Abstract: The Adiabatic Gauge Potential (AGP) is the generator of adiabatic deformations between quantum eigenstates. There are various ways to construct the AGP operator and evaluate the AGP norm. Recently, it was proposed that a Gram-Schmidt-type algorithm can be used to explicitly evaluate the expression of the AGP. We employ a version of this approach by using the Lanczos algorithm to evaluate the AGP operator in terms of Krylov vectors and the AGP norm in terms of the Lanczos coefficients. We discuss various advantages to using this approach and explicitly evaluate the AGP operator for some simple systems by using this approach. We also present a modification of the Variational approach to derive the regulated AGP norm. We approximate the AGP using this and observe different features for different classes of systems. Finally, we compare quantum-chaos-probing capabilities of the AGP norm and the Krylov mechanism and infer some plausible interesting physics with regards to quantum chaotic dynamics.
Abstract: Progress in non-Hermitian physics has revolutionized the traditional quantum mechanics over past decades, because any model for a realistic quantum system should take into account the interactions of the system with its environment. Recently, the interplay between non-Hermitian physics and topological physics leads to anomalous boundary behaviors, called non-Hermitian skin effects. Beyond the fundamental theory, the mathematical equivalence between Schrödinger equation and wave equations, also allows one to simulate non-Hermitian wave physics in various classical systems, e.g., photonics, mechanics, electrical circuits and acoustics.
Here, to give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates, in which translation symmetry is broken due to the open boundary condition. By introducing the Vieta’s theorem for any polynomial equation with arbitrary degree, our approach is widely applicable for arbitrary one-dimensional non-Hermitian tight-binding models. With the non-Hermitian generalized Bloch theorem, we can analyze the condition of existence or non-existence of non-Hermitian skin effects and study the real-space exceptional point at a mathematically rigorous level.
Meanwhile, at an engineering level, we design and simulate a two-dimensional topolectrical circuit lattice with non-reciprocal interaction and observe various types of exceptional rings. We also illustrate the significant role of pseudo-Hermitian symmetry, which protects the exceptional rings in two-dimensional models, and also protects the bulk-boundary correspondence between the exceptional rings and topological behaviors.
Abstract: In any computation, noise and decoherence is inevitable. To this end, methods need to be devised for reliable computation. One way is to protect the states of the qubit by exploiting topology via architecture or circuits. One such design is the 0-pi qubit. But to manipulate it’s states, one needs to find suitable frequencies for tuning. We then study the effect of external flux on the 0-pi qubit as well as it’s electrical conductivity.
Another way to control errors in a qubit is to control the transition of a qubit itself such that we have sufficient time to manipulate it. One work presented by Minev et al. tries to achieve this using transmons to create a three-level system as proposed by Dehmelt and devised by Cook. This work helped achieve reversal of a qubit transition which may aid correction of an error. Building upon this, the dynamics of a qubit was studied, which evolves in time and simultaneously interacts with an environment. It then gets projected onto a state, giving an output of the measurement observable of the environment. A system which is continuously being monitored, freezes in time, displaying quantum Zeno effect. We discuss two regimes, one in which measurement frequency is lower than the system frequency, and one in which system is being monitored more frequently than its characteristic Rabi frequency. Thus being evolved on the Bloch sphere, it gives us coupled state update equations in time, using which a dynamic Hamiltonian can be constructed. This further leads us to creating phase space trajectories of the evolving qubit interacting with the environment, displaying an inherent level in the qubit where the system sits for a while, providing us with time for manipulations and corrections.
Encryption of codewords to form logical qubits is an idea which follows from classical error correction. A stabilizer algebra was designed to study logical operations in quantum systems. Kitaev’s idea of toric code led to the study of a new stabilizer code – the surface code. The surface code is a genus one code which helps encrypt one logical qubit by exhausting a large number of qubits. In one of our works, we propose a double-toric code, a genus two code, which uses six pi/3-2pi/3 rhombus as the fundamental domain and can tessellate the whole plane (a major idea to help achieve scalability). Using this topology, we could reach an encryption rate of 0.5 and even increase the distance of the code. Even a single unit of the code produces 2 logical qubits by exhausting only 6 physical qubits.
We believe that these proposed ideas will lead one to achieve scalability as well as reliability in the near future.
Abstract: Since its first synthesis, graphene has opened new exciting research prospects in the context of solid state physics. Despite the simplicity of its structure, this material hosts a rich variety of phenomena and physical properties. In particular, in the low energy limit, it exhibits massless Dirac fermions, typical of 2D Weyl semimetals. However, the semimetallic nature of graphene is generally detrimental for the realization of electronic devices. Therefore it reveals important to find ways to generate a gap in its band structure. In this thesis, employing a tight-binding description, we review the well-known graphene model and the possibility of engineering a spectral gap by applying mechanical strain to its honeycomb structure. This serves as a blueprint to generalize the discussion to the kagomé systems, a novel class of 2D Weyl semimetals for which we construct the effective Dirac theory and classify all the possible mass terms based on the symmetries they preserve or break.
Abstract: In this thesis, we try to combine machine learning and quantum computing in order to simultaneously perform different readings of a sentence. In the first part, we introduce a procedure to obtain a distributional tensor represen- tation for adjectives seen as endomorphisms on the noun space. We accomplish this by discretizing the surface of the n-sphere, where the noun embeddings lie, and finding local approximations. We show how the analysis of their activity distributions can give us some information about their action in the noun space. We also provide different options to approximate their local behavior and visually represent their activity. This approach could, in principle, be applied to any kind of transformation in the sense of the types of categorial grammars. The second section, which is devoted to the quantum approach to the problem, explains how these classical representations can be effectively encoded into quantum states. Additionally, it involves the introduction of some quantum circuits, which, when used in conjunction with a traditional machine learning strategy, enable us to simultaneously perform several readings of ambiguous sentences using index contractions and to assign them a likelihood score.
Abstract: In this talk, I will start with my Masters thesis where we use the stabilizer formalism in order to implement the Hayden-Preskill protocol for recovering information from black holes. Inspired by the AdS/CFT literature, we take the black hole as a scrambling unitary and for the decoding of the scrambled information, we use the Yoshida-Kitaev decoder. We exploit the stabilizer formalism and the properties of Clifford unitaries to demonstrate that it is possible to implement this decoding algorithm without the need for any quantum advantage.
Near the end of my talk, I will also describe the work I am currently engaged in, which explores the characteristics of the Wigner quasiprobability distribution (particularly, its log negativity and spread over phase space) to study on the one-hand non-stabilizerness (magic) of quantum field theories as well as quantum chaotic properties of the SYK model.
Abstract:While enormously successful at describing the microscopic world, quantum mechanics remains largely unexplored at scales that exceed the mass of a few thousand atoms. Recent progress in the quantum control of the mechanical degrees of freedom of solids suspended in a vacuum suggests that this situation might change in the near to mid-term future. Containing billions of atoms, levitated nanoparticles might be able to perform quantum experiments in an unprecedented mass regime, and thus, interrogate Nature about fundamental aspects of physics for which we do not have an answer, for example, does the linearity of quantum mechanics hold at macroscopic scales? or, can a source of the gravitational field be placed in a spatial superposition? In my talk, I will examine the opportunities and challenges that this nascent quantum platform presents to address these fascinating questions.
First, I will present a collection of proposed experimental techniques that can both extend the coherence times and shorten the duration of experiments aimed at realizing matter-wave interferometry with levitated solids. Secondly, I will discuss the prospects of exploring quantum aspects of gravity with tabletop, quantum-optical experiments. In particular, I will present two routes towards this goal, one which relies on the generation of entanglement through gravitational interaction and a second one that can test the quantumness of gravity without the generation or detection of entanglement.
References: [1] J. S. Pedernales, G. W. Morley, and M. B. Plenio, Motional dynamical decoupling for interferometry with macroscopic particles, Physical Review Letters 125 (2), 023602 (2020).
[2] F. Cosco, J. S. Pedernales, and M. B. Plenio, Enhanced force sensitivity and entanglement in periodically driven optomechanics, Phys. Rev. A 103, 061501 (2021).
[3] J. S. Pedernales, K. Streltsov, and M. B. Plenio, Enhancing Gravitational Interaction between Quantum Systems by a Massive Mediator, Phys. Rev. Lett. 128 (11), 110401 (2022).
[4] J. S. Pedernales and M. B. Plenio, Robust Macroscopic Matter-Wave Interferometry with Solids, Phys. Rev. A 105, 063313 (2022).
[5] L. Lami, J. S. Pedernales and M. B. Plenio, Testing the quantumness of gravity without entanglement, arXiv:2302.03075 (2023)
Abstract: I investigate the nonequilibrium behavior of driven non-interacting chaotic Fermi systems both in a random matrix theory framework and in two-dimensional Anderson models. I concentrate on the statistical properties of the work performed on the system, the adiabatic time evolution, and on the extension of universality to non-equilibrium systems. I derive a determinant formula to calculate the characteristic function of work statistics and the probability of adiabaticity. Next, I show that the instantaneous occupation numbers, the work statistics, and the probability of adiabaticity follow universal curves that depend only on the average work and the temperature both in the driven random matrix and Anderson models. In addition, I show that a classical energy space diffusion model accurately describes the nonequilibrium dynamics and also explains the observed universal properties. Within this framework, using bosonization and mean field methods, I derive approximate analytical expressions for the work statistics at zero temperature. I also show that as the thermal energy becomes larger than the average work the probability of adiabaticity exhibits a cross-over from stretched exponential to exponential behavior, while the fluctuations of work turn from superdiffusive to diffusive, and the work statistics converges to a Gaussian distribution in the small work limit. In these small and large work limits, I also provide approximate analytical expressions for the occupation numbers.
Abstract: We consider the dynamics of a one-dimensional quantum system in the presence of a localized defect. We prepare the system in a short-range entangled state, we let it evolve ballistically, and we study the entanglement across the defect. Linear growth of the entanglement entropy is observed, whose slope depends both on the scattering properties of the defect and the initial state. The protocol above is characterized by Conformal Field Theory, and the Rényi entropies are related to the correlation functions of twist fields in a bounded two-dimensional geometry. Moreover, we investigate a particular lattice realization in a free-fermion chain, giving a prediction for the linear slope via a quasi-particle picture.
This talk is based on joint work with Viktor Eisler.
Abstract: In this talk, I will present my work on spinor Bose-Einstein condensates (BEC) using mean-field theory: energetic stability of vortex dissociation in spin- 1 Bose-Einstein condensates (BEC) [1] and microscopic derivation of Stoner-Wohlfarth model in spinor BEC with magnetic dipole-dipole interaction [2].
Due to the internal spin degree of freedom, spinor BEC has the U(1) global gauge symmetry and the SO(3) spin rotational symmetry. Hence the mass circulation along a closed path around the core of the vortex can be quantized in fractional units of h/M where h is the Planck constant and M is the mass of the BEC particle. When the quadratic Zeeman coefficient is changed from the positive to negative value, the order parameter of the spin-1 BEC can be changed from the polar phase to the antiferromagnetic phase. In this process, single-quantum vortices in the polar phase are dissociated into half-quantum vortices in the antiferromagnetic phase [3]. We studied the energetic stability of this vortex dissociation using mean-field theory and found out that the ratio of the density-density interaction coefficient (c0) and the spin-spin interaction coefficient (c2) in the spin-1 BEC determines its energetic stability. Also, we found out that the critical ratio (c2/c0)cr depends on the size of the system [1].
In order to describe the finite lifetime of the collective oscillation in BEC, Pitaevskii introduced the damping coefficient Γ in the mean-field theory for scalar BEC [4] and this Γ is estimated to be 0.03 in the scalar 23 BEC [5]. However, even though Γ is introduced for scalar BEC and its value might depend on the type of the BEC system, it has been applied to the mean-field theory for spinor BEC with Γ ≃ 0.03 for any system. Here, starting from this introduction of Γ to the mean-field theory for spinor BEC with magnetic dipole-dipole interaction, we show that one can microscopically derive the Landau-Lifshitz- Gilbert equation (phenomenological equation to describe the motion of magnetization) [6, 7] and the Stoner-Wohlfarth model (model for the magnetization of single-domain ferromagnets) [8]. Additionally, we show that the Γ affects the switching time of the magnetization in a single-domain spinor BEC under the external magnetic field [2], which implies that one can measure Γ in spinor BEC with magnetic dipole-dipole interaction.
For detailed review on mean-field theory for spinor Bose-Einstein condensates, please refer to [9].
References:
[1] S.-H. Shinn and U. R. Fischer, Phys. Rev. A 98, 053602 (2018).
[2] S.-H. Shinn, D. Braun, and U. R. Fischer, Phys. Rev. A 102, 013315 (2020).
[3] S. W. Seo, S. Kang, W. J. Kwon, and Y.-i. Shin, Phys. Rev. Lett. 115, 015301 (2015).
[4] L. P. Pitaevskii, Sov. Phys.-JETP 8, 282 (1959).
[5] S. Choi, S. A. Morgan, and K. Burnett, Phys. Rev. A 57, 4057 (1998).
[6] L. Landau and E. Lifshitz, Phys. Z. Sowjetunion 8, 153 (1953).
[7] T. L. Gilbert, IEEE Transactions on Magnetics 40, 3443 (2004).
[8] E. C. Stoner and E. P. Wohlfarth, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 240, 599 (1948).
[9] Y. Kawaguchi and M. Ueda, Physics Reports 520, 253 (2012).
Abstract: Height models and random tiling are well-studied objects in classical statistical mechanics and combinatorics that lead to many interesting phenomena, such as arctic curve, limit shape and Kadar-Parisi-Zhang scaling. We introduce quantum dynamics to the classical hexagonal dimer, six-, and nineteen-vertex models to construct frustration-free Hamiltonians with unique ground state being a superposition of discrete random surfaces subject to a Dirichlet boundary configuration. The local Hilbert space is further decorated by a color degree of freedom, matched in pairs between lattice sites of the same height, generating long range entanglement that makes area law violation of entanglement entropy possible. The scaling of entanglement entropy between half systems is analyzed with the gradient surface tension in the scaling limit and under a q-deformation that weighs random surfaces by the volume below, it undergoes a phase transition from area law to volume scaling. At the critical point, the scaling is L logL due to the so-called "entropic repulsion” of Gaussian free fields conditioned to stay nonnegative. An exact holographic tensor network description of the ground state is proposed with one extra dimension perpendicular to the lattice. I will also discuss an alternative realisation with vertex models, inhomogeneous deformation to obtain sub-volume intermediate scaling, and possible generalizations to higher dimension
Abstract: The Variational Quantum Eigensolver (VQE) algorithm is part classical and part quantum. It is based on the Rayleigh Ritz variational principle and was proposed to calculate the ground state energies of quantum many body systems. It has been successfully applied to find the ground state energies of small systems including atoms and molecules. In this work, we extend the VQE algorithm to the relativistic regime and carry out quantum simulations to obtain ground state energies as well as molecular permanent electric dipole moments of single-valence diatomic molecules, from the light BeH molecule to the heavy radioactive RaH molecule.
Abstract: Black holes are the most mysterious objects in nature. They are believed to be the fastest scrambler of information, as they destroy local correlations and spread information throughout the system. Unscrambling this information is possible, given a perfect knowledge of the black hole internal dynamics[arXiv:1710.03363]. This work shows that information can be efficiently decoded from an unknown black hole by observing the outgoing Hawking radiation. Surprisingly, black holes admit Clifford decoders: the salient properties of a scrambling unitary can be efficiently described even if exponentially complex, as long as it is not fully chaotic. This is possible because all the redundant complexity can be described as an entropy, and for non-chaotic black holes it can be efficiently pushed away, just like in a refrigerator. This entropy is not due to thermal fluctuations but to the non-stabilizer behavior of the scrambler
Abstract: Despite its importance to experiments, numerical simulations, and the development of theoretical models, the problem of lack of self-averaging in many-body quantum systems out of equilibrium is often overlooked. Usually, in the chaotic regime, self-averaging is taken for granted. The numerical and analytical results that I will present force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function used in experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.
Abstract: I show an explicit construction of a Hamiltonian that, given access to a measurement record, reproduces the stochastic trajectory of a continuously monitored quantum system. This provides a tool to engineer quantum control protocols by exploiting measurement feedback. For example, via suitably chosen feedback Hamiltonians, this allows to mitigate the production of qubit errors with smaller ancilla overheads than traditional quantum error correction techniques if one has access to the environment responsible for the errors.
Abstract: Ensembles of quantum chaotic systems are expected to exhibit random matrix universality in their energy spectrum. The presence of this universality can be diagnosed by looking for a linear in time 'ramp' in the spectral form factor, but for realistic systems this feature is typically only visible after a sufficiently long time. Given the wide prevalence of this random matrix behavior, it is natural to ask for an effective field theory which predicts the ramp and computes corrections to it arising from physical constraints. I will present such an effective theory based on fluctuating hydrodynamics and will discuss its application to a wide variety of systems including systems with a diffusive pole, a sound pole, spontaneously broken symmetry, and glassy dynamics.
Abstract: In this talk I will give a brief overview of quantum adiabatic theorems valid in the open system setting. I will discuss the possibility of diminishing the adiabatic error using the so-called Boundary Cancellation (BC) protocol, which amounts to using schedules with a number of vanishing derivatives at the end of the anneal. Moreover, in order to be able to apply the BC theorem to existing annealing hardware, the BC theorem needs to be generalized to include the case where the Liouvillian gap vanishes and we will also consider the effect of dynamical freezing of the evolution, a known shortcoming of current annealers. We experimentally test the predictions of the boundary cancellation theorem using D-Wave devices, and find qualitative agreement with the predicted error suppression despite using annealing schedules that only approximate the required smooth schedules. Performance is further improved by using quantum annealing correction, and we demonstrate that the boundary cancellation protocol is significantly more robust to parameter variations than protocols which employ pausing to enhance the probability of finding the ground state.
Ref: Demonstration of error-suppressed quantum annealing via boundary cancellation, Humberto Munoz-Bauza, Lorenzo Campos Venuti, Daniel Lidar, arXiv:2206.14269
Abstract: Many-body effects can present new opportunities, as well as non-trivial challenges, in developing many-body quantum technologies. In this talk I will focus on many-body quantum thermal engines. I will discuss control in quantum engines operating close to quantum phase transitions, and how collective effects can allow us to develop highly reliable many-body quantum engines.
Abstract: When does a closed quantum many-body system thermalize? In this talk we will focus on the dynamics of systems in the presence of kinetic constraints. We will first show that the combination of charge and dipole conservation leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead to a breakdown of thermalization. As a concrete example, we will investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total Sz) and its associated dipole moment. More generally, we will classify these systems as weakly or strongly fragmented, and obtain additional dynamical features for each scenario. At this point, one might wonder how realistic dipole-conserving systems are. We will find that such systems naturally arise as effective descriptions of interacting systems in the presence of a strong tilted field, and briefly discuss recent experimental results.
Abstract: The evolution of Heisenberg operators in a chaotic system could be interpretated as the falling of particles into the extra dimension in holography. We use the Krylov-complexity in the Sachdev-Ye-Kitaev (SYK) model and the volume-complexity in Jackiw-Teitelboim (JT) gravity to characterized the evolution of operators. Both quantities show an exponential-to-linear growth behavior. We also calculate the size of operators and further relate it to the growth of complexities.
Abstract: We introduce a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Such minimization can be solved in practice, and the measure is controlled by the ``survival amplitude'' for a state to remain unchanged. It can be efficiently computed in theories with discrete spectra. We describe our methods for the harmonic and inverted oscillators, particles on group manifolds, the Schwarzian theory, the SYK model, and random matrix models. For time-evolved thermofield double states in chaotic systems our measure shows four regimes: a linear "ramp'' up to a "peak'' that is exponential in the entropy, followed by a "slope" down to a "plateau". These regimes arise in the same physics producing the slope-dip-ramp-plateau structure of the Spectral Form Factor. Specifically, the complexity slope arises from spectral rigidity, distinguishing different random matrix ensembles.
ABSTRACT: We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Thanks to the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states. In the latter case, depending on interaction strength and temperature, we identify various dynamical regimes where the current oscillates, is self-trapped or decays with time and involve phase slips of thermal or quantum nature. We finally link the current oscillations in the large barrier limit to quantum shock waves.
Abstract: Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. In this talk I present both the theoretical [1] and experimental [2] works where we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a programmable quantum sensor operating close to the fundamental limits imposed by the laws of quantum mechanics. We achieve this by using low-depth, parametrized quantum circuits implementing optimal input states and measurement operators for a sensing task on a trapped ion experiment. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions. We further perform 'on-device' quantum-classical feedback optimization to 'self-calibrate' the programmable quantum sensor with comparable performance. Such 'on-device’ optimization can also be performed in regimes not accessible to classical computations and in the presence of imperfections.
[1] Phys. Rev. X 11, 041045
[2] arXiv:2107.01860 (accepted to Nature)
ABSTRACT: One dimensional (1D) strongly correlated quantum systems are nowadays the subject of intense theoretical and experimental activity due to the incredible experimental control offered by ultra-cold atoms setups. In such systems, the momentum distribution is a powerful probe of both gas statistics and of the intertwined effect of interactions between particles and the effective dimensionality they move in.
A remarkable momentum distribution feature, in all dimensions, is the presence of universal power-law tails n(k)~k^{-4} for a gas where interactions can be schematized as contact ones (as it is the case for most standard cold gases experiments). The weight of such tails, denoted as Tan's contact, can be put into relation with several many-body quantities, ranging from the interaction energy to the depletion rate by inelastic collisions.
In our study, we provide a complete characterization of the Tan's contact for one-dimensional bosons under harmonic confinement for arbitrary interaction strength, number of particles, temperature and trap frequency. Using a combination of thermal Bethe-ansatz solutions with local-density approximation and exact numerical calculations, we demonstrate that the contact is a universal function of only two scaling parameters and determine the scaling function. Moreover we consider the case of fermionic mixtures. We show that for the case of zero-temperature mixtures, the Tan's contact is determined by the mixture particle-exchange symmetry. The scaling properties derived for the Tan's contact for a single-component bosonic gas are also valid for a fermionic (or bosonic) mixtures at zero temperature and in the limit of large temperatures. However, the universal scaling is lost at small temperatures, where states with different symmetries contributes to the Tan's contact in a non-trivial way.
ABSTRACT: Quantum complexity is expected to have a specific time-dependent profile for finite quantum chaotic systems. In this talk we will introduce Krylov complexity and its associated mathematical objects, the Krylov space and the Lanczos sequence. We will show that it is a good candidate for a concrete notion of quantum complexity as it exhibits the expected time-dependent features at all time scales, for finite quantum chaotic systems.
We will then present novel numerical results for Krylov complexity in the maximally chaotic SYK4 model, as well as in the strongly interacting but integrable XXZ model. We will identify a form of 'Anderson localization' effect on the systems' Krylov complexity profiles, and show that this effect is enhanced in the integrable case. We will suggest that this is a general feature of integrable systems, and thus that studying a system's Krylov complexity profile may serve as a 'probe' for integrability vs chaos.
REFERENCES:
https://arxiv.org/abs/2112.12128
https://arxiv.org/abs/2009.01862
https://arxiv.org/abs/1907.05393.
ABSTRACT: Stochastic Schrödinger equations that govern the dynamics of open quantum systems are given by the equations for signal processing. In particular, the Brownian motion that drives the wave function of the system does not represent noise, but provides purely the arrival of new information. Thus the wave function of an open system is guided by the optimal signal detection about the conditions of the environments under noisy observation. This behaviour is similar to biological systems that detect environmental cues, process this information, and adapt to them optimally by minimising uncertainties about the conditions of their environments. In this talk I will postulate that information-processing capability is a fundamental law of nature, and hence that models describing open quantum systems can equally be applied to biological systems to model their dynamics. For illustration, simple stochastic models are considered to capture heliotropic and gravitropic motions of plants. The advantage of such dynamical models is that it allows for the quantification of information processed by the plants. By considering the consequence of information erasure, it is argued that biological systems can process environmental signals relatively close to the Landauer limit of computation, and that loss of information must lie at the heart of ageing in biological systems.
ABSTRACT: In this talk, I will describe the notion of the operator growth and Krylov complexity. In particular, I will discuss its geometric interpretation and possible applications to holographic CFTs.
REFERENCES:
[1] Pawel Caputa, Javier M. Magan, Dimitrios Patramanis; Geometry of Krylov Complexity arXiv:2109.03824 [hep-th]
[2] Pawel Caputa, Shouvik Datta; Operator growth in 2d CFT arXiv:2110.10519 [hep-th]
ABSTRACT: Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. In this talk, I will discuss gate-based simulation using Trotter - Suzuki approximation, and describe how studying the simulator as a driven Floquet system can lead to novel insights into the emergence of errors in the device. An example of this appears when the system being simulated is such that the Floquet map underlying the Trotter decomposition becomes quantum chaotic. I will present results on a recent work studying quantum simulation of spin systems with long-range multi-body interactions, where we identify a novel regime where error proliferation occurs even in the absence of chaos. In this regime, errors appear due to ‘structural instabilities’ in the Floquet operator, which undergoes sharp changes even for a small variation of the Trotter step size. This phenomenon, which becomes more common as the degree of the interaction is increased, appears typically at intermediate Trotter step sizes and in the weakly-interacting regime and is thus complementary to the chaotic regime. I will also illustrate how the deviations between the Trotterized dynamics and the Hamiltonian dynamics can be related to the emergence of a robust subharmonic periodic response of a periodically driven system, akin to Floquet time crystals.
ABSTRACT: We derive generalized quantum speed limit inequalities that represent limitations on the time evolution of quantum states. They are extensions of the original inequality and are applied to the overlap between the time-evolved state and an arbitrary state. We can discuss the lower limit of the overlap, in addition to the upper limit as in the original inequality, which allows us to estimate the minimum time for the evolution to a target state. The inequalities are written by using an arbitrary reference state and are flexibly used to derive a tight bound. We demonstrate these properties by using several simple models.
REFERENCES:
[1] K Suzuki and K. Takahashi, Phys. Rev. Res. 2, 032016(R) (2020)
[2] K. Takahashi, arXiv: 2112.12631
ABSTRACT: In this talk, we study the mean-field dynamics of a general class of quantum many-body systems with stochastically fluctuating interactions. Our findings reveal a universal algebraic decay of the order parameter m(t)~t^{-\chi} with an exponent \chi=1/3 that is independent of most system details including the strength of the stochastic driving, the energy spectrum of the undriven systems, the initial states and even the driving protocols. It is shown that such a dynamical universality class can be understood as a consequence of a diffusive process with a time-dependent diffusion constant which is determined self-consistently during the evolution. The finite-size effect, as well as the relevance of our results with current experiments in high-finesse cavity QED systems are also discussed.
ABSTRACT: The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability, but the associated methods cannot be readily applied when integrability is broken. After an introduction to superdiffusion I will examine spin transport in such a spin-1/2 chain in which the exchange couplings fluctuate in space and time, breaking integrability but not spin symmetry, showing that operator dynamics in the strong noise limit can be analyzed using conventional perturbation theory. I will argue that the spin dynamics undergo enhanced diffusion with some interesting transient behavior rather than superdiffusion, comparing the dynamics with both a hydrodynamic approach and tensor network simulations.
REFERENCE:
[1] Pieter W. Claeys, Austen Lamacraft, Jonah Herzog-Arbeitman, Absence of superdiffusion in certain random spin models, arXiv:2110.06951
ABSTRACT: Recently, the notion of quantum scrambling, the process by which interaction spreads initially localized quantum information into its many degrees of freedom, has become very popular in understanding chaotic properties of quantum systems. In this talk, I will focus on Krylov Complexity as a tool to correctly quantify this rate of information spreading and will discuss both analytic results from SYK physics and how to compute it in general. I will then argue that operator delocalization — the mechanism by which a simple operator evolves into a superposition of many different operators with time — has probably been overlooked in our understanding of scrambling. Finally, I will show preliminary results pointing towards the notion of proximity to quantum chaos in free many-body systems.
REFERENCES:
[1] Joonho Kim, Jeff Murugan, Jan Olle, Dario Rosa, Operator Delocalization in Quantum Networks, arXiv:2109.05301
ABSTRACT: We consider the Luttinger liquid (which can be thought of as bosonization of a 1d Fermi gas) interacting with an environment. Dynamics of the system is Markovian and governed by the Lindblad equation. For a closed system, correlations in the ground state are described by the free boson theory. This theory is conformal, which is reflected by a simple algebraic form of correlations functions. Our main finding is that for a specific choice of dissipation the steady state has remarkable properties compatible with conformal symmetry (albeit being a non-trivial mixed density matrix). Namely, correlation functions of primary operators have the same simple universal form as in the vacuum state, yet with modified scaling exponents. During the talk I will outline the necessary basics of conformal field theory and detail some of the technical steps that allowed to solve the model in the presence of dissipation, in particular the convenience of working in the Heisenberg picture.
ABSTRACT: We study the universality of work statistics of a system quenched through a quantum critical surface. By using the adiabatic perturbation theory, we obtain the general scaling behavior for all cumulants of work. These results extend the studies of KZM scaling of work statistics from an isolated quantum critical point to a critical surface. As an example, we study the scaling behavior of work statistics in the 2D Kitaev honeycomb model featured with a critical line. By utilizing the trace formula for quadratic fermionic Hamiltonian, we obtain the exact characteristic function of work of the 2D Kitaev model at zero temperature. The results confirm our prediction.
REFERENCES:
[1] Z. Fei, N. Freitas, V. Cavina, H. T. Quan, and M. Esposito, Phys. Rev. Lett. 124, 170603 (2020)
ABSTRACT: In the first part of my talk [1], I will discuss correlations present deep in the spectrum of many-body-localized systems (isolated). An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two models exhibiting many-body localization: a disordered quantum spin chain and a phenomenological l-bit model based on the existence of local integrals of motion. I will discuss a universal regime that is insensitive to the global density of states as well as spectral edge effects.
In the second part of my talk [2], I will discuss localization/self-trapping in open quantum systems. I will show that a careful engineering of drive, dissipation and Hamiltonian results in achieving indefinitely sustained self-trapping. I will demonstrate that the intricate interplay between drive, dissipation and light-matter interaction results in requiring an optimal window of drive strengths in order to achieve such non-trivial steady states.
REFERENCES:
[1] A. Prakash, J. H. Pixley, M. Kulkarni, Phys. Rev. Research 3, L012019, Letters (2021), Editors' Suggestion
[2] A. Dey, M. Kulkarni, Phys. Rev. A 101, 043801 (2020)
ABSTRACT: Active matter has emerged recently as the class of nonequilibrium systems where every component extracts energy from its environment to produce sustained motion. This leads to collective effects without any equilibrium equivalent, such as the phase separation of purely repulsive particles. While the phase diagrams of these nonequilibrium transitions have been studied extensively, only little is known about how to optimally *control* active systems. I will discuss some specific control protocols which rely on applying external perturbations at optimal cost. First, I will consider the design of engines extracting work from active matter. Second, I will present a systematic framework for optimal control in finite time, with potential to drive phase transitions externally. These examples illustrate how to find the best trade-off between internal driving, governed by particle-based energy consumption, and external driving, controlled by perturbations, in active matter.
ABSTRACT: Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of N-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence, that is a generalization of h the mechanism of decoherence, which transforms a quantum state into a classical one. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification, that is a generalization of the scheme used to construct a quantum state out of a classical one, to obtain Lindblad operators out of Kolmogorov ones.
REFERENCES:
[1] W. Tarnowski, I. Yusipov, T. Laptyeva, S. Denisov, D. Chruściński, K. Życzkowski, arXiv:2105.02369 (2021)
ABSTRACT: The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior in the vicinity of quantum phase transitions (QPTs). It is now well understood for one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by fundamental differences of the associated QPTs and their underlying conformal field theories. In this work [1], we take the first steps towards exploring the QKZM in two-dimensional spin systems. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods, including artificial neural networks and tensor networks. As a central result, we quantify universal QKZM behavior close to the QPT. However, upon traversing further into the ferromagnetic regime, we observe deviations from the QKZM prediction. We explain the observed behavior by proposing an extended QKZM taking into account spectral information as well as phase ordering. Our work provides a starting point towards the exploration of dynamical universality in higher-dimensional quantum matter.
REFERENCES:
[1] M. Schmitt, M.M. Rams, J. Dziarmaga, M. Heyl, W.H. Zurek, arXiv:2106.09046
ABSTRACT: I will describe a simple scheme for finding quantum critical points, which is based on studies of a nonequilibrium susceptibility during finite-rate quenches taking the system from one phase to another. I will assume that two such quenches are performed in opposite directions and argue that they lead to the formation of peaks of a nonequilibrium susceptibility on opposite sides of a critical point. Its position will be then narrowed to the interval marked off by these values of the parameter driving the transition, at which the peaks are observed. Universal scaling with the quench time of precision of such an estimation will be derived and verified in two exactly solvable models. Possible relevance of these results to localization of classical critical points will be mentioned.
ABSTRACT: The one-dimensional Heisenberg model with onsite disorder has become paradigmatic in the analysis of many-body localization. In this talk, I will show how the evolution, time scales, and self-averaging properties of different observables depend on the disorder strength of this model. Emphasis will be given to the survival probability, but I plan to discuss also the behavior of the inverse participation ratio, spin auto-correlation function, and connected spin-spin correlation function, which are quantities measured in experiments with cold atoms and ion traps. The survival probability exhibits a power-law behavior with an exponent that coincides with the multifractal dimension of the eigenstates [1]. After the power-law decay, it develops the correlation hole, whose starting point defines the Thouless time. This time grows exponentially with the disorder strength and approaches the Heisenberg time as the system gets closer to the localized phase [2]. The survival probability is non-self-averaging at any time scale and for any disorder strength, which implies that averages over a large number of disorder realizations are needed no matter how large the system size is [3].
REFERENCES:
[1] E. J. Torres-Herrera, Lea F. Santos, Physical Review B 92, 014208 (2015).
[2] Mauro Schiulaz, E. J. Torres-Herrera, Lea F. Santos, Physical Review B 99, 174313 (2019).
[3] E. J. Torres-Herrera, Giuseppe De Tomasi, Mauro Schiulaz, Francisco Pérez-Bernal, Lea F. Santos, Physical Review B 102, 094310 (2020).
ABSTRACT: Collective strong coupling of N ≫ 1 molecular excitations to an optical cavity mode gives rise to 2 polariton states and N – 1 dark states. The polariton states are hybrid light-matter in nature and are shifted in energy relative to the bare molecular states. These properties make polaritons promising for altering chemical and material properties. In contrast, the dark states are energetically unchanged from their bare counterparts and are essentially purely molecular. Nevertheless, the dark states greatly outnumber the polaritons and can serve as an energy sink for the polariton states, thereby enriching the relaxation dynamics. In this talk, I will discuss our efforts to model and predict new chemical phenomena arising from strong light-matter coupling, specifically the interplay between polariton and dark states.
First, I will share our comprehensive exploration of scenarios in which strong coupling can (and cannot) enable long-range energy transfer between donor and acceptor dye molecules [1].
Next, I will present our theoretically designed “remote control” of chemistry. The proposed device enables photoexcitation of molecules in one optical cavity to modify the photoisomerization efficiency of molecules in a second optical cavity [2].
Last, I will highlight our efforts to provide insight on experiments showing that vibrational strong coupling can modify the kinetics of thermally activated chemical reactions (i.e., without photoexcitation). Using nonadiabatic electron transfer as a model reaction, we reveal distinct mechanisms—for two-molecule [3] and many-molecule [4] systems—by which VSC can promote thermalization and thereby suppress nonequilibrium effects that influence reactivity.
REFERENCES:
[1] M. Du, L. A. Mart nez-Mart nez, R. F. Ribeiro, Z. Hu, V. M. Menon and J. Yuen-Zhou, Chem. Sci., 9, 6659 (2018).
[2] M. Du, R. F. Ribeiro and J. Yuen-Zhou, Chem, 5, 1167 (2019).
[3] M. Du, J. A. Campos-Gonzalez-Angulo, J. Yuen-Zhou, J. Chem. Phys., 154, 084108 (2021).
[4] M. Du, J. Yuen-Zhou, arXiv:2104.07214
ABSTRACT: Reservoir computing is a machine learning approach based on the framework of neural networks. This unconventional computing approach allows for excellent performance with an easy training strategy. Recent developments of quantum reservoir computing and extreme learning machines are moving from classical to quantum implementations, being these proposals also good candidates for NISQ devices. In this seminar, I will introduce both bosonic and spin networks models and first results about their performance.
ABSTRACT: In quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. We show examples of the opposite by considering spin-1/2 chains which contain antiferromagnetic interactions and are set on a ring with an odd number of sites a setting inducing topological frustration. In particular, we focus on spin chains which possess a global SU(2) symmetry with parity symmetries in this setting, a quite common property in the absence of external fields, an example being the quantum XY chain. These conditions allow studying symmetry breaking without thermodynamic limit and symmetry breaking fields. The ground state is degenerate already in a nite system, for which we compute the magnetization, and afterwards track it towards the thermodynamic limit. We nd in this way that topological frustration can destroy local order, create a site-dependent magnetization which varies in space with an incommensurate pattern, induce a new quantum phase transition and modify the existing one.
REFERENCES:
[1] V. Marić, S. M. Giampaolo, D. Kuić, & F. Franchini, The Frustration of being Odd: How Boundary Conditions can destroy Local Order, New J. Phys 22 083024 (2020).
[2] V. Marić, S. M. Giampaolo, & F. Franchini, Quantum Phase Transition induced by Topological Frustration, Communications Physics 3, 220 (2020).
[3] G. Torre, V. Marić, F. Franchini & S. M. Giampaolo, Effects of defects in the XY chain with frustrated boundary conditions, Phys. Rev. B 103, 014429 (2021).
[4] V. Marić, S. M. Giampaolo & F. Franchini, Absence of local order in topologically frustrated spin chains, arXiv:2101.07276.
[5] V. Marić, G. Torre, F. Franchini & S. M. Giampaolo, Topological Frustration can modify the nature of a Quantum Phase Transition, arXiv:2101.08807.
VM acknowledges support from the European Regional Development Fund the Competitiveness and Cohesion Operational Programme and from the Croatian Science Foundation (HrZZ).
ABSTRACT: Trade-off relations involving the relative uncertainty of currents and the associated entropy production have been of enormous interest in the last few years in the field of non-equilibrium stochastic thermodynamics. It is now realized, for example, that the optimization of heat engines should balance power, efficiency as well as power fluctuations. In this talk, I will first present our results for the steady-state thermodynamic uncertainty relation (TUR) for quantum charge and energy transport. In the second part of my talk, I will show that, for multi-affinity driven continuous thermal machines, the relative fluctuations of individual currents are not independent but follow strict bounds, giving rise to a new bound for the mean efficiency of an engine. I will also talk about the extension of this bound for finite-time Otto cycles.
REFERENCES:
[1] Bounds on fluctuations for finite-time quantum Otto cycle, S. Saryal and Bijay Agarawalla, arXiv: 2104.121732.
[2] Universal bounds on Fluctuations in continuous thermal machines, S. Saryal et al arXiv:2103.13513
[3] Papers related thermodynamic uncertainty relations: Phys. Rev. Research (Rapid Communication) 2, 022044 (2020), Phys. Rev. E 100, 042101 (2019), Phys. Rev. B 98, 155438 (2018).
ABSTRACT: In this talk, I will attempt to cover two seemingly unrelated topics. Yet, the key is that they are related, as will be explained.
Recently, we theoretically unveiled an unexplored flexibility of nonlinear optics that a shaped laser pulse can drive a quantum system to emit light as if it were an arbitrary different system. This realizes an aspect of the alchemist’s dream to make different elements look alike, albeit for the duration of a laser pulse. To understand this methodology, we need to define what “looking alike” means. One visually perceives a physical system due to a difference between light before (i.e., the optical input) and after (i.e., the optical response) interacting with the system of interest. Thus, to make two different systems look alike is equivalent to be able to match their optical responses. This finding has received broad public coverage in such scientific outlets as Physics, PhysicsWorld, Nature Materials, Quanta Magazine, Wired, etc
Erik Verlinde's theory of entropic gravity, postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultra-cold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. We show that the proposed master equation is fully compatible with the qBounce experiment for ultra-cold neutrons. In addition, comparing our mode of entropic gravity to the Diosi-Penrose model for gravity induced decoherence indicates that the two theories are incompatible.
ABSTRACT: Describing complex interacting quantum systems is a daunting task. One very fruitful approach to this problem, developed for unitary dynamics, is to represent the Hamiltonian of a generic system by a large random matrix. This eventually led to the development of the field of quantum chaos. Here, we will discuss the recent application of (non-Hermitian) random matrix theory to open quantum systems, where dissipation and decoherence coexist with unitary dynamics. First, we consider the Lindblad generator of Markovian dissipation, for which a characteristic lemon-shaped spectrum has been identified in a variety of settings [1-3]. This allows us to characterize and constrain the timescales for relaxation and dissipation. Then, we focus on periodically driven open quantum systems and their discrete-time Kraus map representation [4]. We find a transition in the shape of the support of the spectrum of the Kraus map, occurring at a critical value of the dissipation strength. The steady state, on the contrary, is not affected by the spectral transition, and its properties coincide with those of random Lindbladians, indicating universality. Finally, we briefly discuss how this work and its extensions [4--6] help in laying the foundations for systematic studies of generic open quantum systems. Of particular interest is the search for signatures of dissipative quantum chaos [5] and the study of more realistic local dissipative systems modeled as, e.g., quantum circuits [4,6].
REFERENCES:
[1] Sá, L., Ribeiro, P., and Prosen, T. (2020). Spectral and steady-state properties of random Liouvillians, J. Phys. A: Math. Theor. 53 305303 (2020).
[2] Denisov, S., Laptyeva, T., Tarnowski, W., Chruscinski, D., and Zyczkowski, K. (2019). Universal Spectra of Random Lindblad Operators, Phys. Rev. Lett. 123, 140403 (2019).
[3] Wang, K., Piazza, F., and Luitz, D. J. (2020). Hierarchy of Relaxation Timescales in Local Random Liouvillians, Phys. Rev. Lett. 124, 100604.
[4] Sá, L., Ribeiro, P., Can, T., and Prosen, T. (2020). Spectral transitions and universal steady states in random Kraus maps and circuits, Phys. Rev. B 102, 134310.
[5] Sá, L., Ribeiro, P., and Prosen, T. (2020). Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos, Phys. Rev. X 10, 021019.
[6] Sá, L., Ribeiro, P., and Prosen, T. (2021). Integrable nonunitary open quantum circuits, Phys. Rev. B 103, 115132.
L.S. is supported by FCT through Grant No. SFRH/BD/147477/2019.
ABSTRACT: In this talk, I will review several different experiments on quench dynamics of random spin models in different cold atom and NV center systems. In these experiments, two distinct and universal phenomena are observed. We point out that a unified understanding of these two phenomena emerges naturally in a holographic theory where these spin models are connected to a gravity theory with a traversable wormhole. We also show the prediction of this theory that can be verified in future experiments. This work shows an example of the frontier of physics research at the interdisciplinary of quantum matter, quantum information, and quantum gravity.
ABSTRACT: The goal of quantum metrology is the precise estimation of physical parameters using quantum properties such as entanglement. This estimation usually consists of three steps: initial state preparation, time evolution during which information of the parameters is imprinted in the state, and readout of the state. Decoherence during the time evolution typically degrades the performance of quantum metrology and is considered to be one of the major obstacles to realizing entanglement-enhanced sensing. We show, however, that under suitable conditions, this decoherence can be exploited to improve the sensitivity [1]. In this talk, I will introduce a sensing scheme utilizing Markovian collective dephasing. Assume that we have two axes, and our aim is to estimate the relative angle between them. Our results reveal that the use of Markvoian collective dephasing to estimate the relative angle between the two directions affords Heisenberg-limited sensitivity. Moreover, our scheme is robust against environmental noise: it is possible to achieve the Heisenberg limit even under the effect of independent dephasing.
REFERENCES:
[1] S. Kukita, Y. Matsuzaki, & Y. Kondo, arXiv:2103.11612 [quant-ph]
ABSTRACT: I will present a dynamic scaling theory aimed at carefully addressing the out-of-equilibrium behavior of many-body systems in proximity of quantum phase transitions of any order. This can be obtained by suitably extending the equilibrium scaling laws ruled either by the critical exponents at continuous transitions, or by the energy gap of the lowest levels at first-order transitions. I will also discuss some aspects related to the effects of dissipative mechanisms, highlighting a nontrivial competition that may arise between the coherent dynamics at quantum transitions and some non-unitary perturbations, such as the coupling with an external Markovian bath or to a quantum measurement apparatus.
REFERENCE:
[1] D. Rossini and E. Vicari, arXiv:2103.02626 [review paper]
ABSTRACT: We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultra-strong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics [1]. The time-dependent quantum Rabi model is simulated by applying parametric amplification [2,3] to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrödinger cat states, through a process which is 10 times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables to freely design the parametric drive, so that the target state can be generated in the lab frame. A largely detuned light-matter coupling makes the protocol robust against imperfections of the operation times in experiments.
REFERENCES:
[1] Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, Phys. Rev. Lett. 126, 023602 (2021);
[2] W. Qin, A. Miranowicz, P.-B. Li, X.-Y. Lü, J. Q. You, and F. Nori, Phys. Rev. Lett. 120, 093601 (2018);
[3] C. Leroux, L. C. G. Govia, and A. A. Clerk, Phys. Rev. Lett. 120, 093602 (2018).
Funding Acknowledgement: This work was supported in part by NTT, JST, CREST, JSPS, ARO, AOARD, FQXi.
ABSTRACT: One should be amazed with an unreasonable effectiveness of random matrix theory to describe spectral fluctuations in simple non-integrable many-body systems, say one dimensional spin 1/2 chains with local interactions. I will discuss a class of Floquet (periodically driven) quantum spin chains - specifically, dual unitary Floquet circuits - where the random matrix result for the spectral form factor can be derived or even rigorously proven. Several other nontrivial exactly solvable features of the presented models, such as dynamical correlations or entanglement dynamics, will be discussed.
ABSTRACT: Heat engines are devices that convert thermal energy into mechanical work in a consecutive manner. Advances in technology so far have enabled us to downsize heat engines, and current state-of-the-art experiments have reached the stage to realize heat engines with a single colloidal particle or macromolecule [1], where fluctuations in thermodynamic quantities are non-negligible [2]. To characterize the performance of such microscopic heat engines, it is essentially important to go beyond the description by mean values done in the conventional thermodynamics for macroscopic systems, and capture their higher-order statistical properties.
We attack this issue of microscopic classical heat engines [3]. Namely, we study the higher-order statistical properties of the Carnot cycle whose working substance consists of a small, classical system. We show that the ratio between the fluctuations of work and heat is given by an universal form depending solely on the temperature ratio between the hot and cold heat baths. Moreover, we show that the Carnot cycle provides the upper bound on this fluctuation ratio for cycles consisting of quasistatic strokes. These results serve as a guiding principle in the design and optimization of fluctuations in small heat engines.
REFERENCES:
[1] I. A. Martínez, É. Roldán, L. Dinis, and R. A. Rica, Soft Matter 13, 22 (2017).
[2] K. Sekimoto, F. Takagi, and T. Hondou, Phys. Rev. E 62, 7759 (2000).
[3] K. Ito, C. Jiang, and G. Watanabe, arXiv:1910.08096 (2019).
ABSTRACT: In equilibrium thermodynamics, the Boltzmann entropy serves as a complete thermodynamic potential that characterizes state convertibility in a necessary and sufficient manner. In this talk, I will present our result [1,2] that a complete thermodynamic potential emerges for quantum many-body systems under physically reasonable assumptions, even in out-of-equilibrium and fully quantum situations. Our proof is based on the resource-theoretic formalism of thermodynamics and the quantum ergodic theorem. The complete thermodynamic potential is in general given by a quantity called the spectral divergence rate, while under the above-mentioned assumptions it reduces to the Kullback-Leibler (KL) divergence rate. In addition, I will discuss the case where an auxiliary system called a catalyst is introduced, and show that the KL divergence again serves as a complete thermodynamic potential if a small amount of correlation is allowed between the system and the catalyst [3].
REFERENCES:
[1] P. Faist, T. Sagawa, K. Kato, H. Nagaoka, F. Brandao, Phys. Rev. Lett. 123, 250601 (2019).
[2] T. Sagawa, P. Faist, K. Kato, K. Matsumoto, H. Nagaoka, F. Brandao, arXiv:1907.05650
[3] N. Shiraishi, T. Sagawa, arXiv:2010.11036, to appear in PRL.
ABSTRACT: Inspired by recent findings on quantum simulation, we derive general results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time at most poly(N) implies the existence of "quantum many-body scars". These are energy eigenstates with energies placed in an equally-spaced ladder and with Rényi entanglement entropy scaling as log(N) any region of the lattice. This shows that quantum many-body scars are a necessary condition for revivals, independent of particularities of the Hamiltonian leading to them. We also present further general results of the behavior of the fidelity in many-body systems, and explore their consequences for the revivals. In particular, we show that the average fidelity decreases quickly with time and system size, and as a consequence find that the duration of revivals must be vanishingly short.
REFERENCES:
Álvaro M. Alhambra, Anurag Anshu, and Henrik Wilming, Phys. Rev. B 101, 205107 (2020)
ABSTRACT: Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. In this talk, I will motivate the study of many-body chaos from the context of quantum thermalization and discuss its surprising connections with the quantum dynamics of black holes. I will then describe a numerical study of many-body chaos in the Sachdev-Ye-Kitaev (SKY) model, in which we leveraged massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators for previously inaccessible system sizes. Our numerical results verified analytical predictions on the thermalization dynamics of the SYK model and provided direct numerical evidence for many-body chaos, including the universal bound on its rate.
REFERENCES:
ABSTRACT: We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at a fixed temperature and chemical potential. Our method works at a finite temperature, beyond linear response and weak system-reservoir coupling, and allows for nonquadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped toward thermal equilibrium, in order to represent continuum baths, and a novel tensor-network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well-known Landauer-Büttiker theory for efficiency and power. We then simulate a three-site machine with nonquadratic interactions; remarkably, these lead to power enhancement without being detrimental to the efficiency. Finally, we demonstrate the capability of our method to tackle complex many-body systems by extracting the superdiffusive exponent for high-temperature transport in the isotropic Heisenberg model.
REFERENCES:
[1] M. Brenes, J.J. Mendoza-Arenas, A. Purkayastha, M.T. Mitchison, S.R. Clark and J. Goold, Phys. Rev. X 10, 032040 (2020)
[2] A. Levy and W. Dou, Physics 13, 129 (2020)
ABSTRACT: Future photonic quantum technologies and the fundamental understanding of macroscopic quantum phenomena require a generation of many photons, their propagation in large optical networks, and a subsequent detection and analysis of sophisticated quantum features. In this talk, we report on a recent experimental implementation of such a large-scale quantum system and its theoretical characterization. To this end, we benchmark our time-multiplexing framework that includes a high-performance source of multiphoton states and a large multiplexing network, together with unique detectors with high photon-number resolution, readily available for distributing quantum light and measuring complex quantum correlations. By exploiting symmetry and using powerful analysis tools, we can directly analyze quantum effects that would be inaccessible by classical means otherwise because of an exponential scaling. In particular, we produce on the order of ten photons, distribute them over 64 modes, determine correlation functions up to the 128th order, and certify nonclassicality with statistical significances of up to 20 standard deviations.
REFERENCES:
J. Tiedau, M. Engelkemeier, B. Brecht, J. Sperling, and C. Silberhorn. Phys. Rev. Lett. 126, 023601 (2021).
ABSTRACT: Controlling the dynamics of quantum systems with high-fidelity is becoming a necessity to advance quantum science and technology. Techniques known as shortcuts to adiabaticity (STA) tailor excitations in nonadiabatic processes to prepare a given state in a finite time, without the requirement of slow driving. Their developments in isolated quantum systems have found broad applications. I will first present an experimental demonstration of STA in the control of compression and expansion of a Fermi gas, which results into friction-free strokes that can be implemented to increase the power output of a heat machine while maintaining a high efficiency [1].
STA are however severely limited to isolated systems. Extending such control techniques to open systems is highly desirable in view of applications to cooling, and more generally, in finite-time thermodynamics. I will present a universal scheme for the control of open systems, defining a trajectory-based equation of motion that allows for the control of any arbitrary dynamics [2]. Its application will be given for controlling the temperature and squeezing of a single-particle thermal state in a harmonic trap [3.4].
REFERENCES:
[1] S. Deng, A. Chenu, P. Diao,F. Lu, S. Yu, I. Coulamy, A. del Campo, H. Wu. Superadiabatic quantum friction suppression in finite-time thermodynamics, Sci. Adv. 4:5909 (2018).
[2] S. Alipour, A. Chenu, A. Rezakhani, A. del Campo. Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution. Quantum, 4:336 (2020)
[3] L. Dupays, I. L. Egusquiza, A. del Campo, and A. Chenu. Superadiabatic thermalization of a quantum oscillator by engineered dephasing , Phys. Rev. Res. 2:033178 (2020)
[4] L. Dupays and A. Chenu. Dynamical engineering of squeezed thermal state, ArXiv2008.033027 (2020)
ABSTRACT: We investigate the normal mode spectrum of a trapped ion crystal at finite temperatures near the symmetry-breaking linear to zigzag transition. Experimentally, we excite and measure normal mode oscillations by amplitude modulating the Doppler cooling laser. The expected mode softening at the critical point, a signature of the second-order transition, is not observed. With the help of numerical simulations this is attributed to the finite temperature of the crystal, that leads to jumps between the two degenerate ground-states of the zigzag crystal. We develop an effective analytical model, which allows us to reproduce the low-frequency spectrum as a function of the temperature close to the transition point. The frequency shift of the soft mode is due to the higher order coupling to high frequency modes, which are in a thermal equilibrium at finite temperatures. This study could of importance for near ground-state cooling and maybe the normal mode spectrum near other symmetry-breaking transitions at finite temperature.
REFERENCES:
Jan Kiethe, Lars Timm, Haggai Landa, Dimitri Kalincev, Giovanna Morigi, Tanja E. Mehlstäubler, arXiv:2012.11236 (2020)
ABSTRACT: Recently, thermodynamic uncertainty relation has attracted broad interest in classical stochastic thermodynamics. In this talk, I introduce a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the system-environment interaction, I derive a quantum thermodynamic uncertainty relation via quantum estimation theory. The obtained relation holds for general open quantum systems with any counting observable and any initial state. I apply the relation to continuous measurement and the quantum walk to find that the system's quantum nature can enhance precision.
REFERENCES:
Yoshihiko Hasegawa, Phys. Rev. Lett. 126, 010602 (2021)
ABSTRACT: Squeezed state in harmonic systems can be generated through a variety of techniques, including varying the oscillator frequency or using nonlinear two-photon Raman interaction. We focus on these two techniques to drive an initial thermal state into a final squeezed thermal state with controlled squeezing parameters —amplitude and phase— in arbitrary time. The protocols are designed through reverse engineering for both unitary and open dynamics. Control of the dissipation is achieved using stochastic processes, readily implementable via e.g. continuous quantum measurements. Importantly, this allows for control of entropy and can yield to fast thermalization. So the developed protocols are suited to generate squeezed thermal states at controlled temperature in arbitrary time.
REFERENCES:
L. Dupays and A. Chenu, arXiv:2008.03307 (2020)
ABSTRACT: We introduce a dynamical picture, referred to as correlation picture, which connects a correlated bipartite state to its uncorrelated counterpart. This picture allows us to derive an exact dynamical equation for a general open-system dynamics with system-environment correlations included. This exact dynamics is in the form of a Lindblad-like equation even in the presence of initial system-environment correlations. For explicit calculations, we also develop a weak-correlation expansion that allows us to introduce systematic perturbative approximations. This expansion provides approximate master equations that can feature advantages over existing weak-coupling techniques. As a special case, we derive a Markovian master equation, which is different from existing approaches. We compare our equations with corresponding standard weak-coupling equations using two examples, for which our correlation-picture formalism is more accurate, or at least as accurate as the weak-coupling equations.
REFERENCES: