Research

Quantum Synchronization

Synchronization processes are ubiquitous in nature from the flashing of fireflies to the firing of neurons in the brain. Despite a plethora of work on classical synchronization, the idea of quantum synchronization has only recently gained attention. Unlike classical synchronization which has a well-defined notion, quantum synchronization has several facets. For example, discrete quantum systems are said to be in synchrony when the coherences of the density matrix synchronize, giving us the phase space definition of synchronization. Alternatively, continuous quantum systems that have a well-defined classical limit are said to synchronize when their classical counterparts mimic a known classical synchronization model. We study discrete and continuous synchronization models through the lens of quantum thermodynamics. In the discrete case we generalized the Scovil and Schulz-DuBois three level maser heat engine to a general N-level scenario and showed how the two different mechanisms of synchronization, i.e.,  entrainment and mutual synchronization, can either cooperate or compete depending on the thermodynamic operating regime of the heat engine.  Moreover, the cooperation and competition between these mechanisms of synchronization is technologically vital since it lower bounds the efficiency of the engine. In the continuous case scenario, we applied the idea of quantum speed limits to find the minimal time and energy cost of synchronizing a quantum system in non-Hermitian quantum open systems. In the case of a coupled waveguide model we found the minimal energy cost of synchronizing a quantum system and moreover showed that the quantumness of the system allows it to be synchronized for parameters where classical synchronization is impossible. Our results highlight the intricate connections between quantum thermodynamics and synchronization and show how synchronization can be made useful in the quantum regime.

• T. Murtadho, J. Thingna, and S. Vinjanampathy, Phys. Rev. A 108, 012205 (2023).

• T. Murtadho, S. Vinjanampathy, and J. Thingna, Phys. Rev. Lett. 131, 030401 (2023).

• M. Aifer, J. Thingna, and S. Deffner, Phys. Rev. Lett. 133, 020401 (2024). 

Quantum Measurements

Unlike classical systems, a measurement performed on a quantum system always alters its state. Thus, any diagnostic method that involves measuring a quantum device will affect its performance, and a prior the impact on the performance metrics is not clear.  Hence, with the advancement of quantum technologies and quantum devices becoming a reality, improvement in diagnostic tools is the need of the hour. We focus our attention on developing novel diagnostic tools tailored to specific types of measurements in quantum devices. To measure the sum of values of an observable we introduce a repeated contact scheme in which an ancillary system (aka a pointer) repeatedly interacts with the quantum device exchanging information about the measured observable. Once the required number of interactions, determined by the upper limit (N) of the sum of values of the observable, is performed the pointer is finally measured out yielding information about the entire sum in a single readout.  The repeated contact scheme maintains the precision of the pointer and does not lead to a deterioration in precision with N like other standard schemes. We apply this approach to study quantum heat engines and show that all performance metrics like work output, efficiency, maximum power, and reliability are enhanced with the repeated contact scheme. Another example we consider is a parasitic relation between two quantum devices, namely an Otto engine that charges a quantum battery. In this case, monitoring the battery enhances certain performance metrics (charging speed) while not monitoring the battery allows other performance metrics to be enhanced (amount of useful charge stored in the battery aka ergotropy). The enhancements arise due to the possibility of coherence propagating in between the strokes of the engine cycle, an impossibility with other standard methods. Our results highlight the importance of taking into account the nature of diagnostic tools for monitoring quantum devices.

• J. Thingna and P. Talkner, Phys. Rev. A 102, 012213 (2020).

• J. Son, P. Talkner, and J. Thingna, Phys. Rev. X Quantum 2, 040328 (2021).

• J. Son, P. Talkner, and J. Thingna, Phys. Rev. A 106, 052202 (2022).

• D. Šafránek and J. Thingna, Phys. Rev. A 108, 032413 (2023).

Many-body open systems

Many-body systems refer to structures containing a large number of interacting particles whose individual properties may (or may not) be simple, but their collective behaviour poses a complex challenge. Over the last few decades, several interesting physical phenomena like localization or synchronization have been discovered in such systems, but very little is known about the interplay of the mechanisms that lead to these effects and dissipation due to a thermal environment. In the classical case, we treat such many-body open systems using the traditional Gillespie approach and envisage a complex network of thermal machines that undergo a phase transition between a stable fixed point to the synchronizing regime. The presence of the collective synchronizing behavior tends to make the machine efficient with maximum power output, indicating that a complex network of machines is better off. Similar results are observed in effective nonlinear models of synchronization, namely, the inertial Stuart-Landau model that displays a complex phase diagram with bistable regions. On the other hand, the quantum many-body open systems are notoriously difficult due to their increased computational complexity. Hence, we develop a robust Matrix Product Operator (MPO) based algorithm to treat physical systems connected to thermal baths relying on the minimum number of approximations (Redfield-based MPO approach). This allows us to explore parameter regimes beyond the standard Lindblad-based MPO approaches that tend to neglect the strong interactions in these many-body systems. Thus the toolsets we develop not only help explore classical many-body systems but also help understanding the complex dynamics of quantum many-body systems.

• T. Herpich, J. Thingna, and M. Esposito, Phys. Rev. X 8, 031056 (2018).

• X. Xu, J. Thingna, C. Guo, and D. Poletti, Phys. Rev. A 99, 012106 (2019).

• J.-W. Ryu, A. Lazarescu, R. Marathe, and J. Thingna, New J. Phys. 23, 105005 (2021).

Landau-Zener approach to open systems

Systems in contact with a large reservoir equilibriate when all their independent degrees of freedom simultaneously interact with infinite degrees from the reservoir. Such an interaction leads to dissipation and the system relaxes to a canonical state (weak system reservoir coupling) governed by the temperature and chemical potential of the reservoir. In order for the system to reach the canonical/Gibbs state, two properties are of utmost importance: 1.) Sufficient mixing between system and reservoir (i.e., the finite system interacts with infinite reservoir degrees simultaneously), and 2.) (local-)detailed balance condition for the transition rates of the reservoir. These conditions are also essential to obtain a reduced description of the system dynamics commonly known as a master equation. How do these conditions differ if the reservoir is finite and/or the system is driven? In general, this is still an open question but for a sub class of systems that are linearly driven such that they interact with reservoir degrees sequentially we can obtain a master equation that is of a Lindblad form in the diabatic limit. In other words, a system interacting with infinite degrees of the reservoir simultaneously (traditional picture) is equivalent to a system interacting with a single reservoir degree one after the other but infinitely fast. The latter picture requires Landau-Zener physics and we can also relax the diabatic condition to obtain a Markov chain that is valid for finite reservoirs. This regime of validity of the Landau-Zener Markov chain is contrasting to the tradition picture and interestingly in both regimes we can obtain a complete nonequilibrium thermodynamic description of the problem. The driven system can then be used as a machine that utilizes the coherences and converts them into useful work.

• J. Thingna, F. Barra, and M. Esposito, Phys. Rev. E 96, 052132 (2017).

• J. Thingna, M. Esposito, and F. Barra, Phys. Rev. E 99, 042142 (2019).

Symmetries in open quantum systems

Symmetries is a fundamental property of nature. In physical chemistry, structural symmetry often manifests in spectral, polarity, chirality, etc. but little attention is directed towards its role in non-equilibrium transport processes. Our work represents a major effort to extend the concept of symmetry from equilibrium to non-equilibrium dynamics in realistic chemical systems affected by static disorder or dynamical noise. In this work we show that any single-body system having geometrical symmetries in the structure possess invariant sub-spaces that can lead to multiple steady-states. These excess steady-states due to symmetries correspond to the anti-symmetric subspace and hence do not transmit energy or particles in a non-equilibrium system. Disorder typically breaks the perfect symmetry but the reminiscence of the structure is encapsulated in the long-time quasi-stationary state dynamics. Thus, even for disordered systems the underlying symmetry can be detected via the dynamical currents. We also investigate the effect of external fields, like magnetic, that could break the perfect symmetry of the system. The interplay between the presence of symmetries and its systematic breaking via the magnetic field enables us to propose a fully-connected network that could act as a switch to change the steady-state currents without changing the affinities.

• J. Thingna, D. Manzano, and J. Cao, Scientific Reports 6, 28027 (2016).

• J. Thingna, D. Manzano, and J. Cao, New J. Phys. 22, 083026 (2020).

• Á. Tejero, J. Thingna, and D. Manzano, J. Phys. Chem. C 125, 7518 (2021).

• J. Thingna and D. Manzano, Chaos 31, 073114 (2021).

Asymptotic states of open quantum systems

Statistical mechanics has been one of the corner stones of physics where the distribution of a system, weakly interacting with a thermal bath, is the well-known Gibbs distribution. However, when the coupling to the thermal bath is not weak the emergence of the generalized Gibbs distribution from dynamical laws presents itself as a formidable problem. In this work we address this problem using the tools of quantum open systems; we first show that for all perturbative second-order master equations the steady state solution is correct only up to zeroth-order in the system-bath coupling. Hence in order to obtain the steady state result correct up to second-order in coupling strength we develop a novel scheme using analytical continuity techniques and the Redfield master equation. For the one bath case we analytically show that our approach results in the well-known generalized Gibbs distribution. For the multiple bath problem exact results are highly non-trivial except the case of harmonic oscillator for which our approach gives the correct non-equilibrium distribution. We also address the non-trivial problem of time-dependent systems and find that under certain conditions the system follows an effective Floquet-Gibbs state. The Hamiltonian describing the Floquet-Gibbs state is given by the Magnus expansion of the time-dependent Floquet Hamiltonian. The characterization of the asymptotic state allows us then to extend the basic laws of thermodynamics to the time-dependent scenario.

• J. Thingna, J.-S. Wang, and P. Hänggi, J. Chem. Phys. 136, 194110 (2012). 

• J. Thingna, J.-S. Wang, and P. Hänggi, Phys. Rev. E 88, 052127 (2013).

• T. Shirai, J. Thingna, T. Mori, S. Denisov, P. Hänggi, and S. Miyashita, New J. Phys. 18, 053008 (2016).

• X. Xu, J. Thingna, and J.-S. Wang, Phys. Rev. B 95, 035428 (2017).

• T. Becker, A. Schnell, and J. Thingna, Phys. Rev. Lett. 129, 200403 (2022).

Thermal transport

The role of anharmonic interactions in thermal transport has attracted considerable theoretical interest due to its crucial role in phononic devices. To date, there have been only a handful of approaches which can handle anharmonic effects based on a microscopic quantum theory. One of the most promising of these approaches is the quantum master equation (QME) approach which handles the anharmonicity exactly but treats the system-bath coupling perturbatively. The QME approach was applied to study small molecular junctions interacting via a quartic or double-well potential and photonic cavities with photons interacting via two-photon hopping. Exotic properties such as negative differential thermal conductance (NDTC) and a phase transition from heating to cooling phase were observed. Another approach we developed is based on the famous Feynmann-Jenson inequality, where we try to use the equilibrium properties of an anharmonic system to describe non-equilibrium effects. The approach termed as quantum self-consistent phonon theory (QSCPT) converts the anharmonic problem to an effective harmonic one by treating the anharmonicity only via the first order Feynmann diagram self-consistently . A variant of QSCPT based on non-equilibrium Green's function approach [Quantum self-consistent mean field (QSCMF)] is also proposed which can handle the system-bath coupling exactly, but is limited to the first order Feynmann diagram while treating the anharmonicity. Both QSCPT and QSCMF have been used to study rectification effects in small molecular systems.

• J. Thingna, J. L. García-Palacios, and J.-S. Wang, Phys. Rev. B 85, 195452 (2012).

• L. Zhang, J. Thingna, D. He, J.-S. Wang, and B. Li, EPL 103, 64002 (2013).

• J. Thingna, H. Zhou, and J.-S. Wang, J. Chem. Phys. 141, 194101 (2014). 

• D. He, J. Thingna, J.-S. Wang, and B. Li, Phys. Rev. B 94, 155411 (2016).

• D. He, J. Thingna, and J. Cao, Phys. Rev. B 97, 195437 (2018).

• J.-Y. Han, D. Leykam, D. G. Angelakis, and J. Thingna, Phys. Rev. A 104, 052220 (2021).

Thermoelectric transport

Thermoelectric properties of systems have been investigated for a long time using the Onsager transport matrix. The transport matrix, along with the Onsager reciprocal relations, were used to explore the effect of nonlinearity on the steady-state thermoelectric current, i.e., electric current generated by a thermal gradient. The nonlinearity was introduced by considering nanoelectromechanical systems (NEMS), wherein the interaction strength between the electronic degrees of freedom and the mechanical oscillator can be manipulated. Tuning the interaction strength helped switch directions of the thermoelectric current and hence achieve a knob to mechanically control the currents. Contrary to Joule heating, that always heats the oscillator, the thermoelectric current induces a backaction to cool the oscillator. The effect of time-dependent external gate voltage was also examined and it was found that the external driving violates the critical Onsager reciprocal relations. The violation could lead a significant boost in the thermoelectric efficiency and help build devices that could efficiently convert heat to electricity.

• H. Zhou, J. Thingna, J.-S. Wang, and B. Li, Phys. Rev. B 91, 045410 (2015).

• H. Zhou, J. Thingna, P. Hänggi, J.-S. Wang, and B. Li, Scientific Reports 5, 14870 (2015).

• G. Tang, J. Thingna, and J. Wang, Phys. Rev. B 97, 155430 (2018).

Spin transport 

Spintronics has been one of the most rapidly growing fields of the past two decades. The field has initially dealt with the engineering of devices with itinerant spin carriers, namely electrons, based on phenomenological models to deal with mesoscopic systems. In order to study the effect of device geometries we developed a generalised three-dimensional spin drift diffusion model and investigated the effect on the spin-injection ratio. Our calculations indicate that once the device dimensions are close to the spin-diffusion length, the simplistic model breaks down and three-dimensional simulations become essential. In recent times the interest has been diverted from itinerant spin carriers to the nonitenerant systems mainly due to the low power dissipation. These nonitenerant systems or magnetic insulators can be easily modelled by the spin-1/2 XXZ model making them  lucrative candidates for theoretical studies. To study such magnetic insulators we proposed a unique model to inject pure spin currents using a thermal drive via the spin-Seebeck effect. Spin-rectification was the main quantity of interest and novel effects of oscillation with system-size and high range of tunability with external magnetic field were found, hopefully guiding experimentalists to build better spin-based diodes and transistors. 

• J. Thingna and J.-S. Wang, J. Appl. Phys. 109, 124303 (2011).

• J. Thingna and J.-S. Wang, EPL 104, 37006 (2013).

• G. Tang, J. Thingna, and J. Wang, Phys. Rev. B 97, 155430 (2018).