Research
Bayesian parameter estimation using Gaussian states and measurements
Simon Morelli, Ayaka Usui, Elizabeth Agudelo, Nicolai Friis Quantum Sci. Technol. 6 025018. [arXiv:2009.03709]
For parameter estimation, local estimation is commonly used, but its drawback is that it is not well defined when no initial information about the parameter to be estimated is available, e.g., when few measurements are performed. On the other hand, Bayesian estimation can be applied no matter how much initial information is present. In this work, we considered three parameter estimation scenarios (estimation of displacements, phases, and squeezing strengths) in continuous-variable quantum metrology and implemented Bayesian estimation. For each of these scenarios, we investigated the precision achievable with single-mode Gaussian states under homodyne or heterodyne detection and determined the probe state that provides the best performance. This work did not focus on revealing optimal sets of probe state and measurement schemes to achieve asymptotic scaling advantages, i.e. the Heisenberg limit. These sets are often difficult to prepare or carry out. Rather, our strategy was to achieve good performance in a single shot using feasible states and measurements. This comprehensive study provides an important reference point for Bayesian parameter estimation and will be a good basis for more advanced investigation into more complicated setups.
Spin-orbit coupling in the presence of strong atomic correlations
Ayaka Usui, Thomás Fogarty, Steve Campbell, Simon. A. Gardiner, and Thomas Busch, New J. Phys. 22 013050 (2020) [arXiv].
An article for non-physicists is [here].
Spin–orbit coupling (SOC) is an effect that was initially discussed in systems of charged particles. It is of large prominence in condensed matter physics and underlies, for example, the appearance of the spin Hall effect or of topological insulator states. The recent progress in implementing synthetic SOC in systems of cold neutral atoms has led to significant progress in this respect and controllable systems with long coherence times and a lack of impurities are now experimentally available.
A lot of research about SOC of cold atoms has focused on many-particle systems such as Bose-Einstein condensates (BECs) by, for example, expressing the systems under the mean-field approximation and dealing with effective single-particle states. It is shown that by changing parameters such as SOC strength, BECs with SOC can undergo phase transition and go through three phases, the stripe phase, magnetised phase, and single minimum phase [Y. Li, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 108, 225301 (2012)]. In the stripe phase, the ground state is given by superposition between a state with positive momentum and one with negative momentum. The momentum difference generates interference pattern in total density profile, which leads to supersolid. In the magnetised phase, the ground state is degenerate between the positive-momentum state and the negative-momentum state. In the single minimum phase, the ground state is just a stationary state.
A problem we point out is that discussion in mean-field regime is limited to weak contact interactions and does not fully explain many-body effects. It is important to reveal strong contact interaction regime because strong interactions are ingredients of quantum correlations such as entanglement. Moreover, in general, the system is described with operators, but with the mean-field approximation the system is simplified with classical fields, which unable one to see quantum correlations.
Few-particle systems can help one address these problems because these systems enable one to explore the systems exactly and cover strong interaction regime perfectly. A simple system is two-particle system. We investigate the ground state in two interacting particle system with SOC in one dimension to compare it with the ground state in mean-filed regime and see a unique effect of strong interactions.
In short, what we have discovered is the ground state not seen in the mean-field regime. The ground state can include a contribution from the anti- symmetric spin state, even though the system is bosonic. The global entanglement shared between the real- and pseudo-spin spaces changes drastically at a transition to another phase.
Quantum probe spectroscopy for cold atomic systems
Ayaka Usui, Berislav Buča, and Jordi Mur-Petit, New J. Phys. 20 103006 (2018) *video abstract is available [arXiv]
Atomic gases trapped in optical lattices are great platforms for quantum simulation of strongly correlated phases of matter. A powerful tool to study these systems is quantum gas microscope. Since there are various experimental techniques to study condensed matter systems, a wide range of techniques to characterise a quantum simulator are required, probing for instance its density, multi- particle correlations, temperature, or excitation spectrum. The progress in control and measurement methods at the single-atom level provides an approach based on utilising quantum impurities (e.g. single atoms in a different internal state or belonging to an entirely distinct atomic species [A. Recati, P. O. Fedichev, W. Zwerger, J. von Delft, and P. Zoller, Phys. Rev. Lett. 94, 040404] as nondestructive quantum probes of many-body quantum systems.
I studied a two-level impurity coupled locally to a quantum gas on an optical lattice (See Fig, 1), and I aimed to explore information encoded in the impurity dynamics. I solved the von Neumann equation analytically by assuming that the density matrix of the composite system is separable at all times. The assumption is rigorously justified for weak coupling and short evolution times. Also, for a more realistic situation, dephasing of the probe (the impurity) was investigated. This can be modelled using the standard Markovian approach to open quantum systems, and the time-evolved state is obtained by solving the Lindblad master equation. As a result, it was found that the evolution of the impurity encodes information on the local excitation spectrum of gas at the coupling site. Based on this, I designed a nondestructive method to probe the lattice system's excitations in a broad range of energies by measuring the state of the probe using standard atom optics methods. This protocol constitutes a new tool to characterise atomic gases in optical lattices.
Since I have contributed to the whole discussion except for the dephasing, I will focus on its result. Let me consider that there is a superposition of four eigenstates in a lattice and all of the four eigenstates overlap at the coupled site to the probe. The probing protocol is the following (See Fig. 1): the probe is initialised in its ground state, and follows a Ramsey sequence, interacting with the lattice for a while before being measured in the pseudo- spin basis. By performing Fourier transformation of the population of the excited state of the probe, it is seen that each peak of them corresponds to each difference between the eigenenergies of the lattice state (See Fig. 2). In this way, the probe’s evolution tells one information on excitation spectrum of the lattice.
Dynamical phase transitions and temporal orthogonality in one-dimensional hard-core bosons: from the continuum to the lattice
Thomás Fogarty, Ayaka Usui, Thomas Busch, Alessandro Silva, and John Goold, New J. Phys. 19, 113018 (2017). [arXiv]
The realisation of isolated system of cold atoms has motivated one to investigate non- equilibrium phenomena and quantum thermodynamics, which are usually inaccessible in conventional condensed matter physics. Recently, Heyl et al. have reported that there is equivalence between equilibrium phase transitions (EPTs) and dynamical phase transitions (DPTs) [M. Heyl, A. Polkovnikov, and S. Kehrein, Phys. Rev. Lett. 110, 135704] (See the below diagram). In EPTs the partition function 𝑍(𝛽) gives zero, which results in that free energy 𝐹(𝛽) shows singularities. On the other hand, in DPTs the survival function g(𝑡) gives zero, which results in that the rate function 𝑓(𝑡) shows singularities. Since the work was published, DPTs have been studied in various models. However, there was no research of DPTs in the original experiments which started the field of non-equilibrium dynamics, i.e. phase transition across the superfluid to Mott insulator and the dynamics in strongly interacting gas in one dimension.
To fill the void, it is necessary to investigate DPTs triggered by superfluid-Mott-insulator transition. This situation can be realised by giving a quench such as suddenly turning on a lattice potential, which undergoes a pinning transition to an insulator. I considered infinite strongly interacting particles in one dimension, Tonks-Girardeau (TG) gas, are trapped in a box potential. TG gases allow one to map the system into free fermions due to the Bose-Fermi mapping theorem and describe some many-particle quantities with the single-particle states. Zeros of the survival probability have been suggested to indicate DPTs. A natural question is whether the DPTs can be detected. To address the question, I investigated whether such zeros can be tied to the dynamics of physically observables in the systems.
It was found that in general the periodicity of the momentum distribution does not agree with the non-analyticities in the rate function (See Fig. 1). This means that the orthogonality of the time-evolved state to the initial state, connecting to the DPT, cannot be detected by looking at the temporal behaviour of local observables.
Rabi-coupled countersuperflow in binary Bose-Einstein condensates
Ayaka Usui and Hiromitsu Takeuchi, Phys. Rev. A 91, 063635 (2015). [arXiv]
A feature of Bose-Einstein condensates (BECs) is superfluidity. Flow in superfluid becomes unstable for larger relative velocity with an external potential than a critical value. The realisation of multi-component BECs enables one to study mixture of different kinds of superfluid. In the mixture, two counter-propagating flow is called coundersuperflow. Hammer et al. applied a magnetic field to a one-dimensional BEC with a coherent coupling between components [C. Hamner, Yongping Zhang, J. J. Chang, Chuanwei Zhang, and P. Engels, Phys. Rev. Lett. 111, 264101], called Rabi coupling. The group considered that the magnetic field made the Rabi coupling non-uniform. However, it is also expected that the magnetic field accelerated each component differently and generated a countersuperflow.
To analyse the experiment, it is necessary to study countersuperflow with Rabi coupling. I aimed to reveal what kind of state is stabilised in Rabi-coupled countersuperflow. A point is how the instability of coutersuperflow is modulated by Rabi coupling. I solved the non-linear Schrodinger equation analytically and numerically, called Gross-Pitaevskii (GP) equation, which describes wave functions of BECs in mean-field regime.
I found that a soliton is stabilised in the system. This kind of structure is not specific to this system, and for example it is known to be stabilised between two vortices in the vortex-molecule structure in rotating Rabi-coupled two-component BECs. It is worth investigating the stability of such a structure. I showed that a periodic density pattern is stabilised in countersuperflow under Rabi coupling (See Fig. 1). For the coupling, the relative velocity between components is localised around density depressions. The soliton becomes unstable when the localised relative velocity exceeds a critical value. The stability-phase diagram of this system is evaluated with a stability analysis of countersuperflow.
In four years, K. Ihara et al. investigated the same instability analytically [K. Ihara and K. Kasamatsu, Phys. Rev. A 100, 013630 (2019)].
