|speaker||Dr. Maximilian Prüfer and Mr. Stefan Lannig (Heidelberg University)|
|title||Quantum field simulations with spinor Bose-Einstein condensates|
In this talk we will present the recent results from the Rubidium BEC experiment in Heidelberg. In our
experiments we employ 87Rb spinor Bose-Einstein condensates in quasi-one-dimensional trapping
potentials. We will start by introducing our experimental setup and our newly developed read-out
schemes for complex-valued spin fields .
In the first part of the talk we present a method for extracting the equal-time quantum effective action from experimental observations . We exemplify our method experimentally in a regime far from equilibrium where we observed universal dynamics recently . The experimental results reveal a strong suppression of the four-vertex at low momenta emerging in the highly occupied regime.
In the second part we present our recent findings concerning the creation of vector solitons . We deterministically prepare three-component vector solitons by employing local spin rotations. The coherent nature of the multi-component solitons gives rise to a vector degree of freedom. We observe striking collisional properties which are quantitatively described by the integrable repulsive threecomponent Manakov model.
 Kunkel, P. et al., PRL 123, 063603 (2019).
 Prufer, M. et al., Nature Physics 1-5 (2020).
Prufer, M. et al., Nature 563, 217-220 (2018).
 Lannig, S. et al, arXiv: 2005.13278 (2020), accepted in PRL.
|title||Theoretical study of binary Bose-Einstein condensates under synthetic gauge fields|
In ultracold atomic gases composed of two component, synthetic gauge fields have been realized. The parallel magnetic fields are created by the mechanical rotation and the antiparallel fields are created by the optical dressing of the atoms. When the magnetic fields are sufficiently strong, the vortex lattices with different structures depending on the ratio of the intercomponent interaction to intracomponent one appears in the mean-field theory. While the phase diagram for parallel and antiparallel fields are the same in the mean-field theory, the ground states are different in the quantum Hall regime where the magnetic field is strong.
In this seminar, we discuss the vortex lattices in binary BECs in the lowest-Landau-level approximation from the effective field theory and the Bogoliubov theory. By renormalizing the coupling constants, we present the rescaling relation of the excitation spectra and the elastic constants by fitting them to the analytical expression. We show the fraction of the quantum depletion increases logarithmically as a function of a vortex number. We demonstrate the boundaries between different vortex-lattice phases shift by calculating the correction to the ground-state energy from the zero-point fluctuation in the Bogoliubov theory. We obtain the intercomponent entanglement spectra of vortex lattices in binary BECs which exhibit square root dispersion relations related to the emergence of the long-range interactions in the entanglement Hamiltonian. We also present the intercomponent entanglement entropy (EE) of vortex lattices for parallel (antiparallel) fields are larger than the other for repulsive (attractive) intercomponent interaction and EE increases logarithmically as a function of vortex number.
|title||Quantum coherence gap: confinement-deconfinement transition in quantum coherence|
|abstract||Relaxation dynamics of open quantum systems are controlled by the balance between coherent time evolution described by the Hamiltonian of the system and stochastic time evolution resulting from the interaction with an environment. A dynamical transition from Hamiltonian-driven coherent relaxation to dissipation-driven incoherent relaxation has been referred to as the coherent-incoherent transition. In this study, we show that the coherent-incoherent transition is closely related to a structural transition in the spectrum of the Liouvillian superoperator that describes the time evolution of the density matrix. A novel ingredient that plays a primary role in this study is “quantum coherence gap”. The eigenvalues of the Liouvillian can be classified into the following two groups: incoherent eigenvalues, whose eigenmodes are exponentially localized at the diagonal elements in the matrix representation, and coherent eigenvalues, whose eigenmodes are uniformly delocalized over the off-diagonal elements. The quantum coherence gap is defined as the minimal distance between the coherent and incoherent spectra along the real axis. From analytical arguments and exact diagonalization, we show that, while there exists a nonzero quantum coherence gap for a sufficiently strong dissipation, it closes below a critical dissipation strength. This quantum coherence gap closing is accompanied by a localization-delocalization transition at the diagonal elements of the eigenmodes. If the density matrix is mapped to a vector in the tensor product space between the bra-space and ket-space, the localization-delocalization transition in the density matrix is interpreted as a transition from a “confined” state, in which degrees of freedom in the ket-space and bra-space are strongly correlated, to a “deconfined” state, in which these degrees of freedom are uniformly delocalized in each space. In this picture, the quantum coherence gap corresponds to the minimal binding energy of the confined state, and its closing implies the onset of a confinement-deconfinement transition in the eigenmodes. The geometrical structure of the spectrum on the complex plane is related to the relaxation dynamics of open quantum systems. By numerically solving the quantum master equation, we demonstrate that the quantum coherence gap closing leads to a dynamical transition from an overdamped regime, in which an inhomogeneous initial state exponentially relaxes to the uniform steady state, to an underdamped regime, in which the particle density shows temporal oscillations.|
|title||\eta pairing of light-emitting fermions|
|abstract||Spontaneous emission of light is a fundamental consequence of the coupling between matter and quantized light. In this presentation, we show that strongly interacting fermions that spontaneously emit photons develop superfluid pairing correlations in the nonequilibrium steady state. The superfluid is characterized by pairing, which was shown to be an exact eigenstate of the Fermi-Hubbard model in the seminal work by C. N. Yang . We elucidate that an interplay between the Fermi statistics and spontaneous emission of light leads to the nonequilibrium pairing, which is distinct from the conventional BCS pairing in thermal equilibrium. Experimental implementation with ultracold atoms in an optical lattice is discussed.
 C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989).
|title||Test of eigenstate thermalization hypothesis based on local random matrix theory|
Recent developments in experiments have enabled us to realize isolated quantum systems with unprecedented accuracy, and local relaxations of such a system to thermal ensembles have been observed.
On the other hand, the state of an isolated quantum system remains pure if it is initially in a pure state.
How can we reconcile this discrepancy and justify the use of thermal ensembles that are mixed state?
The eigenstate thermalization hypothesis asserts that the eigenstates of many-body Hamiltonians are itself in thermal equilibrium, thereby reconciling the use of thermal ensembles with the unitary dynamics.
A mathematical argument based on ''typicality'' is proposed to justify this hypothesis . However, almost all Hamiltonians considered in that argument contain highly non-local and too-many-body correlations, and its result cannot extend to realistic situations with the locality of interactions .
In this talk, we numerically verify that the eigenstate thermalization hypothesis typically holds even with the locality of interactions while the fraction of systems which does not satisfy the hypothesis is significantly larger than that proposed before.
 P.Reimann, Phys. Rev. Lett.115.010403 (2015)
 R.Hamazaki and M.Ueda, Phys. Rev. Lett.120.080603 (2018)
|title||Embedding of the Lee-Yang Quantum Criticality in Open Quantum Systems|
|abstract||The Lee-Yang edge singularity has long been known as a critical phenomenon accompanied by anomalous scaling laws. Conventionally, this critical phenomenon has been discussed mainly from mathematical points of view because it involves concepts regarded as unphysical in classical systems, such as an imaginary magnetic field. In this seminar, we discuss the physical realization of the Lee-Yang edge singularity in quantum systems based on the quantum-classical correspondence and show that such realization is achieved in open quantum systems. Specifically, we embed the non-Hermitian quantum system in an extended Hermitian system by introducing an ancilla as an environment, and we find that the essential origin of the singularity is the fact that the physical quantity to be evaluated is the expectation value conditioned on the measurement outcomes of the ancilla and that the probability of the successful postselection of the events corresponding to this critical phenomenon becomes close to zero in the vicinity of the critical point. Moreover, we have derived unconventional scaling laws for finite-temperature dynamics, which are experimentally relevant and unique to quantum systems, as well as reproducing, for the zero temperature, the conventional scaling laws known in classical systems.|
|speaker||Prof. Haruki Watanabe (the University of Tokyo)|
|title||Review of recent developments of Lieb-Schultz-Mattis theorem|
|abstract||The Lieb-Schultz-Mattis theorem is a no-go theorem prohibiting the unique ground state with a nonzero excitation gap under certain conditions. The theorem was originally formulated for the S=1/2 Heisenberg spin chain more than a half century ago. Over years, the theorem has been refined in many important ways and it became a very powerful and general constraint applicable to much wider classes of Hamiltonians. In this talk, as requested, I will review the historical development of the theorem and try to cover as many recent refinements as possible.|
|title||Nonconvergence of Deep Q-Learning and Alternative Solutions|
|abstract||We notice that the conventional deep Q-learning which has been widely applied to various tasks as a reinforcement learning strategy actually does not have guaranteed convergence. Although it can produce state-of-the-art results on a few modern tasks, its performance may not improve steadily in the training process and may oscillate endlessly, and as a result, whether it finally produces good performance heavily relies on manual fine-tuning of the settings of its training, and the performance can also change dramatically from trial to trial due to the randomness. In this seminar, we review the general TD (temporal difference)-type value-based reinforcement learning and the convergence results thereof, and we show that the widely applied deep Q-learning algorithm actually does not have convergence guarantee, while another large-scale reinforcement learning algorithm A3C has. However, A3C is too data-inefficient to work as a substitute for deep Q-learning. Therefore, we try to propose alternative methods to deal with the nonconvergence issue of deep Q-learning while keeping its efficiency. We discuss the properties and the performances of our alternative methods and compare them with the conventional deep Q-learning.|
|title||Stochastic Gradient Descent with Large Learning Rate|
As a simple and efficient optimization method in deep learning, stochastic gradient descent (SGD) has attracted tremendous attention. In the vanishing learning rate regime, SGD is now relatively well-understood, and the majority of theoretical approaches to SGD set their assumptions in the continuous-time limit. However, the continuous-time predictions are unlikely to reflect the experimental observations well because the practice often runs in the large learning rate regime, where the training is faster and the generalization of models are often better. In this work , we propose to study the basic properties of SGD and its variants in the non-vanishing learning rate regime. The focus is on deriving exactly solvable results and relating them to experimental observations. The main contributions of this work are to derive the stable distribution for discrete-time SGD in a quadratic loss function with and without momentum. We then apply our theory to study the approximation error of variants of SGD, the effect of mini-batch noise, and the escape rate from a sharp minimum.
 K. Liu*, L. Ziyin*, and M. Ueda, in preparation.
|title||Rigorous bounds on the heating rate under Thue-Morse quasi-periodic driving and its randomized variants|
Recent theoretical studies revealed that a periodically driven system exhibits prethermalization when the frequency of the driving field is much larger than a typical local energy scale. It has also been proved that a prethermal state under fast periodic driving has an astonishingly long lifetime: it scales exponentially in the frequency. These theoretical results are obtained by utilizing the Magnus expansion [1,2].
It is an important yet challenging problem to understand what happens when the driving filed changes rapidly but not periodically. It is known that an isolated system often immediately heats up to infinite temperature under random driving, while some works show that prethermalization happens under certain quasi-periodic driving. In this talk, I briefly review some recent works towards this direction, and talk about our recent study on a rigorous upper bound on the heating rate for quantum many-body systems under quasi-periodic Thue-Morse driving and its randomized variants introduced in [3,4]. Although the driving is not periodic in time, the Magnus expansion is a useful tool to evaluate the heating time.
 T. Kuwahara, T. Mori, and K. Saito, Ann. Phys. 367, 96 (2016)
 T. Mori, T. Kuwahara, and K. Saito, Phys. Rev. Lett. 116, 120401 (2016)
 S. Nandy, A. Sen, and D. Sen, Phys. Rev. X 7, 031034 (2017)
 H. Zhao, F. Mintert, R. Moessner, and J. Knolle, arXiv:2007.07301
|title||A Few Topics on Discrete-Time Stochastic Gradient Descent|
|abstract||Recently, we have studied the nature of the stochastic gradient descent (SGD) in the discrete-time regime. This enables finding analytical solutions to the SGD in simple settings. This presentation builds on that work. In particular, we discuss (1) how discrete-time SGD in anharmonic potential leads to chaos and (2) exact solutions to the minibatch noise for a linear regression.|
|title||Game-Theoretical Models and Emergence of Cooperation|
|abstract||Game theory is commonly used to explain human decision-making processes and has an important role in economics, biology and other various fields. In this seminar, I would introduce two game-theoretical models: an independent multi-agent reinforcement learning model and a population dynamics model. We mainly focus on what is called the prisoner's dilemma game, where two rational players are likely to mutually defect and fail to reach the optimal choices for both players. From learning trajectories of reinforcement learners, we can see how they change their strategies with time and result in converging to mutual defection. We then demonstrate the emergence of mutual cooperation in a population dynamics model and the observation that a large-population setting can enhance and stabilize mutual cooperation.|
|title||Topological Field Theory of Non-Hermitian Systems|
We develop a field-theoretic description of intrinsic non-Hermitian topological phases. Because of the dissipative and nonequilibrium nature of non-Hermiticity, the theory is formulated solely in terms of spatial degrees of freedom, which contrasts with the conventional theory defined in spacetime. It describes and predicts unique non-Hermitian topological phenomena, such as the unidirectional transport in one dimension and the chiral magnetic skin effect in three dimensions. From the field-theoretic perspective, the non-Hermitian skin effect, which is anomalous localization due to non-Hermiticity, is shown to be a signature of an anomaly.
Reference: K. Kawabata, K. Shiozaki, and S. Ryu, arXiv:2011.11449.
|title||Fluctuation Dissipation Theorem and Quantum Fisher Information|
In this seminar, I would like to talk about the attempt to give operational meaning to quantum Fisher information by introducing these existing studies about the fluctuation-dissipation theorem (FDT) and quantum Fisher information (QFI).
The FDT  shows a universal relation between linear response functions and fluctuations represented by time correlations both in classical and quantum systems. More specifically, FDT relates canonical time correlations (can-TCs) and symmetrized time correlations (sym-TCs), which correspond to response functions and fluctuations, respectively. However, in quantum systems, fluctuations calculated from measured values need not coincide with sym-TCs or can-TCs because of the disturbance by measurements. This fact has already been mentioned in Ref. .
The recent study showed the coincidence between sym-TCs and time correlations calculated from measured values in macroscopic systems . In Ref. , the measurement with the minimal disturbance (quasiclassical measurement) is introduced. The time correlations between two physical quantities can be calculated from the expectation value of the product of two values measured by the quasiclassical measurement of the first quantity and the quasiclassical measurement of the second quantity after the first one. This calculated time correlation coincides with the sym-TC in the thermodynamic limit when the system and physical quantities satisfy the cluster conditions for the quantum central limit theorem . This result assures the operational meaning of sym-TCs , which correspond to SLD quantum Fisher information, in the macroscopic equilibrium systems.
Moreover, I review the relation between FDT and quantum information geometry. In a system at equilibrium, quantum Fisher information can be determined by measuring linear response function through the generalized Kubo formula, which relates Fourier components of can-TCs and other correlation functions defined by quantum Fisher information .
 R. Kubo, Journal of the Physical Society of Japan 12, 570 (1957).
 A. Shimizu and K. Fujikura, J. Stat. Mech. (2017) 024004.
 D. Goderis and P. Vets, Commun. Math. Phys. 122, 249 (1989).
 T. Shitara and M. Ueda, Phys. Rev. A 94, 062316 (2016).