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In isolated quantum systems satisfying ETH and in quantum open systems where the detailed balance conditions hold, the initially nonequilibrium state relaxes to thermal equilibrium state after long time. On the other hand, quantum open systems that do not satisfy the detailed balance condition generally have non-trivial non-equilibrium stationary states. Theoretical studies of such systems are rapidly developing, inspired by recent experimental techniques (quantum measurement, control of external dissipation, etc.).
・Novel transitions in Non-Unitary Boson Sampling Dynamics
Non-hermitian quantum mechanics has been actively studied in the past few years as one of the descriptions of open quantum systems, and many experiments exist, including those on optical systems. However, the fundamental question of to what extent non-Hermitian quantum mechanics exhibits quantum nature has rarely been discussed.
In the unitary dynamics, quantum properties can be discussed in terms of computational complexity. In particular, in the boson sampling problem, we consider the distribution of the output of a boson that passes through a quantum optical system. If this distribution cannot be efficiently sampled classically, it implies a certain quantum supremacy.
We consider non-unitary boson sampling in quantum optical systems and find that non-unitarity enhances the classical property as well as novel transitions related to computational complexity. In particular, PT symmetry breaking, which is unique to non-unitary dynamics, has a great effect on the transition of the efficiency. First, when PT symmetry is unbroken, we find only one dynamical transition, upon which the distribution of bosons ceases to be approximated by a efficiently computable one of distinguishable particles. If the system enters a PT -broken phase, the threshold time for the transition is suddenly prolonged. Furthermore, this phase also exhibits a notable dynamical transition on a longer time scale, at which the boson distribution again becomes computable.
K. Mochizuki and R. Hamazaki, Phys. Rev. Research 5, 013177 (2023). [arXiv:2207.12624]
Discrete-time crystals in open quantum systems in cavity QED and circuit QED systems. In the former case, for which the number of atoms is large, there appears a phase where the spin and other oscillations are stabilized for a long time. In the latter case, where the number of atoms is small, the tendency remains for a short time.
・Dissipative discrete time crystals
A discrete-time crystal is a quantum many-body system in which the oscillations of a physical quantity with period nT (n=2,3,...) are stabilized by the many-body effect, even though it is driven by period T. Before our work, discrete-time crystals have been realized only in isolated quantum systems and have been thought to be unstable in open systems.
We have investigated the time evolution of the periodically driven open Dicke model, which is realized by cavity QED. We found that when the number of atoms is very large, several different discrete-time crystal phases are stabilized, reflecting the semiclassical bifurcation. We also found that even when the number of atoms is finite and quantum effects are strong, the discrete-time crystal phases can be stabilized to exponentially long times by dissipation only when the interaction is strong.
Z. Gong, R. Hamazaki, and M. Ueda. Phys. Rev. Lett. 120, 040404 (2018). [arxiv:1708.01472]
・Neural stationary states for open quantum many-body systems
Numerical calculations of open quantum many-body systems are more difficult than those of isolated systems, and effective numerical methods for general systems have long been desired. Based on the recent application of machine learning techniques to isolated quantum many-body systems, we have demonstrated that neural-network states can be used to describe the steady state of open quantum systems. We particularly confirmed that our method can be used to describe the steady state of one-dimensional and two-dimensional quantum dissipative spin models. In fact, it is more efficient than the exact Lanczos method for finding the steady state.
N. Yoshioka and R. Hamazaki. Phys. Rev. B 99, 214306 (2019). [arXiv:1902.07006]
Neural-network stationary states described by the restricted Boltzmann machine.
・Liouvillian skin effect and its relation to the relaxation time and the spectral gap
It is well known that the relaxation time of an isolated system is given by the inverse of the spectral gap. Similarly, it has been believed that the gap of the Liouvillian product of the dynamics is given by the inverse of the relaxation time even in open systems. We have shown that this relation is violated in open systems when "skin effects" occur, where particles localize at the edges of the system (due to the non-Hermitian nature unique to dissipative systems). Instead, we derived a new generalized relation between the relaxation time, the spectral gap, and the localization length of the system.
T. Haga, M. Nakagawa, R. Hamazaki, and M. Ueda. Phys. Rev. Lett. 127, 070402 (2021). [arXiv:2005.00824]
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