Session S33: Open Quantum Systems I

Coherence resonance in open quantum systems

In this study, we demonstrate that coherence resonance, in which regularity of the oscillatory response of a nonlinear system is maximized at a certain optimal noise intensity, occurs in open quantum systems. We numerically demonstrate that quantum coherence resonance occurs in a quantum van der Pol system subjected to squeezing. We first demonstrate that quantum coherence resonance occurs in the semiclassical regime, namely, the regularity of the system's oscillatory response is maximized at an optimal intensity of quantum fluctuations, and interpret this phenomenon by analogy with classical noisy excitable systems using semiclassical stochastic differential equations. We further investigate the stronger quantum regimes and demonstrate that the regularity of the system's response can exhibit the second peak as the intensity of the quantum fluctuations is further increased. We show that this second peak of resonance is a strong quantum effect that cannot be interpreted by a semiclassical picture, in which only a few energy states participate in the system dynamics.   

Distributed-Memory Tensor Network Algorithms for Simulating Open Quantum Systems

Open quantum systems, typically governed by the Linblad quantum master equation (LQME), are a useful model for simulating a real quantum computer with noise. We investigate the non-equilibrium dynamics of open quantum systems under the LQME using tensor network states. Using the Cyclops Tensor Framework (CTF), a distributed memory tensor contraction library, we simulate the evolution of a quantum system by representing the density matrix as a matrix product state (MPS) under a Choi isomorphism. The massively parallel nature of our algorithm will let us perform tensor operations at a faster rate than traditional libraries. This will allow us to use larger tensors, thus obtaining a more accurate ansatz. We will use this simulation to gauge the fidelity of noisy quantum computers more efficiently.   

Unfolding Correlation from Open-Quantum-System Master Equations.

Understanding system-bath correlations in open quantum systems is essential for various quantum information and technology applications. Derivations of most master equations (MEs) for the dynamics of open systems require approximations that mask dependence of the system dynamics on correlations since the MEs focus on reduced system dynamics. Here we demonstrate that the most common MEs indeed contain hidden information about explicit system-environment correlation. We unfold these correlations by recasting the MEs into a universal form in which the system-bath correlation operator appears. The equations include the Lindblad, Redfield, second-order time-convolutionless, second-order Nakajima-Zwanzig, and second-order universal Lindblad-like cases. We further illustrate our results in an example, which implies that the second-order universal Lindblad-like equation captures correlation more accurately than other standard techniques.   

Clustering of steady-state correlations in open systems with long-range interactions

Lieb-Robinson bounds are powerful tools which  constrain the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from "reversibility"—naturally satisfied for thermal environments—we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open  directions regarding the application of Lieb-Robinson bounds to dissipative systems.   

Auxilliary particle field theory for generalised and non-Markovian Jaynes-Cummings Models

The interaction of photons with molecules or atoms coupled to vibrations are often described by Jaynes-Cummings or spin-boson models. Commonly, these models are treated via a rate-equation approach [1] due to the non-canonical dynamics of the (spin-like) electronic excitations. However, this approach does not account for non-Markovian dynamics of the internal vibrational states. We introduce a novel auxilliary-particle formulation for the electronic and vibrational state of the molecules. This field-theoretical approach can be applied in and out of equilibrium and can capture non-Markovian dynamics, large reservoir sizes as well as spontaneously broken U(1) symmetry due to Bose-Einstein condensation. We present results for a pump cavity system filled with a dilute dye solution showing a BEC transition of photons [2]. Further generalisations of this formulation can be applied to various open or closed multi-level systems.

[1] P. Kirton, J. Keeling, Phys. Rev. Lett. 111, 100404 (2013).

[2] J. Klaers, J. Schmitt, F. Vewinger, M. Weitz, Nature 468, 545 (2010).   

Thermalizing open systems show "transient democratization" of states.

A general expression for thermalization of arbitrary systems through a Lindbladian operator is formulated in terms of the system's energy levels. Upon application to some bosonic or fermionic system, we find that thermalization of the states is achieved in a time inversely proportional to the strength of the Lindblad operator. A remarkable feature of the results, which invites experimental testing, is the initial overshooting of the entropy over its long-term value, a phenomenon which appears to recur in all our numerical experimentations. It may be termed a "transient democratization", in that transiently more energy states participate in excitation,than in the long-term state.   

Observation of Decoherence Induced Exceptional Points in the Dynamics of a Dissipative Superconducting Qubit

Exceptional point degeneracies have been extensively studied in many dissipative systems with energy or particle loss where the dynamics are governed by non-Hermitian Hamiltonians. This Hamiltonian formalism, however, cannot capture the effect of decoherence that plays an essential role in quantum systems. Recently, Liouvillian superoperators have been proposed to take account of both energy loss and decoherence. The degeneracies of the (generically non-Hermitian) Liouvillian are also exceptional points, which are associated with critical dynamics as a dissipative quantum system approaches steady state. Here, we study the dynamics of a dissipative superconducting qubit and observe two different types of Liouvillian exceptional points that arise from the interplay of energy loss and decoherence, or purely due to decoherence. Further, by dynamically tuning the Liouvillian superoperators in real time we observe non-Hermiticity-induced chiral state transfer. This study opens new avenues for exploring non-Hermitian physics in open quantum systems and may help harness non-Hermitian dynamics into quantum control.   

Non-hermitian topology and directional amplification

Directional amplification, in which signals are selectively amplified depending on their propagation direction, has attracted much attention as a key resource for applications, including quantum information processing. Recently, several, physically very different, directional amplifiers have been proposed and realized in the lab. In this talk, I will present a unifying framework based on topology to understand non-reciprocity and directional amplification in driven-dissipative cavity arrays. Specifically, we unveil a one-to-one correspondence between a non-zero topological invariant defined on the spectrum of the dynamic matrix and regimes of directional amplification, in which the end-to-end gain grows exponentially with the number of cavities. I will also show that the correspondence between topology and directional amplification still holds in the presence of disorder as long as the size of the point gap is larger than the disorder.   

Optimal control for state preparation in a noisy environment via the most-likely path

One of the stepping stones to quantum technologies is the ability to actively control and prepare desired quantum states with high success rates. In open quantum systems, state preparation can be a challenging task due to the unpredictability of environmental noises. The conventional approach is to search for optimal controls based on the Lindblad master equation. The equation describes the system's average evolution over noise realizations and can be used to maximize the average fidelity to a target state in the state preparation task. However, the Lindblad evolution does not always capture the best estimate of the bona fide noisy state evolution. In this work, we propose an optimal control protocol for the state preparation based on the most-likely state evolution (path). We apply the least action principle to the stochastic path integral constructed for a noisy quantum dynamics. We then investigate the qubit state preparation under the dephasing noise, and analytically obtain the Rabi drive that maximizes the likelihood of reaching the target state. Our most-likely path approach can lead to controls with higher success rates than the conventional Lindblad approach based on the average fidelity.   

Entanglement phases of monitored circuits via spacetime duality

Quantum systems subject to monitoring by an outside observer have been shown to exhibit interesting entanglement phases in their quantum trajectories, giving a new paradigm for phase structure out of equilibrium. However, observing these phases is quite challenging, as it requires tracking one out of exponentially many quantum trajectories. I will discuss how key aspects of these measurement-induced phases (including the emergence of a dynamically-generated quantum error correcting code that supports the entangling phase) are present in unitary circuits without any monitoring, and are accessible via the idea of "spacetime duality", i.e. by exchanging the roles of space and time in the dynamics. This opens the door to practical laboratory realizations and also enables the derivation of new monitored phases with "fractal" scaling of entanglement, not generically found in many-body unitary dynamics.   

Many-body quantum state diffusion for non-Markovian dynamics in structured environments

Experimental systems in quantum optics offer a controllable way of probing the effects of dissipative processes on the dynamics of many-body systems, beyond the typical Born-Markov approximation. Developing numerical tools for theoretically analysing these systems is important for understanding such experiments, and is generally a challenging problem -- especially for strongly-interacting many-body systems. By combining non-Markovian quantum state diffusion techniques and tensor network methods, we study environments that have power law spectral densities (e.g. Ohmic) such as those that can be realised in many physical situations, including impurity atoms immersed in Bose-Einstein condensates. We benchmark these methods, applying them to a Hubbard-Holstein model with dissipative phonon modes, where we are now able to capture features in the spreading of correlation functions that go beyond what is simulable within standard open quantum system techniques.   

Quantum Parametric Oscillator Heat Engines in Squeezed Thermal Baths: Foundational Theoretical Issues

In this work, we examine some foundational issues of a class of quantum engines where the system consists of a single quantum parametric oscillator, operating in an Otto cycle consisting of 4 stages of two alternating phases: the isentropic phase is detached from any bath where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system is put in contact with one or two squeezed baths of different temperatures, whose nonequilibrium dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian motion. Taking advantage of the fact that the HPZ master equation is an exact nonMarkovian equation, we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. Our aim here is not to present ways for attaining higher efficiency but to build a more solid theoretical foundation for quantum engines of continuous variables covering a broader range of parameter spaces hopefully of use for exploring such possibilities.