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Physical Review A

Nondemolition quasiprobabilities of work and heat in the presence of a non-Markovian environment

Haiping Li, Jian Zou, Bin Shao

Published Mar 29, 2024• 2 citations
Publisher

Abstract

We consider a collision model representation of nonequilibrium dynamics for an externally driven open quantum system. Specifically we investigate the nondemolition quasiprobability distributions (QPDFs) of work and heat in both Markovian and non-Markovian regimes. In this model, work and heat correspond to different evolution processes, and their contributions can be distinguished. For the system state with initial coherence, in both Markovian and non-Markovian regimes, negative quasiprobabilities at half of the energy gap of the system for work and the variation of internal energy appear, which is considered to be a witness of the quantumness of the system. We also find that when the external driving speed slows down, the quantumness of the system is weakened, and when the driving speed is slow enough, the negative quasiprobability will disappear and the results of the QPDF coincide with those of the two-measurement protocol. Most importantly, we find that non-Markovianity can enhance the quantumness of the system.

DOI
10.1103/physreva.109.032228

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We consider a collision model representation of nonequilibrium dynamics for an externally driven open quantum system. Specifically we investigate the nondemolition quasiprobability distributions (QPDFs) of work and heat in both Markovian and non-Markovian regimes. In this model, work and heat correspond to different evolution processes, and their contributions can be distinguished. For the system state with initial coherence, in both Markovian and non-Markovian regimes, negative quasiprobabilities at half of the energy gap of the system for work and the variation of internal energy appear, which is considered to be a witness of the quantumness of the system. We also find that when the external driving speed slows down, the quantumness of the system is weakened, and when the driving speed is slow enough, the negative quasiprobability will disappear and the results of the QPDF coincide with those of the two-measurement protocol. Most importantly, we find that non-Markovianity can enhance the quantumness of the system.
Abstract We determine the Kirkwood–Dirac quasiprobability (KDQ) distribution associated to the stochastic instances of internal energy variations for the quantum system and environment particles in coherent Markovian collision models. In the case the interactions between the quantum system and the particles do not conserve energy, the KDQ of the non-energy-preserving stochastic work is also derived. These KDQ distributions can account for non-commutativity, and return the unperturbed average values and variances for a generic interaction-time, and generic local initial states of the quantum system and environment particles. Using this nonequilibrium-physics approach, we certify the conditions under which the collision process of the model exhibits quantum traits, and we quantify the rate of energy exchanged by the quantum system by looking at the variance of the KDQ energy distributions. Finally, we propose an experimental test of our results on a superconducting quantum circuit implementing a qubit system, with microwave photons representing the environment particles.
We discuss an approach to determine averages of the work, dissipated heat, and variation of internal energy of an open quantum system driven by an external classical field. These quantities are measured by coupling the quantum system to a quantum detector at different times. This approach allows us to preserve the full quantum features of the evolution. From the measured phase, we are able to obtain a quasicharacteristic function and a quasiprobability density function for the corresponding observables. Despite the fact that these quasiprobability density functions are not the results of direct measurements, they reproduce the expected value of the physical quantities. Analogously to the Wigner function, the negative regions of these quasiprobability density functions are directly related to pure quantum processes which are not interpretable in classical terms. We use this feature to show that in the limit of fast dissipation, the quantum features vanish and interpret this as the emergence of the classical limit of the energy exchange process. Our analysis explains and confirms the behavior observed in recent experiments performed on IBMQ devices [P. Solinas et al., Phys. Rev. A 103, L060202 (2021)]. The possibility to discriminate between classical and quantum features makes the proposed approach an excellent tool to determine if, and in which conditions, quantum effects can be exploited to increase the efficiency in an energy exchange process at the quantum level.
We investigate the steady state properties arising from the open system dynamics described by a memoryless (Markovian) quantum collision model, corresponding to a master equation in the ultra-strong coupling regime. By carefully assessing the work cost of switching on and off the system-environment interaction, we show that only a coupling Hamiltonian in the energy-preserving form drives the system to thermal equilibrium, while any other interaction leads to non-equilibrium steady states that are supported by steady-state currents. These currents provide a neat exemplification of the housekeeping work and heat. Furthermore, we characterize the specific form of system-environment interaction that drives the system to a steady-state exhibiting coherence in the energy eigenbasis, thus, giving rise to families of states that are non-passive.
Abstract We consider a microscopic collision model, i.e., a quantum system interacts with a hierarchical environment consisting of an auxiliary system and a reservoir. We show how the non-Markovian character of the system is influenced by the coupling strength of system-auxiliary system and auxiliary system-reservoir, coherence of environment and initial system-environment correlations. And we study the non-Markovianity induced by coherence of environment from the perspective of energy, further the relationship between information backflow and energy flux is obtained. Then we study the effect of non-Markovianity on thermodynamic properties. By studying the entropy change of system especially that from heat exchanges with the environment, we reveal the essence of entropy change between positive and negative values during non-Markovian evolution is due to the contribution of heat flux induced by coherence. And compared with the case of Markovian dynamics, we observe that the entropy production decreases in some specific time intervals under non-Markovian dynamics induced by the coupling strength. And this is different to the case of non-Markovianity caused by initial system-environment correlation, that we show the possibility of positive entropy production during the whole dynamics.
Despite the increasing interest, the research field which studies the concepts of work and heat at the quantum level has suffered from two main drawbacks: first, the difficulty to properly define and measure the work, heat, and internal energy variation in a quantum system and, second, the lack of experiments. Here, we report a full characterization of the dissipated heat, work, and internal energy variation in a two-level quantum system interacting with an engineered environment. We use the IBMQ quantum computer to implement the driven system's dynamics in a dissipative environment. The experimental data allow us to construct quasiprobability distribution functions from which we recover the correct averages of work, heat, and internal energy variation in the dissipative processes. Interestingly, by increasing the environment coupling strength, we observe a reduction of the pure quantum features of the energy exchange processes that we interpret as the emergence of the classical limit. This makes the present approach a privileged tool to study, understand, and exploit quantum effects in energy exchanges.
Quantum non-Markovianity represents memory during system dynamics, which is typically weakened by temperature. We study here the effects of environmental temperature on the non-Markovianity of an open quantum system by virtue of collision models. The environment is simulated by a chain of ancillary qubits that are prepared in thermal states with a finite temperature TTT. Two distinct non-Markovian mechanisms are considered via two types of collision models, one where the system SSS consecutively interacts with ancillas and a second where SSS collides only with an intermediate system ${S}^{\ensuremath{'}}$, which in turn interacts with the ancillas. We show that in both models the relation between non-Markovianity and temperature is nonmonotonic. In particular, revivals of non-Markovianity may occur as temperature increases. We find that the physical reason behind this behavior can be revealed by examining a peculiar system-environment coherence exchange, leading to ancillary qubit coherence larger than system coherence, which triggers information backflow from the environment to the system. These results provide insights into the mechanisms underlying the counterintuitive phenomenon of temperature-enhanced quantum memory effects.