System-bath Correlations Research Articles

Effective modeling of open quantum systems by low-rank discretization of structured environments.

The accurate description of the interaction of a quantum system with its environment is a challenging problem ubiquitous across all areas of physics and lies at the foundation of quantum mechanics theory. Here, we pioneer a new strategy to create discrete low-rank models of the system-environment interaction, by exploiting the frequency and time domain information encoded in the fluctuation-dissipation relation connecting the system-bath correlation function and the spectral density. We demonstrate the effectiveness of our methodology by combining it with tensor-network methodologies and simulating the quantum dynamics of complex excitonic systems in a highly structured bosonic environment. The new modeling framework sets the basis for a leap in the analysis of open quantum systems, providing controlled accuracy at significantly reduced computational costs, with benefits in all connected research areas.

Non-Hermitian pseudomodes for strongly coupled open quantum systems: Unravelings, correlations, and thermodynamics

The pseudomode framework provides an exact description of the dynamics of an open quantum system coupled to a non-Markovian environment. Using this framework, the influence of the environment on the system is studied in an equivalent model, where the open system is coupled to a finite number of unphysical pseudomodes that follow a time-local master equation. Building on the insight that this master equation does not need to conserve the hermiticity of the pseudomode state, we here ask for the most general conditions on the master equation that guarantee the correct reproduction of the system's original dynamics. We demonstrate that our generalized approach decreases the number of pseudomodes that are required to model, for example, underdamped environments at finite temperature. We also provide an unraveling of the master equation into quantum jump trajectories of non-Hermitian states, which further facilitates the utilization of the pseudomode technique for numerical calculations by enabling the use of easily parallelizable Monte Carlo simulations. Finally, we show that pseudomodes, despite their unphysical nature, provide a natural picture in which physical processes, such as the creation of system-bath correlations or the exchange of heat, can be studied. Hence, our results pave the way for future investigations of the system-environment interaction leading to a better understanding of open quantum systems far from the Markovian weak-coupling limit. Published by the American Physical Society 2024

Influence of initial correlations on evolution over time of an open quantum system

A novel approach to accounting for the influence of initial system–bath correlations on the dynamics of an open quantum system, based on the conventional projection operator technique, is suggested. To avoid the difficulties of treating the initial correlations, the conventional Nakajima–Zwanzig inhomogeneous generalized master equations (GMEs) for a system’s reduced statistical operator and correlation function are exactly converted into the homogeneous GMEs (HGMEs), which take into account the initial correlations in the kernel governing the evolution of these HGMEs. In the second order (Born) approximation in the system–bath interaction, the obtained HGMEs are local in time and valid at all timescales. They are further specialized for a realistic equilibrium Gibbs initial (at t=t0) system+bath state (for a system reduced statistical operator an external force at t>t0 is applied) and then for a bath of oscillators (Boson field). As an example, the evolution of a selected quantum oscillator (a localized mode) interacting with a Boson field (Fano-like model) is considered at different timescales. It is shown explicitly how the initial correlations influence the oscillator evolution process. In particular, it is shown that the equilibrium system’s correlation function acquires at the large timescale the additional constant phase factor conditioned by survived initial system–bath correlations.

System-bath correlations and finite-time operation enhance the efficiency of a dissipative quantum battery

The reduced state of a small system strongly coupled to a thermal bath may be athermal and used as a small battery once disconnected. The unitarily extractable energy (a.k.a. ergotropy) will be negligible if the disconnecting process is too slow. To study the efficiency of this battery, we consider the cycle of disconnecting, extracting, and connecting the battery back to the bath. Efficiency, i.e. the ratio between ergotropy and connecting plus disconnecting work, is a function of disconnecting time. We consider the Caldeira–Leggett model of a quantum battery in two scenarios. In the first scenario, we assume that the discharged battery is uncorrelated to the bath when connecting back and find that the efficiency peaks at an optimal disconnecting time. In the second scenario, the discharged battery is correlated to the bath, and see that the optimal efficiency corresponds to an instantaneous disconnection. On top of these results, we analyze various thermodynamic quantities for these Caldeira–Leggett quantum batteries and express the first and second laws of thermodynamics for the cycles in simple form despite the system-bath initial correlations and strong coupling regime of the working device.

Quantum non-Markovianity of a qubit in presence of state dependent bath

In the field of quantum information theory, the intersection of the complex dynamics related to non-Markovianity and information is a crucial frontier. Non-Markovian effects, which take memory and temporal correlations into account, challenge conventional wisdom in the fields of quantum biology, metrology, cryptography, and communication. In this work, we analyze the non-Markovian dynamics of a dephasing model in presence of initial system-bath (SB) correlations. These SB correlations are generated via projective measurements on a predefined equilibrium state. Using the non-Markovian measures based on trace distance and quantum Fisher information, it is shown that these correlations have significant impact in the non-Markovian regime at high temperatures while it does not play any role in the Markovian case. Furthermore, it is shown that the oscillatory behaviour of the decoherence function does not always show non-Markovian behaviour.

Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations

Irreversibility, crucial in both thermodynamics and information theory, is naturally studied by comparing the evolution—the (forward) channel—with an associated reverse—the reverse channel. There are two natural ways to define this reverse channel. Using logical inference, the reverse channel is the Bayesian retrodiction (the Petz recovery map in the quantum formalism) of the original one. Alternatively, we know from physics that every irreversible process can be modeled as an open system: one can then define the corresponding closed system by adding a bath (“dilation”), trivially reverse the global reversible process, and finally remove the bath again. We prove that the two recipes are strictly identical, both in the classical and in the quantum formalism, once one accounts for correlations formed between system and the bath. Having established this, we define and study special classes of maps: (including ), for which no such system-bath correlations are formed for some states; and , when the reverse channel can be implemented with the same devices as the original one. We establish several general results connecting these classes, and a very detailed characterization when both the system and the bath are one qubit. In particular, we show that, when reverse channels are well defined, product preservation is a sufficient but not necessary condition for tabletop reversibility; and that the preservation of local energy spectra is a necessary and sufficient condition to generalized thermal operations. Published by the American Physical Society 2024

Microscopic contributions to the entropy production at all times: from nonequilibrium steady states to global thermalization

Based on exact integration of the Schrödinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scales, including the nonequilibrium steady state regime and the final stage of global thermalization. We find that the entropy production is dominated for most times by microscopic deviations from thermality in the baths and the correlation between (but not inside) the baths. Despite these microscopic deviations from thermality, the temperatures and chemical potentials of the baths thermalize as expected, even though our model is integrable. Importantly, this observation is confirmed for both initially mixed and pure states. We further observe that the bath-bath correlations are quite insensitive to the system-bath coupling strength contrary to intuition. Finally, the system-bath correlation, small in an absolute sense, dominates in a relative sense and displays pure quantum correlations for all studied parameter regimes.

Stochastic Schrödinger Equation Approach to Real-Time Dynamics of Anderson-Holstein Impurities: An Open Quantum System Perspective.

We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.

Dephasing effects on quantum correlations and teleportation in presence of state dependent bath

Quantum information protocols are often designed in the ideal situation with no decoherence. However, in real setup, these protocols are subject to the decoherence and thus reducing fidelity of the measurement outcome. In this work, we analyze the effect of state-dependent bath on the quantum correlations and the fidelity of a single qubit teleportation. We model our system-bath interaction as qubits interacting with a common bath of bosons, and the state dependence of the bath is generated through a projective measurement on the joint state in thermal equilibrium. The analytic expressions for the time evolution of entanglement, discord and average fidelity of quantum teleportation are calculated. It is shown that due to the presence of initial system-bath correlations, the system maintains quantum correlations for long times. Furthermore, due to the presence of finite long-time entanglement of the quantum channel, the average fidelity is shown to be higher than its classical value.

Engineering a heat engine purely driven by quantum coherence

The question of whether quantum coherence is a resource beneficial or detrimental to the performance of quantum heat engines has been thoroughly studied but remains undecided. To isolate the contribution of coherence, we analyze the performance of a purely coherence-driven quantum heat engine, a device that does not include any heat flow during the thermodynamic cycle. The engine is powered by the coherence of a multiqubit system, where each qubit is charged via interaction with a coherence bath using the Jaynes-Cummings model. We demonstrate that optimal coherence charging and hence extractable work is achieved when the coherence bath has an intermediate degree of coherence. In our model, the extractable work is maximized when four copies of the charged qubits are used. Meanwhile, the efficiency of the engine, given by the extractable work per input coherence flow, is optimized by avoiding the coherence being stored in the system-bath correlations that is inaccessible to work. We numerically find that the highest efficiency is obtained for slightly lower temperatures and weaker system-bath coupling than those for optimal coherence charging.

Time evolution of quantum correlations in presence of state dependent bath

The emerging quantum technologies heavily rely on the understanding of dynamics in open quantum systems. In the Born approximation, the initial system-bath correlations are often neglected which can be violated in the strong coupling regimes and quantum state preparation. In order to understand the influence of initial system-bath correlations, we study the extent to which these initial correlations and the distance of separation between the qubits influence the dynamics of quantum entanglement and coherence. It is shown that at low temperatures, the initial correlations have no role to play while at high temperatures, these correlations strongly influence the dynamics. Furthermore, we have shown that the distance of separation between the qubits in presence of a collective bath helps to maintain entanglement and coherence at long times.

Capturing non-Markovian dynamics with the reaction coordinate method

The reaction coordinate (RC) technique is emerging as a significant tool in the study of quantum dissipative dynamics and quantum thermodynamics. With the objective to further establish this tool, here we explore to what extent the method can capture non-Markovian dynamics of open quantum systems. As a case study, we focus on the pure decoherence model of a spin coupled to a harmonic reservoir. We compare the spin dynamics and measures for non-Markovianity from the exact analytical solution to simulations based on the RC method at the level of a second-order quantum master equation. We find that the RC method can quantitatively capture non-Markovian effects at strong system-bath coupling and for structured baths. This is rationalized by the fact that the collective RC bath mode, which is made part of the system, maintains system-bath correlations. Lastly, we apply our RC method and study the spin-boson model in the non-Markovian regime.

Effect of memory on the violation of Leggett–Garg inequality

The Leggett-Garg inequalities impose restrictions on the values taken by some combinations of the two-time correlation functions of observables in order to be explainable by a noninvasive-realist classical model. While in the unitary dynamics, it is straightforward to compute these correlation functions, open system effects bring in subtleties. Specifically, for non-Markovian dynamics, which involves setting up of system-bath correlations, the Leggett-Garg measurements disrupt these correlations, making a full system-bath Hamiltonian approach natural. However, here we point out that the problem can also be dealt with from a reduced dynamics perspective. The key point is that the noise superoperator acting on the system must be suitably updated after measurement interventions. Also considered is the effect of Markovian versus non-Markovian behavior as well as classically non-Markovian processes on the violation of Leggett-Garg inequalities.

Non-Markovianity of a Central Spin Interacting with a Lipkin-Meshkov-Glick Bath via a Conditional Past-Future Correlation.

Based on conditional past–future (CPF) correlations, we study the non-Markovianity of a central spin coupled to an isotropic Lipkin–Meshkov–Glick (LMG) bath. Although the dynamics of a system is always non-Markovian, it is found that some measurement time intervals considering a specific process, with respect to a particular set of CPF measurement operators, can be zero, which means that in this case the non-Markovianity of the system could not be detected. Furthermore, the initial system–bath correlations only slightly influence the non-Markovianity of the system in our model. Significantly, it is also found that the dynamics of the system for LMG baths, initially in the ground states corresponding to the symmetric phase and symmetry broken phase, exhibit different properties, and the maximal value of the CPF at the critical point is the smallest, independent of the measurement operator, which means that the criticality can manifest itself by the CPF. Moreover, the effect of bath temperature on the quantum criticality of the CPF depends on the measurement operator.

Steady-State Analysis of Light-Harvesting Energy Transfer Driven by Incoherent Light: From Dimers to Networks.

The question of how quantum coherence facilitates energy transfer has been intensively debated in the scientific community. Since natural and artificial light-harvesting units operate under the stationary condition, we address this question via a nonequilibrium steady-state analysis of a molecular dimer irradiated by incoherent sunlight and then generalize the key predictions to arbitrarily complex exciton networks. The central result of the steady-state analysis is the coherence-flux-efficiency relation: η = c∑i≠jFijκj = 2c∑i≠jJijIm[ρij]κj, where c is the normalization constant. In this relation, the first equality indicates that the energy transfer efficiency, η, is uniquely determined by the trapping flux, which is the product of the flux, F, and branching ratio, κ, for trapping at the reaction centers, and the second equality indicates that the energy transfer flux, F, is equivalent to the quantum coherence measured by the imaginary part of the off-diagonal density matrix, that is, Fij = 2JijIm[ρij]. Consequently, maximal steady-state coherence gives rise to optimal efficiency. The coherence-flux-efficiency relation holds rigorously and generally for any exciton network of arbitrary connectivity under the stationary condition and is not limited to incoherent radiation or incoherent pumping. For light-harvesting systems under incoherent light, the nonequilibrium energy transfer flux (i.e., steady-state coherence) is driven by the breakdown of detailed balance and by the quantum interference of light excitations and leads to the optimization of energy transfer efficiency. It should be noted that the steady-state coherence or, equivalently, efficiency is the combined result of light-induced transient coherence, inhomogeneous depletion, and the system-bath correlation and is thus not necessarily correlated with quantum beatings. These findings are generally applicable to quantum networks and have implications for quantum optics and devices.

Excitation energy transfer with initial system-bath correlations for coherent initial conditions in a toy donor-acceptor model

A theory of coherent resonant energy transfer with initial system-bath correlations [Qin et al., Phys. Rev. A 99, 032111 (2019)] is extended for a coherent initial system condition, which is a linear superposition of donor and acceptor excitations, and is more general and actual in many respects. The nonequilibrium bath state, containing initial system-bath correlations, is expanded in powers of coupling strength within the polaron formalism of second-order time-convolutionless quantum master equation. Detailed expressions for both homogeneous and inhomogeneous terms are derived and calculations are performed under the assumption of super-Ohmic spectral densities where the case of common bath modes is also included. Numerical results indicate that, for certain initial system conditions, the nonequilibrium due to the initial system-bath correlations brings about larger amplitude of population oscillation. And the initial system condition is of crucial importance in determining whether the initial system-bath correlations would play a significant role in the transfer dynamics. We identify a sensitive window in which the transfer dynamics is especially vulnerable to the bath such that there exists a greatly obvious difference between the dynamics with and without initial correlations. Besides, the system-bath coupling strength, the evolution time, and the nature of common bath modes are also shown to contribute to these effects. Rate equations based on F\orster-Dexter energy transfer theory are derived for comparison.

Excitation-energy transfer from weak to strong coupling: Role of initial system-bath correlations

Excitation-energy transfer problems in molecular aggregates have attracted intensive research interests for their fundamental importance. It is usually supposed that the total density operator at time $t=0$ is a factorized product of single-excitation system state and thermal equilibrium bath state. The Franck-Condon principle ensures that it is a good approximation for a rapid photoexcitation. For natural photosynthesis, however, the transfer process in light-harvesting complexes mostly is initialized from an excited molecule, not direct absorption of a photon. Such intermolecular excitations span the same time scale as the transfer dynamics, and longer than the characteristic time of bath relaxation. Therefore, the initial system-bath correlations should be reconsidered. This work extends the coherent resonant energy transfer theory by including initial system-bath correlations. Within the approach of a second-order time-convolutionless quantum master equation in the polaron frame, a general time evolution equation for the reduced system density operator is obtained, including detailed expressions for both homogeneous and inhomogeneous terms. Two essentially distinct kinds of nonequilibrium are identified: one stems from subsistent initial system-bath correlations, while the other is from the theory of polaron transformation itself. The two kinds of nonequilibrium can accelerate or slow down the dynamical evolution for different energetic situations. Rate equations based on F\orster-Dexter theory with and without initial correlations are also derived for comparison. Besides, our conclusions provide a positive perspective accounting for the quantum coherence induced by initial system-bath correlations, which may help to clarify the long-lasting issue of whether quantum phenomenons might be observed under natural conditions of excitation by incoherent solar light, and deepen understandings of the physical mechanisms underlying the natural photosynthesis process.

No Thermalization without Correlations.

The proof of the long-standing conjecture is presented that Markovian quantum master equations are at odds with quantum thermodynamics under conventional assumptions of fluctuation-dissipation theorems (implying a translation invariant dissipation). Specifically, except for identified systems, persistent system-bath correlations of at least one kind, spatial or temporal, are obligatory for thermalization. A systematic procedure is proposed to construct translation invariant bath models producing steady states that well approximate thermal states. A quantum optical scheme for the laboratory assessment of the developed procedure is outlined.

Quantum Speed Limit for Dynamics of Central Spin Model with Initial System-Bath Correlations

We investigate the quantum speed limit (QSL) time of an electronic spin coupled to a bath of nuclear spins. We consider three types of initial states with different correlations between the system and bath, i.e., quantum correlation, classical correlation, and no any correlation. Interestingly, we show that the QSL times of the central spin for these three types of initial correlations are identical when the couplings are homogeneous. However, it is remarkable different for inhomogenous couplings. The QSL time of the central spin is sensitive to the initial states, the average coupling strength, the distribution of the couplings between the system and bath and the number of the nuclear spins in the bath. Furthermore, we find that the coherence in the initial state has significant influences on the QSL time of the system, and can lead to the increase of QSL time for homogeneous couplings.

Effects of initial system-environment correlations on open-quantum-system dynamics and state preparation

We investigate the preparation of a target initial state for a two-level (qubit) system from a system-environment equilibrium or correlated state by an external field. The system-environment equilibrium or correlated state results from the inevitable interaction of the system with its environment. An efficient method in an extended auxiliary Liouville space is introduced to describe the dynamics of the non-Markovian open quantum system in the presence of a strong field and an initial system-environment correlation. By using the time evolutions of the population difference, the state trajectory in the Bloch sphere representation and the trace distance between two reduced system states of the open quantum system, the effect of initial system-environment correlations on the preparation of a system state is studied. We introduce an upper bound and a lower bound for the trace distance within our perturbation formalism to describe the diverse behaviors of the dynamics of the trace distance between various correlated states after the system state preparation. These bounds that are much more computable than similar bounds in the literature give a sufficient condition and a necessary condition for the increase of the trace distance and are related to the witnesses of non-Markovianity and initial system-bath correlation.