Strong System-bath Coupling Research Articles

Kink Sum for Long-Memory Small Matrix Path Integral Dynamics.

The small matrix decomposition of the real-time path integral (SMatPI) allows for numerically exact and efficient propagation of the reduced density matrix (RDM) for system-bath Hamiltonians. Its high efficiency lies in the small size of the SMatPI matrices employed in the iterative algorithm, whose size is equal to that of the full RDM. By avoiding the storage and multiplication of large tensors, the SMatPI algorithm is applicable in multistate systems under a variety of conditions. The main computational effort is the evaluation of path sums within the entangled memory length to construct the SMatPI matrices. A number of methods are available for this task, each with its own favorable parameter regime, but calculations with strong system-bath coupling and long memory at low temperatures remain out of reach. The present paper evaluates the path sums by binning the paths (in forward time only) based on their amplitudes, which depend on the number and type of kinks they contain. The algorithm is very efficient, leading to a dramatic acceleration of path sums and significantly extending the accessible memory length in the most challenging regimes.

Stochastic learning control of adiabatic speedup in a non-Markovian open qutrit system

Precise and efficient control of quantum systems is essential to perform quantum information-processing tasks. In terms of adiabatic speedup via leakage elimination operator approach, for a closed system, the ideal pulse control conditions have been theoretically derived by P-Q partitioning technique. However, it is a challenge to design the corresponding control pulses for an open system, which requires noisy environments to be addressed. In this paper, we apply the stochastic search procedures to an open qutrit system and successfully obtain the optimal control pulses for significant adiabatic speedup. The calculation results show that these optimal pulses allow us to acquire higher fidelities than the ideal pulses. The improvement of fidelity is large for relatively strong system-bath coupling strength and high bath temperature. For certain coupling strength and bath temperature, the maximal improvement can be achieved for a critical characteristic frequency which represents the memory time of the environment. Our investigation indicates that the stochastic search procedures are powerful tools to design control pulses for combating the detrimental effects of the environment.

Optimal linear cyclic quantum heat engines cannot benefit from strong coupling.

Uncovering whether strong system-bath coupling can be an advantageous operation resource for energy conversion can facilitate the development of efficient quantum heat engines (QHEs). Yet, a consensus on this ongoing debate is still lacking owing to challenges arising from treating strong couplings. Here, we conclude the debate for optimal linear cyclic QHEs operated under a small temperature difference by revealing the detrimental role of strong system-bath coupling in their optimal operations. We analytically demonstrate that both the efficiency at maximum power and maximum efficiency of strong-coupling linear cyclic QHEs are upper bounded by their weak-coupling counterparts with the same degree of time-reversal symmetry breaking. Under strong time-reversal symmetry breaking, we further reveal a quadratic suppression of the optimal efficiencies relative to the Carnot limit when away from the weak-coupling regime, along with a quadratic enhancement of the mean entropy production rate.

Nonadiabatically driven open quantum systems under out-of-equilibrium conditions: Effect of electron-phonon interaction

In this paper we explore the effects of nonadiabatic external driving on the dynamics of an electronic system coupled to two electronic leads and to a phonon mode, with and without damping. In the limit of slow driving, we establish nonadiabatic corrections to thermodynamic and transport quantities. In particular, we study the first-order correction to the work done by the driving, the charge current, and the vibrational excitation using a perturbative expansion. We then compare the results to the numerically exact hierarchical equations of motion (HEOM) approach. Furthermore, the HEOM analysis spans both the weak and strong system-bath coupling regime and the slow- and fast-driving limits. We show that the electronic friction and the nonadiabatic corrections to the charge current provide a clear indicator for the Franck-Condon effect and for nonresonant tunneling processes. We also discuss the validity of the approximate quantum master equation approach and the benefits of using HEOM to study nonadiabatically driven open quantum systems out of equilibrium.

Strong system-bath coupling effects in quantum absorption refrigerators.

We study the performance of three-level quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equationmethod, which treats system-bath interactions beyond weak coupling, we demonstrate that in a broad range of parameters the cooling window at strong coupling can be captured by a weak-coupling theory, albeit with parameters renormalized by the system-bath coupling energy. As a result, at strong system-bath couplings the window of cooling is significantly reshaped compared to predictions of weak-coupling treatments. We further show that strong coupling admits direct transport pathways between the thermal reservoirs. Such beyond-second-order transport mechanisms are typically detrimental to the performance of quantum thermal machines. Our study reveals that it is inadequate to claim for either a suppression or an enhancement of the cooling performance as one increases system-bath coupling-when analyzed against a single parameter and in a limited domain. Rather, a comprehensive approach should be adopted so as to uncover the reshaping of the operational window.

Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion.

The theory of hierarchical equations of motion (HEOM) is one of the standard methods to give exact evaluations of the dynamics as coupled to harmonic oscillator environments. However, the theory is numerically demanding due to its hierarchy, which is the set of auxiliary elements introduced to capture the non-Markovian and non-perturbative effects of environments. When system-bath coupling becomes relatively strong, the required computational resources and precision move beyond the regime that can be currently handled. This article presents a new representation of HEOM theory in which the hierarchy is mapped into a continuous space of a collective bath coordinate and several auxiliary coordinates as the form of the quantum Fokker-Planck equation. This representation gives a rigorous time evolution of the bath coordinate distribution and is more stable and efficient than the original HEOM theory, particularly when there is a strong system-bath coupling. We demonstrate the suitability of this approach to treat vibronic system models coupled to environments.

Improving the efficiency of open-quantum-system simulations using matrix product states in the interaction picture

Modeling open quantum systems---quantum systems coupled to a bath---is of value in condensed-matter theory, cavity quantum electrodynamics, nanosciences, and biophysics. The real-time simulation of open quantum systems was advanced significantly by the recent development of chain mapping techniques and the use of matrix product states that exploit the intrinsic entanglement structure in open quantum systems. The computational cost of simulating open quantum systems, however, remains high when the bath is excited to high-lying quantum states. We develop an approach to reduce the computational costs in such cases. The interaction representation for the open quantum system is used to distribute excitations among the bath degrees of freedom so that the occupation of each bath oscillator is ensured to be low. The interaction picture also causes the matrix dimensions to be much smaller in a matrix product state of a chain-mapped open quantum system than in the Schr\"odinger picture. Using the interaction representation accelerates the calculations by one to two orders of magnitude over the existing matrix-product-state method. In the regime of strong system-bath coupling and high temperatures, the speedup can be as large as three orders of magnitude. The approach developed here is especially promising to simulate the dynamics of open quantum systems in high-temperature and strong-coupling regimes.

Steady state in strong system-bath coupling regime: Reaction coordinate versus perturbative expansion.

Motivated by the growing importance of strong system-bath coupling in several branches of quantum information and related technological applications, we analyze and compare two strategies currently used to obtain (approximately) steady states in strong-coupling regime. The first strategy is based on perturbative expansions while the second one uses reaction coordinate mapping. Focusing on the widely used spin-boson model, we show that the predictions of these two strategies coincide in many situations. This confirms and strengthens the relevance of both techniques. Beyond that, it is also crucial to know precisely their respective range of validity. In that perspective, thanks to their different limitations, we use one to benchmark the other. We introduce and successfully test some very simple validity criteria for both strategies, bringing some answers to the question of the validity range.

Quantum-parametric-oscillator heat engines in squeezed thermal baths: Foundational theoretical issues.

In this paper 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 four stages of two alternating phases: the isentropic phase is detached from any bath (thus a closed system) where the natural frequency of the oscillator is changed from one value to another, and the isothermal phase where the system (now rendered open) 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. The HPZ equation is an exact non-Markovian equation which preserves the positivity of the density operator and is valid for (1) all temperatures, (2) arbitrary spectral density of the bath, and (3) arbitrary coupling strength between the system and the bath. Taking advantage of these properties we examine some key foundational issues of theories of quantum open and squeezed systems for these two phases of the quantum Otto engines. This includes (1) the non-Markovian regimes for non-Ohmic, low-temperature baths, (2) what to expect in nonadiabatic frequency modulations, (3) strong system-bath coupling, as well as (4) the proper junction conditions between these two phases. 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 that we hope are of use for exploring such possibilities.

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.

Strong coupling effects in quantum thermal transport with the reaction coordinate method

We present a semi-analytical approach for studying quantum thermal energy transport at the nanoscale. Our method, which is based on the reaction coordinate method, reveals the role of strong system-bath coupling effects in quantum energy transport. Considering as a case study the nonequilibrium spin-boson model, a collective coordinate is extracted from each thermal environment and added into the system to construct an enlarged system (ES). After performing additional Hamiltonian’s truncation and transformation, we obtain an effective two-level system with renormalized parameters, resulting from the strong system-bath coupling. The ES is weakly coupled to its environments, thus can be simulated using a perturbative Markovian quantum master equation approach. We compare the heat current characteristics of the effective two-state model to other techniques, and demonstrate that we properly capture strong system-bath signatures such as the turnover behavior of the heat current as a function of system-bath coupling strength. We further investigate the thermal diode effect and demonstrate that strong couplings moderately improve the rectification ratio relative to the weak coupling limit. The effective Hamiltonian method that we developed here offers fundamental insight into the strong coupling behavior, and is computationally economic. Applications of the method toward studying multi-level quantum thermal machines are anticipated.

Stabilization of adiabatic population transfer by strong coupling to a phonon bath

We investigate the influence of the environment on the rapid adiabatic passage scheme for optimal population transfer in a two-level system. To cope with strong coupling to an external phonon bath with super-Ohmic spectral density, we are solving the time-dependent Schr\odinger equation of the extended system, including a finite number of bath modes using the multi-Davydov D2 ansatz. This allows for the treatment of the non-Markovian reduced dynamics of the two-level subsystem. Surprisingly, it is found that strong system-bath coupling stabilizes the transition probability from the lower to the upper level as a function of the area under the laser pulse. This dissipative engineering effect could only be uncovered by a non-Markovian treatment. For strong coupling, the transition probability then becomes a monotonically increasing function of the pulse area at zero temperature of the heat bath. Finite temperatures break the monotonicity in the range of pulse areas that we studied, but not the stability of the observed effect.

Recovery of Purity in Dissipative Tunneling Dynamics.

The time evolution of purity for an initially localized state of a symmetric two-level system coupled to a dissipative bath is investigated using numerically exact real-time path integral methods. With strong system-bath coupling and high temperature, the purity decays monotonically to its fully mixed value, with a short-time Gaussian behavior, which is subsequently followed by exponential evolution. However, under low-temperature and weak coupling conditions, a substantial recovery of purity is observed. A simple theoretical analysis reveals three contributions that correspond to a completely incoherent, eigenstate population difference and rate terms. The last two of these terms can counter the early drop of purity and are responsible for its rebound. These findings caution against using purity as a measure of decoherence in the dynamics of quantum dissipative systems.

A polaron theory of quantum thermal transistor in nonequilibrium three-level systems**Project supported by the National Natural Science Foundation of China (Grant Nos. 11704093 and 11705008) and Beijing Institute of Technology Research Fund Program for Young Scholars, China.

We investigate the quantum thermal transistor effect in nonequilibrium three-level systems by applying the polaron-transformed Redfield equation combined with full counting statistics. The steady state heat currents are obtained via this unified approach over a wide region of system–bath coupling, and can be analytically reduced to the Redfield and nonequilibrium noninteracting blip approximation results in the weak and strong coupling limits, respectively. A giant heat amplification phenomenon emerges in the strong system–bath coupling limit, where transitions mediated by the middle thermal bath are found to be crucial to unravel the underlying mechanism. Moreover, the heat amplification is also exhibited with moderate coupling strength, which can be properly explained within the polaron framework.

Dissipative Majorana Quantum Wires.

SummaryIn this paper, we formulate and quantitatively examine the effect of dissipation on topological systems. We use a specific model of Kitaev quantum wire with an onsite Ohmic dissipation and perform a numerically exact method to investigate the effect of dissipation on the topological features of the system (e.g., the Majorana edge mode) at zero temperature. We find that even though the topological phase is robust against weak dissipation as it is supposed to be, it will eventually be destroyed by sufficiently strong dissipation via either a continuous quantum phase transition or a crossover depending on the symmetry of the system. The dissipation-driven quantum criticality has also been discussed.

A new perspective for nonadiabatic dynamics with phase space mapping models.

Based on the recently developed unified theoretical framework [J. Liu, J. Chem. Phys. 145(20), 204105 (2016)], we propose a new perspective for studying nonadiabatic dynamics with classical mapping models (CMMs) of the coupled multistate Hamiltonian onto the Cartesian phase space. CMMs treat the underlying electronic state degrees of freedom classically with a simple physical population constraint while employing the linearized semiclassical initial value representation to describe the nuclear degrees of freedom. We have tested various benchmark condensed phase models where numerically exact results are available, which range from finite temperature to more challenging zero temperature, from adiabatic to nonadiabatic domains, and from weak to strong system-bath coupling regions. CMMs demonstrate overall reasonably accurate dynamics behaviors in comparison to exact results even in the asymptotic long time limit for various spin-boson models and site-exciton models. Further investigation of the strategy used in CMMs may lead to practically useful approaches to study nonadiabatic processes in realistic molecular systems in the condensed phase.

Strong system-bath coupling induces negative differential thermal conductance and heat amplification in nonequilibrium two-qubit systems.

Quantum heat transfer is analyzed in nonequilibrium two-qubits systems by applying the nonequilibrium polaron-transformed Redfield equation combined with full counting statistics. Steady-state heat currents with weak and strong qubit-bath couplings are clearly unified. Within the two-terminal setup, the negative differential thermal conductance is unraveled with strong qubit-bath coupling and finite qubit splitting energy. The partially strong spin-boson interaction is sufficient to show the negative differential thermal conductance. Based on the three-terminal setup, in which two qubits are asymmetrically coupled to three thermal baths, a giant heat amplification factor is observed with strong qubit-bath coupling. Moreover, the strong interaction of either the left or right spin-boson coupling is able to exhibit the apparent heat amplification effect.

Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach.

We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperature difference. Results are compared to perturbative treatments and demonstrate good agreement in the appropriate limits. The challenge of converging nonequilibrium quantities, currents and high order cumulants, is discussed in detail. The iFCSPI, a numerically exact technique, naturally captures strong system-bath coupling and non-Markovian effects of the environment. As such, it is a promising tool for probing fundamental questions in quantum transport and quantum thermodynamics.

Interfacial thermal transport with strong system-bath coupling: A phonon delocalization effect

We study the effect of system-bath coupling strength on quantum thermal transport through the interface of two weakly coupled anharmonic molecular chains using quantum self-consistent phonon approach. The heat current shows a resonant to bi-resonant transition due to the variations in the interfacial coupling and temperature, which is attributed to the delocalization of phonon modes. Delocalization occurs only in the strong system-bath coupling regime and we utilize it to model a thermal rectifier whose ratio can be non-monotonically tuned not only with the intrinsic system parameters but also with the external temperature.

A strongly coupled open system with a non-linear bath: fluctuation–dissipation and Langevin dynamics

The study of Langevin dynamics and fluctuation–dissipation relation (FDR) for a generic probe system (represented by a mass ), bilinearly coupled to a bath of harmonic oscillators, has been a standard paradigm for the microscopic theory of stochastic processes for several decades. The question that we probe in this paper is, how robust the structure of the classical FDR is, when one replaces the harmonic bath by an anharmonic one in the limit of strong system-bath coupling? Such a picture carries the signature of the probe system in the zeroth order through a nonlocal time kernel. We observe that the two-time noise correlations hold a rich structure from which the usual FDR emerges only in the leading order of perturbation. Beyond this order, multiple time scales and nontrivial dependence on the temperature starts to manifest. These new aspects conspire to break the time-translational invariance of the noise-correlations. Several other interesting features show up and we discuss them methodically through rigorous calculations order-by-order in perturbation. This formalistic derivation along with a specific example of non-linearity can be easily applied to a huge range of processes and statistical observables that fall under the purview of a system-reservoir theory.