Weak System-bath Coupling Research Articles

Accelerated adiabatic quantum search algorithm via pulse control in a non-Markovian environment

Adiabatic quantum computation requires that the system remains in its ground state. However, an adiabatic process often loses partly or entirely its quantumness, such as entanglement in its long runtime, due to the system-environment interactions. Here we put forward an effective quantum control technique to realize the adiabatic quantum search algorithm in a nonadiabatic regime and in the presence of environment. Using the non-Markovian quantum state diffusion equation approach, we numerically study the system dynamics characterized by the success probability. The results show that the probability increases with decreasing coupling strength and temperature. In particular, non-Markovianity from the environment can help to enhance the success probability. By choosing a suitable pulse intensity and period, a high success probability can be obtained in a short runtime for weak system-bath coupling, low temperature, and strong non-Markovian heat baths.

Long memory effects in excitonic systems dynamics: Spectral relations and excitation transport.

The main quantity that controls excitation relaxation and transport in molecular systems is the environment-induced fluctuation correlation function. Commonly used models assume the exponentially decaying correlation function, characterized by a given characteristic time, which allows us to define the Markovian conditions and, hence, allows us to use rate equations for excitation dynamics. A long memory fractional correlation function is studied in this paper as an alternative model. Such a function has an infinite characteristic decay time, and thus, system decay to equilibrium becomes poorly defined. Consequently, it becomes impossible to define the Markovian regime. By assuming the weak system-bath coupling regime, we apply the non-Markovian equations of motion to describe the equilibration process in an excitonic molecular aggregate. The long memory model causes a weaker decay of coherent components in excitonic system relaxation dynamics. Nevertheless, the short time dynamics, which is important in optical spectroscopy, depends on the short time interval of the fluctuation correlation function. Excitation relaxation in this window appears to be well described by non-Markovian approaches.

Optimal population inversion of a single dissipative two-level system

Optimal population inversion of a single two-level system (TLS) coupled to an Ohmic boson bath via off-diagonal TLS-bath coupling is studied by using optimal control theory. In the weak system-bath coupling regime where the Bloch-Redfield formalism is applicable, we derive the Bloch equation for describing the evolution of the dissipative TLS in the presence of a time-dependent external control field. By using the automatic differentiation technique to compute the gradient for the cost functional, we calculate the optimal energy difference profile that can achieve an ideal inversion. Further we examine the robustness of driving-induced tunneling oscillations (DITO) in presence of dissipation.

Non-Abelian Berry phase for open quantum systems: Topological protection versus geometric dephasing

We provide a detailed theoretical analysis of the adiabatic evolution of degenerate open quantum systems, where the dynamics is induced by time-dependent fluctuating loop paths in control parameter space. For weak system-bath coupling, the fluctuations around a deterministic base path obey Gaussian statistics, where we assume that the quantum adiabatic theorem is also satisfied for fluctuating paths. We show that universal non-Abelian geometric dephasing (NAGD) contributions are contained in the fluctuation-averaged evolution operator. This operator plays a key role in all experimental protocols proposed in this work for the detection of NAGD. In particular, we formulate interference measurements providing full access to NAGD. Apart from a factor due to the dynamic phase and its fluctuations, the averaged evolution operator contains the averaged Berry matrix. A polar decomposition of this non-unitary matrix into the product of a unitary, $V$, and a positive semi-definite Hermitian matrix, $R$, reveals the physics of the NAGD contributions. Unlike the conventional dynamic dephasing rate, the NAGD eigenrates encoded by $R$ depend on the loop orientation sense and, in particular, change sign under a reversal of the direction. A negative rate then implies amplification of coherences as compared to the ones when only dynamic dephasing is present. The non-Abelian character of geometric dephasing is rooted in the non-commutativity of $V$ and $R$ and causes smoking-gun signatures in interference experiments. We also clarify why systems subject to topological protection do not show geometric dephasing. Without full protection, however, geometric dephasing can arise and has to be taken into account. As concrete application, we propose spin-echo NAGD detection protocols for modified Majorana braiding setups.

Interplay of Direct and Indirect Charge-Transfer Pathways in Donor-Bridge-Acceptor Systems.

Charge transfer in donor-bridge-acceptor (DBA) structures typically takes place through the combination of donor-bridge and bridge-acceptor overlap integrals forming an effective, indirect electronic coupling between the donor (D) and acceptor (A) moieties. Here we examine the effects of an additional direct DA electronic coupling of charge-transfer processes in DBA systems with local interaction with thermal baths. First, using the exact Nakajima-Zwanzig master equation (NZME) for the reduced density matrix, we rigorously define probability currents as the coherent part of the NZME, thereby allowing us to quantify the contribution of the different electronic pathways (direct and indirect) to the charge-transfer dynamics. Focusing on two minimal DBA systems of three sites (V and Λ models) and adopting well-developed methods, we find that the interplay between different transfer pathways can be assessed by the McConnell formula in the weak system-bath coupling regime. We then demonstrate that the combination of indirect and direct donor-acceptor coupling either enhances or leads to a destructive quantum interference effect on charge-transport processes, depending on the energy landscape of the DBA system.

Time-dependent Markovian quantum master equation

We construct a quantum Markovian Master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the propagator of the driven system. This enables the validity of the Master equation to be extended beyond the adiabatic limit. The Non-Adiabatic Master Equation (NAME) is derived employing the weak system-bath coupling limit. The NAME is valid when a separation of timescales exists between the bath dynamics and the external driving. In contrast to the adiabatic Master equation, the NAME leads to coupled equations of motion for the population and coherence. We employ the NAME to solve the example of an open driven time-dependent harmonic oscillator. For the harmonic oscillator the NAME predicts the emergence of coherence associated with the dissipation term. As a result of the non-adiabatic driving the thermalization rate is suppressed. The solution is compared with both numerical calculations and the adiabatic Master equation.

Quantum mechanical response to a driven Caldeira-Leggett bath

We determine the frequency-dependent response characteristics of a quantum system to a driven Caldeira-Leggett bath. The bath degrees of freedom are explicitly driven by an external time-dependent force, in addition to the direct time-dependent forcing of the system itself. After general considerations of driven Caldeira-Leggett baths, we consider the Rubin model of a chain of quantum particles coupled by linear springs as an important model of a quantum dissipative system. We show that in the presence of time-dependent driving of the chain, this model can be mapped to a quantum system which couples to a driven Caldeira-Leggett bath. The effect of the bath driving is captured by a time-dependent force on the central system, which is, in principle, non-Markovian in nature. We study two specific examples, the exactly solvable case of a harmonic potential and a quantum two-state system for which we assume a weak system-bath coupling. We evaluate the dynamical response to a periodic driving of the system and the bath. The dynamic susceptibility is shown to be altered qualitatively by the bath drive: The dispersive part is enhanced at low frequencies and acquires a maximum at zero frequency. The absorptive part develops a shoulder-like behavior in this frequency regime. These features seem to be generic for quantum systems in a driven Caldeira-Leggett bath.

Symmetry-protected coherent relaxation of open quantum systems

We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1/2 XXZ Heisenberg chain, as the system evolves after a N\'eel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between $\mathbb{PT}$ symmetry and weak symmetries, which strengthens previous predictions for $\mathbb{PT}$-symmetric Liouvillian dynamics. Requirements are a non-degenerate $\mathbb{PT}$-symmetric generator of time evolution $\hat{\mathcal{L}}$, a weak parity symmetry and an observable that is anti-symmetric under this parity transformation. The spectrum of $\hat{\mathcal{L}}$ then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.

Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model

The Nakajima-Zwanzig generalized master equation provides a formally exact framework to simulate quantum dynamics in condensed phases. Yet, the exact memory kernel is hard to obtain and calculations based on perturbative expansions are often employed. By using the spin-boson model as an example, we assess the convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation. The exact memory kernels are calculated by combining the hierarchical equation of motion approach and the Dyson expansion of the exact memory kernel. High order expansions of the memory kernels are obtained by extending our previous work to calculate perturbative expansions of open system quantum dynamics [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. It is found that the high order expansions do not necessarily converge in certain parameter regimes where the exact kernel show a long memory time, especially in cases of slow bath, weak system-bath coupling, and low temperature. Effectiveness of the Padé and Landau-Zener resummation approaches is tested, and the convergence of higher order rate constants beyond Fermi's golden rule is investigated.

On the number of Bose-selected modes in driven-dissipative ideal Bose gases.

In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240405]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.

Qubit absorption refrigerator at strong coupling

We demonstrate that a quantum absorption refrigerator (QAR) can be realized from the smallest quantum system, a qubit, by coupling it in a non-additive (strong) manner to three heat baths. This function is un-attainable for the qubit model under the weak system-bath coupling limit, when the dissipation is additive. In an optimal design, the reservoirs are engineered and characterized by a single frequency component. We then obtain closed expressions for the cooling window and refrigeration efficiency, as well as bounds for the maximal cooling efficiency and the efficiency at maximal power. Our results agree with macroscopic designs and with three-level models for QARs, which are based on the weak system-bath coupling assumption. Beyond the optimal limit, we show with analytical calculations and numerical simulations that the cooling efficiency varies in a non-universal manner with model parameters. Our work demonstrates that strongly-coupled quantum machines can exhibit function that is un-attainable under the weak system-bath coupling assumption.

Nonperturbative environmental influence on dephasing

Environmental noise leads to dephasing and relaxation in a quantum system. Often, a rigorous treatment of multiple noise sources within a system-bath approach is not possible. We discuss the influence of environmental fluctuations on a quantum system whose dynamics is dephasing already due to a phenomenologically treated additional noise source. For this situation, we develop a path-integral approach, which allows us to treat the system-environment coupling in a numerically exact way, and additionally we extend standard perturbative approaches. We observe strong deviations between the numerically exact and the perturbative results even for weak system-bath coupling. This shows that standard perturbative approaches fail for additional, even weak, system-bath couplings if the system dynamics is already dissipative.

Effects of system-bath coupling on a photosynthetic heat engine: A polaron master-equation approach

In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect charge transfer processes in Photosystem II reaction center (PSII RC) inspired quantum heat engine (QHE) model in a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in details. The results show a variety of dynamical behaviours. We interpret these results in terms of noise-assisted transport effect and dynamical localization which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms is manifestations of dual role played by bath-induced fluctuations within respective parameter range. In addition, we find that the effec- tive voltage of QHE exhibits superior robustness with respect to the bath noise as long as the system-coupling strength is not too large.

Charge and spin current statistics of the open Hubbard model with weak coupling to the environment.

Based on generalization and extension of our previous work [Phys. Rev. Lett. 112, 067201 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.067201] to multiple independent Markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. Only the next-to-leading and higher orders depend on the Hubbard interaction parameter. The physical results are related to those for the XXZ model in the analogous setup implying a certain universality, which potentially holds in this class of nonequilibrium models.

Quantum thermal transport through anharmonic systems: A self-consistent approach

We propose a feasible and effective approach to study quantum thermal transport through anharmonic systems. The main idea is to obtain an {\it effective} harmonic Hamiltonian for the anharmonic system by applying the self-consistent phonon theory. Using the effective harmonic Hamiltonian we study thermal transport within the framework of nonequilibrium Green's function method using the celebrated Caroli formula. We corroborate our quantum self-consistent approach using the quantum master equation that can deal with anharmonicity exactly, but is limited to the weak system-bath coupling regime. Finally, in order demonstrate its strength we apply the quantum self-consistent approach to study thermal rectification in a weakly coupled two segment anharmonic system.

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system–environment partition. To achieve this goal we make use of the reaction coordinate (RC) mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the RC), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system–bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.

Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach

The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi’s golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.

Optimal state transfer of a single dissipative two-level system

Optimal state transfer of a single two-level system (TLS) coupled to an Ohmic boson bath via off-diagonal TLS-bath coupling is studied by using optimal control theory. In the weak system-bath coupling regime where the time-dependent Bloch-Redfield formalism is applicable, we obtain the Bloch equation to probe the evolution of the dissipative TLS in the presence of a time-dependent external control field. By using the automatic differentiation technique to compute the gradient for the cost functional, we calculate the optimal transfer integral profile that can achieve an ideal transfer within a dimer system in the FennaMatthews-Olson (FMO) model. The robustness of the control profile against temperature variation is also analyzed.

Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov D1 states

Dynamics of the sub-Ohmic spin-boson model is investigated by employing a multitude of the Davydov D1 trial states, also known as the multi-D1 Ansatz. Accuracy in dynamics simulations is improved significantly over the single D1 Ansatz, especially in the weak system-bath coupling regime. The reliability of the multi-D1 Ansatz for various coupling strengths and initial conditions is also systematically examined, with results compared closely with those of the hierarchy equations of motion and the path integral Monte Carlo approaches. In addition, a coherent-incoherent phase crossover in the nonequilibrium dynamics is studied through the multi-D1 Ansatz. The phase diagram is obtained with a critical point sc = 0.4. For sc < s < 1, the coherent-to-incoherent crossover occurs at a certain coupling strength, while the coherent state recurs at a much larger coupling strength. For s < sc, only the coherent phase exists.

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method.

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S2(ππ*)-S1(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system-bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system-bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system-bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S2) is very efficiently quenched by the system-bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode-mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system-bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system-bath coupling as well as the field-matter coupling.