We study the dynamics of an open quantum system interacting with a non-thermal bath. Here, "non-thermal" means that the bath modes do not need to have the same temperature, but they have an effective temperature distribution. We find that, when a quantum system is interacting with such a non-thermal bath far from thermal equilibrium, it is no longer proper to use any coarse-grained Markovian description for the system, even when their coupling strength is quite weak. Especially, when there is coherent transition with strong interference strength in the quantum system, the Markovian master equation would bring in a serious problem of negative probability. After we consider some proper non-Markovian corrections, the problem can be naturally resolved.
We study the dynamics of an open quantum system interacting with a non-thermal bath. Here, "non-thermal" means that the bath modes do not need to have the same temperature, but they have an effective temperature distribution. We find that, when a quantum system is interacting with such a non-thermal bath far from thermal equilibrium, it is no longer proper to use any coarse-grained Markovian description for the system, even when their coupling strength is quite weak. Especially, when there is coherent transition with strong interference strength in the quantum system, the Markovian master equation would bring in a serious problem of negative probability. After we consider some proper non-Markovian corrections, the problem can be naturally resolved.
It is known that the origin of the deviations from standard thermodynamics proceed from the strong coupling to the bath. Here, it is shown that these deviations are related to the power spectrum of the bath. Specifically, it is shown that the system thermal-equilibrium-state cannot be characterized by the canonical Boltzmann's distribution in quantum mechanics. This is because the uncertainty principle imposed a lower bound of the dispersion of the total energy of the system that is dominated by the spectral density of the bath. However, in the classical case, for a wide class of systems that interact via central forces with pairwise-self-interacting environment, the system thermal equilibrium state is exactly characterized by the canonical Boltzmann distribution. As a consequence of this analysis and taking into account all energy scales in the system and reservoir interaction, an effective coupling to the environment is introduced. Sample computations in different regimes predicted by this effective coupling are shown. Specifically, in the strong coupling effective regime, the system exhibits deviations from standard thermodynamics and in the weak coupling effective regime, quantum features such as stationary entanglement are possible at high temperatures. Moreover, it is known that the spectrum of thermal baths depends on the non-Markovian character. Hence, non-Markovian interactions have a important role in the thermal equilibrium state of physical systems. For example, in quantum optomechanics is looked up to cool the mechanical system through an auxiliary system which generally is a cavity. This cooling process takes into account the non-Markovian interaction and as it is shown here, it is more effective than if we use only the Markovian approximation in the equation of motion for the different modes.
Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that in quantum mechanics, these deviations originate from the uncertainty principle and are supported by the non-Markovian character of the dynamics. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum; therefore, quantum mechanics inhibits the system thermal-equilibrium-state from being described by the canonical Boltzmann's distribution. We show for a wide class of systems, systems interacting via central forces with pairwise-self-interacting environments; this general observation is in sharp contrast to the classical case, for which the thermal equilibrium distribution, irrespective of the interaction strength, is exactly characterized by the canonical Boltzmann distribution; therefore, no dependence on the bath power spectrum is present. We define an effective coupling to the environment that depends on all energy scales in the system and reservoir interaction. Sample computations in regimes predicted by this effective coupling are demonstrated. For example, for the case of strong effective coupling, deviations from standard thermodynamics are present and for the case of weak effective coupling, quantum features such as stationary entanglement are possible at high temperatures.
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
The interplay between non-Markovian dynamics and driving fields in the survival of entanglement between two non-degenerate oscillators is considered here. Based on exact analytical results for the non-Markovian dynamics of two parametrically coupled non-degenerate oscillators in contact with non-identical independent thermal baths, the out-of-equilibrium quantum limit derived in [ Phys. Rev. Lett. 105 180501 (2010)] is generalised to the non-Markovian regime. Specifically, it is shown that non-Markovian dynamics, when compared to the Markovian case, allow for the survival of stationary entanglement at higher temperatures, with larger coupling strength to the baths and at smaller driving rates. The effect of the asymmetry of the (i) coupled oscillators, (ii) coupling strength to the baths at equal temperature, and (iii) temperature at equal coupling strength is discussed. In particular, it is shown that the non-Markovian character of the dynamics is capable of beating the resonant condition that states that the driving frequency equals the sum of the natural frequencies for the maximum rate of squeezing generation; hence, squeezing generation is more robust under non-Markovian dynamics.
We generalize the classical theory of Brownian motion so as to reckon with non-Markovian effects on both Klein-Kramers and Smoluchowski equations. For a free particle and a harmonic oscillator, it is shown that such non-Markovian effects account for the differentiability of the Brownian trajectories as well as the breakdown of the energy equipartition of statistical mechanics at short times in some physical situations. This non-Markovian approach is also extended to look at anomalous diffusion. Next, we bring in the dynamical-quantization method for investigating open quantum systems, which does consist in quantizing the classical Brownian motion starting directly from our non-Markovian Klein-Kramers and Smoluchowski equations, without alluding to any model Hamiltonian. Accordingly, quantizing our non-Markovian Klein-Kramers in phase space gives rise to a non-Markovian quantum master equation in configuration space, whereas quantizing our non-Markovian Smoluchowski equation in configuration space leads to a non-Markovian quantum Smoluchowski equation in phase space. In addition, it is worth noticing that non-Markovian quantum Brownian motion takes place in presence of a generic environment (e.g. a non-thermal quantum fluid). As far as the special case of a heat bath comprising of quantum harmonic oscillators is concerned, a non-Markovian Caldeira-Leggett master equation and a thermal quantum Smoluchowski equation are derived and extended to bosonic and fermionic heat baths valid for all temperatures.
An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..