We use a master equation to provide a proof of interference between noninteracting baths on a system’s reduced dynamics, agreeing with a result in . Here, we provide a formula for the details of leading-order interference. We illustrate the use of such interference toward suppressing (even freezing) decoherence with a simplest example and identify what determines the extent of decoherence suppression. However, we find that interference of baths vanishes (up to second order) as long as the baths are initially separable, thereby identifying a “low-bar” condition for noninterference. This finding provides strong justification for the widely used “additive assumption” in weak coupling regime. We discuss how this noninterference finding sheds light on the “puzzle” of vanishing second-order interference in the joint scenario of quantum and classical noises in . We also provide a general proof of interference between two baths under stochastic coupling, in contrast to the study of deterministic coupling in the literature. We demonstrate decoherence suppression with an example of a central spin stochastically coupled to two environmental spins. We find that two baths will cease to interfere (up to second order) if the two baths are initially separable and the system’s stochastic coupling strengths with the two baths are uncorrelated.
We use a master equation to provide a proof of interference between noninteracting baths on a system’s reduced dynamics, agreeing with a result in . Here, we provide a formula for the details of leading-order interference. We illustrate the use of such interference toward suppressing (even freezing) decoherence with a simplest example and identify what determines the extent of decoherence suppression. However, we find that interference of baths vanishes (up to second order) as long as the baths are initially separable, thereby identifying a “low-bar” condition for noninterference. This finding provides strong justification for the widely used “additive assumption” in weak coupling regime. We discuss how this noninterference finding sheds light on the “puzzle” of vanishing second-order interference in the joint scenario of quantum and classical noises in . We also provide a general proof of interference between two baths under stochastic coupling, in contrast to the study of deterministic coupling in the literature. We demonstrate decoherence suppression with an example of a central spin stochastically coupled to two environmental spins. We find that two baths will cease to interfere (up to second order) if the two baths are initially separable and the system’s stochastic coupling strengths with the two baths are uncorrelated.
We provide an alternative derivation of a master equation formalism for open quantum systems and apply it to illustrative examples. Using this formalism, we show that generally there can be interference between non-interacting baths on a system's reduced dynamics, confirming results in Phys. Rev. A 89, 042117 (2014). However, we also find that, up to second order, such interference vanishes as long as the baths are initially statistically independent, thereby identifying a satisfiable condition for non-interference. We use a two-dimensional series expansion method to develop a master equation formalism that deals with the effects of both system-environment interaction and classical noise on a system's dynamics in a unified manner. We apply this formalism to the example of a Zeeman-splitted atom in a stochastic B-field interacting with an optical cavity and find that the atom's total decoherence rate is, up to second order, a simple sum of the decoherence rate due to the atom-cavity interaction alone and that due to the stochastic B-field alone. We also develop a formalism for the dynamics of the (marginal) probability density of open classical systems in a similar fashion as the master equation formalism for open quantum systems.
We develop a new master equation as a unified description of the effects of both quantum noise (system-bath interaction) and classical noise on a system's dynamics, using a two-dimensional series expansion method. When quantum and classical noises are both present, their combined effect on a system's dynamics is not necessarily a simple sum of the two individual effects. Thus previous master equations for open systems and those for classical noise, even when jointly used, may not capture the full physics. Our formalism can determine whether there is interference between quantum and classical noises and will be able to capture and describe such interference if there is any (in a perturbative manner). We find that, interestingly, second-order interference between quantum and classical noises vanishes identically. This work thus also serves to justify simple additive treatments of quantum and classical noises, especially in the weak coupling regime. For a Zeeman-splitted atom in a stochastic magnetic field interacting with an optical cavity, we use the formalism developed herein to find the overall decoherence rate between the atom's energy levels.
Control of decoherence in open quantum systems has become a topic of great interest due to the emergence of quantum technologies that depend on quantum coherent effects. In this work, we investigate the decoherence dynamics of systems coupled to multiple baths through noncommuting systems' operators, and beyond the weak system-bath coupling limit. By building on cooperative effects between baths, we propose a novel strategy to mitigate rapid decoherence. Concretely, we study the dynamics of a qubit coupled to multiple environments with arbitrary interaction strengths, and along different coordinates. Based on insights gained on the decoherence dynamics from the analytical Effective Hamiltonian method, we carry out numerical simulations using the Reaction Coordinate quantum master equation method. In contrast to standard expectations, we show that when the system strongly interacts with a decohering bath, increasing its coupling to a second, dissipative bath slows down the decoherence dynamics. Our work offers insights into the preservation of quantum coherences in open quantum systems based on frustration effects, by utilizing cooperative effects between different heat baths.
The generalized quantum master equation provides an exact equation of motion for the reduced density operator of a quantum system coupled to one or more baths, with all bath-induced effects encoded in a memory kernel superoperator. In this paper, we investigate whether the memory kernel for a system coupled simultaneously to multiple independent baths can be written as a sum of memory kernels associated with the corresponding single-bath problems. We show that such additivity holds in the weak system-bath coupling limit, where the second-order memory kernel separates into independent bath contributions. Beyond this limit, however, the baths become dynamically correlated through their mutual coupling to the system, and the exact multi-bath memory kernel is no longer equal to the sum of exact single-bath memory kernels. We demonstrate this non-additivity for a two-level system linearly coupled to hot and cold harmonic baths, using the hierarchical equations of motion method to construct the memory kernels. The results show that non-additivity increases with system-bath coupling strength and is process-dependent: coherence damping remains comparatively well described by an additive kernel, whereas population-coherence and coherence-coherence transfer exhibit pronounced non-additive behavior. These findings clarify the limitations of additive multi-bath descriptions and highlight the ambiguity of decomposing heat flow into independent bath-resolved contributions beyond weak system-bath coupling.
It has recently been shown that interactions among the spins of a bath can result in an effective suppression of the decoherence of a single qubit embedded in a multi-spin environment. However, the effects of such intrabath interaction on the dynamics of entanglement are still not well understood. Here we study the dynamics of a system composed of two entangled qubits coupled to (1) independent self-interacting spin baths, and (2) a common self-interacting spin bath. We find that, as in the case of a single qubit, strong interactions among the spins in the bath may induce an effective decoupling between the bath and the system—this in turn suppresses the loss of entanglement that a non-, or weakly, interacting bath would typically cause. However we find that the intrabath interaction strength needed to achieve such effects is much larger than in the single qubit case, especially when the two qubits share the same environment. Our results illustrate the system's size effects in the entanglement sharing condition, where the entanglement within the bath limits the entanglement between the bath and the system.
Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.