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arXiv:2002.04234 · Photonics

Topological Protection and Control of Quantum Markovianity

Gian Luca Giorgi, Salvatore Lorenzo, Stefano Longhi

Published Feb 8, 2020• 11 citations
arXivHTMLPDF

Abstract

Under the Born–Markov approximation, a qubit system, such as a two-level atom, is known to undergo a memoryless decay of quantum coherence or excitation when weakly coupled to a featureless environment. Recently, it has been shown that unavoidable disorder in the environment is responsible for non-Markovian effects and information backflow from the environment into the system owing to Anderson localization. This turns disorder into a resource for enhancing non-Markovianity in the system–environment dynamics, which could be of relevance in cavity quantum electrodynamics. Here we consider the decoherence dynamics of a qubit weakly coupled to a two-dimensional bath with a nontrivial topological phase, such as a two-level atom embedded in a two-dimensional coupled-cavity array with a synthetic gauge field realizing a quantum-Hall bath, and show that Markovianity is protected against moderate disorder owing to the robustness of chiral edge modes in the quantum-Hall bath. Interestingly, switching off the gauge field, i.e., flipping the bath into a topological trivial phase, allows one to re-introduce non-Markovian effects. Such a result indicates that changing the topological phase of a bath by a tunable synthetic gauge field can be harnessed to control non-Markovian effects and quantum information backflow in a qubit-environment system.

DOI
10.3390/photonics7010018

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Under the Born–Markov approximation, a qubit system, such as a two-level atom, is known to undergo a memoryless decay of quantum coherence or excitation when weakly coupled to a featureless environment. Recently, it has been shown that unavoidable disorder in the environment is responsible for non-Markovian effects and information backflow from the environment into the system owing to Anderson localization. This turns disorder into a resource for enhancing non-Markovianity in the system–environment dynamics, which could be of relevance in cavity quantum electrodynamics. Here we consider the decoherence dynamics of a qubit weakly coupled to a two-dimensional bath with a nontrivial topological phase, such as a two-level atom embedded in a two-dimensional coupled-cavity array with a synthetic gauge field realizing a quantum-Hall bath, and show that Markovianity is protected against moderate disorder owing to the robustness of chiral edge modes in the quantum-Hall bath. Interestingly, switching off the gauge field, i.e., flipping the bath into a topological trivial phase, allows one to re-introduce non-Markovian effects. Such a result indicates that changing the topological phase of a bath by a tunable synthetic gauge field can be harnessed to control non-Markovian effects and quantum information backflow in a qubit-environment system.
Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.
As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence, when an atom interacts with a disordered lattice, one indeed observes a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario, we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath.
Non-Markovian effects arising in open quantum system evolution have been a subject of increasing interest over the past decade. One of the most appealing features of non-Markovianity (NM) is that it captures scenarios where loss of information and coherence are reversible, and thus a temporary backflow of information from the environment to the system is possible. In this work we study the interplay between the degree of non-Markovianity and the action of time-dependent control fields in an open two-level quantum system. We find that periodical modulation of a field acting solely on the system can greatly enhance the degree of non-Markovianity with respect to the undriven case. We show that this effect is present only when the coupling between system and environment is weak. Remarkably, the enhancement disappears at strong coupling, which is usually the regime where non-Markovian effects are expected to be more pronounced.
Non-Markovian effects arising in open quantum system evolution have been a subject of increasing interest over the past decade. One of the most appealing features of non-Markovianity (NM) is that it captures scenarios where loss of information and coherence are reversible, and thus a temporary backflow of information from the environment to the system is possible. In this work we study the interplay between the degree of non-Markovianity and the action of time-dependent control fields in an open two-level quantum system. We find that periodical modulation of a field acting solely on the system can greatly enhance the degree of non-Markovianity with respect to the undriven case. We show that this effect is present only when the coupling between system and environment is weak. Remarkably, the enhancement disappears at strong coupling, which is usually the regime where non-Markovian effects are expected to be more pronounced.
Manipulating the dynamics of open quantum systems is a crucial requirement for large-scale quantum computers. Finding ways to overcome or extend decoherence times is a challenging task. Already at the level of a single two-level atom, its reduced dynamics with respect to a larger environment can be very complex. Structured environments, for instance, can lead to various regimes other than memoryless Markovian spontaneous emission. Here, we consider an atom coupled to an array of coupled cavities in the presence of on-site correlated disorder. The correlation is long-ranged and associated with the trace of a fractional Brownian motion following a power-law spectrum. With the cavity modes playing the role of the environment, we study the dynamics of the spontaneous emission. We observe a change from non-Markovian to Markovian decay in the presence of disorder by tuning the correlation parameter. This is associated with a localization-delocalization transition involving the field modes. Two dissipative models that effectively reproduce the behavior of the non-Markovianity are discussed. The dissipation dynamics of the atom can thus be used to extract information about the phase of the environment. Our results provide a direction in the engineering of disordered quantum systems to function as controllable reservoirs.
It was recently shown [S. Lorenzo, F. Lombardo, F. Ciccarello and M. Palma, Sci. Rep. 7 (2017) 42729] that the presence of static disorder in a bosonic bath — whose normal modes thus become all Anderson-localized — leads to non-Markovianity in the emission of an atom weakly coupled to it (a process which in absence of disorder is fully Markovian). Here, we extend the above analysis beyond the weak-coupling regime for a finite-band bath so as to account for band edge effects. We study the interplay of these with static disorder in the emergence of non-Markovian behavior in terms of a suitable non-Markovianity measure.