Enabling quantum non-Markovian dynamics by injection of classical colored noise

Abstract

The non-Markovian nature of quantum systems recently turned to be a key subject for investigations on open quantum system dynamics. Many studies, from its theoretical grounding to its usefulness as a resource for quantum information processing and experimental demonstrations, have been reported in the literature. Typically, in these studies, a structured reservoir is required to make non-Markovian dynamics to emerge. Here, we investigate the dynamics of a qubit interacting with a bosonic bath and under the injection of a classical stochastic colored noise. A canonical Lindblad-like master equation for the system is derived, using the stochastic wavefunction formalism. Then, the non-Markovianity of the evolution is witnessed using the Andersson, Cresser, Hall and Li measure. We evaluate the measure for three different noises and study the interplay between environment and noise pump necessary to generate quantum non-Markovianity, as well as the energy balance of the system. Finally, we discuss the possibility to experimentally implement the proposed model.

A systematic path to non-Markovian dynamics: new response probability density function evolution equations under Gaussian coloured noise excitation

“…[8], [9], Sec. IX.7, [10][11][12][13][14][15][16]. Despite the difficulties, various methods seeking to formulate response pdf evolution equations for systems under coloured noise excitation have been proposed and developed.…”

When can quantum decoherence be mimicked by classical noise?

“…Due to the conceptual and technical complexities in dealing with the system plus environment fully quantum mechanically, an alternative approach is to simply consider that the effect of the environment is to introduce classical noise in the system's degrees of freedom [17][18][19][20][21][22][23][24][25]. In this picture, quantum dissipation is mimicked by stochastic terms in the equation of motion that introduce random transitions between system energy eigenstates.…”

“…However, unless this difference is probed explicitly, the noise model can mimic well the effects of decoherence since they both effectively lead to a damping of coherences. In fact, this stochastic picture with classical noise has been widely used in chemistry and physics to capture the loss of interference [19,25], optical line shapes [20,21], noise-assisted energy transport [22], non-Markovian dynamics [23], Landau-Zener [27,28] and central-spin problems [18] and in the quantum simulation of open many-body systems [24].…”

Quantum critical probing and simulation of colored quantum noise

“…Experimental developments have brought the notion of a quantum simulator to firmer grounds in different architectures, including trapped-ions [4][5][6][7], ultra-cold atoms [9][10][11][12], and superconducting circuits [13]. The simulation of the nonequilibrium dynamics of quantum systems coupled to complex environments is receiving increasing attention [15][16][17][18][19][20][21][22][23][24]26]. Several proposals have emerged that include an environment producing a classical noise [23,24] or even a quantum noise [15-22, 25, 26] which may therefore yield to dissipation in the open system [28].…”