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arXiv:1802.07715 · New Journal of Physics

Theory of open quantum dynamics with hybrid noise

Anatoly Yu. Smirnov, M. H. S. Amin

Published Oct 11, 2018• 23 citations
arXivHTMLPDF

Abstract

We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components.One part of the system-bath interaction is treated in a perturbative manner, whereas the other part is considered exactly.This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch-Redfield and Marcus formulas.Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment.As an illustration, we apply the theory to the 16 qubit quantum annealing problem with dangling qubits (Dickson et al 2013 Nat.Commun.4 1903) and show qualitative agreement with experimental results.

DOI
10.1088/1367-2630/aae79c

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We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components.One part of the system-bath interaction is treated in a perturbative manner, whereas the other part is considered exactly.This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch-Redfield and Marcus formulas.Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment.As an illustration, we apply the theory to the 16 qubit quantum annealing problem with dangling qubits (Dickson et al 2013 Nat.Commun.4 1903) and show qualitative agreement with experimental results.
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 theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master equations, respectively. We derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process, respectively. For the pure decoherence case with no tunneling coupling, the expressions of the decoherence factor we obtained are consistent with the well-known existing ones. The results are significant to quantum information processing and helpful for further understanding the quantum dynamics of open quantum systems.
Data of the numerical solution of the time-dependent Schrödinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects inasmuch the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-type equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this perturbatively derived equation quantitatively differs from the numerically estimated Markovian master equation, the results of which agree very well with the solution of the time-dependent Schrödinger equation.
In this paper we demonstrate how to generate the strong-coupling master equations for open quantum systems of continuous variables. These are the dissipative master equations of quantum Brownian particles for which the environmental noise is stronger than other system forces. Our strong-coupling master equations are very different from other so-called "strong-coupling" master equations (e.g. the quantum Smoluchowski equation) which are perturbing off a limit in which the system energy is taken to be perturbative and thus the dynamics is principally Markovian. Such approximations also require the system mass to be asymptotically large (even as compared to the ratio of noise and induced system frequencies) and thus they do not fully categorize the regime of what one might consider to be strong coupling. Our master equations are highly non-Markovian and radically different for different system potentials, admitting no apparent generic form. This result is quite exciting as it brings forth a new regime for theoretical exploration: the regime of strong noise and dissipation yet non-Markovian, such as strong coupling to a low-temperature environment with large 1/f fluctuations.
Abstract This chapter is dedicated to open quantum systems. We explain the origin of non-unitary time evolution by studying different interactions between a qubit and the environment. The first part of the chapter introduces the time evolution equation of an open quantum system, also called the Born-Markov master equation and the Redfield equation. We then study the interaction between a qubit and a thermal bath of harmonic oscillators and introduce the qubit relaxation and the dephasing times. After discussing the relationship between relaxation and dephasing times of a qubit and the power spectral density of the noise source, we present the Hahn echo and the Carr-Purcell-Meiboom-Gill experiments, two protocols that provide information about the noise spectrum. The chapter ends with a discussion of the driven evolution of a qubit subject to spontaneous emission and dephasing
In this paper, we investigate the dynamics of an open qubit model by solving two sets of its reduced dynamical equations. One set of the equations is the well-known Bloch equations and the other is the widely investigated master equations of Redfield form. Both of them are obtained from the perturbation approximation which demands the system of interest weakly coupled to its environment. It is shown that the qubit has a longer decoherence and relaxiation time as the dynamics is described by the Redfield equantions.