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Nanosystems Physics Chemistry Mathematics

Hidden polarization in open quantum systems

A.D. Vatutin, George P. Miroshnichenko, Alexander Trifanov

Published Dec 30, 2023• 0 citations
Publisher

Abstract

In this work, we explore the master equation governing open quantum systems dynamics in an alternative form, which preserves the normal-ordered representation of the averaged normal-ordered operators.We derive a linear system of differential equations for the fourth-order moments of corresponding bosonic operators.Polarization moments of the first and the second orders are investigated using plane rotation transformation.We also evaluate the dynamics of the hidden polarization in comparison with the dynamics of usual polarization within open quantum dynamics.

DOI
10.17586/2220-8054-2023-14-2-626-632

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In this work, we explore the master equation governing open quantum systems dynamics in an alternative form, which preserves the normal-ordered representation of the averaged normal-ordered operators.We derive a linear system of differential equations for the fourth-order moments of corresponding bosonic operators.Polarization moments of the first and the second orders are investigated using plane rotation transformation.We also evaluate the dynamics of the hidden polarization in comparison with the dynamics of usual polarization within open quantum dynamics.
It is well known that the state operator of an open quantum system can be generically represented as the solution of a time-local equation — a quantum master equation. Unraveling in quantum trajectories offers a picture of open system dynamics dual to solving master equations. In the unraveling picture, physical indicators are computed as Monte Carlo averages over a stochastic process valued in the Hilbert space of the system. This approach is particularly adapted to simulate systems in large Hilbert spaces. We show that the dynamics of an open quantum system generically admits an unraveling in the Hilbert space of the system described by a Markov process generated by ordinary stochastic differential equations for which rigorous concentration estimates are available. The unraveling can be equivalently formulated in terms of norm-preserving state vectors or in terms of linear “ostensible” processes trace preserving only on average. We illustrate the results in the case of a two level system in a simple boson environment. Next, we derive the state-of-the-art form of the Diósi-Gisin-Strunz Gaussian random ostensible state equation in the context of a model problem. This equation provides an exact unraveling of open systems in Gaussian environments. We compare and contrast the two unravelings and their potential for applications to quantum error mitigation.
We study the quantum dynamics of mixed polarization states represented by the two-mode boson system interacting with an environment. Using the form of general dynamical equations for averaged operators that preserve normal ordering, we show that the dynamical regimes of the averaged Stokes operators crucially depend on the anisotropy of the relaxation operator resulting from the intermode coupling induced by the anisotropic environment. We analyze how this coupling impacts the quantum bit error rate in the well-known single-photon polarization-coding quantum key distribution protocol BB84.
Understanding system-environment correlations in open quantum systems is vital for various quantum information and technology applications. However, these correlations are often overlooked or hidden in derivations of open-quantum-system master equations, especially when applying the Born approximation. To address this issue, given a microscopic model, we demonstrate how to retain system-environment correlation within commonly used master equations, such as the Markovian Lindblad, Redfield, second-order time convolutionless, second-order Nakajima-Zwanzig, and second-order universal Lindblad-like equations. We show that each master equation corresponds to a particular approximation on the system-environment correlation operator. In particular, our analysis exposes the form of the hidden system-environment correlation in the Markovian Lindblad equation derived using the Born approximation. We also identify that the processes leading to the Redfield equation yield an inaccurate initial-time system-environment correlation approximation. By fixing this problem, we propose a corrected Redfield equation with an improved prediction for early stages of the time evolution. We further illustrate our results in two examples, which imply that the second-order universal Lindblad-like equation captures correlation more accurately than the other standard master equations. Published by the American Physical Society 2024
Master equations describing open quantum dynamics are typically first-order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the generator of the corresponding master equation becomes singular while the dynamical map becomes noninvertible. The first-order, time-local, homogeneous master equations then fail to describe the dynamics beyond the singular point. Retaining time locality in the master equation necessitates a reformulation in terms of higher-order differential equations. We formulate a method to eliminate the divergent behavior of the generator by using a combination of higher-order derivatives of the generator with suitable weights and illustrate it with several examples. We also present a detailed study of the central spin model and we propose the average rate of information inflow in non-Markovian processes as a quantity that captures a different aspect of non-Markovian dynamics.
We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation values of observables evaluated in a coherent state representation. We examine a model of a quantum nonlinear oscillator with a density-density interaction with a collection of environmental oscillators at finite temperature. We derive the exact solution for dynamics of observables and demonstrate a consistent perturbation approach.