Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1712.06795

Non-Markovian quantum interference in multilevel quantum systems: Exact master equation approach

Yusui Chen, J. Q. You, Ting Yu

Published Dec 19, 2017• 2 citations
arXivHTMLPDF

Abstract

We study the non-Markovian quantum interference phenomenon of a multi-state atomic system coupled to a bosonic dissipative environment by using the exact master equations derived in this paper. Two examples involving four-level systems with or without external control fields are investigated. Our results show that non-Markovian master equations are capable of exhibiting quantum interference phenomena in a temporal domain that has not fully explored before. In particular, we show that the environmental memory is instrumental in the onset of non-Markovian quantum interference pattern in different time scales.

DOI
10.48550/arxiv.1712.06795

Related papers

Non-Markovian quantum interference in multilevel quantum systems: exact master equation approach

Yusui Chen, J. Q. You, Ting Yu

We study the non-Markovian dynamics of multilevel quantum systems coupled with a bosonic dissipative environment. Based on the known exact quantum-state diffusion (QSD) equations, we propose a systematic approach to derive exact time-convolutionless master equations for multilevel quantum systems. Through a combination of analytical and numerical approaches, we extract the non-Markovian dynamics of quantum interference in different time scales. Also, we demonstrate the evolution of quantum interference in a four-level system controlled by an external electromagnetic field. Our findings are extended to few-body quantum networks, with a universal formalism established.

Quantum Information and Computation•Dec 1, 2018•4 citations

Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach

Yusui Chen, J. Q. You, Ting Yu

A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative $N$-qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.

arXiv:1408.1475•Physical Review A•Nov 5, 2014•50 citations

Time-local quantum-state-diffusion equation for multilevel quantum systems

Jun Jing, Xinyu Zhao, J. Q. You +1 more

An open quantum system with multiple levels coupled to a bosonic environment at zero temperature is investigated systematically using the non-Markovian quantum-state-diffusion (QSD) method [W. T. Strunz, L. Di\'osi, and N. Gisin, Phys. Rev. Lett. 82, 1801 (1999)]. We have established exact time-local QSD equations for a set of interesting multilevel open systems, including high-spin systems, multiple-transition atomic models, and multilevel atomic models driven by time-dependent external fields. These exact QSD equations have paved the way to evaluate the dynamics of open multilevel atomic systems in the general non-Markovian regimes without any approximation.

arXiv:1201.6558•Physical Review A•Apr 6, 2012•41 citations

Non-Markovian Dynamics of Qubit Systems: Quantum-State Diffusion Equations Versus Master Equations

Yusui Chen, Ting Yu

In this review we discuss recent progress in the theory of open quantum systems based on non-MarkovianNon-Markovian quantum state diffusionQuantum state diffusion equation and master equationsMaster equation. In particular, we show that an exact master equation for an open quantum system consisting of a few qubits can be explicitly constructed by using the corresponding non-Markovian quantum state diffusion equation. The exact master equation arises naturally from the quantum decoherence dynamics of qubit systems collectively interacting with a colored noise. We illustrate our general theoretical formalism by the explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This exact qubit master equation accurately characterizes the time evolution of the qubit system in various parameter domains, and paves the way for investigation of the memory effect of an open quantum system in a non-Markovian regime without any approximation.

Nanoscience and technology•Nov 20, 2015•2 citations

Master equation and dispersive probing of a non-Markovian process

Li‐Ping Yang, C. Y. Cai, Dazhi Xu +2 more

For a bosonic (fermionic) open system in a bath with many bosonic (fermionic) modes, we derive the exact non-Markovian master equation in which the memory effect of the bath is reflected in the time-dependent decay rates. In this approach, the reduced density operator is constructed from the formal solution of the corresponding Heisenberg equations. As an application of the exact master equation, we study the active probing of the non-Markovianity of the quantum dissipation of a single bosonic mode of an electromagnetic field in a cavity-QED system. The non-Markovianity of the bath of the cavity is explicitly reflected by the atomic decoherence factor.

arXiv:1209.5510•Physical Review A•Jan 11, 2013•26 citations

Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach

Jun Jing, Ting Yu

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schrödinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.

arXiv:1009.5301•Physical Review Letters•Dec 8, 2010•136 citations
We study the non-Markovian quantum interference phenomenon of a multi-state atomic system coupled to a bosonic dissipative environment by using the exact master equations derived in this paper. Two examples involving four-level systems with or without external control fields are investigated. Our results show that non-Markovian master equations are capable of exhibiting quantum interference phenomena in a temporal domain that has not fully explored before. In particular, we show that the environmental memory is instrumental in the onset of non-Markovian quantum interference pattern in different time scales.
We study the non-Markovian dynamics of multilevel quantum systems coupled with a bosonic dissipative environment. Based on the known exact quantum-state diffusion (QSD) equations, we propose a systematic approach to derive exact time-convolutionless master equations for multilevel quantum systems. Through a combination of analytical and numerical approaches, we extract the non-Markovian dynamics of quantum interference in different time scales. Also, we demonstrate the evolution of quantum interference in a four-level system controlled by an external electromagnetic field. Our findings are extended to few-body quantum networks, with a universal formalism established.
A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative NNN-qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.
An open quantum system with multiple levels coupled to a bosonic environment at zero temperature is investigated systematically using the non-Markovian quantum-state-diffusion (QSD) method [W. T. Strunz, L. Di\'osi, and N. Gisin, Phys. Rev. Lett. 82, 1801 (1999)]. We have established exact time-local QSD equations for a set of interesting multilevel open systems, including high-spin systems, multiple-transition atomic models, and multilevel atomic models driven by time-dependent external fields. These exact QSD equations have paved the way to evaluate the dynamics of open multilevel atomic systems in the general non-Markovian regimes without any approximation.
In this review we discuss recent progress in the theory of open quantum systems based on non-MarkovianNon-Markovian quantum state diffusionQuantum state diffusion equation and master equationsMaster equation. In particular, we show that an exact master equation for an open quantum system consisting of a few qubits can be explicitly constructed by using the corresponding non-Markovian quantum state diffusion equation. The exact master equation arises naturally from the quantum decoherence dynamics of qubit systems collectively interacting with a colored noise. We illustrate our general theoretical formalism by the explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This exact qubit master equation accurately characterizes the time evolution of the qubit system in various parameter domains, and paves the way for investigation of the memory effect of an open quantum system in a non-Markovian regime without any approximation.
For a bosonic (fermionic) open system in a bath with many bosonic (fermionic) modes, we derive the exact non-Markovian master equation in which the memory effect of the bath is reflected in the time-dependent decay rates. In this approach, the reduced density operator is constructed from the formal solution of the corresponding Heisenberg equations. As an application of the exact master equation, we study the active probing of the non-Markovianity of the quantum dissipation of a single bosonic mode of an electromagnetic field in a cavity-QED system. The non-Markovianity of the bath of the cavity is explicitly reflected by the atomic decoherence factor.
The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schrödinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.