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Non-Markovian dynamics of a three-level atom in a stochastic field with finite correlation time due to initial correlations

Victor Mikhailov, Nikolay V. Troshkin

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Dynamics of a three-level atom interacting with a stochastically fluctuating environment characterized by finite correlation time is investigated in the cases of a product initial state and a correlated initial state. The correlated initial state is obtained by the state reduction caused by the von Neumann measurement on the quantum system evolved from the product initial state and surrounded by the initially stationary stochastic environment. It is shown that in case of a pure dephasing process under the influence of a Kubo-Anderson type stochastic environment, the projective measurement causes the emergence of correlations between previously independent stochastic processes, their non-stationarity, and also causes the transition from a Markovian-type evolution to a non-Markovian one.

DOI
10.1051/epjconf/201922003031

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Dynamics of a three-level atom interacting with a stochastically fluctuating environment characterized by finite correlation time is investigated in the cases of a product initial state and a correlated initial state. The correlated initial state is obtained by the state reduction caused by the von Neumann measurement on the quantum system evolved from the product initial state and surrounded by the initially stationary stochastic environment. It is shown that in case of a pure dephasing process under the influence of a Kubo-Anderson type stochastic environment, the projective measurement causes the emergence of correlations between previously independent stochastic processes, their non-stationarity, and also causes the transition from a Markovian-type evolution to a non-Markovian one.
Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic Liouville equation is shown to be derived from the quantum master equation of the Lindblad under certain conditions. Relaxation processes of single and bipartite quantum systems which are initially correlated with a stochastic environment are investigated. It is shown the possibility that the stochastic fluctuation can create coherence and entanglement of a quantum system with the assistance of the initial correlation. The results are examined in the pure dephasing processes of qubits, which are caused by the nonstationary Gauss-Markov process and two-state jump Markov process.
The character of evolution of an open quantum system is often encoded in the correlation function of the environment or, equivalently, in the spectral density function of the interaction. When the environment is heterogeneous, e.g., consists of several independent subenvironments with different spectral functions, one of the subenvironments can be considered auxiliary and used to control decoherence of the open quantum system in the remaining part of the environment. The control can be realized, for example, by adjusting the character of interaction with the subenvironment via suitable parameters of its spectral density. We investigate non-Markovian evolution of a two-level system (qubit) under influence of three independent decoherence channels: two of them have classical nature and originate from interaction with a stochastic field, and the third is a quantum channel formed by interaction with a bosonic bath. By modifying spectral densities of the channels, we study their impact on steady states of the two-level system, evolution of its density matrix, and the equilibrium emission spectra. Additionally, we investigate the impact of the rotation-wave approximation applied to the bath channel on accuracy of the results.
The reduced time evolution of a single qubit under the influence of a classical environment is studied by means of the stochastic Liouville equation. The qubit initially correlates with the environment, which is created by a preparation process of an initial state. The phase fluctuation caused by the environment is characterized by means of the Gauss-Markov process and the two-state-jump Markov process. It is shown that depending on values of the parameters, the initial correlation enhances or reduces the decoherence of the qubit. In the case of the slow modulation, the effect of the initial preparation of the qubit becomes significant and it cannot be ignored in the reduced time evolution of the qubit.
In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.
Relaxation of a three-level atom with non-equidistant spectrum interacting with a thermostat and an external stochastic field is studied. The master equation for the reduced density matrix and its solution in the first order of the perturbation theory are obtained. Using quantum regression theorem, explicit formulas for two-time correlation functions and shapes of radiation lines are derived for all types of three-level atoms and the following stochastic processes: a delta-correlated process and a Kubo-Anderson process. The influence of stochastic perturbations of atom’s energy levels and damping constants of adjacent transitions on width of radiation lines is shown.
We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, of which the statistical properties are both non-stationary and non-Markovian. Due to the time-homogeneous property in the master equations for the multi-time probability distribution, the decoherence factor induced by the generalized RTN with a modulatable-type memory kernel can be exactly derived by means of a closed fourth-order differential equation with respect to time. In some special limit cases, the decoherence factor recovers to the expression of the previous ones. We analyzed in detail the environmental effect of memory modulation in the dynamical dephasing in four types of dynamics regimes. The results showed that the dynamical dephasing of the quantum system and the conversion between the Markovian and non-Markovian characters in the dephasing dynamics under the influence of the generalized RTN can be effectively modulated via the environmental memory kernel.