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arXiv:2202.01726 · Quantum Information Processing

Quantum coherence dynamics of displaced squeezed thermal state in a non-Markovian environment

Md. Manirul Ali, Chandrashekar Radhakrishnan, S. S. Naina Mohammed

Published May 1, 2022• 5 citations
arXivHTMLPDF
DOI
10.1007/s11128-022-03535-4

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The transient dynamics of quantum coherence of Gaussian states are investigated. The state is coupled to an external environment which can be described by a Fano-Anderson type Hamiltonian. Solving the quantum Langevin equation, we obtain the Greens functions which are used to compute the time evolved first and second moments of the quadrature operators. From the quadrature operator moments, we construct the covariance matrix which is used to measure the coherence in the system. The coherence is measured using the relative entropy of coherence measure. We consider three different classes of spectral densities in our analysis viz, the Ohmic, the sub-Ohmic, and the super-Ohmic densities. In our work, we study the dynamics of the coherent state, squeezed state, and displaced squeezed state. For all these states we observe that when the coupling with the system and the environment is weak, the coherence monotonically decreases and eventually vanishes in a long time. Thus all the states exhibit Markovian evolution in the weak coupling limit. In the strong coupling limit, the dynamics for the initial period is Markovian and after a certain period, it becomes non-Markovian where we observe an environmental backaction on the system. Thus in the strong coupling limit, we observe a dynamical crossover from Markovian nature to non-Markovian behavior. This crossover is very abrupt under some environmental conditions and for some parameters of the quantum state. Using a quantum master equation approach we verify the crossover from the dynamics of the dissipation and fluctuation parameters and the results endorse those obtained from coherence dynamics.
Understanding how quantum systems equilibrate is a fundamental question with implications for quantum technologies, such as state preparation for quantum computing. However, linear response theory fails to explain the thermal relaxation of far-from-equilibrium classical and quantum systems. In this context, recent studies have reported a relaxation asymmetry, where heating is faster than cooling for initial states that are thermodynamically equidistant from equilibrium, but understanding how quantum resources affect this asymmetry is still an open question. In this work, we investigate the heating and cooling asymmetry in discrete and continuous-variable quantum systems. For the discrete case, we study two interacting qubits coupled to a global bosonic bath, focusing on the effects of initial coherences, steady state correlations generated by the dynamics and local non-Markovianity. For the continuous case, we consider Gaussian states and compare the thermal relaxation asymmetry of displaced and squeezed states. Our results for the discrete case indicate that non-Markovianity may accelerate thermal relaxation, while the initial coherences do not change the equilibration time. In Gaussian systems, applying the displacement operator in the initial states does not affect the asymmetry, but applying the squeezing operator reduces the asymmetry. Additionally, we show an invertion of the asymmetry, making cooling faster than heating, by squeezing the hotter state and displacing the cooler state.
We apply the stochastic Schr\"odinger equation approach to study the non-Markovian dynamics of quantum systems coupled to a squeezed environment. We derive the non-Markovian quantum-state-diffusion equation using coherent-state unraveling and the associated zeroth-order master equation for general models in a microscopic quantum context. Focused on a dissipative optical cavity coupled with a squeezed vacuum, the numerical simulations demonstrate the time evolution of photon numbers in an optical cavity. We observe that the long-time limits of the non-Markovian dynamics are significantly different from those of the Markovian dynamics for various memory factors and squeezing factors. Additionally, non-Markovian dynamics exhibit a distinct pattern of behavior when parameters change. Our work provides a method to study the impact of multiple parameters on the non-Markovian dynamics and long-time limits in a joint manner. The method can be further extended to squeezed finite-temperature environments.