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arXiv:1801.09310 · Physical Review A

Metastable decoherence-free subspace and pointer states in mesoscopic quantum systems

F. Lastra, C. E. López, J. C. Retamal

Published Apr 24, 2018• 3 citations
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Abstract

Two initially correlated coherent states, each interacting with its own independent dissipative environment, exhibit a sudden transition from classical to quantum decoherence. This change in the dynamics is a turning point in the decoherence in the sense that depending on the average number of photons of each harmonic oscillator, decoherence can even be suppressed. Indeed, the quantum state is time independent for a time span in the mesoscopic regime, revealing a decoherence-free subspace. Furthermore, the absence of decoherence is manifested in the apparition of a metastable pointer-state basis.

DOI
10.1103/physreva.97.042123

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Two initially correlated coherent states, each interacting with its own independent dissipative environment, exhibit a sudden transition from classical to quantum decoherence. This change in the dynamics is a turning point in the decoherence in the sense that depending on the average number of photons of each harmonic oscillator, decoherence can even be suppressed. Indeed, the quantum state is time independent for a time span in the mesoscopic regime, revealing a decoherence-free subspace. Furthermore, the absence of decoherence is manifested in the apparition of a metastable pointer-state basis.
The dynamic of correlations in a system composed of a two-mode quantum field coupled with the environment is studied. The quantum field corresponds to two entangled coherent states whose amplitude we vary up to the mesoscopic regime. We show that under the onset of decoherence, correlations in the quantum field are not lost but transferred to the environment. We also found that sudden transitions in the decoherence regimes appear along with the dynamics depending on the coherent states' amplitude. Increasing the amplitude of the entangled coherence state results in the apparition of a metastable decoherence-free subspace (DFS) in the field subsystem, and the transference of classical correlations freezes. This subspace only exists during a time interval that depends on the average number of photons. Interestingly, the reservoir subsystem also experiences the apparition of a DFS. Only quantum correlations are transferred while the DFS exists.
We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t \bar{t}, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time \bar{t} the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.
We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t<[symbol: see text]. In this initial time interval classical correlations decay. For t>[symbol: see text], on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time [symbol: see text] the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.
We study the dynamics of quantum and classical correlations in a two-qutrit system coupled to independent reservoirs. In particular, we address the differences in the dynamics of Markovian and non-Markovian regimes and show that for specific initial states, classical correlations exhibit abrupt changes along the dynamics. A particular sudden change occurs when the classical correlations freeze to a certain value at a given time, revealing the apparition of a pointer-state basis. After this given time, the decoherence only affects quantum correlations. Here we identify two regimes in the decoherence dynamics: a mixed regime when both classical and quantum correlations decay and a quantum regime when only quantum correlations decay. We show that the freezing of classical correlations can be stable or metastable depending on the system-reservoir parameters. In the long-time limit, we find analytical expressions for the pointer-state basis the system settles in and consequently for classical and quantum correlations.
We analyze the dynamics of metastable Markovian open quantum systems by unraveling their average dynamics into stochastic trajectories. We use quantum reset processes as examples to illustrate metastable phenomenology, including a simple three-state model whose metastability is of classical type, and a two-qubit model that features a metastable decoherence-free subspace. In the three-state model, the trajectories exhibit classical metastable phenomenology: fast relaxation into distinct phases and slow transitions between them. This extends the existing correspondence between classical and quantum metastability. It enables the computation of committors for the quantum phases, and the mechanisms of rare transitions between them. For the two-qubit model, the decoherence-free subspace appears in the unraveled trajectories as a slow manifold on which the quantum state has a continuous slow evolution. This provides a classical (nonmetastable) analog of this quantum effect. We discuss the general implications of these results, and we highlight the useful role of quantum reset processes for analysis of quantum trajectories in metastable systems. Published by the American Physical Society 2024
The coupling of a mesoscopic system with its environment usually causes total decoherence: at long times the reduced density matrix of the system evolves in time to a limit which is independent of its initial value, losing all the quantum information stored in its initial state. Under special circumstances, a subspace of the system's Hilbert space remains coherent, or "decoherence free", and the reduced density matrix approaches a non-trivial limit which contains information on its initial quantum state, despite the coupling to the environment. This situation is called "partial decoherence". Here we find the conditions for partial decoherence for a mesoscopic system (with NNN quantum states) which is coupled to an environment. When the Hamiltonian of the system commutes with the total Hamiltonian, one has "adiabatic decoherence", which yields N-1 time-independent combinations of the reduced density matrix elements. In the presence of a magnetic flux, one can measure circulating currents around loops in the system even at long times, and use them to retrieve information on the initial state. For N=2, we demonstrate that partial decoherence can happen only under adiabatic decoherence conditions. However, for N>2N>2N>2 we find partial decoherence even when the Hamiltonian of the system does not commute with the total Hamiltonian, and we obtain the general conditions for such non-adiabatic partial decoherence. For an electron moving on a ring, with N>2N>2N>2 single-level quantum dots, non-adiabatic partial decoherence can arise only when the total flux through the ring vanishes (or equals an integer number of flux quanta), and therefore there is no asymptotic circulating current.