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arXiv:1502.02446 · Scientific Reports

Role of initial system-bath correlation on coherence trapping

Yingjie Zhang, Wei Han, Yun‐Jie Xia, Yanmei Yu, Heng Fan

Published Aug 25, 2015• 68 citations
arXivHTMLPDF

Abstract

We study the coherence trapping of a qubit correlated initially with a non-Markovian bath in a pure dephasing channel. By considering the initial qubit-bath correlation and the bath spectral density, we find that the initial qubit-bath correlation can lead to a more efficient coherence trapping than that of the initially separable qubit-bath state. The stationary coherence in the long time limit can be maximized by optimizing the parameters of the initially correlated qubit-bath state and the bath spectral density. In addition, the effects of this initial correlation on the maximal evolution speed for the qubit trapped to its stationary coherence state are also explored.

DOI
10.1038/srep13359

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We study the coherence trapping of a qubit correlated initially with a non-Markovian bath in a pure dephasing channel. By considering the initial qubit-bath correlation and the bath spectral density, we find that the initial qubit-bath correlation can lead to a more efficient coherence trapping than that of the initially separable qubit-bath state. The stationary coherence in the long time limit can be maximized by optimizing the parameters of the initially correlated qubit-bath state and the bath spectral density. In addition, the effects of this initial correlation on the maximal evolution speed for the qubit trapped to its stationary coherence state are also explored.
We study the interplay between coherence trapping, information backflow and the form of the reservoir spectral density for dephasing qubits. We show that stationary coherence is maximized when the qubit undergoes non-Markovian dynamics, and we elucidate the different roles played by the low- and high-frequency parts of the environmental spectrum. We show that the low frequencies fully determine the presence or absence of information backflow while the high frequencies dictate the maximal amount of coherence trapping.
Abstract The emerging quantum technologies heavily rely on the understanding of dynamics in open quantum systems. In the Born approximation, the initial system-bath correlations are often neglected which can be violated in the strong coupling regimes and quantum state preparation. In order to understand the influence of initial system-bath correlations, we study the extent to which these initial correlations and the distance of separation between the qubits influence the dynamics of quantum entanglement and coherence. It is shown that at low temperatures, the initial correlations have no role to play while at high temperatures, these correlations strongly influence the dynamics. Furthermore, we have shown that the distance of separation between the qubits in presence of a collective bath helps to maintain entanglement and coherence at long times.
Variations of the bath energy are compared with the information flow in local dephasing channels. Special correlated initial conditions are prepared from the thermal equilibrium of the whole system, by performing a selective measurement on the qubit. The spectral densities under study are ohmic-like at low frequencies and include logarithmic perturbations of the power-law profiles. The bath and the correlation energy alternately increase or decrease, monotonically, over long times, according to the value of the ohmicity parameter, following logarithmic and power laws. Consider initial conditions such that the environment is in a thermal state, factorized from the state of the qubit. In the superohmic regime the long-time features of the information flow are transferred to the bath and correlation energy, by changing the initial condition from the factorized to the specially correlated, even with different temperatures. In fact, the low-frequency structures of the spectral density that provide information backflow with the factorized initial condition, induce increasing (decreasing) bath (correlation) energy with the specially correlated initial configuration. By performing the same change of initial conditions, the spectral properties providing information loss, produce decrease (increase) of the bath (correlation) energy.
We investigate the reduced dynamics of a qubit subject to correlated longitudinal and transverse noise arising from its coupling to a shared bosonic bath. The environmental fluctuations are characterized by a positive-semidefinite matrix-valued spectral density, whose complex off-diagonal elements encode correlations between dephasing and relaxation channels in the frequency domain. Within the second-order time-convolutionless framework, we derive closed time-local equations for the Bloch-vector components of the reduced density matrix. The numerical implementation is validated against the exact pure-dephasing solution and the established behavior of the transverse-coupling spin-boson model. When both noise channels are present, the cross-spectral terms couple the otherwise distinct dephasing and relaxation sectors, producing dynamics that cannot be reproduced by adding independent noise contributions. In particular, the correlations generate non-monotonic population relaxation and a transient revival of coherence following its initial decay. The strength, bandwidth, delay, and phase of the cross spectrum provide control parameters for the magnitude and temporal structure of these effects. Our results demonstrate that correlated multi-axis noise can redistribute coherence loss and energy relaxation in time, thereby providing finite temporal windows of enhanced coherence or suppressed relaxation within the weak-coupling regime.
We study a model of dephasing (decoherence) in a two-state quantum system (qubit) coupled to a bath of harmonic oscillators. An exact analytic solution for the reduced dynamics of a two-state system in this model has been obtained previously for factorizing initial states of the combined system. We show that the model admits exact solutions for a large class of correlated initial states which are typical in the theory of quantum measurements. We derive exact expressions for the off-diagonal elements of the qubit density matrix, which hold for an arbitrary strength of coupling between the qubit and the bath. The influence of initial correlations on decoherence is considered for different bath spectral densities. Time behavior of the qubit entropy in the decoherence process is discussed.
The influence of the initial preparation on dephasing in open quantum dynamics is studied using an exactly solvable model of a two-level system (qubit) interacting with a bosonic bath. It is found that, for some classes of nonselective preparation measurements, qubit-bath correlations lead to a significant enhancement of coherence in the qubit at the initial stage of evolution. The time behavior of the qubit purity and entropy in the regime of enhancement of coherence is considered for different temperatures and coupling strengths.