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arXiv:1311.0699 · Physical Review A

Coherence trapping and information backflow in dephasing qubits

Carole Addis, Gregoire Xavier Brebner, Pinja Haikka, Sabrina Maniscalco

Published Feb 5, 2014• 98 citations
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Abstract

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.

DOI
10.1103/physreva.89.024101

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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.
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 investigate the relationship between non-Markovianity and the effectiveness of a dynamical decoupling (DD) protocol for qubits undergoing pure dephasing. We consider an exact model in which dephasing arises due to a bosonic environment with a spectral density of the Ohmic class. This is parametrized by an Ohmicity parameter by changing which we can model both Markovian and non-Markovian environments. Interestingly, we find that engineering a non-Markovian environment is detrimental to the efficiency of the DD scheme, leading to a worse coherence preservation. We show that each DD pulse reverses the flow of quantum information and, on this basis, we investigate the connection between DD efficiency and the reservoir spectral density. Finally, in the spirit of reservoir engineering, we investigate the optimum system-reservoir parameters for achieving maximum stationary coherences.
The flow of quantum information in local dephasing channels is analyzed over short and long times in case the structured reservoir of frequency modes exhibits a spectral gap in the density of modes over low frequencies. The presence of the low-frequency gap with upper cut-off frequency [Formula: see text] produces an infinite sequence of long-time intervals over which information backflow appears. Though generally irregular, the time intervals exhibit, under certain conditions, upper bounds: the [Formula: see text]th episode of information backflow has already started at the instant [Formula: see text], and already ended at the instant [Formula: see text], for every [Formula: see text]. The intervals become regular over long times, tend to the asymptotic length [Formula: see text], as the supremum value, and are described analytically in terms of the structure of the spectral density near the upper cut-off frequency of the spectral gap. Consequently, engineering structured reservoirs of frequency modes with a spectral gap over low frequencies produces in local dephasing channels regular sequences of information backflow and recoherence over long times, along with non-Markovian evolution.
We investigate the dynamics of quantum information flow in one and two impurity qubits trapped in a double-well potential and interacting with a one-dimensional ultracold Bose-Bose mixture reservoir. For a single qubit immersed in a binary Bose mixture, we show that the system maintains coherence over finite timescales and exhibits non-Markovian dynamics, particularly in the upper branch of the environment. We explore the transition from Markovian to non-Markovian dephasing through the Ohmicity of the spectral density functions, which are significantly influenced by interspecies interactions. In the case of two spatially separated qubits coupled to the Bose-Bose mixture reservoir, we demonstrate that collective decoherence affects the system dynamics, leading to prolonged coherence survival in both branches of the mixture. The intricate evolution of the decoherence factors is reflected in the density spectral functions and their Ohmicity characteristics. We find that the decoherence functions and spectra oscillate with increasing distance between the qubits, modifying the information flow dynamics. Additionally, we conduct a thorough investigation of the entanglement dynamics between the two qubits induced by the binary Bose mixture reservoir in both branches, underscoring the critical role of interspecies interactions.
How quantum coherence influences thermodynamic behavior remains an open question in quantum thermodynamics. Here we investigate this relation within the pure dephasing framework, where a central qubit interacts with a finite Ising-like spin environment. Although the system's internal energy remains constant, the interaction induces decoherence and gives rise to nontrivial thermodynamic features. Within the two-point measurement approach, we show that the heat dissipated into the environment matches the coherent energy contribution appearing in a reformulated first law of quantum thermodynamics. Numerical calculations reveal oscillatory coherence dynamics, with revivals associated with information backflow and non-Markovian effects, as quantified by the Breuer-Laine-Piilo measure. We find that heat and coherence exhibit intertwined temporal behavior, with enhanced heat dissipation during coherence decay and reduced heat during revivals. These results suggest a connection between coherence dynamics and thermodynamic quantities in finite, closed composite systems undergoing pure dephasing.
We derive an analytical relation between the von Neumann entropy rate and the coherence dynamicsof a qubit undergoing pure dephasing without assuming Markovianity. The result expresses˙S(t) solely in terms of the ℓ1-coherence C(t) and its time derivative ˙C (t), for fixed populations. TheMarkovian exponential decay is recovered as a special case. In non-Markovian regimes, the formulapredicts intervals of negative entropy rate associated with coherence revivals, providing a compactlink between information backflow and entropy dynamics.