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arXiv:1411.3382 · New Journal of Physics

Quantum limit for driven linear non-Markovian open-quantum-systems

Andres Estrada, Leonardo A. Pachón

Published Mar 27, 2015• 31 citations
arXivHTMLPDF

Abstract

The interplay between non-Markovian dynamics and driving fields in the survival of entanglement between two non-degenerate oscillators is considered here. Based on exact analytical results for the non-Markovian dynamics of two parametrically coupled non-degenerate oscillators in contact with non-identical independent thermal baths, the out-of-equilibrium quantum limit derived in [ Phys. Rev. Lett. 105 180501 (2010)] is generalised to the non-Markovian regime. Specifically, it is shown that non-Markovian dynamics, when compared to the Markovian case, allow for the survival of stationary entanglement at higher temperatures, with larger coupling strength to the baths and at smaller driving rates. The effect of the asymmetry of the (i) coupled oscillators, (ii) coupling strength to the baths at equal temperature, and (iii) temperature at equal coupling strength is discussed. In particular, it is shown that the non-Markovian character of the dynamics is capable of beating the resonant condition that states that the driving frequency equals the sum of the natural frequencies for the maximum rate of squeezing generation; hence, squeezing generation is more robust under non-Markovian dynamics.

DOI
10.1088/1367-2630/17/3/033038

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Abstract Entanglement being a foundational cornerstone of quantum sciences and the primary resource in quantum information processing, understanding its dynamical evolution in realistic conditions is essential. Unfortunately, numerous model studies show that degradation of entanglement from a quantum system’s environment, especially thermal noise, is almost unavoidable. Thus the appellation ‘hot entanglement’ appears like a contradiction, until Galve et al. [Phys. Rev. Lett. 105, 180501 (2010)] announced that entanglement can be kept at high temperatures if one considers a quantum system with time-dependent coupling between the two parties, each interacting with its individual bath. With the goal of understanding the sustenance of entanglement at high temperatures, working with the same model and set up as Galve et al, namely, parametrically-driven coupled harmonic oscillators interacting with their own Markovian baths, this work probes into the feasibility of ‘hot entanglement’ from three aspects listed in the subtitle. Our findings show that 1) hot entanglement functions only in the unstable regimes, 2) instability is a necessary but not sufficient condition, and 3) the power intake required by the drive operating in the unstable regime to sustain entanglement increases exponentially. The last factor indicates that hot entanglement under this modeling is theoretically untenable and its actual implementation likely unattainable.
We study non-Markovian dynamics of an open quantum system system interacting with a nonstationary squeezed bosonic reservoir. We derive exact and approximate descriptions for the open system dynamics. Focusing on the spin boson model, we compare exact dynamics with Redfield theory and a quantum optical master equation for both short and long time dynamics and in non-Markovian and Markov regimes. The squeezing of the bath results in asymptotic oscillations in the stationary state, which are captured faithfully by the Redfield master equation in the case of weak coupling. Furthermore, we find that the bath squeezing direction modifies the effective system-environment coupling strength and, thus, the strength of the dissipation.
Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies. In this regard, we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent (Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field. Then, we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure. It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency, the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies (central detuning) in both non-Markovian and Markovian reservoirs. While the central detuning has a constructive role, the detuning between the qubit and the classical field (laser detuning) affects negatively on the entanglement protection. The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir. We demonstrate that, in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.
Abstract The non-Markovian dynamics of a qubit dephasing in a squeezed thermal environment with general Ohmic spectral density are investigated, and the analytical solution is presented for the models with sub-Ohmic, Ohmic, and super-Ohmic spectral densities in the zero-temperature limit. We study the non-Markovianity of the open qubit system, and find that it is very large in a certain regime of the squeezed parameters and almost vanishes outside this regime, given the parameters of the environmental spectrum. Furthermore, the non-Markovianity can be enhanced to surpass that of the unsqueezed case by adjusting the squeezing parameters. More interestingly, we find that given the other parameters, the non-Markovianity of a small coupling constant between the qubit and its environment may be larger than in the case of a large coupling constant; this is dependent on the competition between the coupling constant and the Ohmicity parameter of the environment. We also discuss the influence of squeezing operator on the quantum speed limit (QSL) time for the considered model, and find that the QSL time can be reduced via the adjustment of the squeezing operator.
Abstract We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime. However, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale ( ) than in the Markovian regime ( ). Moreover, although the singular coupling limit of non-Markovian dynamics yields Markovian ones, we show that the same limit does not lead from non-Markovian entanglement generation conditions to Markovian ones. Also, entanglement generation conditions do not depend on the initial time for non-Markovian open dynamics resulting from couplings to bosonic Gaussian baths, while they may depend on time for open dynamics originated by couplings to classical, stochastic Gaussian environments.
We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.