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arXiv:1405.5321 · Physical Review B

Bipartite entanglement dynamics of two-level systems in sub-Ohmic reservoirs

Denis Kast, Joachim Ankerhold

Published Sep 23, 2014• 9 citations
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Abstract

The quantum dynamics of pairs of two-level systems immersed in dissipative reservoirs with sub-Ohmic spectral distributions is studied by means of numerically exact path integral Monte Carlo methods. It is shown that this class of reservoirs, relevant for generic properties of strongly non-Markovian environments with possible realizations in solid state structures at cryogenic temperatures, supports bipartite entanglement in broad ranges of parameter space and even for broken symmetries and in the presence of thermal noise. The sensitivity of the creation of entanglement in nonequilibrium on the initial preparations of the reservoir is investigated in detail.

DOI
10.1103/physrevb.90.100301

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The quantum dynamics of pairs of two-level systems immersed in dissipative reservoirs with sub-Ohmic spectral distributions is studied by means of numerically exact path integral Monte Carlo methods. It is shown that this class of reservoirs, relevant for generic properties of strongly non-Markovian environments with possible realizations in solid state structures at cryogenic temperatures, supports bipartite entanglement in broad ranges of parameter space and even for broken symmetries and in the presence of thermal noise. The sensitivity of the creation of entanglement in nonequilibrium on the initial preparations of the reservoir is investigated in detail.
The dissipative quantum dynamics of a two-level system interacting with a structured reservoir consisting of a damped harmonic mode is investigated by means of the numerically exact path integral Monte Carlo method. This approach provides benchmark results in a broad range of parameter space, in particular, in those domains which are not accessible by approximate methods and alternative numerical schemes, that is, strong coupling between system and harmonic mode and from low to high temperatures. For low temperatures the numerical data are quantitatively in agreement with the noninteracting blip approximation only in the regimes of very weak and very strong coupling. It turns out that the entangled dynamics of the two-level system and the harmonic mode is relatively robust so that its signatures are observable up to relatively strong friction and high temperatures. Nonequilibrium initial preparations of the reservoir with respect to the initial state of the system give rise, for strong interactions, to a stepwise decay of the population, thus displaying coherent dynamics of the bath. The impact of an additional Ohmic bath coupled directly to the two-level system is studied as well, including the case where both reservoirs carry different temperatures.
The quantum dynamics of a two-state system coupled to a bosonic reservoir with sub-Ohmic spectral density is investigated for strong friction. Numerically exact path integral Monte Carlo methods reveal that a changeover from coherent to incoherent relaxation does not occur for a broad class of spectral distributions. In nonequilibrium coherences associated with substantial system-reservoir entanglement exist even when strong dissipation forces the thermodynamic state of the system to behave almost classically. This may be of relevance for current experiments with nanoscale devices.
We study the non-Markovian dynamics of a two-mode bosonic system interacting with two uncorrelated thermal bosonic reservoirs. We present the solution to the exact microscopic Master equation in terms of the quantum characteristic function and study in detail the dynamics of entanglement for bipartite Gaussian states. In particular, we analyze the effects of short-time system-reservoir correlations on the separability thresholds and show that the relevant parameter is the reservoir spectral density. If the frequencies of the involved modes are within the reservoir spectral density, entanglement persists for a longer time than in a Markovian channel. On the other hand, when the reservoir spectrum is out of resonance, short-time correlations lead to a faster decoherence and to the appearance of entanglement oscillations.
In this work, I study the dynamics of spin-1/2 systems in contact with dissipative bosonic reservoirs. Investigations are motivated by recent progress in designing and controling atomic and solid state structures of growing complexity. The interplay between the bare system and the environment is of substantial importance for understanding the dynamics of such devices. Spin systems that are embedded in bosonic reservoirs are described by the famous spin-boson model and have been studied for several decades. Recent work has shown that two-level systems in contact with sub-Ohmic reservoirs are of fundamental interest in view of both theoretical considerations and their experimental relevance. This is why I focus on the dynamics of systems that couple to a sub-Ohmic environment. Additionally, impressive experimental progress in embedding quantum dots into photonic crystals encouraged me to investigate the dynamics of two-level systems coupled to surroundings with spectral gaps.
This study advances the theoretical understanding of decoherence mechanisms in open quantum systems by modelling entanglement dynamics under localised environmental interactions relevant to emerging quantum technologies in Tunisia. A unified analytical framework is developed that bridges Markovian and non-Markovian regimes, quantifying the resilience of bipartite entanglement against structured environmental noise. Considering a system of two non-interacting qubits coupled to a common bosonic reservoir, a generalised master equation incorporating a memory kernel is derived from a structured spectral density function with tunable ohmicity. An analytical expression for the time-dependent concurrence is obtained for an initial Bell state, revealing a crossover from monotonic decay to oscillatory behaviour with entanglement revivals as the reservoir cutoff frequency is lowered relative to the qubit splitting. In the sub-ohmic regime, entanglement decay is slower and revivals are more pronounced, demonstrating that the spectral density cutoff frequency acts as a control parameter for entanglement preservation. The framework incorporates a local noise temperature parameter to represent cryostat fluctuations typical of Tunisian laboratory conditions, allowing the model to capture the phenomenology of entanglement evolution under constraints of limited cryogenic infrastructure and higher ambient noise levels. Crucially, the results show that standard Markovian models systematically overestimate the rate of entanglement loss, particularly in sub-ohmic environments, and that non-Markovian memory effects can temporarily restore quantum correlations after periods of apparent death. These findings challenge the assumption that decoherence is irreversible, revealing a form of quantum memory that could be harnessed for error correction or state protection. The framework provides a practical tool for predicting coherence lifetimes in solid-state and photonic systems, offering a comparative benchmark for experimental platforms within Tunisia's nascent quantum optics community and informing the design of robust quantum information protocols in the North African research context.
We study the decoherence properties of an entangled bipartite qubit system, represented by two two-level atoms that are individually coupled to non-Markovian reservoirs. This coupling ensures that the dynamical equations of the atoms can be treated independently. The non-Markovian reservoirs are described by a model which leads to an exact non-Markovian master equation of the Nakajima-Zwanzig form [J. Salo, S. M. Barnett, and S. Stenholm, Optics Commun. 259, 772 (2006)]. We consider the evolution of the entanglement of a two-atom state that is initially completely entangled, quantified by its concurrence. Collapses and revivals in the concurrence, induced by the memory effects of the reservoir, govern the dynamics of the entangled quantum system. These collapses and revivals in the concurrence are a strong manifestation of the non-Markovian reservoir.