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arXiv:0809.4906 · Physical Review E

Dynamic entanglement in oscillating molecules and potential biological implications

Jianming Cai, Sandu Popescu, Hans J. Briegel

Published Aug 25, 2010• 82 citations
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Abstract

We demonstrate that entanglement can persistently recur in an oscillating two-spin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a nonequilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of decoherence, which we expect, e.g., for biological systems. Our results also suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current state-of-the-art quantum technologies.

DOI
10.1103/physreve.82.021921

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We demonstrate that entanglement can persistently recur in an oscillating two-spin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a nonequilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of decoherence, which we expect, e.g., for biological systems. Our results also suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current state-of-the-art quantum technologies.
We demonstrate that entanglement can persistently recur in an oscillating two-spin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a non-equilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of de-coherence, which we expect e.g. for biological systems. Our results furthermore suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current state-of-the-art quantum technologies.
Very recently (Cai et al 2010 Phys. Rev. E 82 021921), a simple mechanism was presented by which a molecule subjected to forced oscillations, out of thermal equilibrium, can maintain quantum entanglement between two of its quantum degrees of freedom. Crucially, entanglement can be maintained even in the presence of very intense noise, so intense that no entanglement is possible when the forced oscillations cease. This mechanism may allow for the presence of nontrivial quantum entanglement in biological systems. Here we significantly enlarge the study of this model. In particular, we show that the persistent generation of dynamic entanglement is not restricted to the bosonic heat bath model, but can also be observed in other decoherence models, e.g. the spin gas model, and in non-Markovian scenarios. We also show how conformational changes can be used by an elementary machine to generate entanglement even in unfavorable conditions. In biological systems, similar mechanisms could be exploited by more complex molecular machines or motors.
Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gas-type systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states. We develop master equations to describe the system and its interaction with an environment, study toy models with two particles (qubits), where the master equation can often be solved analytically, and finally examine larger systems with possibly fluctuating particle numbers. We find that in gas-type systems, the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment, while this is not true in strongly coupled systems. But even then, the temperature range where one can find entangled steady states is typically much higher with the reset mechanism.
Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gas-type systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states. We develop master equations to describe the system and its interaction with an environment, study toy models with two particles (qubits), where the master equation can often be solved analytically, and finally examine larger systems with possibly fluctuating particle numbers. We find that in gas-type systems, the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment, while this is not true in strongly coupled systems. But even then the temperature range where one can find entangled steady states is typically much higher with the reset mechanism.
The possibility of maintaining entanglement in a quantum system at finite, even high, temperatures – the so-called ‘hot entanglement’ – has obvious practical interest, but also requires closer theoretical scrutiny. Since quantum entanglement in a system evolves in time and is continuously subjected to environmental degradation, a nonequilibrium description by way of open quantum systems is called for. To identify the key issues and the contributing factors that may permit ‘hot entanglement’ to exist, or the lack thereof, we carry out a model study of two spatially-separated, coupled oscillators in a shared bath depicted by a finite-temperature scalar field . From the Langevin equations we derived for the normal modes and the entanglement measure constructed from the covariance matrix we examine the interplay between direct coupling, field-induced interaction and finite separation on the structure of late-time entanglement. We show that the coupling between oscillators plays a crucial role in sustaining entanglement at intermediate temperatures and over finite separations. In contrast, the field-induced interaction between the oscillators which is a non-Markovian effect becomes very ineffective at high temperature. We determine the critical temperature above which entanglement disappears to be bounded in the leading order by the inverse frequency of the center-of-mass mode of the reduced oscillator system, a result not unexpected, which rules out hot entanglement in such settings.
Decoherence due to contact with a hot environment typically restricts quantum phenomena to the low temperature limit, k_{B}T/ℏω≪1 (ℏω is the typical energy of the system). Here we report the existence of a nonequilibrium state for two coupled, parametrically driven, dissipative harmonic oscillators which, contrary to generalized intuition, has stationary entanglement at high temperatures. This clarifies the role of temperature and could lighten the burden on quantum experiments requiring delicate precooling setups.