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International Conference on Quantum Information

Bringing Entanglement to the High Temperature Limit

Fernando Galve, Leonardo A. Pachón, David Zueco

Published Jan 1, 2011• 4 citations
Publisher

Abstract

Decoherence due to contact with a hot environment typically restricts quantum phenomena to the low temperature limit, kBT/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.

DOI
10.1364/icqi.2011.qmi24

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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.

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Decoherence due to contact with a hot environment typically restricts quantum phenomena to the low temperature limit, kBT/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.
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.
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.
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.
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.
This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.