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arXiv:quant-ph/0609139

Gravitationally Induced Decoherence of Optical Entanglement

Timothy C. Ralph, Gerard J Milburn, T. G. Downes

Published Sep 18, 2006• 5 citations
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Abstract

We propose an experiment in which an entangled pair of optical pulses are propagated through non-uniform gravitational fields. A field operator calculation of this situation predicts decoherence of the optical entanglement under experimentally realistic conditions.
DOI
10.48550/arxiv.quant-ph/0609139

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We investigate the effect of quantum metric fluctuations on qubits that are gravitationally coupled to a background spacetime. In our first example, we study the propagation of a qubit in flat spacetime whose metric is subject to flat quantum fluctuations with a Gaussian spectrum. We find that these fluctuations cause two changes in the state of the qubit: they lead to a phase drift, as well as the expected exponential suppression (decoherence) of the off-diagonal terms in the density matrix. Although in principle observable, the current state of technology prohibits the experimental demonstration of the phase drift. Second, we calculate the decoherence of a qubit in a circular orbit around a Schwarzschild black hole. The no-hair theorems suggest a quantum state for the metric in which the black hole's mass fluctuates with a thermal spectrum at the Hawking temperature. Again, we find that the orbiting qubit undergoes decoherence and a phase drift that both depend on the temperature of the black hole. Third, we study the interaction of coherent and squeezed gravitational waves with a qubit in uniform motion. Finally, we investigate the decoherence of an accelerating qubit in Minkowski spacetime due to the Unruh effect. In this case decoherence is not due to fluctuations in the metric, but instead is caused by coupling (which we model with a standard Hamiltonian) between the qubit and the thermal cloud of Unruh particles bathing it. When the accelerating qubit is entangled with a stationary partner, the decoherence should induce a corresponding loss in teleportation fidelity.
We investigate gravity-induced entanglement between the output optical fields of two red-detuned pulsed optomechanical systems with their masses coupled by mutual gravitational interaction. For each individual system, the optomechanical interaction realizes a beam-splitter state swap between an incident optical pulse and its mechanical mode. Using two rectangular pulses for each system -- the first to imprint a nonclassical state on the mechanical modes and the second to read the gravitationally generated entanglement back onto the outgoing light -- we show that the amount of entanglement can be amplified by preparing the input in a squeezed or Fock state. However, the threshold for entanglement generation is set by the competition between the gravitational coupling and thermal decoherence, gG>2γmNthg_G>2γ_m N_{\rm th}gG​>2γm​Nth​, and cannot be lowered by any choice of input state. We prove this bound for two-mode Gaussian inputs and show that it continues to hold for Fock-state inputs. We further analyze how imperfect detection modifies the threshold and identify the entanglement-annihilating and entanglement-breaking regimes, which are set by the thermal decoherence accumulated over the interaction time, independent of the gravitational coupling.
We analyze the dynamics of a gravity-induced entanglement for NNN massive particles. Considering the linear configuration of these particles, we investigate the entanglement between a specific pair of particles under the influence of the gravitational interaction between the massive particles. As the particle number increases, the specific particle pair decoheres more easily due to the gravitational interaction with other particles. The timescale of the gravity-induced decoherence is analytically determined. We also discuss the entanglement dynamics of initially entangled particles, which exemplify the monogamy of the gravity-induced entanglement.