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arXiv:0803.3995 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Disentanglement of two harmonic oscillators in relativistic motion

Shih-Yuin Lin, Chung-Hsien Chou, B. L. Hu

Published Dec 19, 2008• 63 citations
arXivHTMLPDF

Abstract

We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in $(3+1)\mathrm{D}$ Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time (``sudden death''). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob's proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice's coordinate, but the shorter in Rob's coordinate.

DOI
10.1103/physrevd.78.125025

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•Dec 23, 2008•4 citations
We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D(3+1)\mathrm{D}(3+1)D Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time (``sudden death''). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob's proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice's coordinate, but the shorter in Rob's coordinate.
We study the full entanglement dynamics of two uniformly accelerated Unruh-DeWitt detectors with no direct interaction in between but each coupled to a common quantum field and moving back-to-back in the field vacuum. For two detectors initially prepared in a separable state our exact results show that quantum entanglement between the detectors can be created by the quantum field under some specific circumstances, though each detector never enters the other's light cone in this setup. In the weak coupling limit, this entanglement creation can occur only if the initial moment is placed early enough and the proper acceleration of the detectors is not too large or too small compared to the natural frequency of the detectors. Once entanglement is created it lasts only a finite duration, and always disappears at late times. Prior result by Reznik [B. Reznik, Found. Phys. 33, 167 (2003).] derived using the time-dependent perturbation theory with extended integration domain is shown to be a limiting case of our exact solutions at some specific moment. In the strong coupling and high acceleration regime, vacuum fluctuations experienced by each detector locally always dominate over the cross correlations between the detectors, so entanglement between the detectors will never be generated.
We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance ddd. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation ddd. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on ddd. The detectors separated at those ddd with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small ddd, the two detectors can have residual entanglement even if they initially were in a separable state, while for ddd a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.
Based on our results for the detector-field system in Gaussian states, I am addressing the following issues about the quantum dynamics of atoms or detectors moving in a relativistic quantum field: First, the dynamics of the detectors as an open quantum quantum system, hence the entanglement creation and sudden death processes between the detectors, are non-Markovian in general. Second, the excitations of the accelerated detectors in the Unruh effect depend only on the kinematics of the detectors. The event horizon for the detector is not essential in this effect, and the particle notion of the quantum field is not needed here. Third, entanglement dynamics of the detectors are independent of time-slicing scheme. Local projective measurements on point-like detectors are also consistent in different time-slicing schemes even in the presence of relativistic quantum fields.
A bstract We study two accelerating Unruh-DeWitt detectors coupled linearly or quadratically with a scalar field, by using an approach different from previous ones. We use Rindler frame, and integrate over the spacetime coordinates before over the momenta. In this way, the divergent problem previously encountered is avoided. We show that entanglement between the detectors can be created by coupling with the field, and is divergent only in the limit that the two detectors coincide in spacetime. For linear coupling, entanglement increases monotonically with the decrease of acceleration, as previously found, while for quadratic coupling, entanglement behaves non-monotonically, as noted for the first time.
We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance ddd. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation ddd. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on ddd. The detectors separated at those ddd with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small ddd, the two detectors can have residual entanglement even if they initially were in a separable state, while for ddd a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.