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arXiv:1606.03412

Numerical Evaluation of Accelerated-Assisted Entanglement Harvesting

Andrew Eric Brainerd, BRIAN R. GREENE

Published Jun 10, 2016• 0 citations
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Abstract

We consider acceleration-assisted entanglement harvesting as evidenced in correlations between two accelerating Unruh detectors coupled to a scalar field. We elaborate on earlier studies, which in a stationary phase approximation calculated the entanglement dependence on two parameters $c_1 = κL$, and $c_2 = κΩσ^2$, where $κ$ describes the detector's acceleration, $L$ their separation and $Ω$ the energy splitting in a pair of two state Unruh detectors. Here, we go beyond the stationary phase approximation by performing a numerical calculation of entanglement harvesting, allowing us to present the dependence on $c_3 = σΩ$, where $σ$ denotes the half width of a Gaussian window function specifying the field-detector interaction, and show agreement with earlier work the large $c_3$ limit.

DOI
10.48550/arxiv.1606.03412

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We consider acceleration-assisted entanglement harvesting as evidenced in correlations between two accelerating Unruh detectors coupled to a scalar field. We elaborate on earlier studies, which in a stationary phase approximation calculated the entanglement dependence on two parameters c1=κLc_1 = κLc1​=κL, and c2=κΩσ2c_2 = κΩσ^2c2​=κΩσ2, where κκκ describes the detector's acceleration, LLL their separation and ΩΩΩ the energy splitting in a pair of two state Unruh detectors. Here, we go beyond the stationary phase approximation by performing a numerical calculation of entanglement harvesting, allowing us to present the dependence on c3=σΩc_3 = σΩc3​=σΩ, where σσσ denotes the half width of a Gaussian window function specifying the field-detector interaction, and show agreement with earlier work the large c3c_3c3​ limit.
We explore whether acceleration assists entanglement harvesting for a pair of uniformly accelerated detectors in three different acceleration scenarios, i.e., parallel, antiparallel and mutually perpendicular acceleration, both in the sense of the entanglement harvested and harvesting-achievable separation between the two detectors. Within the framework of entanglement harvesting protocols and the Unruh-DeWitt model of detectors locally interacting with massless scalar fields via a Gaussian switching function with an interaction duration parameter, we find that, in the sense of the entanglement harvested, acceleration is a mixed blessing insofar as it increases the harvested entanglement for a large detector energy gap relative to the interaction duration parameter, whilst inhibiting the entanglement harvested for a small energy gap. Regarding the harvesting-achievable separation range between the detectors, we further find that for very small acceleration and large energy gap, both relative to the duration parameter, acceleration-assisted enhancement can happen in all three acceleration scenarios. This is in sharp contrast to what was argued previously: that the harvesting-achievable range can be enhanced only for antiparallel acceleration. However, for a not too small acceleration relative to the duration parameter and an energy gap larger than the acceleration, we find that only detectors in parallel acceleration possess a harvesting-achievable range larger than those at rest.
We study entanglement harvested from a quantum field through local interaction with Unruh–DeWitt detectors undergoing linear acceleration. The interactions allow entanglement to be swapped locally from the field to the detectors. We find an enhancement in the entanglement harvesting by two detectors with anti-parallel acceleration over those with inertial motion. This enhancement is characterized by the presence of entanglement between two detectors that would otherwise maintain a separable state in the absence of relativistic motion (with the same distance of closest approach in both cases). We also find that entanglement harvesting is degraded for two detectors undergoing parallel acceleration in the same way as for two static, comoving detectors in a de Sitter universe. This degradation is known to be different from that of two inertial detectors in a thermal bath. We comment on the physical origin of the harvested entanglement and present three methods for determining distance between two detectors using properties of the harvested entanglement. Information about the separation is stored nonlocally in the joint state of the accelerated detectors after the interaction; a single detector alone contains none. We also find an example of entanglement sudden death exhibited in parameter space.
We make a detailed comparison between entanglement harvesting for uniformly accelerated detectors in vacuum and static ones in a thermal bath at the Unruh temperature and find that, for a small energy gap relative to the Heisenberg energy of the detectors, static detectors in the thermal bath can harvest more entanglement and possess a comparatively larger harvesting-achievable range than the uniformly accelerated ones; however, as the energy gap grows sufficiently large, the uniformly accelerated detectors are instead likely to harvest more entanglement and possess a relatively larger harvesting-achievable range than inertial ones in the thermal bath. In comparison with static detectors in vacuum, there exist phenomena of acceleration-assisted entanglement harvesting but never that of thermal-noise-assisted one. A notably interesting feature is that, although both the amount of entanglement harvested and the harvesting-achievable interdetector separation for static detectors in a thermal bath are always a decreasing function of temperature, they are not always so for uniformly accelerated detectors as acceleration (Unruh temperature) varies, suggesting the existence of the anti-Unruh effect in the entanglement harvesting phenomena of the accelerated detectors.
We study the properties of the transition probability and entanglement harvesting phenomenon for circularly accelerated detectors locally interacting with massless scalar fields. The dependence of the transition probability on the parameters associated with the circular motion is first analyzed in detail. By a cross-comparison with the situation of the uniformly accelerated motion, we obtain that the transition probability and the possible thermalization behavior for detectors rotating with an extremely large circular radius are analogous to that for uniformly accelerated detectors, but for a very small linear speed and a large acceleration, the effective temperature which characterizes the detectors' thermalization in a finite duration is much lower than that for uniformly accelerated detectors. We then focus on the phenomenon of entanglement harvesting in two special situations of circular trajectories, i.e., the coaxial rotation and the mutually perpendicular axial rotation by examining the concurrence as the entanglement measure in detail. We find that when two circularly accelerated detectors have equivalent acceleration and size of circular trajectory, the harvested entanglement rapidly decays with increasing acceleration or separation between two detectors. In contrast with the situation of uniform acceleration, the angular velocity would have significant impacts on entanglement harvesting. Especially for those detectors circularly moving in different directions, both the acceleration and trajectory radius play an important inhibiting role in entanglement harvesting. When two circularly accelerated detectors have different values of acceleration or angular velocity, we find that the entanglement can still be extracted by such detectors, even in the situation that one detector is at rest and the other is in a circular motion.
We study, in the framework of entanglement harvesting protocols, the entanglement harvesting of a pair of uniformly accelerated detectors locally interacting with vacuum massless scalar fields subjected to a perfectly reflecting plane boundary. We find that the presence of the boundary generally degrades the amount of the harvested entanglement when two detectors are very close to the boundary for all three acceleration scenarios of the detectors with respect to the boundary, i.e., parallel, anti-parallel and mutually perpendicular acceleration. However, when the distance between detectors and the boundary becomes comparable to the interaction duration parameter, the amount of harvested entanglement may approach a peak, which even goes beyond that without a boundary. Remarkably, the parameter space of the detectors' separation and the magnitude of acceleration that allows entanglement harvesting to occur is enlarged due to the presence of the boundary. In this sense, the boundary plays a double-edged role on entanglement harvesting, degrading in general the amount of entanglement while enlarging the harvesting-achievable parameter space. A comparison of three different acceleration scenarios shows that the phenomena of entanglement harvesting crucially depends on the magnitude of acceleration, the separation between two detectors and the detectors' distance from the boundary.
Abstract We study, in the framework of the entanglement harvesting protocol, the entanglement harvesting of both a pair of inertial and uniformly accelerated detectors locally interacting with vacuum massless scalar fields subjected to a perfectly reflecting plane boundary. We find that the presence of the boundary generally degrades the harvested entanglement when two detectors are very close to the boundary. However, when the distance between detectors and the boundary becomes comparable to the interaction duration parameter, the amount of the harvested entanglement approaches a peak, which even goes beyond that without a boundary. Remarkably, the parameter space of the detectors’ separation and the magnitude of acceleration that allows entanglement harvesting to occur is enlarged due to the presence of the boundary. In this sense, the boundary plays a double-edged role on entanglement harvesting, degrading in general the harvested entanglement while enlarging the entanglement harvesting-achievable parameter space. A comparison of three different acceleration scenarios of the detectors with respect to the boundary, i.e., parallel, anti-parallel and mutually perpendicular acceleration, shows that the phenomenon of entanglement harvesting crucially depends on the acceleration, the separation between two detectors and the detectors’ distance from the boundary.