Role of thermal field in entanglement harvesting between two accelerated Unruh-DeWitt detectors

Abstract

A general consensus is -two causally disconnected Unruh-DeWitt detectors, depending upon their motions, can be entangled through interaction with a common background field. Here we investigate the effects of field temperature T (f ) on the entanglement harvesting between two uniformly accelerated detectors. In the case of their parallel motion, the thermal nature of fields does not produce any entanglement, and therefore, the outcome is the same as the non-thermal situation. On the contrary, background temperature T (f ) does affect entanglement harvesting when the detectors are in anti-parallel motion, i.e., one detector is in the right Rindler wedge (detector A), and the other one is in the left Rindler wedge (detector B). While for T (f ) = 0 entanglement harvesting is possible for all acceleration values aA of detector A, in the presence of temperature, the situation is quite different. In the latter case, entanglement harvesting is possible only within a narrow range of aA. For (1 + 1) dimensions, the range starts from a certain value and extends to infinity, and as we increase T (f ) , the required value of aA for starting entanglement increases. Moreover, above a critical value aA = ac harvesting increases as we increase T (f ) , which is just opposite in nature for accelerations below it. This feature does not change even if both the detectors move with equal acceleration. In the (1 + 3) dimensions, we found many critical values of aA when the detectors are moving with different accelerations. In addition, there exist several discrete ranges of aA, contrary to the single range in (1 + 1) dimensions, for certain fixed values of T (f ) within which the entanglement harvesting is possible. Interestingly, for detectors moving with equal acceleration, instead of multiple critical values one again has a single critical point, with nature quite similar to (1 + 1) dimensional results.

Fate of entanglement between two Unruh-DeWitt detectors due to their motion and background temperature

“…To avoid such scenario here we adopt the Wightman functions corresponding to Rindler modes with vacuum is taken to be that for Unruh modes, which is incidentally Minkowski here. In this case the required functions are time translational invariant with respect to Rindler proper time [17,32,34]. Therefore all our observations of this study strictly valid for later modes.…”

“…There has been plenty of work in the area of entanglement harvesting for different spacetimes and setups of different kind of observers [11][12][13][14][15][16]. A very recent work also deals with entanglement harvesting from vacuum in presence of a thermal background field [17].…”

“…With this motivation, we analyze variation of entanglement dynamics with temperature of the background field? As seen in [17], presence of thermal fields give rise to several interesting features in the entanglement harvesting phenomenon, so it might be interesting to look at how the presence of a thermal field will effect the dynamics of entanglement as well. To the best of our knowledge, no such study exists in present literature.…”

“…We obtain the time-evolved density matrix of the system of UD detectors, following the approach given in [16], and compute the eigenvalues of the partially transposed matrix. To obtain the eigenvalues we compute the Greens functions following [32] and compute certain integrals as in [17]. We finally analyze Negativity by numerical analysis of upto O(C 2 ), where C is the coupling parameter between the detector and the field.…”

Entanglement harvesting from conformal vacuums between two Unruh-DeWitt detectors moving along null paths

“…It resulted in the introduction of the Feynman propagator rather than the Wightman function in some places of the estimated eigenvalues. We mention that the entanglement harvesting condition and the measure of the harvested entanglement depends on the background geometry [32][33][34][49][50][51], boundary conditions [15,50,52], the two detectors' trajectories [6,49,53], etc.…”