Kinematic entanglement degradation of fermionic cavity modes

We analyze the entanglement and the nonlocality of a ($1+1$)-dimensional massless Dirac field confined to a cavity on a world tube that consists of inertial and uniformly accelerated segments, for small accelerations but arbitrarily long travel times. The correlations between the accelerated field modes and the modes in an inertial reference cavity are periodic in the durations of the individual trajectory segments, and degradation of the correlations can be entirely avoided by fine-tuning the individual or relative durations of the segments. Analytic results for selected trajectories are presented. Differences from the corresponding bosonic correlations are identified, and extensions to massive fermions are discussed.

Figure 1

Spacetime diagram of cavity motion is shown. Rob’s cavity is at rest initially (Region I), then undergoes a period of uniform acceleration from $t=0$ to $\eta ={\eta }_1$ (Region II) and is thereafter again inertial (Region III). Alice’s cavity overlaps with Rob’s cavity in Region I and remains inertial throughout.

Figure 2

The plot shows $f_k/h^2$ as a function of $u≔\frac{1}{2}{\eta }_1/\ln (b/a)=h{\tau }_1/[4\delta \mathrm{atanh}(h/2)]$, over the full period $0\le u\le 1$. The solid curve (black) is for $s=0$ with $k=\pm 1$. The dashed, dash-dotted and dotted curves are, respectively, for $s=\frac{1}{4}$, $s=\frac{1}{2}$, and $s=\frac{3}{4}$, for $k=1$ (blue) above the solid curve and for $k=-1$ (red) below the solid curve.

Figure 3

The plot shows ${\tilde{\tilde{f}}}_k$ as a function of $u≔h{\tau }_1/[4\delta \mathrm{atanh}(h/2)]$ and $v≔{\tau }_2/(2\delta )$ over the full period $0\le u\le 1$ and $0\le v\le 1$, for $s=0$ and $k=1$. Note the zeroes at $u\equiv 0$ mod 1 and at $u+v\equiv 0$ mod 1.