Quantum gates and multipartite entanglement resonances realized by nonuniform cavity motion

We demonstrate the presence of genuine multipartite entanglement between the modes of quantum fields in nonuniformly moving cavities. The transformations generated by the cavity motion can be considered as multipartite quantum gates. We present two setups for which multimode entanglement can be generated for bosons and fermions. As a highlight we show that the genuine bosonic multipartite correlations can be resonantly enhanced. Our results provide fundamental insights into the structure of Bogoliubov transformations and suggest strong links between quantum information, quantum fields in curved spacetimes and gravitational analogues by way of the equivalence principle.

Figure 1

Space-time diagram of the multicavity setup: While Alice’s and Charlie’s cavities remain at rest Rob’s cavity undergoes nonuniform motion. Rob’s cavity of width $\delta =(b-a)$ follows a world tube that consists of alternating segments of inertial motion (red, parallel lines) and uniform acceleration (green, confocal hyperbolae). The individual segments in this example travel scenario are of equal duration $\tau /2$ and equal acceleration $h/\delta$ as measured at the center of Rob’s cavity. The dashed lines indicate the light cone at $(t,x)=(0,0)$.

Figure 2

Illustration of the bosonic resonances: The linear coefficients $|{\beta }_{mn}^{(1)}|$ for the bosonic Bogoliubov transformations, are shown for a real, massless scalar field in ($1+1$) dimensions. The travel scenario has $N$ segments of uniform acceleration $h/\delta$ and duration $\tau /2$ as measured at the cavity’s center, separated by ($N-1$) segments of inertial coasting of the same duration (to first order in $h$), as illustrated in Fig. 1 for $N=2$. The curves in Fig. 2 are plotted for $N=15$, $(m,n)=(k,k^{\prime })=(1,2)$ (blue, solid) and $(m,n)=(k^{\prime },k^{\prime \prime })=(2,3)$ (red, dashed) and $u≔h\tau /[4\delta \mathrm{atanh}(h/2)]$. The vertical dashed lines indicate the potential resonance times for $(k,k^{\prime })$ and $(k^{\prime },k^{\prime \prime })$ respectively. The explicit form of the Bogoliubov coefficients can be found in Refs. 6, 10.