Collective Effects in Casimir-Polder Forces

We study cooperative phenomena in the fluctuation-induced forces between a surface and a system of neutral two-level quantum emitters prepared in a coherent collective state, showing that the total Casimir-Polder force on the emitters can be modified via their mutual correlations. Particularly, we find that a one-dimensional chain of emitters prepared in a super- or subradiant state experiences an enhanced or suppressed collective vacuum-induced force, respectively. The collective nature of dispersion forces can be understood as resulting from the interference between the different processes contributing to the surface-modified resonant dipole-dipole interaction. Such cooperative fluctuation forces depend singularly on the surface response at the resonance frequency of the emitters, thus being easily maneuverable. Our results demonstrate the potential of collective phenomena as a new tool to selectively tailor vacuum forces.

Figure 1

(a) Schematic representation of $N$ two-level quantum emitters prepared in a collective state, interacting with the vacuum EM field in the presence of a planar half-space medium. (b) Constructive (destructive) interference between the two processes shown in green and red leads to superradiance (subradiance) in the surface-mediated resonant dipole-dipole interactions.

Figure 2

(a) Collective Casimir-Polder force (in units of $\hslash {\mathrm{\Gamma }}_0{k}_0$) and (b) spontaneous emission (in units of ${\mathrm{\Gamma }}_0$), on a system of two emitters near a gold surface, as a function of the separation between the emitters. Here the distance of the emitters from the surface is assumed to be $k_0{z}_0=0.01$. (c) [(d)] Collective Casimir-Polder force and (e) [(f)] spontaneous emission on two emitters as a function of their distance from the surface and their mutual separation, for the dipoles prepared in the superradiant [subradiant] state $|{\mathrm{\Psi }}_{\sup }⟩$ [$|{\mathrm{\Psi }}_{\mathrm{sub}}⟩$]. For reference, the ground state Casimir-Polder force on the two emitters at point $P$ is roughly $|F_g|\sim {10}^4\hslash {\mathrm{\Gamma }}_0{k}_0$. The surface is described by the Drude model with a plasma frequency ${\omega }_p\approx 1.37\times {10}^{16}\mathrm{Hz}$ (9 eV) and loss parameter $\gamma \approx 5.31\times {10}^{13}\mathrm{Hz}$ (35 meV) for gold [60].

Figure 3

Superradiant boost of the time-dependent total attractive $CP$ force on a linear chain of $N$ SiV emitters initially prepared in the excited level of the 737 nm transition with a lifetime of 1.7 ns [61], placed $z_0\approx 10\mathrm{nm}$ from a gold surface [47, 62]. The inset shows the absolute value of the maximum boost as a function of the number of emitters, illustrating the $N^2$ scaling of the force for the superradiant state $|J=N/2,M=0⟩$.