Quantum metasurfaces as probes of vacuum particle content

TL;DR

The paper introduces a quantum metasurface made from a two-dimensional sub-wavelength atomic array controlled by a Rydberg ancilla to create coherent superpositions of transmissive and reflective cavity boundary conditions. By mapping vacuum particle content generated under highly non-perturbative boundary changes onto a measurable frequency shift of the control atom, it provides a concrete, near-term path to observe vacuum-particle creation beyond classical mirror modulation. The work analyzes slow and fast switching regimes, derives the relevant Bogoliubov-type mode mixing, and proposes an extraction protocol, supported by realistic atomic-species parameters and error considerations. The approach offers a quantum-enhanced probe of vacuum entanglement and non-perturbative boundary-condition physics with potential implications for quantum sensing and fundamental tests of quantum field theory in novel regimes.

Abstract

The quantum vacuum of the electromagnetic field is inherently entangled across distinct spatial sub-regions resulting in entangled particle content across these sub-regions. However accessing this particle content in a controlled laboratory experiment has remained out of experimental reach. Here we propose to overcome this challenge with a quantum mirror made from a two-dimensional sub-wavelength array of atoms that divides a photonic cavity. The array response to light is tunable between transmissive and reflective states by a control atom that is excited to a Rydberg state. We find that vacuum photon content from non-perturbative changes of the boundary conditions and therefore distinct spatial sub regions of the vacuum causes subtle frequency shifts that are accessible to sub-wavelength atom array platforms. This novel approach for probing vacuum particle content stems from the unique ability to create coherent dynamics of superpositions of transmissive and reflective states providing a quantum enhanced platform for observing vacuum particle creation from highly non-perturbative boundary condition changes of the electromagnetic field vacuum.

Figures (5)

• Figure 1: (a) When the reflectivity of the two-dimensional atomic array changes, it leads to particle creation from the vacuum. This vacuum-induced effect causes a frequency shift, denoted by $\delta_R$, in the transition frequency $\nu$ of the control atom. The shift occurs when the control atom is driven by an external field with drive frequency $\omega_D$. As we show in this work, the frequency shift can be much larger than the linewidth $\gamma$ of the control atom. (b) A quantum metasurface acts as a quantum-controlled mirror within a photonic cavity, where dynamical superpositions of reflective $(\ket{R})$ and transmissive $(\ket{T})$ states are created by driving the control Rydberg atom between its ground and excited state respectively. This dynamical superposition prepares superpositions of the cavity's boundary conditions, leading to observable frequency shifts of the control atom. These effects serve as a witness of particle content from entangled spatial sub-regions of the electromagnetic field vacuum, achievable without the need for classical rapid mirror motion. We note that while the array can be positioned at any place in the cavity, for practical realization we will consider it to be placed off-centre.
• Figure 2: Analytical estimate for the frequency shift as a function of the ratio of the left sub-cavity length to the global cavity length given in Eq. \ref{['analyticest']}. The asymmetry in the frequency shift arises because the mirror only reflects a single frequency - higher order modes have a comparatively negligible contribution, leaving only the contribution from the fundamental mode which has this characteristic curve.
• Figure 3: (a) Plot of the switching profile $r(t) = 1 - \theta(t)$ as a function of time, where $r = 1$ corresponds to perfect reflection. The orange curve depicts an effective reflectivity $r_\mathrm{eff} = 0.95$. (b) Plot of the particle content of the $m$th sub-cavity mode in the global vacuum state as a function of the effective reflectivity $r_\mathrm{eff}$. We have plotted this difference for a cavity with walls at $x = \pm a/2$ with $a = 1$. The dashed lines correspond to $r_\mathrm{eff} = 0.95$. (c) Plot of the estimated frequency shift re-normalised to the sub-cavity frequency $\omega_1$, $\frac{\delta_R}{\omega_1} = \sum_n | \beta_{1,n} |^2$ obtained within our toy model, as a function of the switching parameter $\lambda$. The inset plots the frequency shift in the slow-switching regime corresponding to low effective reflectivities $r_\mathrm{eff} \sim 10^{-4}$. Recall that $\lambda$ serves a dual purpose: it determines both the proximity of the mirror’s final state to perfect reflectivity and the speed at which the mirror is activated.
• Figure 4: (a) Time-dependence of the reflectivity of the atomic array initialised in the EIT dark state, after a speed of light switch on of the Rydberg potential energy $V^R$. The time is renormalised to the linewidth, with $\Omega_p = 10\Gamma_e$, $V^R = 10^5\Gamma_e$, $\Gamma_e = \Gamma_r$. (b) Time-dependence of the reflectivity of the atomic array initialised in the EIT dark state, after a speed of light switch on of the Rydberg potential energy $V^R$. The time is renormalised to the linewidth, with $\Omega_p = 10^4\Gamma_e$, $V^R = 10^3\Gamma_e$, $\Gamma_e = \Gamma_r$. In this regime, the Rydberg interaction is not strong enough to switch the array to near unit reflectivity. However, fast oscillations are observed before reaching the steady state, on a time-scale proportional to $\Omega_p$. (c) Time-dependence of the reflectivity after initialising in the highly reflective state with the Rydberg shift on in the regime $V^R \gg \frac{\Omega_p^2}{\Gamma_r}$, and a speed of light switch-off of the Rydberg interaction energy, in this regime for which $\Omega_p = 10^4\Gamma_e \gg \Gamma_e$, fast oscillations are observed on the time-scale $\Omega_p$, with a decay envelope on the time-scale of the linewidth. (d) Inset into the fast oscillations displayed in (c). Code for the simulations is attached as an ancillary file. Scaling the EIT control beam coupling strength all the way down to $\mathrm{MHz}$ coupling strengths yields the same qualitative behaviour in (b) and (c) with slower oscillation speeds, this enables parametric particle production in this regime going from $\mathrm{MHz} - \mathrm{GHz}$ scale oscillation speeds.
• Figure 5: An atom array in a photonic cavity that is highly reflective within some frequency band-width $\Delta$, can trap standing waves of frequency $\omega_1 \in \Delta$ of the left sub-cavity, and $\bar{\omega}_k \in \Delta$ of the right sub-cavity. The Hamiltonian for an atom array that is highly reflective in this frequency band-width can be constructed as the sum of free Hamiltonian terms of the left and right sub-cavities, including vacuum terms.