Polaron-Polaritons in Subwavelength Arrays of Trapped Atoms

TL;DR

This work introduces polaron-polaritons as the fundamental excitations in subwavelength arrays of trapped atoms, coupling collective polariton modes to lattice vibrations through a Fröhlich-type interaction in the Lamb-Dicke regime. By combining analytical polaron theory with numerical simulations, it shows that resonant phonon-assisted scattering governs how motion alters dispersion, decay, and transport, while off-resonant processes can be engineered to preserve or enhance light–matter coupling. The study reveals that dark-state transport remains robust across a broad range of trap frequencies when resonant scattering is suppressed, and that high reflectivity in 2D atomic mirrors is achievable (≳99%) by avoiding resonant phonon sidebands and tuning geometry. Moreover, motion can be harnessed to directly excite subradiant states, offering new spectra for spectroscopic studies and potential for phonon-mediated nonlinearities, with direct implications for quantum memories and photon-atom interfaces in all-atomic nanophotonic devices.

Abstract

Subwavelength arrays of atoms trapped in optical lattices or tweezers are inherently susceptible to deformations: Optomechanical forces produce lattice distortions, which, in turn, modify the optical response of the array. We show that this coupling hybridizes collective atomic excitations (polaritons) with phonons, forming polaron-polaritons -- the fundamental quasiparticles governing light-matter interactions in arrays of trapped atoms. Using analytical polaron theory and numerical simulations, we show that: (1) phonons can strongly enhance the decay of subradiant states, but also enable their efficient excitation; (2) transport of dark excitations remains remarkably robust even at low trap frequencies, except when a polariton can resonantly scatter phonons; and (3) motion reduces the reflectivity of a two-dimensional atomic mirror, however, we identify mechanisms that mitigate this degradation and restore reflectivity above 99% in some cases. Our findings lay the foundation for analyzing motional effects in key applications and suggest new ways to harness them in state-of-the-art experiments.

Figures (12)

• Figure 1: Motion in subwavelength arrays. (a) Subwavelength arrays of trapped atoms: recoil due to emission and absorption couples dipole excitation to atomic motion. (b) Propagation of a subradiant excitation in a 2D array. The frozen motion approximation may predict a breakdown of transport in the limit $\nu \ll \gamma_0$ (left panel). We identify conditions where the propagation of a polaron-polariton remains robust over a broad range of trap frequencies $\nu\sim \gamma_0$ (central panel). In these cases, transport is similar to the case of fast motion $\nu\gg\gamma_0$ (right panel). (c) Atomic mirrors exhibit near perfect reflectivity when atoms are pinned (left). Phonon-assisted scattering leads to reduced reflectivity (right). High reflectivities can nevertheless be obtained by suppressing resonant scattering to motional sidebands.
• Figure 2: Polaron-polaritons properties in 2D arrays. (a) Dispersion relation, (b) decay rate and (c) quasiparticle weight for a polaron-polariton in 2D arrays for perpendicularly polarized light relative to the array [see schematic array representation in the top left corner of (a)] and for indicated values of trapping frequency, $\nu$. The inset in (a) shows the symmetric lines in the first Brillouin zone outside of the light cone (blue disk region). The black dashed line in (a) and (b) show respectively the unperturbed value $J_\mathbf{p}^{(0)}$ and the fast motion correction $\eta^2\gamma_0$ to the decay rate. (d) Decay rate vs trap frequency for indicated quasimomenta and dipole polarizations, and with lattice spacing $d = \lambda_0/4$. These are further compared to the contribution from the zero-point motion, $\eta^2\gamma_0$, which they approach for $\nu \gg \gamma_0$ (black line). The divergences for $\mathbf{p} = (0.8\pi,0.8\pi)$ and $\mathbf{p} = (\pi,0)$ are logarithmic, appearing due to a resonant coupling to a saddle-point in the dispersion, $J_\mathbf{q}$. For (e) perpendicular and (f) parallel polarization, we indicated (colors) the modes which admit a logarithmic divergence at a particular value $\nu/\gamma_0$. The pink circles show the light cone at $k = k_0$. In panels (a) and (c), we use $\eta = 0.2$.
• Figure 3: Transport in a 1D array. We consider $N=400$ with $d=\lambda_0/4$, perpendicular polarization, and $\eta=0.05$. (a) Propagation of the normalized spin population along the array for different values of the trap frequency $\nu/\gamma_0$ at indicated times. (b) Evolution of the center of the wave-packet compared to the pinned atom (black solid line) and to the frozen motion approximation (black dashed line) (c) Dispersion relation for the zero phonon band (solid blue) and for the one phonon sideband (dashed orange) with $\nu/\gamma_0=0.5$. (d) Trap frequency dependence of the bare polariton damping rate ($\Gamma_p$), total radiative decay rate ($\Gamma_\text{rad}$) and phonon-scattering rate ($\Gamma_\text{ph}$). The numerically extracted values of $\Gamma_p$ in blue markers show excellent agreement with the polaron result (black line) calculated from Eqs. \ref{['eq:main_Self_Energy_1D_res']}-\ref{['eq:main_Self_Energy_1D_offres']}. (e) Decay of the excitation as a function of time for different values of the trap frequencies (colored markers) and for the fast (dash-dotted line) and frozen motion approximations (dashed line). Other parameters: $k_s=0.8\pi/d$, and $\sigma_k = (\pi/d-k_s)/2$. The frozen motion simulations are averaged over 1000 realization for Gaussian disorder with standard deviation $\eta/k_0$.
• Figure 4: Transport in a 2D array. (a) Snapshots of the spin population distribution at different times (increasing from left to right starting at $\gamma_0 t=0$) for an array of $24\times 24$ atoms polarized perpendicular to the array plane. (b) Trap frequency dependence of the polariton damping $\Gamma_\mathbf{p}$ (blue circles) and of the radiative scattering rate $\Gamma_\text{rad}$ (orange square) compared to the polaron theory in \ref{['eq:second_order_energy_D_dimension']} for $\mathbf{p}=(0.8,0.8)\pi/d$. (c) Decay of $\vert \vert\ket{\psi(t)}\vert\vert^2$ as a function of time for: pinned atoms (solid line), fast motion (dashed line), frozen motion (dash-dotted line) and $\nu=0.1\gamma_0$ (blue dots). Other parameters: $\eta=0.05$, $d/\lambda_0=0.25$, $\mathbf{k}_s = (0.8,0.8)\pi/d$. For the frozen motion calculation, we average over 1000 realizations.
• Figure 5: Effect of motion on a 2D atomic mirror. Reflection $R$ (a), transmission $T$ (b), and loss $L$ (c,d) coefficients as a function of detuning for two experimental setups based on $^{87}$Rb in an optical lattice (red) and $^{88}$Sr in a tweezer array (blue) compared to the perfectly pinned case (black). In both cases the atomic dipoles are circularly polarized in the plane of the array (inset in (a)). The detuning is set relative to the resonance frequency, $J_{\bf 0}$, and in units of the collective decay rate, $\Gamma_{\bf 0}$, for pinned atoms. The insets in (c) show the dispersion relation for circularly polarized dipoles in case of Rubidium (left inset) and Strontium (right inset). The resonances appearing in the loss spectrum are directly related to energy ranges where the density of states is large in correspondence of flat dispersions (triangles and squares). (d) Loss coefficients for the $^{88}$Sr setup and indicated out-of-plane Lamb-Dicke parameters by varying the trap frequency $\nu_z$. These correspond to (top to bottom) $\nu_z/2\pi \simeq 19 {\rm\, kHz}, 75 {\rm\, kHz}, 300 {\rm \,kHz}$. The main loss suppression results from moving the phononic sideband out of resonance (black arrow).