Cavity-mediated charge and pair-density waves in a unitary Fermi gas

Abstract

Coherent light-matter interactions between a quantum gas and light in a high-finesse cavity can drive self-ordering phase transitions. To date, such phenomena have involved exclusively single-atom coupling to light, resulting in coupled charge-density or spin-density wave and superradiant order. In this work, we engineer simultaneous coupling of cavity photons to both single atoms and fermionic pairs, which are also mutually coupled due to strong correlations in the unitary Fermi gas. This interplay gives rise to an interference between the charge-density wave and a pair-density wave, where the short-range pair correlation function is spontaneously modulated in space. We observe this effect by tracking the onset of superradiance as the photon-pair coupling is varied in strength and sign, revealing constructive or destructive interference of the three orders with a coupling mediated by strong light-matter and atom-atom interactions. Our observations are compared with mean-field theory where the coupling strength between atomic- and pair-density waves is controlled by higher-order correlations in the Fermi gas. These results demonstrate the potential of cavity quantum electrodynamics to produce and observe exotic orders in strongly correlated matter, paving the way for the quantum simulation of complex quantum matter using ultracold atoms.

Fig. 1. Coupled order parameters.

a Charge-density wave (Θ), pair-density wave (Π), and in-phase cavity-field quadrature (X) represent the three coupled orders. Λ, the strength of the dispersive atom-cavity coupling, is controlled via the pump strength V₀. r denotes the relative strength of the dispersive coupling of atoms and pairs to the cavity. Θ and Π are mutually coupled by strong atom-atom interactions with a strength U. b Schematic phase boundary separating the normal (X = 0) from the superradiant phase (X ≠ 0) as a function of V₀ and −1/r, showing a characteristic Fano-type profile. c Single atoms (left) and pairs of atoms (right) in a unitary Fermi gas within the mode of a high-finesse cavity can scatter photons from a transverse pump into the cavity and vice versa. The pump (red arrows) forms a standing wave with a wavevector ${\overrightarrow{k}}_p$. The dispersive coupling strengths Λ and rΛ are determined by the detuning Δ_a between the pump (p) and the atomic resonance (a), and the detuning Δ_m between the pump and a photo-association resonance (m), respectively.

Fig. 2. Ordering close to a photo-association transition.

a Dispersive shift δ_c measured by transmission spectroscopy as a function of the molecular detuning Δ_m, showing the avoided crossing pattern characteristic of strong light-matter coupling. b Photon flux traces as a function of pump strength V₀ while varying Δ_m across the photoassociation transition at fixed Δ_c/2π = −5.5 MHz. The blue-red line indicates the Fano-type phase boundary predicted in Fig. 1b, with an overall scaling factor left as a free parameter for the V₀ axis, and the other parameters calculated using a mean-field theory. The two sharp features located around Δ_m/2π = 150 and 180 MHz are due to another weakly coupled photoassociation transition, leading to sharp losses without significantly affecting the atom-cavity coupling.

Fig. 3. Critical light-matter coupling strength.

a Cavity photon count rate as a function of ${\tilde{\mathrm{\Delta }}}_{\mathrm{c}}$ and pump strength V₀, for Δ_m/2π = −100 MHz (red) and +100 MHz (blue), showing the onset of superradiance above a critical pump strength. The growing offset between the two phase boundaries between positive and negative Δ_m is a manifestation of the intertwining of density and contact-density wave order. b Normalized inverse critical coupling strength ${\mathcal{D}}_{0\mathrm{C},a}/{\mathcal{D}}_{0\mathrm{C}}$ as a function of the inverse detuning 2π/Δ_m at unitarity (open circles). The measurements agree with the predictions of the zero-momentum model (dashed green line) and the mean-field (solid yellow light), including trap averaging, within our error bars. The inset depicts measurements away from unitarity at 1/k_Fa = 0.22 (blue square) and 1/k_Fa = −0.16 (pink diamond) and the respective mean-field models (solid blue line, solid pink line).