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arXiv:2212.04402 · Nature

Density-wave ordering in a unitary Fermi gas with photon-mediated interactions

Victor Helson, Timo Zwettler, Farokh Mivehvar, Elvia Colella, Kévin Roux, Hideki Konishi, Helmut Ritsch, Jean-Philippe Brantut

Published May 24, 2023• 45 citations
arXivHTMLPDF

Abstract

Abstract A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering1, pairing and superfluidity2, and the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose–Einstein condensate3. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen–Cooper–Schrieffer superfluid and Bose–Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.

DOI
10.1038/s41586-023-06018-3

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Abstract A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical analysis. In the past decades, tunable quantum Fermi gases have served as model systems for exploring the physics of strongly interacting fermions, including most notably magnetic ordering1, pairing and superfluidity2, and the crossover from a Bardeen–Cooper–Schrieffer superfluid to a Bose–Einstein condensate3. Here, we realize a Fermi gas featuring both strong, tunable contact interactions and photon-mediated, spatially structured long-range interactions in a transversely driven high-finesse optical cavity. Above a critical long-range interaction strength, DW order is stabilized in the system, which we identify via its superradiant light-scattering properties. We quantitatively measure the variation of the onset of DW order as the contact interaction is varied across the Bardeen–Cooper–Schrieffer superfluid and Bose–Einstein condensate crossover, in qualitative agreement with a mean-field theory. The atomic DW susceptibility varies over an order of magnitude upon tuning the strength and the sign of the long-range interactions below the self-ordering threshold, demonstrating independent and simultaneous control over the contact and long-range interactions. Therefore, our experimental setup provides a fully tunable and microscopically controllable platform for the experimental study of the interplay of superfluidity and DW order.
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. Cavity-mediated interactions lead to collective effects and ordering in ultracold atomic systems. Here, the authors demonstrate the interplay of different ordered states of ultracold Fermi gases in a cavity, resulting from an intriguing coexistence of photon coupling with both atoms and atom-pairs.
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.
Recent quantum gas cavity-QED experiments demonstrated simultaneous coupling of photons to single atom transitions as well as correlated pairs of ultracold fermions trapped inside optical cavities. This enables simultaneous control over density ordering and pairing. Using extensive numerical simulations, we show that in a transversely driven, two-component degenerate Fermi gas, the interplay of cavity-induced and bare atom--atom interactions controls not only the power threshold for self-organization, but also the type of spatial ordering in the Z2\mathbb Z_2Z2​-symmetry-broken superradiant state. In the repulsive interaction regime, unpaired or weakly paired fermions first self-organize through a charge-density-wave instability, and finite-momentum pairing only occurs at much stronger pump strengths. In contrast, an attractive superfluid undergoes a joint density--pairing instability, directly entering into intertwined phase with charge-density-wave and pair-density-wave orders. At strong pumping the photon-enhanced pair interaction generates localized density and pairing order even when the bare contact interaction is repulsive. In this cavity-dominated regime strong spatial localization suppresses the long range superfluid coherence. Our results identify the role of cavity-induced atomic interactions in supporting intertwined fermionic orders and pave the way for exploring exotic states with multiple orders in highly controlled hybrid light-matter systems.
This thesis reports on quantum simulation experiments conducted on strongly correlated fermionic atoms coupled to light in an optical cavity. To this day, the quantum-mechanical description of strongly correlated many-body systems remains a considerable theoretical challenge. Quantum simulation experiments with ultracold atoms contribute to the understanding of such systems through controlled studies of complex, engineered many-body states. Advances in measurement and control techniques continuously drive the development of this field, enabling the creation, detection, and manipulation of novel states of matter. The experiments presented in this thesis build upon the prior observation of cavity-induced density-wave ordering in a gas of strongly interacting 6Li atoms. In particular, we report on an extension of the cavity quantum electrodynamics setup through the implementation of a high-resolution imaging system. The imaging setup enables the in situ observation of the density waves through resonant absorption imaging within a single experimental realization. Using this technique, we investigate ordering both following adiabatic preparation and after a quench of the cavity-induced long-range interaction. Our observations support the expectation of a density modulation with a single spatial frequency and phase that extends across the entire atomic cloud. We further present a correlation study between atomic and photonic observables, confirming their correspondence and thereby directly testing the theoretical foundation of cavity-mediated interactions. By imaging density waves in the vicinity of the first higher-order transverse cavity mode, we demonstrate the capability of the imaging setup to reveal local order beyond global observables. Additionally, this thesis presents two studies of density-wave ordering based on measurements of the cavity photon leakage. The first study focuses on the dynamics of order formation following an instantaneous quench. We observe an exponential growth of the order parameter, with a growth rate predominantly governed by the quench strength, in agreement with a theoretical description based on a random phase approximation. In the second study, we realize a system of three mutually coupled orders, enabled by the simultaneous coupling of light to atoms and atom pairs via a photoassociation resonance. In combination with the strong correlations present in the gas, this gives rise to three coupled order parameters: the cavity photon field, a density wave, and a pair-density wave. The mutual competition and enhancement between these orders result in a measurable shift of the density-wave order phase boundary. We conclude the thesis by reporting on recent experimental advances in the implementation of a homogeneous trapping potential, leading to a uniform atomic density along two spatial directions. This represents work towards an ideal starting point for a range of exciting future experiments, including spectroscopic measurements, local potential patterning, and correlation studies in long-range interacting Fermi gases, leveraging the numerical aperture of the imaging system.
We study a Fermi gas with strong, tunable interactions dispersively coupled to a high-finesse cavity. Upon probing the system along the cavity axis, we observe a strong optomechanical Kerr nonlinearity originating from the density response of the gas to the intracavity field and measure it as a function of interaction strength. We find that the zero-frequency density response function of the Fermi gas increases by a factor of two from the Bardeen-Cooper-Schrieffer to the Bose-Einstein condensate regime. The results are in quantitative agreement with a theory based on operator-product expansion, expressing the density response in terms of universal functions of the interactions, the contact, and the internal energy of the gas. This provides an example of a driven-dissipative, strongly correlated system with a strong nonlinear response, opening up perspectives for the sensing of weak perturbations or inducing long-range interactions in Fermi gases.
We propose that the evolution of superfluidity from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime can be realized using ultracold Fermi gas coupled to a single-mode cavity. By the functional integral formalism, we derive an effective atom-only action, which mimics the two-component Fermi gas with tunable two-body interaction. First, we address the features of the cavity-mediated interaction. We find that the matter-light coupling creates an effective sss-wave scattering whose sign and amplitude are controlled by parameters of the cavity. Second, we discuss the fermionic superfluidity on the mean-field level, including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, and dissociation temperature. It is shown that by varying the atom-cavity detuning, a BCS to BEC crossover occurs. In addition, the influences of the atomic collaborative effect and external pumping field on the pairing correlation are also studied.