We demonstrate high-resolution in situ imaging of density-wave ordering induced by cavity-mediated interactions in a unitary Fermi gas. We observe long-range spatial correlations throughout the formation of density waves, both for adiabatic preparation and following a quench, with a pattern controlled by the cavity mode structure. Our single-shot microscopic images together with the real-time readout of the cavity photons provide access to atom-photon correlations. We use this capability to investigate order fluctuations as a function of time following a quench and to directly confirm the correspondence between optical and atomic observables. Our system opens rich perspectives, from local patterning to correlation measurements in long-range interacting quantum gases.
We demonstrate high-resolution in situ imaging of density-wave ordering induced by cavity-mediated interactions in a unitary Fermi gas. We observe long-range spatial correlations throughout the formation of density waves, both for adiabatic preparation and following a quench, with a pattern controlled by the cavity mode structure. Our single-shot microscopic images together with the real-time readout of the cavity photons provide access to atom-photon correlations. We use this capability to investigate order fluctuations as a function of time following a quench and to directly confirm the correspondence between optical and atomic observables. Our system opens rich perspectives, from local patterning to correlation measurements in long-range interacting quantum gases.
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.
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.
Atom-based quantum simulators offer a unique platform that enables the imaging of each particle in a many-body system. Until now, however, this capability has been limited to quantum systems in discretized space such as optical lattices and tweezers, where spatial degrees of freedom are quantized. Here, we introduce a novel method for imaging atomic quantum many-body systems in the continuum, allowing for in situ resolution of every particle. We demonstrate the capabilities of our approach on a two-dimensional atomic Fermi gas. We probe the density correlation functions, resolving their full spatial functional form, and reveal the shape of the Fermi hole arising from Pauli exclusion as a function of temperature. Our method opens the door to probing strongly correlated quantum gases in the continuum with unprecedented spatial resolution, providing in situ access to spatially resolved correlation functions of arbitrarily high order across the entire system.
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.
We obtain the universal form of spatial density and phase correlations after a quantum quench in dilute ultracold Bose gases, and give compact time-dependent expressions for the most visible effects. A Bogoliubov description in a local density approximation is used. It is demonstrated that density correlations can be observed even with imaging resolution well below healing length, and estimated that the conditions in existing 1D experiments allow observation of the long-range density correlation wave. This would allow one to directly measure counterpropagating atom pairs in situ.
We investigate the interplay between cavity-induced density-wave ordering and controllable disorder in a trapped two-dimensional gas of ultracold fermions. The atoms are dispersively coupled to an optical cavity and transversely driven by a pump beam, while an additional speckle beam spatially modulates the atom-light coupling through an AC-Stark shift of the atomic transition. In momentum space, this disorder converts the usual coupling between the cavity mode and a discrete set of density-wave Fourier components into a coupling to a continuum of fermionic density modes, weighted by the spectrum of the speckle pattern. Using linear response theory, we derive the superradiant threshold and show that the disordered interaction renormalizes the effective light-matter coupling, lowering the critical pump strength on average, with the threshold becoming self-averaging for short speckle correlation lengths. We complement this analysis with a numerical mean-field treatment that gives access to the intracavity photon number and to the real-space fermion density across the transition. These results confirm that the disorder shifts the photonic phase boundary and, above threshold, distorts the density-wave crystal by populating Fourier components beyond those selected by the clean cavity geometry. Our findings identify both the emitted cavity light and in situ density images as probes of engineered disorder in fermionic matter coupled to optical cavities.