Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator

Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions

Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein-Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.

Momentum-exchange interactions in a Bragg atom interferometer suppress Doppler dephasing

Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction-enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields.

Tuning Photon-Mediated Interactions in a Multimode Cavity: From Supersolid to Insulating Droplets Hosting Phononic Excitations

Ultracold atoms trapped in laser-generated optical lattices serve as a versatile platform for quantum simulations. However, as these lattices are infinitely stiff, they do not allow to emulate phonon degrees of freedom. This restriction can be lifted in emerged optical lattices inside multimode cavities. Motivated by recent experimental progress in multimode cavity QED, we propose a scheme to implement and study supersolid and droplet states with phononlike lattice excitations by coupling a Bose gas to many longitudinal modes of a ring cavity. The interplay between contact collisional and tunable-range cavity-mediated interactions leads to a rich phase diagram, which includes elastic supersolid as well as insulating droplet phases exhibiting roton-type mode softening for a continuous range of momenta across the superradiant phase transition. The nontrivial dynamic response of the system to a local density perturbation further proves the existence of phononlike modes.

Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms

We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.

Polarization resonance with sub-wavelength switching of random light self-interfering in open-end cavity

Following recent work [Sci. China Phys. Mech. Astron.66, 274213 (2023)10.1007/s11433-023-2097-9] that revealed the sub-wavelength scale resonance phenomenon in scalar random beams counterpropagating in an open-end cavity, we extend the analysis to the vectorial domain and show a similar effect for the polarization properties. We found that, in contrast with the changes in the scalar properties, being of harmonic nature, changes in polarization involve alternating regions of constant values followed by sharp and complex changes.

Heating a dipolar quantum fluid into a solid

Raising the temperature of a material enhances the thermal motion of particles. Such an increase in thermal energy commonly leads to the melting of a solid into a fluid and eventually vaporises the liquid into a gaseous phase of matter. Here, we study the finite-temperature physics of dipolar quantum fluids and find surprising deviations from this general phenomenology. In particular, we describe how heating a dipolar superfluid from near-zero temperatures can induce a phase transition to a supersolid state with a broken translational symmetry. We discuss the observation of this effect in experiments on ultracold dysprosium atoms, which opens the door for exploring the unusual thermodynamics of dipolar quantum fluids.

Entanglement-enhanced matter-wave interferometry in a high-finesse cavity

An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit^1–3 set by projections of individual atoms. Large amounts of entanglement^4–6 involving the internal degrees of freedom of laser-cooled atomic ensembles^4–16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\,.\,{4}_{-0.9}^{+1.1}$$\end{document}3.4−0.9+1.1 dB and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\,.\,{5}_{-0.6}^{+0.6}$$\end{document}2.5−0.6+0.6 dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\,.\,{7}_{-0.5}^{+0.5}$$\end{document}1.7−0.5+0.5 dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors^17,18, searches for new physics, particles and fields^19–23, future advanced gravitational wave detectors^24,25 and accessing beyond mean-field quantum many-body physics^26–30.

A matter-wave interferometer is demonstrated with an interferometric phase noise below the standard quantum limit, combining two core concepts of quantum mechanics, that a particle can simultaneously be in two places at once and entanglement between distinct particles.

Limit cycles and chaos in the hybrid atom-optomechanics system

We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force. The atoms are intrinsically two-level systems that can absorb or emit photons, but the dynamics of their position and momentum are treated classically. On the other hand, the membrane, the cavity field, and the intrinsic two-level atoms are treated quantum mechanically. We show that the mean excitation of the three systems can be stable, periodically oscillating, or in a chaotic state depending on the strength of the coupling between them. We define regular, limit cycle, and chaotic phases, and present a phase diagram where the three phases can be achieved by manipulating the field-membrane and field-atom coupling strengths. We also computed other observable quantities that can reflect the system's phase such as position, momentum, and correlation functions. Our proposal offers a new way to generate and tune the limit cycle and chaotic phases in a well-established atom-optomechanics system.

Supersolid gap soliton in a Bose-Einstein condensate and optical ring cavity coupling system

The system of a transversely pumped Bose-Einstein condensate (BEC) coupled to a lossy ring cavity can favor a supersolid steady state. Here we find the existence of supersolid gap soliton in such a driven-dissipative system. By numerically solving the mean-field atom-cavity field coupling equations, gap solitons of a few different families have been identified. Their dynamical properties, including stability, propagation, and soliton collision, are also studied. Due to the feedback atom-intracavity field interaction, these supersolid gap solitons show numerous new features compared with the usual BEC gap solitons in static optical lattices.

Light-Induced Quantum Droplet Phases of Lattice Bosons in Multimode Cavities

Multimode optical cavities can be used to implement interatomic interactions which are highly tunable in strength and range. For bosonic atoms trapped in an optical lattice we show that, for any finite range of the cavity-mediated interaction, quantum self-bound droplets dominate the ground state phase diagram. Their size and in turn density is not externally fixed but rather emerges from the competition between local repulsion and finite-range cavity-mediated attraction. We identify two different regimes of the phase diagram. In the strongly glued regime, the interaction range exceeds the droplet size and the physics resembles the one of the standard Bose-Hubbard model in a (self-consistent) external potential, where in the phase diagram two incompressible droplet phases with different filling are separated by one with a superfluid core. In the opposite weakly glued regime, we find instead direct first order transitions between the two incompressible phases, as well as pronounced metastability. The cavity field leaking out of the mirrors can be measured to distinguish between the various types of droplets.

Collision of two self-trapped atomic matter wave packets in an optical ring cavity

The interaction between atomic Bose-Einstein condensate (BEC) and light field in an optical ring cavity gives rise to many interesting phenomena such as supersolid and movable self-trapped matter wave packets. Here we examined the collision of two self-trapped atomic matter wave packets in an optical ring cavity, and abundant colliding phenomena have been found in the system. Depending on the magnitude of colliding velocity, the collision dynamics exhibit very different features compared with the cavity-free case. When the initial colliding velocities of the two wave packets are small, they correlatedly oscillate around their initial equilibrium positions with a small amplitude. Increasing the collision velocity leads to severe scattering of the BEC atoms; after the collision, the two self-trapped wave packets usually break into small pieces. Interestingly, we found that such a medium velocity collision is of great phase sensitivity, which may make the system useful in precision matter wave interferometry. When the colliding velocity is further increased, in the bad cavity limit, the two wave packets collide phenomenally similar to two classical particles-they first approach each other, then separate with their shape virtually maintained. However, beyond the bad cavity limit, they experience severe spatial spreading.

An optical lattice with sound

Quantized sound waves-phonons-govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (for example, by binding electrons into superconducting Cooper pairs)^1-3. The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff⁴. Optical-lattice realizations of crystals therefore lack some of the central dynamical degrees of freedom that determine the low-temperature properties of real materials. Here, we create an optical lattice with phonon modes using a Bose-Einstein condensate (BEC) coupled to a confocal optical resonator. Playing the role of an active quantum gas microscope, the multimode cavity QED system both images the phonons and induces the crystallization that supports phonons via short-range, photon-mediated atom-atom interactions. Dynamical susceptibility measurements reveal the phonon dispersion relation, showing that these collective excitations exhibit a sound speed dependent on the BEC-photon coupling strength. Our results pave the way for exploring the rich physics of elasticity in quantum solids, ranging from quantum melting transitions⁵ to exotic 'fractonic' topological defects⁶ in the quantum regime.

Classical and Quantum Collective Recoil Lasing: A Tutorial

Collective atomic recoil lasing (CARL) is a process during which an ensemble of cold atoms, driven by a far-detuned laser beam, spontaneously organize themselves in periodic structures on the scale of the optical wavelength. The principle was envisaged by R. Bonifacio in 1994 and, ten years later, observed in a series of experiments in Tübingen by C. Zimmermann and colleagues. Here, we review the basic model of CARL in the classical and in the quantum regime.