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We derive universal relations between thermodynamic quantities and the pair distribution function for bosons interacting via power-law interactions in three and two dimensions. We find beyond mean-field expressions for Tan's contact and establish new connections between the chemical potential and potential energy per particle, characteristic of systems with finite-range interactions. The obtained results are relevant for dipoles, quadrupoles, Rydberg atoms, excitons, van der Waals atoms, and other systems in the dilute limit., Comment: 18 pages, 2 figures

Large exciton-polariton optical nonlinearities present a key mechanism for photonics-based communication, ultimately in the quantum regime. Enhanced nonlinear response from various materials hosting excitons and allowing for their strong coupling with light is therefore the topic of intense studies, both in theoretical and experimental domains. Reports on the scattering rates arising due to various system's nonlinearities, such as the exciton-exciton Coulomb interaction and the Pauli blocking that leads to the saturation of the exciton oscillator strength, however, are contradictory. In this work, we develop a formalism allowing to track the exciton nonlinearities appearing in the regime of strong coupling with photons, that includes finite temperatures, mixing of the exciton excited states, and the dark exciton contributions to saturation self-consistently. The equilibrium path integration approach employed here to address the polariton composite nature, leads to a transparent hierarchy of various contributions to nonlinearity. At the same time, by taking the simplest limit of zero temperature and so-called "rigid" excitons, through our framework we retrieve the expressions derived in conventional approaches for exciton interaction constants. In particular, our theory allows to clearly show that such interaction constants cannot be used as fitting parameters tunable in a wide range of values, as they are strictly defined by the material properties, and that other explanations are due for large optical nonlinearities recently reported., Comment: 22 pages, 1 figure

The macroscopic coherence of quantum fluids enables for the observation of interference effects in their wavefunctions and leads to practical applications based on Josephson tunnelling such as superconductor quantum interference devices. The Josephson effect manifests in both fermionic and bosonic systems and it has been extensively studied in superfluid helium and atomic Bose-Einstein condensates. Exciton-polaritons can facilitate the transition to integrated semiconductor platforms, but realizing weak links in ring geometries has proven to be challenging. Here we realize a Josephson junction in a polariton ring condensate and, leveraging the optical control of the barrier, we impose a net circulation around the ring. Our experiments reveal two distinct regimes of the polariton weak link: a hydrodynamic regime with a linear relation between the phase jump at the barrier and the average current around the ring, and a Josephson regime characterised by a sinusoidal behaviour for which the mass transport through the barrier drops to zero. Our theory in terms of the 'tilted washboard' potential explains the appearance of these regimes from energy considerations using experimental values. These findings show that weak links in ring condensates can be investigated using all-optical configurations and hold potential for exploration even at room temperature., Comment: Main text: 10 pages, 4 figures, and Supplementary Information: 7 pages, 5 figures

We develop the many-body theory of dipolar exciton-polaritons in an optical microcavity in crossed transverse electric and in-plane magnetic fields. Even for relatively weak fields, we reveal the existence of two minima in the bare lower-polariton dispersion, which give rise to the tuneable transition between the polariton Bose-Einstein condensate and that of excitons, produced by the competition between these minima. We predict that such dipolar condensate exhibits a roton-maxon character of the excitation spectrum, never before observed for polaritons. We show that upon the transition between the two condensation regimes, the weak correlations in the polariton gas give way to the intermediate interparticle correlations characteristic for excitons, and that the transition is accompanied by a sharp quenching of photoluminescence as the lifetime is increased by several orders of magnitude. While in the polariton regime, the luminescence peak corresponding to the condensate is shifted to a non-zero angle. The angular dependence of the two-photon decay time in the Hanbury Brown and Twiss experiment is calculated and used as a tool to evidence the formation of the macroscopically-coherent state. Our proposal opens opportunities towards manipulating the superfluid properties and extended-range dipole-dipole correlations of exciton-polariton condensates., Comment: 17 pages, 7 figures

Bose-Fermi systems such as mixtures of electrons with excitons or exciton-polaritons are extensively discussed as candidates to host a variety of intriguing phenomena, including polaron formation, drag effects, supersolidity, and superconductivity. In this work, assuming the strong-coupling regime between the semiconductor excitons and cavity photons, we develop the many-body theory approach addressing the interplay of different types of interaction among various species in such a mixture, wherein we take into account dynamical density responses of both the Bose-condensed exciton-polaritons and the two-dimensional electron gas inside an optical microcavity. As was anticipated previously, at high enough polariton densities the lower hybrid mode of the system's excitation spectrum acquires a roton minimum, making the system prone to superconducting pairing in the vicinity of the roton instability. We analyze the possibility of polariton-BEC-mediated superconductivity in the electron gas taking into account full momentum and frequency dependence of the gap, as well as in the Eliashberg approach where the momentum dependence is neglected, and in the Bardeen-Cooper-Schrieffer approach that discards the frequency dependence and dynamical effects. Considering the interaction screening in Thomas-Fermi and in random-phase approximations, we estimate the critical temperatures of superconductivity to be not larger than 0.1 K in the vicinity of instability. As possible realizations of the coupled polariton-electron system, semiconductor quantum wells and two-dimensional transition metal dichalcogenides are considered., Comment: 19 pages, 8 figures

Quantum vortices are the quantized version of classical vortices. Their center is a phase singularity or vortex core around which the flow of particles as a whole circulates and is typical in superfluids, condensates and optical fields. However, the exploration of the motion of the phase singularities in coherently-coupled systems is still underway. We theoretically analyze the propagation of an interference dislocation in the regime of strong coupling between light and matter, with strong mass imbalance, corresponding to the case of microcavity exciton-polaritons. To this end, we utilize combinations of vortex and tightly focused Gaussian beams, which are introduced through resonant pulsed pumping. We show that a dislocation originates from self-interference fringes, due to the non-parabolic dispersion of polaritons combined with moving Rabi-oscillating vortices. The morphology of singularities is analyzed in the Poincar\'{e} space for the pseudospin associated to the polariton states. The resulting beam carries orbital angular momentum with decaying oscillations due to the loss of overlap between the normal modes of the polariton system., Comment: 9 pages, 6 figures

The Berry curvature provides a powerful tool to unify several branches of science through their geometrical aspect: topology, energy bands, spin and vector fields. While quantum defects -- phase vortices and skyrmions -- have been in the spotlight, as rotational entities in condensates, superfluids and optics, their dynamics in multi-component fields remain little explored. Here we use two-component microcavity polaritons to imprint a dynamical pseudospin texture in the form of a double full Bloch beam, a conformal continuous vortex beyond unitary skyrmions. The Berry curvature plays a key role to link various quantum spaces available to describe such textures. It explains for instance the ultrafast spiraling in real space of two singular vortex cores, providing in particular a simple expression -- also involving the complex Rabi frequency -- for their intricate velocity. Such Berry connections open new perspectives for understanding and controlling highly-structured quantum objects, including strongly asymmetric cases or even higher multi-component fields., Comment: 17 pages, 4 figures, 3 videos

Quantum vortices are the analogue of classical vortices in optics, Bose-Einstein condensates, superfluids and superconductors, where they provide the elementary mode of rotation and orbital angular momentum. While they mediate important pair interactions and phase transitions in nonlinear fluids, their linear dynamics is useful for the shaping of complex light, as well as for topological entities in multi-component systems, such as full Bloch beams. Here, setting a quantum vortex into directional motion in an open-dissipative fluid of microcavity polaritons, we observe the self-splitting of the packet, leading to the trembling movement of its center of mass, whereas the vortex core undergoes ultrafast spiraling along diverging and converging circles, in a sub-picosecond precessing fashion. This singular dynamics is accompanied by vortex-antivortex pairs creation and annihilation, and a periodically changing topological charge. The spiraling and branching mechanics represent a direct manifestation of the underlying Bloch pseudospin space, whose mapping is shown to be rotating and splitting itself. Its reshaping is due to three simultaneous drives along the distinct directions of momentum and complex frequency, by means of the differential group velocities, Rabi frequency and dissipation rates, which are natural assets in coupled fields such as polaritons. This state, displaying linear momentum dressed with oscillating angular momentum, confirms the richness of multi-component and open quantum fluids and their innate potentiality to implement sophisticated and dynamical topological textures of light., Comment: 12 pages, 8 figures, 3 videos

We propose a way to increase the lifetime of two-dimensional direct excitons and show the possibility to observe their macroscopically coherent state at high temperatures. For a single GaAs quantum well embedded in photonic layered heterostructures with subwavelength period, we predict the exciton radiative decay to be strongly suppressed. Quantum hydrodynamic approach is used to study the Berezinskii-Kosterlitz-Thouless crossover in a finite exciton system with intermediate densities. Below the estimated critical temperatures, drastic growth of the correlation length is shown to be accompanied by a manyfold increase of the photoluminescence intensity., Comment: 6 pages of the main text, and 5 pages of the Supplemental Material; 7 figures

Strongly-coupled quantum fields, such as multi-component atomic condensates, optical fields and polaritons, are remarkable systems where the simple dynamics of coupled oscillators can meet the intricate phenomenology of quantum fluids. When the coupling between the components is coherent, not only the particles number, but also their phase texture that maps the linear and angular momentum, can be exchanged. Here, on a system of exciton-polaritons, we have realized a so-called full-Bloch beam: a configuration in which all superpositions of the upper and the lower polariton -- all quantum states of the associated Hilbert space -- are simultaneously present at different points of the physical space, evolving in time according to Rabi-oscillatory dynamics. As a result, the light emitted by the cavity displays a peculiar dynamics of spiraling vortices endowed with oscillating linear and angular momentum and exhibiting ultrafast motion of their cores with striking accelerations to arbitrary speeds. This remarkable vortex motion is shown to result from distortions of the trajectories by a homeomorphic mapping between the Rabi rotation of the full wavefunction on the Bloch sphere and Apollonian circles in the real space where the observation is made. Such full-Bloch beams offer new prospects at a fundamental level regarding their topological properties or in the interpretation of quantum mechanics, and the Rabi-rotating vortices they yield should lead to interesting applications such as ultrafast optical tweezers., Comment: Published version, 18 pages, 8 figures, 4 ancillary movies

Exciton-photon beats known as polariton Rabi oscillations in semiconductor microcavities are usually excited by short pulses of light. We consider a different pumping scheme, assuming a cw pumping of the Rabi oscillator from an exciton reservoir. We account for the initial pulse of light setting the phase, exciton decay due to exciton-phonon and exciton-exciton scattering, photon leakage, and blueshift of the exciton resonance due to interactions. We find non-trivial stationary solutions reminiscent of Kapitza pendulum, where polaritons are accumulated at the upper branch while the lower branch empties., Comment: 11 pages, 10 figures (including Supplemental Material)

We theoretically analyze exciton-photon oscillatory dynamics within a homogenous polariton gas in presence of energy detuning between the cavity and quantum well modes. Whereas pure Rabi oscillations consist of the particle exchange between the photon and excitons states in the polariton system without any oscillations of the phases of the two sub-condensates, we demonstrate that any non-zero detuning results in oscillations of the relative phase of the photon and exciton macroscopic wave functions. Different initial conditions reveal a variety of behaviors of the relative phase between the two condensates, and a crossover from Rabi-like to Josephson-like oscillations is predicted., Comment: 6 pages, 3 figures