Quantum mixtures of ultra-cold atoms are exceptional platforms which allow to investigate a huge variety of phenomena owing to the exquisite control of interactions between atoms. We present here a theoretical investigation of some distinctive phenomena emerging in these systems which highlight their quantum nature. Balanced mixtures at sufficiently low temperatures are superfluid and, when set into rotation, they display topological excitations in the form of quantum vortices. In many physical systems, especially in quantum mixtures, the scenario is richer as the vortex core is filled, either deliberately or accidentally, by particles and then stable massive vortices appear. The finite inertial mass has an unmistakable dynamical signature in the trajectory of vortices in two-dimensional superfluids. On the one hand, in bosonic mixtures massive vortices may appear in the immiscible regime where one (majority) component features topological excitations and the other (minority) component localizes at the vortex cores. On the other hand, in Fermi superfluids vortices are intrinsically massive, due to the presence of normal component at the vortex core. Together with dissipative effects, the core mass is expected to affect the collective properties of many-vortex systems, such as providing a stabilization mechanism for usual shear-flow instabilities that have been currently investigated in experiments. In the strongly imbalanced regime, quantum mixtures offer a unique viewpoint on the well-known impurity problem. In particular, the strongly-interacting system made of an impurity atom in a Fermi sea can be described in terms of a Fermi polaron, the prototypical realization of Landau's fundamental concept of quasiparticle. We study the behaviour of the moving Fermi polaron, finding a breakdown of the effective mass description at finite momentum which finds a solid confirmation in a cold-atom experiment. A novel type of quantum liquid may also appear in ultra-cold bosonic mixtures from a competition between interactions. When the mean-field attraction is balanced by a repulsion induced by quantum fluctuations, the system stabilizes into a self-bound configuration, known as quantum droplet. While this physics has been explored in the context of quantum gases, we predict here the existence of a similar droplet phase in a solid-state system with light-matter interactions. We consider a spin mixture of exciton-polaritons, hybrid light-matter quasiparticles formed from the strong coupling between excitons (bound electron-hole pairs) and photons in a semiconductor microcavity. This exotic phase could open an alternative avenue to achieve the long-sought quantum polaritonic regime.
Quantum mixtures of ultra-cold atoms are exceptional platforms which allow to investigate a huge variety of phenomena owing to the exquisite control of interactions between atoms. We present here a theoretical investigation of some distinctive phenomena emerging in these systems which highlight their quantum nature. Balanced mixtures at sufficiently low temperatures are superfluid and, when set into rotation, they display topological excitations in the form of quantum vortices. In many physical systems, especially in quantum mixtures, the scenario is richer as the vortex core is filled, either deliberately or accidentally, by particles and then stable massive vortices appear. The finite inertial mass has an unmistakable dynamical signature in the trajectory of vortices in two-dimensional superfluids. On the one hand, in bosonic mixtures massive vortices may appear in the immiscible regime where one (majority) component features topological excitations and the other (minority) component localizes at the vortex cores. On the other hand, in Fermi superfluids vortices are intrinsically massive, due to the presence of normal component at the vortex core. Together with dissipative effects, the core mass is expected to affect the collective properties of many-vortex systems, such as providing a stabilization mechanism for usual shear-flow instabilities that have been currently investigated in experiments. In the strongly imbalanced regime, quantum mixtures offer a unique viewpoint on the well-known impurity problem. In particular, the strongly-interacting system made of an impurity atom in a Fermi sea can be described in terms of a Fermi polaron, the prototypical realization of Landau's fundamental concept of quasiparticle. We study the behaviour of the moving Fermi polaron, finding a breakdown of the effective mass description at finite momentum which finds a solid confirmation in a cold-atom experiment. A novel type of quantum liquid may also appear in ultra-cold bosonic mixtures from a competition between interactions. When the mean-field attraction is balanced by a repulsion induced by quantum fluctuations, the system stabilizes into a self-bound configuration, known as quantum droplet. While this physics has been explored in the context of quantum gases, we predict here the existence of a similar droplet phase in a solid-state system with light-matter interactions. We consider a spin mixture of exciton-polaritons, hybrid light-matter quasiparticles formed from the strong coupling between excitons (bound electron-hole pairs) and photons in a semiconductor microcavity. This exotic phase could open an alternative avenue to achieve the long-sought quantum polaritonic regime.
Quantum vortices are pivotal for understanding of phenomena in quantum hydrodynamics. Vortices were observed in different physical systems like trapped dilute Bose-Einstein condensates, liquid helium, exciton-polariton condensates and other types of systems. Foreign particles attached to the vortices often serve for a visualization of the vortex shape and kinematics in superfluid experiments. Fascinating discoveries were made in the field of cold quantum mixtures, where vortices created in one component may interact with the other component. This works raise the fundamental question of the interaction between quantum vortices and matter. The generalized nonlinear Schrodinger equation based formalism is applied here to model three different processes involving the interaction of quantum vortices with foreign particles: propagation of a fast classical particle in a superfluid under the influence of sound waves, scattering of a single fermion by a quantized vortex line and dynamics of vortex pairs doped with heavy bosonic matter. The obtained results allow to to clarify the details of recent experiments and acquire a better understanding of the multicomponent quantum turbulence.
Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.
We consider ultracold imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mixtures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species. In both cases, the number of atoms for each component is allowed to be different, leading to a spin imbalance or a polarization. In the second case, the two different species also give rise to a mass imbalance for the particles. Imbalanced Fermi mixtures play a fundamental role in condensed-matter, nuclear and astroparticle physics. Experimentally, the atomic mixtures are made strongly interacting with the use of two-channel Feshbach resonances. We start out by treating these in more detail. We review the relevant scattering theory, and apply it to the well-studied case of resonant s-wave collisions with zero angular momentum. Furthermore, we discuss the less-studied case of p-wave collisions with nonzero angular momentum, and the inhomogeneous case due to a trapping potential. Having discussed the two-body physics, we turn to the many-body physics. The pioneering experimental studies of Cooper pairing in lithium-6 mixtures with a spin imbalance were performed by Zwierlein et al. [Science 311, 492 (2006)] and Partridge et al. [Science 311, 503 (2006)]. We study the mean-field theory for the polarized Fermi mixture to obtain a qualitative understanding of these experiments. In the unitarity limit, where the scattering length of the interatomic interaction diverges, the theory gives rise to two exotic superfluid phases that are absent in the balanced mixture. These are the gapless superfluid Sarma phase and the phase-separated phase. By using renormalization group techniques to account for the effects of strong interactions, we obtain also quantitative agreement with Monte-Carlo calculations and experiments. We then generalize our knowledge of the solely spin-imbalanced mixture to the mass-imbalanced case, where in particular the mixture consisting of lithium-6 and potassium-40 is experimentally promising. We study the mean-field phase diagram for this mixture in the unitarity limit, where we not only find phase separation and Sarma superfluidity, but also a Lifshitz point. The latter signals an instability towards a supersolid phase. We also include the effects of fluctuations, which do not alter the topology of the phase diagram. However, fluctuation effects lower the critical temperatures with an experimentally relevant factor of three. Finally, we study superfluidity in a fully polarized gas of potassium-40 atoms near a p-wave Feshbach resonance. In particular, we consider coherent Josephson oscillations between the superfluid components in the two channels of the resonance, whose frequencies contain a clear signature of the quantum phase transition that occurs as a function of applied magnetic field.
The most recent advances in the ultracold atoms experimental techniques allowed the production of the ultracold gases mixtures in the laboratory.Motivated by these developments, in this project we study systems involving two ultracold atoms mixtures.In the first part, we consider a Bose-Einstein condensate (BEC) with a vortex lattice weakly interacting with another utracold dilute bosonic gas.We apply the Bose-Hubbard (BH) model to describe the atoms of the minority species trapped in the vortex lattice.As occurs in a static optical lattice, we predict the quantum phase transition between the Mott insulator to superfluid phases, which now can be controlled by changing the intra and inter-species scattering length.Considering the intrinsic lattice dynamics, the Tkachenko modes of the vortex lattice, we derive an extended BH Hamiltonian and analyzed new properties in the phase diagram that arise from a long-range attractive potential and density-dependent hopping.In the second part, we study the properties of a mobile impurity living in two dimensions and interacting with a 2 and 3 BEC cloud.The resulting impurity-bath interaction leads to the formation of a polaron (particle "dressed" by the phonon excitations of the BEC), which is characterized by its spectral function.We determine the energy dispersion, spectral weight, effective mass and lifetime of the polaron.These analysis allowed us to identify a dissipative regime for higher impurity velocities, with an increasing scattering rate of phonons.In addition, we observe a self-localization regime for lower impurity velocities which may be a signature for molecular formation.In spite of qualitatively similar results obtained for the 2 and 3 bath, we had differences related to the self-localization and dissipation limits, that allowed us to conclude that a 2 BEC bath would be a better candidate to observe stable quasi-particle properties.
These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.
Two models are discussed here to illustrate the quantum many-body phenomena in mixtures of ultra-cold atoms in optical lattices. The first model describes a mixture of two species of bosonic atoms of equal masses in optical lattices and the second describes a mixture of heavy bosonic atoms and light fermionic atoms in optical lattices. For both models, we assume the trap is present and use parameters typical in experiment. For the first model, the discussion is aimed at providing a thorough description of the collective behavior of the binary mixture in various interaction regions, with emphasis on two many-body phenomena, pairing and anti-pairing, as a result of the inter-species interaction. The pairing leads to a new type of superfluid order, called the paired superfluid (PSF) and the anti-pairing leads to another type of superfluid order, called the counter-flow superfluid (CFSF). In addition, we discuss the coexistence of charge density wave order with the three superfluid orders in the strong interaction region. We use both Luttinger liquid theory and the time evolving block decimation (TEBD) method to study this model in one dimension. The discussion is organized in three parts: the phase diagram and the correlation functions; the noise correlation functions; and the transport properties. Two phase diagrams are constructed to map the different orders in the parameter space. The correlation functions, include noise correlations, are carefully examined for the determination of the orders and for possible detection methods. In the end, the transport properties of the PSF and CFSF orders are studied through the dipole oscillation induced by trap displacement. For the second model, examining a mixture of heavy bosons and light fermions, the discussion is oriented toward determining the thermal properties of the mixture for attractive inter-species interactions. This work is motivated by experiments creating artificial molecules through optical and magnetic control of ultra-cold atoms. We use the strong coupling (SC) expansion method to evaluate the density profile, the onsite inter-species correlations, the density fluctuations and the entropy per particle. Analytical expressions are derived for all the quantities above as well as the partition function. To benchmark the accuracy, the SC calculations are compared with inhomogeneous dynamical mean field theory (IDMFT) and Monte Carlo (MC) simulation. From the calculations, we find that 1) the efficiency of creating pre-formed molecules is significantly increased by confining the mixtures onto optical lattices; 2) the temperature of the mixtures in optical lattices can be reliably estimated through the density gradient and the density fluctuations.