Ultracold atomic gases provide a unique way for exploring many-body quantum phenomena that are inaccessible to conventional low-temperature experiments. Nearly two decades ago the Bose-Einstein condensate (BEC) - an ultracold gas of bosons in which almost all bosons occupy the same single-particle state - became experimentally feasible. Because a BEC exhibits superfluid properties, it can provide insights into the behavior of low-temperature helium liquids. We describe the case of a single distinguishable atom (an impurity) embedded in a BEC and strongly coupled to the BEC bosons. Depending on the strength of impurity-boson and boson-boson interactions, the impurity self-localizes into two fundamentally distinct regimes. The impurity atom can behave as a tightly localized 'polaron,' akin to an electron in a dielectric crystal, or as a 'bubble,' an analog to an electron bubble in superfluid helium. We obtain the ground state wavefunctions of the impurity and BEC by numerically solving the two coupled Gross-Pitaevskii equations that characterize the system. We employ the methods of imaginary time propagation and conjugate gradient descent. By appropriately varying the impurity-boson and boson-boson interaction strengths, we focus on the polaron to bubble crossover. Our results confirm analytical predictions for the polaron limit and uncover properties of the bubble regime. With these results we characterize the polaron to bubble crossover. We also summarize our findings in a phase diagram of the BEC-impurity system, which can be used as a guide in future experiments.
Ultracold atomic gases provide a unique way for exploring many-body quantum phenomena that are inaccessible to conventional low-temperature experiments. Nearly two decades ago the Bose-Einstein condensate (BEC) - an ultracold gas of bosons in which almost all bosons occupy the same single-particle state - became experimentally feasible. Because a BEC exhibits superfluid properties, it can provide insights into the behavior of low-temperature helium liquids. We describe the case of a single distinguishable atom (an impurity) embedded in a BEC and strongly coupled to the BEC bosons. Depending on the strength of impurity-boson and boson-boson interactions, the impurity self-localizes into two fundamentally distinct regimes. The impurity atom can behave as a tightly localized 'polaron,' akin to an electron in a dielectric crystal, or as a 'bubble,' an analog to an electron bubble in superfluid helium. We obtain the ground state wavefunctions of the impurity and BEC by numerically solving the two coupled Gross-Pitaevskii equations that characterize the system. We employ the methods of imaginary time propagation and conjugate gradient descent. By appropriately varying the impurity-boson and boson-boson interaction strengths, we focus on the polaron to bubble crossover. Our results confirm analytical predictions for the polaron limit and uncover properties of the bubble regime. With these results we characterize the polaron to bubble crossover. We also summarize our findings in a phase diagram of the BEC-impurity system, which can be used as a guide in future experiments.
Polarons, self-localized composite objects formed by the interaction of a single impurity particle with a host medium, are a paradigm of strong interaction many-body physics. We show that dilute gas Bose-Einstein condensates (BEC's) are the first medium known to self-localize the same impurity particles both in a Landau-Pekar polaron state akin to that of self-localized electrons in a dielectric lattice, and in a bubble state akin to that of electron bubbles in helium. We also show that the BEC-impurity system is fully characterized by just two dimensionless coupling constants, and that it can be adiabatically steered from the Landau-Pekar regime to the bubble regime in a smooth crossover trajectory.
We show that repulsive neutral-atom impurities in a dilute gas Bose-Einstein condensate (BEC) can self-localize in bubble polaron states formally analogous to electron bubbles in helium. The BEC is then the first impurity host medium known to exhibit both Landau-Pekar polaron states akin to that of self-localized electrons in a dielectric lattice and self-localized bubble polaron states. We find that the neutral BEC-impurity system is fully characterized by only two dimensionless coupling constants and that a single BEC impurity can be steered adiabatically from the Landau-Pekar to the bubble region. The adiabatic change is that of a crossover, not a transition.
We describe the ground state of a large, dilute, neutral atom Bose–Einstein condensate (BEC) doped with N strongly coupled mutually indistinguishable, bosonic neutral atoms (referred to as 'impurity') in the polaron regime where the BEC density response to the impurity atoms remains significantly smaller than the average density of the surrounding BEC. We find that N impurity atoms with N ≠ 1 can self-localize at a lower value of the impurity–boson interaction strength than a single impurity atom. When the 'bare' short-range impurity–impurity repulsion does not play a significant role, the self-localization of multiple bosonic impurity atoms into the same single particle orbital (which we call co-self-localization) is the nucleation process of the phase separation transition. When the short-range impurity–impurity repulsion successfully competes with co-self-localization, the system may form a stable liquid of self-localized single impurity polarons.
This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas. The latter can be realized by a Bose-Einstein condensate (BEC) of ultracold atoms, or of exciton polaritons in a semiconductor, which has led to a series of experimental observations of Bose polarons near inter-species Feshbach resonances that we survey. Following an introduction to the topic, with references to its historic roots and a presentation of the Bose polaron Hamiltonian, we summarize state-of-the-art experiments. Next we provide a detailed discussion of polaron models, starting from the ubiquitous Fröhlich Hamiltonian that applies at weak couplings. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency (RF) spectra obtained in ultracold atom experiments; to investigations of universal few-body and Efimov states associated with a Feshbach resonance in atomic mixtures; to studies of quantum dynamics and polarons out of equilibrium; Bose polarons in low-dimensional; induced interactions among polarons and bipolaron formation; and to Bose polarons at non-zero temperatures. We end our review by detailed discussions of closely related experimental setups and systems, including ionic impurities, systems with strong light-matter interactions, and variations and extensions of the Bose polaron concepts e.g. to baths with topological order or strong interactions relevant for correlated electrons. Finally, an outlook is presented, highlighting possible future research directions and open questions in the field as a whole.
This review describes the field of Bose polarons, arising when mobile impurities are immersed into a bosonic quantum gas. The latter can be realized by a Bose-Einstein condensate of ultracold atoms, or of exciton polaritons in a semiconductor, which has led to a series of experimental observations of Bose polarons near inter-species Feshbach resonances that we survey. Following an introduction to the topic, with references to its historic roots and a presentation of the Bose polaron Hamiltonian, we summarize state-of-the-art experiments. Next we provide a detailed discussion of polaron models, starting from the ubiquitous Fröhlich Hamiltonian that applies at weak couplings. Already this highly simplified model allows insights into ultra-violet divergencies, logarithmic and power-law, that need to be properly regularized. To capture the physics near a Feshbach resonance, two-phonon scattering terms on the impurity as well as phonon-phonon interactions need to be included. We proceed by a survey of concurrent theoretical methods used for solving strongly interacting Bose polaron problems, ranging from Lee-Low-Pines mean-field theory, Chevy-ansatz, Gross-Pitaevskii-equation to diagrammatic Monte Carlo approaches. The subsequent sections are devoted to the large bodies of work investigating strong coupling Bose polarons, including detailed comparisons with radio-frequency spectra obtained in ultracold atom experiments; to investigations of universal few-body and Efimov states associated with a Feshbach resonance in atomic mixtures; to studies of quantum dynamics and polarons out of equilibrium; Bose polarons in low-dimensional 1D and 2D quantum systems; induced interactions among polarons and bipolaron formation; and to Bose polarons at non-zero temperatures. We end our review by detailed discussions of closely related experimental setups and systems, including ionic impurities, systems with strong light-matter interactions, and variations and extensions of the Bose polaron concepts e.g. to baths with topological order or strong interactions relevant for correlated electrons. Finally, an outlook is presented, highlighting possible future research directions and open questions in the field as a whole.
Bose-Einstein condensation is a macroscopic quantum phenomenon where cooling down a gas of bosonic particles to ultracold temperatures results in the macroscopic occupation of the lowest energy state. This new state of matter has been used as a quantum simulator of many-body phenomena and theories due to its extreme tunability and controllability. An important example of such a many-body system is the polaron which, in its most general form, describes an impurity interacting with a bosonic bath. In the case of ultracold Bose gases, the impurity interacts with and is dressed by the Bogoliubov excitations of the gas. A supersolid is a state of matter that exhibits both superfluidity and crystalline order, which are seemingly irreconcilable properties. It has recently been observed in dipolar ultracold Bose gases, where it arises from the long-range anisotropic dipole-dipole interactions, and also other systems. The breaking of both translational symmetry and gauge symmetry results in multiple excitation modes in the supersolid. In this thesis, the charged Bose polaron and an impurity in a dipolar ultracold Bose gas exhibiting supersolidity (the supersolid Bose polaron) are studied. The ground-state properties of the charged Bose polaron are discussed using a variational path-integral approach. Absorption spectroscopy is proposed as a probe of the charged Bose polaron, and the optical response is studied for weak impurity-boson interactions. Next, the one-dimensional dipolar supersolid Bose polaron is investigated where multiple approaches are used for the derivation of the ground-state properties. The study of the polaron problem with a supersolid background is of particular interest because of the rich excitation spectrum of the supersolid. Interesting phenomena, such as possible localization of the polaron to a single droplet for strong interactions, are observed. The absorption spectrum of a charged impurity in the supersolid is also derived, which, because of the different excitation modes of the supersolid, shows multiple peaks from which information such as the superfluid fraction may be obtained.