We note the similarity between BEC (Bose-Einstein Condensates) formed of atoms between which we have long-range attraction (and shorter-range repulsions) and the field theoretic "Q balls". This allows us in particular to address the stability of various putative particle physics Q balls made of non-relativistic bosons using variational methods of many-body physics.
We note the similarity between BEC (Bose-Einstein Condensates) formed of atoms between which we have long-range attraction (and shorter-range repulsions) and the field theoretic "Q balls". This allows us in particular to address the stability of various putative particle physics Q balls made of non-relativistic bosons using variational methods of many-body physics.
Relativistic scalar field theories with a conserved global charge Q often possess (meta) stable spherically symmetric soliton solutions, called Q-balls. We elaborate on the perfect formal analogy which exists between Q-balls and spherically symmetric solitons in certain non-relativistic atomic Bose-Einstein condensates, for which the dominant interatomic interaction can be tuned attractive. In a harmonic trap, present in existing experiments, the Q-ball solution is modified in an essential way. If the trap is significantly prolongated in one direction, however, then genuine solitons do appear, and actual experimental data can be obtained for some of the Q-ball properties studied numerically in the relativistic cosmological context, such as their formation and collisions. We also suggest conditions under which the same cosmologically relevant analogies could be extended to the fully three-dimensional case.
Relativistic scalar field theories with a conserved global charge Q often possess (meta)stable spherically symmetric soliton solutions, called Q-balls. We elaborate on the perfect formal analogy which exists between Q-balls and spherically symmetric solitons in certain non-relativistic atomic Bose–Einstein condensates, for which the dominant interatomic interaction can be tuned attractive. In a harmonic trap, present in existing experiments, the Q-ball solution is modified in an essential way. If the trap is significantly prolongated in one direction, however, then genuine solitons do appear, and actual experimental data can be obtained for some of the Q-ball properties studied numerically in the relativistic cosmological context, such as their formation and collisions. We also suggest conditions under which the same cosmologically relevant analogies could be extended to the fully three-dimensional case.
Introduction Bose–Einstein condensation (BEC) is one of the most intriguing phenomena in physics. The basic idea goes back to the 1920s, when Einstein made predictions for the behavior of atoms at sufficiently low temperatures and high densities. However, it took seven decades for experimental physicists to realize this phase under the low-density conditions envisioned by Einstein. In the intermediate period there were many experiments in which aspects of BEC played important roles. Therefore, phenomena such as superfluidity and superconductivity were connected to BEC long before its 1995 realization in ultra-cold, low-density atomic vapors. Since BEC can be discussed with very many different backgrounds and applications in mind, the subject can sometimes be overwhelming for interested students. There is a very good reason why a chapter on BEC does not belong in this book. In all the other chapters here, the processes described involve one or at most two atoms, and the interactions that play a role are between the particles that constitute the atom, namely between the nucleus (or nuclei) and their electrons. The interactions are described quantum mechanically by their Hamiltonian that can always be written exactly in non-relativistic terms, and in some cases can even be solved exactly. This makes atoms and molecules a branch of physics where comparisons between theory and experiments become very meaningful since theoretical predictions are often confirmed to very high accuracy. In BEC, it is the interactions among many atoms that are the key for understanding the phenomenon. Although in principle one could write a Hamiltonian for a Bose condensed gas, its large number of particles makes this not very practical. The starting point for the description of a BEC is in the area of many-body physics that belongs to the expertise of condensed-matter physicists. The interactions between ~10 23 electrons in a solid state with a lattice formed by ~10 23 ions resemble the kind of interactions in a BEC much more closely than the simple fewbody interactions in an atom or molecule. Thus all the theoretical models that have been described up to now are not applicable for the contents of this chapter.
Among settings which have recently been elaborated for the creation of stable multidimensional solitons, most advanced, as concerns the theory and experiment alike, is the work with quantum droplets (QDs) in atomic BEC. Important theoretical predictions for fundamental and topologically structured soliton-like (stably self-trapped) QDs have been published in many papers, starting from the pioneering work of Petrov [Phys. Rev. Lett. 115, 155302 (2015)]. Simultaneously, the experimental advancement in the making of QDs in binary BECs, as well as in single-component BECs of atoms carrying magnetic dipole moments, have been really remarkable and unique. Successful experiments followed the first theoretical prediction of the QDs very quickly, and the progress in the experimental work was much faster than in other areas of physics where stable multidimensional solitons were predicted. The basis of these works is a correction to the MF (mean-field) BEC dynamics produced by quantum fluctuations around MF states. The correction was first predicted in 1957 by Lee, Huang, and Yang (LHY). The breakthrough proposal made by Petrov [Phys. Rev. Lett. 115, 155302 (2015)] was to use the effective higher-order (quartic) self-repulsion, produced by the LHY effect in the atomic BEC, as a mechanism arresting the collapse driven by mutual attraction of two self-repulsive components in a binary quantum bosonic gas. The balance between the inter-species attraction and LHY-induced self-repulsion gives rise to stable 3D and quasi-2D (pancake-shaped) localized bound states in the form of the quantum droplets (QDs). In single-component condensates of magnetic atoms, the attraction is provided by the long-range dipole–dipole interaction (Chomaz et al., 2016; Schmitt et al., 2016). The competition between the MF attraction and LHY repulsion maintains a superfluid state whose density (taking very low values) cannot exceed a certain maximum, thus making it effectively incompressible. This is a reason why this quantum macroscopic state of matter is identified as a superfluid. Accordingly, localized states filled by this quantum fluid are called “droplets.” In addition to the 3D QDs, droplets in the effectively 2D setting, which may exist under the action of tight confinement in one direction, imposed by an external potential, were theoretically predicted [Petrov and Astrakharchik, Phys. Rev. Lett. 117, 100401 (2016)] and experimentally created [Cabrera et al., Science 359, 301-304 (2018)] too. This chapter provides a condensed review of basic theoretical results for stable QDs in binary BECs, maintained through the stable balance between the inter-species attraction and intra-species LHY repulsion. Both fundamental modes and ones with embedded vorticity are considered. The presentation is partly based on a review article by Luo et al. [Front. Phys. 16, 32501 (2021)]. In addition to 2D and 3D self-trapped QDs in free space, the present chapter addresses 2D fundamental and vortex modes trapped in a singular attractive potential, ∼−1/r2, which are stabilized by the LHY repulsion. Two subsequent chapters present a summary of experimental findings for QDs in binary BECs and for QDs in single-component BECs of magnetic atoms.
Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.
Abstract We study the formation of a stable self-trapped spherical quantum ball in a binary Bose–Einstein condensate (BEC) with two-body inter-species attraction and intra-species repulsion employing the beyond-mean-field Lee–Huang–Yang and the three-body interactions. We find that either of these interactions or a combination of them can stabilize the binary BEC quantum ball with very similar stationary results, and for a complete description of the problem both the terms should be considered. These interactions lead to higher-order nonlinearities, e.g. quartic and quintic, respectively, in a nonlinear dynamical equation compared to the cubic nonlinearity of the two-body contact interaction in the mean-field Gross–Pitaevskii equation. The higher-order nonlinearity makes the energy infinitely large at the center of the binary ball and thus avoids its collapse. In addition to the formation of stationary binary balls, we also study a collision between two such balls. At large velocities, the collision is found to be elastic, which turns out to be inelastic as the velocity is lowered. We consider the numerical solution of a beyond-mean-field model for the binary ball as well as a single-mode variational approximation to it in this study.