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Quantum droplets have been realized in experiments on binary boson mixtures and dipolar Bose gases. In these systems, the mean-field energy of the Bose-Einstein condensation is attractive, and the repulsive Lee-Huang-Yang energy is crucial…
Stabilized by quantum fluctuations, dipolar Bose-Einstein condensates can form self-bound liquidlike droplets in the mean-field unstable regime. However in the Bogoliubov theory, some phonon energies are imaginary in the long-wavelength…
Quantum droplets are ultradilute liquid states which emerge from the competitive interplay of two Hamiltonian terms, the mean-field energy and beyond-mean-field correction, in a weakly interacting binary Bose gas. We relate the formation of…
In his seminal proposal of quantum droplets in binary Bose mixtures {[}Phys. Rev. Lett. \textbf{115}, 155302 (2015){]}, Dmitry Petrov suggested that the density ratio $n_{2}/n_{1}$ of the two bosonic components are locked to an optimal…
We study the stability of a zero temperature mixture of attractively interacting degenerate bosons and spin-polarized fermions in the absence of confinement. We demonstrate that higher order corrections to the standard mean-field energy can…
Ultradilute quantum droplets are intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of…
We explore the zero-temperature behavior of an assembly of bosons interacting through a zero-range, attractive potential. Because the two-body interaction admits a bound state, the many-body model is best described by a Hamiltonian that…
We systematically investigate the properties of three-dimensional dipolar binary Bose mixture at low temperatures. A set of coupled self-consistent equations of motion are derived for the two condensates. In the homogeneous case, useful…
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…
Attractive Bose-Einstein condensates can host two types of macroscopic self-bound states of different nature: bright solitons and quantum liquid droplets. Here, we investigate the connection between them with a Bose-Bose mixture confined in…
We investigate the formation of quantum droplets at finite temperature in attractive Bose mixtures subject to a strong transverse harmonic confinement. By means of exact path-integral Monte Carlo methods we determine the equilibrium density…
We exploit a few- to many-body approach to study strongly interacting dipolar bosons in the quasi-one-dimensional system. The dipoles attract each other while the short range interactions are repulsive. Solving numerically the multi-atom…
The thermodynamic and superfluid properties of the dilute two-dimensional binary Bose mixture at low temperatures are discussed. We also considered the problem of the emergence of the long-range order in these systems. All calculations are…
We revisit the Bogoliubov theory of quantum droplets proposed by Petrov {[}Phys. Rev. Lett. \textbf{115}, 155302 (2015){]} for an ultracold Bose-Bose mixture, where the mean-field collapse is stabilized by the Lee-Huang-Yang quantum…
We investigate dark solitons in two-component Bose systems with competing interactions in one dimension. Such a system hosts a liquid phase stabilized by the beyond-mean field corrections. Using the generalized Gross-Pitaevskii equation, we…
We study the properties of the Bose-Fermi mixture from the perspective of reaching a state of a self-bound quantum droplet. The variational analysis shows that the system exhibits bistability. For weak repulsion between bosons, one of the…
In the framework of coupled 1D Gross-Pitaevskii equations, we explore the dynamics of a binary Bose-Einstein condensate where the intra-component interaction is repulsive, while the inter-component one is attractive. The existence regimes…
We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the…
In a binary quantum droplet, the interspecies attraction dominates over the intraspecies repulsions and the mean-field energy is unstable. The mechanical stability is restored by the repulsive Lee-Huang-Yang (LHY) energy [1]. In the…
In these lecture notes, we discuss the physics of a two-dimensional binary mixture of Bose gases at zero temperature, close to the point where the two fluids tend to demix. We are interested in the case where one of the two fluids (the…