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We study the statistical mechanics and the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross-Pitaevskii equation. To determine the classical partition function thereof, we leverage the semi-analytical transfer integral operator (TIO) technique. The latter predicts a distribution of the observed wave function amplitudes and yields two-point correlation functions providing insights into the emergent dynamics involving quantum droplets. We compare the ensuing TIO results with the probability distributions obtained at large times of the modulationally unstable dynamics as well as with the equilibrium properties of a suitably constructed Langevin dynamics. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions and consecutively are found to coalesce at large evolution times. Our results from the distinct methodologies are in good agreement aside from the case of low temperatures in the special limit where the droplet widens. In this limit, the distribution acquires a pronounced bimodal character, exhibiting a deviation between the TIO solution and the Langevin dynamics still captured by the modified Gross-Pitaevskii framework.
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The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large `puddles with a broad flat-top plateau. Small droplets collide quasi-elastically, featuring the soliton-like behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. Finally, the stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.
We predict that Lee-Huang-Yang effect makes it possible to create stable quantum droplets (QDs) in binary Bose-Einstein condensates with a hetero-symmetric or hetero-multipole structure, i.e., different vorticities or multipolarities in their components. The QDs feature flat-top shapes when either chemical potential mu_1,2 of the droplet approaches an edge of a triangular existence domain in the (mu_1,mu_2) plane. QDs with different vorticities of their components are stable against azimuthal perturbations, provided that the norm of one component is large. We also present multipole states, in which the interaction with a strong fundamental component balances the repulsion between poles with opposite signs in the other component, leading to the formation of stable bound states. Extended stability domains are obtained for dipole QDs; tripole ones exist but are unstable, while quadrupoles are stable in a narrow region. The results uncover the existence of much richer families of stable binary QDs in comparison to states with identical components.
Ultracold dipolar droplets have been realized in a series of ground-breaking experiments, where the stability of the droplet state is attributed to beyond-mean-field effects in the form of the celebrated Lee-Huang-Yang (LHY) correction. We scrutinize the dipolar droplet states in a one-dimensional context using a combination of analytical and numerical approaches, and identify experimentally viable parameters for accessing our findings for future experiments. In particular we identify regimes of stability in the restricted geometry, finding multiple roton instabilities as well as regions supporting quasi-one-dimensional droplet states. By applying an interaction quench to the droplet, a modulational instability is induced and multiple droplets are produced, along with bright solitons and atomic radiation. We also assess the droplets robustness to collisions, revealing population transfer and droplet fission.
We study two-dimensional (2D) vortex quantum droplets (QDs) trapped by a thicker transverse confinement with a>1um. Under this circumstance, the Lee-Huang-Yang (LHY) term should be described by its original form in the three-dimensional (3D) configuration. Previous studies have demonstrated that stable 2D vortex QDs can be supported by a thin transverse confinement with a<<1um. In this case, the LHY term is described by a logarithm. Hence, two kinds of confinement features result in different mechanisms of the vortex QDs. The stabilities and characteristics of the vortex QDs must be re-identified. In the current system, we find that stable 2D vortex QDs can be supported with topological charge number up to at least 4. We reformulated their density profile, chemical potential and threshold norm for supporting the stable vortex QDs according to the new condition. Unlike the QDs under thin confinement, the QDs in the current system strongly repel each other because the LHY term features a higher-order repulsion than that of the thin confinement system. Moreover, elastic and inelastic collisions between two moving vortex QDs are studied throughout the paper. Two kinds of collisions can be characterized by exerting different values of related speed. The dynamics of the stable nested vortex QD, which is constructed by embedding one vortex QD with a smaller topological number into another vortex QD with a larger number of topological charge, can be supported by the system.
We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale $k$, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter $K_ksim k^theta$ that vanishes with an exponent $theta=z-1$ related to the dynamical critical exponent $z$. The QBL encodes the existence of rare superfluid regions, controls the low-energy dynamics and yields a (dissipative) conductivity vanishing as $omega^2$ in the low-frequency limit. These results reveal the glassy properties (pinning, shocks or static avalanches) of the Bose-glass phase and can be understood within the droplet picture put forward for the description of glassy (classical) systems.
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