The optical lattice plays an important role in the stability and dynamics of quantum droplets. In this article, we investigate the Bogoliubov excitation spectrum of quantum droplets in an optical lattice in the thermodynamic limit. We classify the collective excitations as synchronous modes, Bloch phononic modes, and site-population-imbalanced modes. For synchronous modes, we measure the dipole oscillation frequencies by quench dynamics with a sudden shift of the optical lattice and the breathing frequencies by Floquet dynamics with a periodic change of the lattice depth. Bloch phononic modes are observable from the Landau critical velocity of the droplets. We further discuss the instability induced by site-dependent density fluctuations and calculate the critical filling of atoms where the growth of lattice vacancy breaks down the translational symmetry of the system. This work makes essential steps towards measuring the excitation spectrum and understanding the superfluid nature of quantum droplets in an optical lattice.
The optical lattice plays an important role in the stability and dynamics of quantum droplets. In this article, we investigate the Bogoliubov excitation spectrum of quantum droplets in an optical lattice in the thermodynamic limit. We classify the collective excitations as synchronous modes, Bloch phononic modes, and site-population-imbalanced modes. For synchronous modes, we measure the dipole oscillation frequencies by quench dynamics with a sudden shift of the optical lattice and the breathing frequencies by Floquet dynamics with a periodic change of the lattice depth. Bloch phononic modes are observable from the Landau critical velocity of the droplets. We further discuss the instability induced by site-dependent density fluctuations and calculate the critical filling of atoms where the growth of lattice vacancy breaks down the translational symmetry of the system. This work makes essential steps towards measuring the excitation spectrum and understanding the superfluid nature of quantum droplets in an optical lattice.
Optical lattice plays an important role on stability and dynamics of quantum droplets. In this letter, we investigate the Bogoliubov excitation spectrum of quantum droplets in optical lattice in the thermodynamic limit. We classify the collective excitations as synchronous modes, Bloch phononic modes, and site-density imbalanced modes. For synchronous modes, we measure the dipole oscillation frequencies by quench dynamics with a sudden shift of the optical lattice, and the breathing frequencies by Floquet dynamics with a periodic change of the lattice depth. Bloch phononic modes are observable from the Landau critical velocity of the droplets. We further discuss the instability induced by the site-dependent density fluctuations, and calculate the critical filling of atoms where the growth of lattice vacancy breaks down the translational symmetry of the system. This work makes essential steps towards measuring the excitation spectrum and understanding the superfluid nature of quantum droplets in optical lattice.
The spectral properties and dynamical behaviors of three-dimensional quantum droplets loaded in an optical lattice within a Lee–Huang–Yang fluid are investigated. Using a beyond-mean-field model combined with variational analysis and numerical simulations, we explore the system's ground states and dynamics. Our results demonstrate that lattice anisotropy and quantum fluctuations effectively tune the excitation spectrum and lift the degeneracy of the breathing modes. Through Floquet dynamics, we identify distinct nonlinear features, including higher-order harmonics and frequency-mixing modes. Quench dynamics studies show center-of-mass oscillations characterized by a linear frequency and an additional nonlinear frequency. Additionally, we find that the collision dynamics of droplet pairs strongly depend on their relative phase, resulting in diverse dynamical behaviors. These findings provide valuable insights for understanding and manipulating quantum droplets in optical lattices, offering some reference for exploring quantum fluctuations in periodically confined geometries.
Motivated by recent experiments on light-matter interacting systems, we investigate a dilute Bose gas and self-bound quantum droplets in a one-dimensional optical lattice coupled to a lossy cavity mode. Using a classical-field approach, we determine the stationary states and collective excitations of this non-equilibrium system. Apart from the usual Bogoliubov modes, we identify a polariton-like gapped excitation, the frequency of which softens as a precursor of the density ordering transition. Moreover, its relaxation time diverges as the critical point is approached, signaling the non-equilibrium nature of this transition. Dynamically, this polariton-like mode can be probed by inducing cavity field fluctuations, which in turn generates spatio-temporal oscillations of both the condensate and droplet states. In the droplet regime, we also analyze the bound modes which bear the characteristics of such non-equilibrium self-bound state. In addition, we uncover solitonic non-equilibrium states, including condensate with kink-like configuration and double-droplet state, and investigate their robustness following a sudden quench. Remarkably, although these states become unstable beyond a critical coupling, they continue to manifest in the dynamics, akin to the scarring phenomena. Our results demonstrate that dissipative cavity coupling provides a versatile route for exploring rich non-equilibrium dynamics of condensates and quantum droplets within experimentally accessible settings.
We study the stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time dynamics of dipole oscillations induced by suddenly displacing the trap center. We consider the following two cases: standard soft-core bosons, whose interparticle interactions include the on-site one only; and hard-core bosons with long-range dipole-dipole interactions. For both cases, we show that the dipole oscillation is significantly damped when the maximum local momentum exceeds a certain threshold, which quantitatively agrees with the critical momentum for the dynamical instability in the homogeneous system. In the case of dipolar hard-core bosons, the dynamical instability of dipole oscillations leads to the formation of checkerboard density waves in the superfluid phase near the boundary to the supersolid phase.
Quantum droplets-arising from the delicate balance between repulsive and attractive interactions-continue to be of significant interest in the study of ultracold atomic systems. In this work, we revisit the ground-state properties and collective dynamics of one-dimensional quantum droplets. We identify a critical effective particle number, [Formula: see text], at which the superfluid fraction [Formula: see text] exhibits a distinct inflection point, indicating a structural transition in the ground state. For [Formula: see text], the density profile is sharply peaked, whereas for [Formula: see text], it flattens into a plateau-like shape well-approximated by the Thomas-Fermi model. Additionally, we show that super-Gaussian functions provide excellent fits to the ground-state density profiles, offering a simple and accurate modeling approach. To study the system's dynamical behavior, we develop an analytical framework for quantum droplets subjected to a periodic lattice potential. In the weak-lattice limit ([Formula: see text]), the excitation spectrum reveals a Goldstone gapless phonon mode, characteristic of superfluidity. However, at low densities, the inclusion of Lee-Huang-Yang corrections leads to phonon instabilities, consistent with the transition from a peak- to a plateau-like ground state. In the strong-lattice regime (large [Formula: see text]), a gap opens in the lowest excitation modes, suggesting a crossover from a superfluid to a Mott-insulating phase. Our findings should shed light on key aspects of a low-dimensional quantum droplet.
We consider quantum droplets in dipolar Bose-Einstein condensates embedded in optical lattices within the framework of Gross-Pitaevskii equations. In dipolar BECs, the long-range and isotropic dipole-dipole interaction provides an additional mechanism for self-binding. We analyze the linear stability as well dynamics of quantum droplets. We find an effective potential for the width and show that the optimum width for formation of quantum droplet increases as the dipole-dipole interaction increases. We study dynamics of the stable droplets and see that its width oscillates with time, and the amplitude of oscillation increases with the increase of dipole-dipole interaction. In presence of optical lattices, width of a stable droplet changes quasi-periodically while the location of density profile changes periodically in space. The frequency of oscillation depends sensitively on the lattice parameters. We check dynamical stability of a quantum droplet through numerical simulation.