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arXiv:2103.02891 · Physical Review A

Propagation of phase-imprinted solitons from superfluid core to Mott-insulator shell and superfluid shell

Y. Watanabe, Shohei Watabe, Tetsuro Nikuni

Published Oct 20, 2021• 0 citations
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Abstract

We study phase-imprinted solitons of ultracold bosons in an optical lattice with a harmonic trap exhibiting superfluid (SF) and Mott-insulator shell structures. An earlier study [K. V. Krutitsky, J. Larson, and M. Lewenstein, Phys. Rev. A 82, 033618 (2010)] reported three types of phase-imprinted solitons in the Bose-Hubbard model: in-phase soliton, out-of-phase soliton, and wavelet. In this paper, we uncover the dynamical phase diagram of these phase-imprinted solitons. We also reveal another type of phase-imprinted soliton, the hybrid soliton. In a harmonically trapped system, solitonic excitations created at the SF core cannot penetrate the outer SF shell. This repulsion at the surface of the outer SF shell can be counteracted by imposing a repulsive potential at the center of the trap. These results can be interpreted as a kind of impedance matching of excitations in Bose-Einstein condensates in terms of the effective chemical potentials or local particle numbers in the shell, and analogous results can be observed in sound waves created by a local single-shot pulse potential.

DOI
10.1103/physreva.104.043314

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We study phase-imprinted solitons of ultracold bosons in an optical lattice with a harmonic trap exhibiting superfluid (SF) and Mott-insulator shell structures. An earlier study [K. V. Krutitsky, J. Larson, and M. Lewenstein, Phys. Rev. A 82, 033618 (2010)] reported three types of phase-imprinted solitons in the Bose-Hubbard model: in-phase soliton, out-of-phase soliton, and wavelet. In this paper, we uncover the dynamical phase diagram of these phase-imprinted solitons. We also reveal another type of phase-imprinted soliton, the hybrid soliton. In a harmonically trapped system, solitonic excitations created at the SF core cannot penetrate the outer SF shell. This repulsion at the surface of the outer SF shell can be counteracted by imposing a repulsive potential at the center of the trap. These results can be interpreted as a kind of impedance matching of excitations in Bose-Einstein condensates in terms of the effective chemical potentials or local particle numbers in the shell, and analogous results can be observed in sound waves created by a local single-shot pulse potential.
We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. [Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.
solitons, vortices, and topological excitations. PACS. 03.75.Nt – Other Bose-Einstein condensation phenomena. Abstract. – Motivated by the recent experiment on the Bose-Einstein condensation of 52 Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, i.e., the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them. The recent observation [2] of quantum phase transition of interacting bosons in an optical lattice has given a new impetus to the study of correlated bosons. The possibility of manipulating both the interactions among the constituents as well as disorder in the system
Dark solitons of ultracold bosons in the vicinity of the Mott-insulator--superfluid phase transition are studied. Making use of the Gutzwiller ansatz we have found antisymmetric eigenstates corresponding to standing solitons, as well as propagating solitons created by phase imprinting. Near the phase boundary, superfluidity has either a particle or a hole character depending on the system parameters, which greatly affects the characteristics of both types of solitons. Within the insulating Mott regions, soliton solutions are prohibited by lack of phase coherence between the lattice sites. Linear and modulational stability show that the soliton solutions are sensitive to small perturbations and, therefore, unstable. In general, their lifetimes differ for on-site and off-site modes. For the on-site modes, there are small areas between the Mott-insulator regions where the lifetime is very large, and in particular much larger than that for the off-site modes.
We describe weakly interacting atomic or molecular bosons trapped in harmonically confined optical lattices, which exhibit a wedding cake structure consisting of insulating (Mott) shells. We show that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping and find that the order parameter equation in the superfluid regions is not of the standard Gross-Pitaevskii type except near the insulator-to-superfluid boundaries. We obtain the excitation spectra in the Mott and superfluid regions, and we show that the superfluid shells possess low-energy sound modes with spatially dependent sound velocity described by a local index of refraction directly related to the local superfluid density. Furthermore, we discuss the Berezinskii-Kosterlitz-Thouless transition and vortex-antivortex pairs in thin (wide) superfluid shells (rings) limited by three- (two-) dimensional Mott regions. Last, we propose an experiment to detect superfluid shells using Laguerre-Gaussian beams and Bragg spectroscopy.
Motivated by the recent experiment on the Bose-Einstein condensation of 52^{52}52Cr atoms with long-range dipolar interactions (Werner J. et al., Phys. Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive nearest and next-nearest neighbor interactions in an optical lattice. The ground state phase diagram, calculated using the Gutzwiller ansatz, shows, apart from the superfluid (SF) and the Mott insulator (MI), two modulated phases, \textit{i.e.}, the charge density wave (CDW) and the supersolid (SS). Excitation spectra are also calculated which show a gap in the insulators, gapless, phonon mode in the superfluid and the supersolid, and a mode softening of superfluid excitations in the vicinity of the modulated phases. We discuss the possibility of observing these phases in cold dipolar atoms and propose experiments to detect them.
We use quantum Monte Carlo simulations to show the presence and study the properties of solitons in the one-dimensional soft-core bosonic Hubbard model with near-neighbor interaction in traps. We show that when the half-filled charge density wave (CDW) phase is doped, solitons are produced and quasi-long-range order established. We discuss the implications of these results for the presence and robustness of this solitonic phase in Bose-Einstein condensates on one-dimensional optical lattices in traps and study the associated excitation spectrum. The density profile exhibits the coexistence of Mott insulator, CDW, and superfluid regions.