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Chinese Physics B

Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice*

Ji-Li Ma, X. X. Li, Rui-Jin Cheng, Ai‐Xia Zhang, Ju-Kui Xue

Published Dec 30, 2020• 0 citations
Publisher

Abstract

We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.

DOI
10.1088/1674-1056/abd746

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We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.
We study the stability of the continuous waves in the pancake shaped dipolar Bose-Einstein condensate trapped in the strong optical lattice potential with the coexisting local (the short-range s-wave) interaction and nonlocal (the dipole-dipole) interactions between the condensate atoms.The system is modeled by two two-dimensional discrete models derived from the Gross-Pitaevskii equation accounting the dipole-dipole interactions: discrete nonlinear Schrödinger equation with cubic nonlinearity and nonpolynomial Schrödinger equation.The corresponding dispersion relations are calculated analytically and the regions of the modulation instability in the parametric space are summarized into the stability diagrams.
Motivated by the recent experiment [Nature 530 (2016) 194] in which a stable droplet in a dipolar quantum gas has been created by the interaction-induced instability, we focus on the modulation instability of an optically-trapped dipolar Bose–Einstein condensate with three-body interaction. Within the mean-field level, we analytically solve the discrete cubic-quintic Gross–Pitaevskii equation with dipole–dipole interaction loaded into a deep optical lattice and show how combined effects of the three-body interaction and dipole–dipole interaction on the condition of modulational instability. Our results show that the interplay of the three-body interaction and dipole–dipole interaction can dramatically change the modulation instability condition compared with the ordinary Gross–Pitaevskii equation. We believe that the predicted results in this work can be useful for the future possible experiment of loading a Bose–Einstein condensate of 164 Dy atoms with strong magnetic dipole–dipole interaction into an optical lattice.
We study dipolar Bose–Einstein condensate (BEC) solitons in a one-dimensional optical lattice with the combined effect of local and nonlocal nonlinearities. The local nonlinearity is imposed by a magnetic or optical field via the Feshbach (FB) resonance. In contrast, the nonlocal nonlinearity is created by the long-range dipole–dipole interaction among the condensates. The orientations of the dipoles are directed by a rotatable uniform external field, which gives rise to a controllable nonlocal nonlinearity resulting from the angle θ between the direction of the dipole and the elongation of the lattice. If the lattice is sufficiently deep, this model can be described by the Gross–Pitaevskii equation (GPE) with tunable local and nonlocal nonlinear strengths (ggg and θ respectively). The formation, motion, and collision of the solitons in this system are studied by numerical simulations. The combined effect of the local and nonlocal nonlinearities gives a controllable scheme for all these characteristics via the relation between ggg and θ.
We study theoretically the stability of a trapless dipolar Bose-Einstein condensate (BEC) with temporal modulation of the short-range contact interaction. For this aim, through both analytical and numerical methods, we solve a Gross-Pitaevskii equation with both constant and oscillatory forms of the short-range contact interaction along with long-range, nonlocal, dipole-dipole interaction terms. By using the variational method, we discuss the stability of the trapless dipolar BEC with the presence and absence of both constant and oscillatory contact interactions. We show that the oscillatory contact interaction prevents the collapse of the trapless dipolar BEC. We confirm the analytical prediction through numerical simulations. We also study the collective excitations in the system induced by the effective potential due to the oscillating interaction.
The coherent matter waves of a dipolar condensate in deep two-dimensional (2D) tilted and nontilted optical lattices are studied both analytically and numerically. It is shown that, in tilted lattices, by properly designing the sign and the magnitude of the contact interaction and the dipolar interaction, it is possible to control the decoherence of Bloch oscillations. Contrary to the usual short-range interacting Bose system, long-lived Bloch oscillations of the dipolar condensate are achieved when the dipolar interaction, the contact interaction, and the lattice dimension satisfy an analytical condition. Furthermore, we predict that, in untilted lattices, stable coherent 2D moving soliton and breather states of the dipolar condensate exist. This fact is very different from the purely short-range interacting Bose system (where the moving soliton cannot be stabilized in high-dimensional lattices). The dipolar interaction can lead to some novel phenomena that can not appear in short-range interacting BEC system.
We investigate the dynamical instabilities of a one-dimensional ultracold Bose-Bose mixture with long-range dipole-dipole interactions, trapped in deep optical lattices and subject to periodically varying contact interaction. The effect of beyond-mean-field corrections due to quantum fluctuations is considered. In the tight-binding regime, we employ Wannier functions to derive a discrete nonlinear Schrödinger equation that captures the dynamics of the system. Using linear stability analysis coupled to multiple scale expansion, we systematically study the modulational and parametric instabilities of the system in the miscible regime, identifying the conditions under which these instabilities emerge. The corresponding instability domains are found and examined. The roles of long-range interactions and quantum fluctuations are highlighted, demonstrating their significant impact on the stability and dynamics of the lattice system. Our analytical predictions are validated through direct numerical simulations, which confirm the instability diagrams through the effective onset of instabilities and reveal the intricate interplay between interaction strength, quantum fluctuation, and the long-range nature of the dipole-dipole forces. This work provides insights into the control and manipulation of ultracold quantum gases in optical lattices, which have potential applications in quantum simulation and condensed-matter physics.