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Chinese Physics Letters

Subdiffusion of Dipolar Gas in One-Dimensional Quasiperiodic Potentials

Xiaodong Bai, Ju-Kui Xue

Published Jan 1, 2015• 6 citations
Publisher

Abstract

Considering the discrete nonlinear Schrödinger model with dipole-dipole interactions (DDIs), we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found: both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction (λ 1 ) and DDI (λ 2 ) satisfy λ 1 ≳ 2λ 2 , the property of the subdiffusion depends only on contact interaction; when λ 1 ≳ 2λ 2 , the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v* for different values of contact interaction and DDI. When the disorder strength v ≥ v*, the wave packet is localized. On the contrary, when the disorder strength v ≤ v*, the wave packet is subdiffusive.

DOI
10.1088/0256-307x/32/1/010302

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Considering the discrete nonlinear Schrödinger model with dipole-dipole interactions (DDIs), we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found: both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction (λ 1 ) and DDI (λ 2 ) satisfy λ 1 ≳ 2λ 2 , the property of the subdiffusion depends only on contact interaction; when λ 1 ≳ 2λ 2 , the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v* for different values of contact interaction and DDI. When the disorder strength v ≥ v*, the wave packet is localized. On the contrary, when the disorder strength v ≤ v*, the wave packet is subdiffusive.
The disorder-free localization that occurred in the study of relaxation dynamics in far-from-equilibrium quantum systems has been widely explored. Here we investigate the interplay between the dipole-dipole interaction (DDI) and disorder in the hard-core polar bosons in a one-dimensional lattice. We find that the localized dynamics will eventually thermalize in the clean gas but can be stabilized with the existence of a small disorder proportional to the inverse of DDI strength. From the effective dimer Hamiltonian, we show that the effective second-order hopping of quasiparticles between nearest-neighbor sites is suppressed by the disorder with strength similar to the effective hopping amplitude. The significant gap between the largest two eigenvalues of the entanglement spectrum indicates the dynamical confinement. We also find that the disorder related sample-to-sample fluctuation is suppressed by the DDI. Finally, we extend our research from the uncorrelated random disorder to the correlated quasiperiodic disorder and from the two-dimer model to the half-filling system, obtaining similar results.
Dipolar interactions support the formation of intersite soliton molecules in a stack of quasi-one-dimensional (quasi-1D) traps. We show that the stability and properties of individual solitons and soliton molecules in such a geometry crucially depend on the interplay between contact and dipolar interactions. In particular, two different quasi-1D soliton regimes are possible: a one-dimensional (1D) soliton characterized by purely repulsive dipole-dipole interactions (DDI) and a three-dimensional (3D) soliton for which a sufficiently large dipole moment renders the DDI attractive. Furthermore, we find that in contrast to the dimers of polar molecules the soliton dimers exhibit a nontrivial behavior of the elementary excitations that stems from the competition between onsite and intersite DDI. Finally, we prove the existence of soliton trimers in a regime where molecular trimers do not occur. We demonstrate that the soliton molecules that we report are well feasible under realistic experimental conditions.
We study the behavior of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andr\`e model for particles in a quasiperiodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wave packet as well as the interplay between two competing effects of the interaction, namely, self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters even for weak interaction. Conversely, if the diffusion starts from a Gaussian wave packet, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.
In a recent experiment, Anderson localization was observed directly for non-interacting Bose-Einstein Condensate in one dimension. The experiment was performed using quasiperiodic optical lattice. Their system can be described by the one-dimensional noninteracting Aubry-Andr�e model. This model which simulates disorder with its quasiperiodic potential shows transition from extended to localised states at a critical disorder strength. The ground state gets localised around a single point for disorder larger than the critical value. We find that while inverse participation ratio increases as we increase disorder and rises to one in insulator phase, super uid fraction decreases as we increase disorder and goes to zero sharply in the insulator phase . When we introduce weak repulsive interaction for Bose gas in the model at the mean field level, we see that the ground-state shows multiple-site localization for certain disorder range, which lies above the critical value. For given interaction strength, we find that the inverse participation ratio increases slowly and super uid fraction decreases slowly as we increase disorder. Moreover, by representing our model as a classical two-dimensional nonlinear Hamiltonian map, we distinguish between localised and extended states by studying the trajectories in phase-space. Using this, we find out the localization length of eigenstates as a function of disorder for non-interacting model. Further, we study the time-evolution of a wave-packet in different regimes of disorder and see the effect of interaction on it.
Dipolar quantum gases, encompassing atoms and molecules with significant dipole moments, exhibit unique long-range and anisotropic dipole-dipole interactions (DDI), distinguishing them from systems dominated by short-range contact interactions. This review explores their behavior across dimensions, focusing on magnetic atoms in quasi-2D in comparison to 3D. In 3D, strong DDI leads to phenomena like anisotropic superfluidity, quantum droplets stabilized by Lee-Huang-Yang corrections, and supersolid states with density modulations. In 2D, we discuss a new scenario where DDI induces angle-dependent Berezinskii-Kosterlitz-Thouless transitions and potential supersolidity, as suggested by recent experimental realizations of strongly dipolar systems in quasi-2D geometries. We identify key challenges for future experimental and theoretical work on strongly dipolar 2D systems. The review concludes by highlighting how these unique 2D dipolar systems could advance fundamental research as well as simulate novel physical phenomena.
We investigate the coherence of correlated dipolar gas in the presence of disorder within a three-site Bose–Hubbard model. We show that the interplay between the on-site interaction, the inter-site dipole–dipole interactions (DDI) and the disorder exhibits new and interesting coherence characters that cannot take place in a non-dipolar system. The ratio between the on-site interaction and DDI plays a dominant role in the phase coherence. The resonance character of the coherence against both disorder and interactions emerges. DDI can enhance the coherence at certain values of the disorder and on-site interaction. In the coherence region, the enhancement of the coherence by disorder in a dipolar system is more significant than that in a non-dipolar system. In particular, the on-site interaction and DDI together can enhance the coherence even in the clean dipolar system (i.e. a dipolar system without disorder). However, without the on-site interaction, disorder, DDI or both together suppress the coherence. Furthermore, the relationship between the coherence and the energy gap and the compressibility of the system is also discussed.