Condensates In Optical Lattices Research Articles

Energy spectrum and superfluidity breakdown of Bose–Einstein condensates in optical lattice under density-dependent artificial gauge field

Nonlinear feedback between the gauge field and the material field can yield novel quantum phenomena. Here, the interplay between a density-dependent artificial gauge field and Bose–Einstein condensates (BECs) trapped in an optical lattice is studied. The energy spectrum and superfluidity represented by energetic and dynamical stabilities of the system are systematically discussed. A density-dependent artificial gauge field with a back-action between the BECs dynamics and the gauge field induces an effective atomic interaction that depends on the quasi-momentum and density of the condensates, resulting in a symmetry-broken energy spectrum and exotic stability phase diagram, that is, the system is only stable in a certain range of atoms density and under a limited lattice strength. The density-dependent artificial gauge field changes the sequence for the emergence of energetic and dynamical instability and the regimes of the energetic and dynamical instabilities are significantly separated, offering an efficient way to examine the energetic and dynamical instabilities of superfluids separately. In particular, the density-dependent artificial gauge field, as a mechanism for transferring momentum to the fluid, results in dynamic instability of the condensates even in free space. Our results provide deep insights into the dynamical response of superfluid systems to gauge fields and have potential applications for the coherent control of exotic superfluid states.

Wannier solitons in spin-orbit-coupled Bose-Einstein condensates in optical lattices with a flat band

Wannier solitons in spin-orbit-coupled Bose-Einstein condensates in optical lattices with a flat band

Two-dimensional anisotropic vortex–bright soliton and its dynamics in dipolar Bose–Einstein condensates in optical lattice

We study construction and dynamics of two-dimensional (2D) anisotropic vortex–bright (VB) soliton in spinor dipolar Bose–Einstein condensates confined in a 2D optical lattice (OL), with two localized components linearly mixed by the spin–orbit coupling and long-range dipole–dipole interaction (DDI). It is found that the OL and DDI can support stable anisotropic VB soliton in the present setting for arbitrarily small value of norm N. We then present a new method via examining the mean square error of norm share of bright component to implement stability analysis. It is revealed that one can control the stability of anisotropic VB soliton only by adjusting OL depth for a fixed DDI. In addition, the dynamics of the anisotropic VB soliton was studied by applying the kick to them. The mobility of the single kicked VB soliton is Rabbi-like oscillation. However, for the collision dynamics of two kicked anisotropic VB solitons, their properties mainly depend on their initial distance and OL, and they can realize the transition from the bright component to the vortex component. Our work may provide a convenient way to prepare and manipulate anisotropic VB soliton in high-dimensional space.

Phase-space distributions of Bose–Einstein condensates in an optical lattice: optimal shaping and reconstruction

We apply quantum optimal control to shape the phase-space distribution of Bose–Einstein condensates in a one-dimensional optical lattice. By a time-dependent modulation of the lattice position, determined from optimal control theory, we prepare, in the phase space of each lattice site, translated and squeezed Gaussian states, and superpositions of Gaussian states. Complete reconstruction of these non-trivial states is performed through a maximum likelihood state tomography. As a practical application of our method to quantum simulations, we initialize the atomic wavefunction in an optimal Floquet-state superposition to enhance dynamical tunneling signals.

Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems

Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena and a deeper understanding of them. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice1,2. However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to two-dimensional (2D) systems. Here we introduce an imaging approach where matter wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in three-dimensional (3D) systems. By combining the site-resolved imaging with magnetic resonance techniques for local addressing of individual lattice sites, we demonstrate full accessibility to 2D local information and manipulation in 3D systems. We employ the high-resolution images for precision thermodynamics of Bose–Einstein condensates in optical lattices as well as studies of thermalization dynamics driven by thermal hopping. The sub-lattice resolution is demonstrated via quench dynamics within the lattice sites. The method opens the path for spatially resolved studies of new quantum many-body regimes, including exotic lattice geometries or sub-wavelength lattices3–6, and paves the way for single-atom-resolved imaging of atomic species, where efficient laser cooling or deep optical traps are not available, but which substantially enrich the toolbox of quantum simulation of many-body systems.

Analytical results for the superflow of spin-orbit-coupled Bose-Einstein condensates in optical lattices

In this paper, we show that for sufficiently strong atomic interactions, there exist analytical solutions of current-carrying nonlinear Bloch states at the Brillouin zone edge to the model of spin-orbit-coupled Bose-Einstein condensates (BECs) with symmetric spin interaction loaded into optical lattices. These simple but generic exact solutions provide an analytical demonstration of some intriguing properties which have neither an analog in the regular BEC lattice systems nor in the uniform spin-orbit-coupled BEC systems. It is an analytical example for understanding the superfluid and other related properties of the spin-orbit-coupled BEC lattice systems.

Superfluidity breakdown of Rabi-coupled two-component Bose-Einstein condensates in optical lattices

We demarcate the unstable regimes of superfluids in a Rabi-coupled two-component Bose-Einstein condensate in the presence of optical lattices. We find that the Rabi coupling can stabilize superfluids. A significant separation between Landau and dynamical instabilities is presented in a Rabi-coupled Zeeman lattice.

Polarized and unpolarized phases of spin-orbit-coupled Bose-Einstein condensates in optical lattice

We investigate the phase transition of the Bose-Einstein condensates with equal-weight Rashba and Dresselhaus spin-orbit coupling trapped in one-dimensional optical lattice. Based on the variational and two-mode approximation, the critical condition for phase transition between polarized and unpolarized Bloch wave phase is obtained analytically for the first time, which explicitly reveals rich competitive relationship among spin-orbit coupling, optical lattice and atomic interactions in determining the phase transition of the system. It is shown that the change of the energy minima and the phase transition point by the optical lattice depends on the atomic interactions and spin-orbit coupling. Our results provide a theoretical evidence for deep understanding of the competition mechanism between the optical lattice and spin-orbit coupling for the ground state phase transition of spin-orbit-coupled Bose-Einstein condensates in optical lattice.

Nonlinear energy band structure of spin-orbit coupled Bose-Einstein condensates in optical lattice

<sec>In a recent experiment [Hamner C, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1103/PhysRevLett.114.070401"> 2015 <i>Phys. Rev. Lett.</i> <b>114</b> 070401</ext-link>], spin-orbit coupled Bose-Einstein condensates in a translating optical lattice have been successfully prepared into any Bloch band, and directly proved to be the lack of Galilean invariance in the presence of the spin-orbit coupling. The energy band structure of the system becomes complicated because of the lack of Galilean invariance. At present, the energy band structure of the spin-orbit coupled Bose-Einstein condensates in optical lattice is still an open issue, especially the theoretical evidence for the in-depth understanding of the competition mechanism among the spin-orbit coupling, the Raman coupling, the optical lattice and the atomic interactions of the nonlinear energy band structure has not been clear yet.</sec><sec>In this paper, based on the two-mode approximation and variational analysis, the nonlinear energy band structure and current density of the spin-orbit coupled Bose-Einstein condensates in the one-dimensional optical lattice are investigated. We find that when the spin-orbit coupling, the Raman coupling, the optical lattice, and the atomic interactions satisfy certain conditions, a loop structure in the Brillouin zone edge will emerge. The critical condition for the loop structure emerging in the Brillouin zone edge is obtained in a parameter space. The Raman coupling and the optical lattice suppress the emergence of the loop structure, while the spin-orbit coupling and the atomic interactions promote the emerging of the loop structure and make the energy band structure more complex. Interestingly, the atomic interactions can make the loop structure occur at both the higher-lying bands and the lowest energy band. The energy band structure is closely related to the current density of the system. The spin-orbit coupling causes the current density to be strongly asymmetric and leads the current density distributions of different spin states to be separated from each other in the momentum space near the boundary of the Brillouin zone. The optical lattice strength and the Raman coupling can weaken the asymmetry. The appearance of loop structure breaks the Bloch oscillation and gives rise to the Landau-Zener tunneling. The separation of the current density distributions of different spin states in the momentum space means the emergence of the spin exchange dynamics. Our results are beneficial to the in-depth understanding of the nonlinear dynamics of the spin-orbit coupled Bose-Einstein condensates in optical lattice.</sec>

Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices

Bogoliubov excitations of Bose-Einstein condensates in optical lattices may possess band topology in analogous to topological insulators in class AII of fermions. Using the language of the Krein-space theory, this topological property is shown to be protected by a pseudo-time-reversal symmetry that is pseudo-antiunitary and squares to $-1$, with the associated bulk topological invariant also being a $\mathbb Z_2$ index. We construct three equivalent expressions for it, relating to the Pfaffian, the pseudo-time-reversal polarization, and most practically, the Wannier center flow, all adopted from the fermionic case, defined here with respect to the pseudo inner product. In the presence of an additional pseudo-unitary and pseudo-Hermitian inversion symmetry, a simpler expression is derived. We then study two toy models feasible on cold atom platforms to numerically confirm the bulk-boundary correspondence. The Krein-space approach developed in this work is a universal formalism to study all kinds of symmetry-protected topological bosonic Bogoliubov bands.

Stripe and supersolid phases of spin–orbit coupled spin-2 Bose–Einstein condensates in an optical lattice

We study the ground-state phases of two-dimensional spin–orbit coupled spin-2 Bose–Einstein condensates in a one-dimensional spin-dependent optical lattice. Due to the competition among optical lattice, spin–orbit coupling and spin-exchange interaction, the exotic ground-state phases are found, i.e. three types of the stripe phases and three types of the supersolid phases. The spin-exchange interaction can adjust the direction of the stripe in the stripe phase and generate various vortex lattice structures in the supersolid phase, which shows that the spin-exchange interaction plays an important role in the formation of the stripe and supersolid phases of spin–orbit coupled spin-2 Bose–Einstein condensates in an optical lattice.

Tunable spinful matter wave valve

We investigate the transport problem that a spinful matter wave is incident on a strong localized spin-orbit-coupled Bose-Einstein condensate in optical lattices, where the localization is admitted by atom interaction only existing at one particular site, and the spin-orbit coupling arouse spatial rotation of the spin texture. We find that tuning the spin orientation of the localized Bose-Einstein condensate can lead to spin-nonreciprocal/spin-reciprocal transport, meaning the transport properties are dependent on/independent of the spin orientation of incident waves. In the former case, we obtain the conditions to achieve transparency, beam-splitting, and blockade of the incident wave with a given spin orientation, and furthermore the ones to perfectly isolate incident waves of different spin orientation, while in the latter, we obtain the condition to maximize the conversion of different spin states. The result may be useful to develop a novel spinful matter wave valve that integrates spin switcher, beam-splitter, isolator, and converter. The method can also be applied to other real systems, e.g., realizing perfect isolation of spin states in magnetism, which is otherwise rather difficult.

Formation of nonlinearX-waves in condensed matter systems

X-waves are an example of a localized wave packet solution of the homogeneous wave equation, and can potentially arise in any area of physics relating to wave phenomena, such as acoustics, electromagnetism, or quantum mechanics. They have been predicted in condensed matter systems such as atomic Bose-Einstein condensates in optical lattices, and were recently observed in exciton-polariton condensates. Here we show that polariton X-waves result from an interference between two separating wave packets that arise from the combination of a locally hyperbolic dispersion relation and nonlinear interactions. We show that similar X-wave structures could also be observed in expanding spin-orbit coupled Bose-Einstein condensates.

Multiple-time-scale analysis for pinned breathers in Bose-Hubbard chains.

Localized and pinned discrete breathers in Bose-Einstein condensates in optical lattices or in arrays of optical waveguides oscillate with frequencies which are much higher than those present in the spectrum of the background. Hence, the interaction between localized breathers and their surroundings is extremely weak leading to a multiple-time-scale perturbation expansion. We identify the leading order in the asymptotic expansion of the breather amplitude which does not average to zero after one full oscillation. The reduced model predicts a lower bound of the breather drift times and explains the topological differences between breathers in dimers, trimers, and in spatially extended one-dimensional lattices even in the presence of transport from boundary heat-baths. These analytical boundaries hold true for lattices of any length, due to the highly localized nature of breathers.

Modulated amplitude waves with non-trivial phase of multi-component Bose–Einstein condensates in optical lattices

Modulated amplitude waves with non-trivial phase of multi-component Bose–Einstein condensates in optical lattices

Absence of Landau damping in driven three-component Bose\u2013Einstein condensate in optical lattices

We explore the quantum many-body physics of a three-component Bose-Einstein condensate in an optical lattice driven by laser fields in V and Λ configurations. We obtain exact analytical expressions for the energy spectrum and amplitudes of elementary excitations, and discover symmetries among them. We demonstrate that the applied laser fields induce a gap in the otherwise gapless Bogoliubov spectrum. We find that Landau damping of the collective modes above the energy of the gap is carried by laser-induced roton modes and is considerably suppressed compared to the phonon-mediated damping endemic to undriven scalar condensates

Damping-free collective oscillations of a driven two-component Bose gas in optical lattices

We explore quantum many-body physics of a driven Bose-Einstein condensate in optical lattices. The laser field induces a gap in the generalized Bogoliubov spectrum proportional to the effective Rabi frequency. The lowest lying modes in a driven condensate are characterized by zero group velocity and non-zero current. Thus, the laser field induces roton modes, which carry interaction in a driven condensate. We show that collective excitations below the energy of the laser-induced gap remain undamped, while above the gap they are characterized by a significantly suppressed Landau damping rate.

Parametric instabilities in resonantly-driven Bose–Einstein condensates

Shaking optical lattices in a resonant manner offers an efficient and versatile method to devise artificial gauge fields and topological band structures for ultracold atomic gases. This was recently demonstrated through the experimental realization of the Harper–Hofstadter model, which combined optical superlattices and resonant time-modulations. Adding inter-particle interactions to these engineered band systems is expected to lead to strongly-correlated states with topological features, such as fractional Chern insulators. However, the interplay between interactions and external time-periodic drives typically triggers violent instabilities and uncontrollable heating, hence potentially ruling out the possibility of accessing such intriguing states of matter in experiments. In this work, we study the early-stage parametric instabilities that occur in systems of resonantly-driven Bose–Einstein condensates in optical lattices. We apply and extend an approach based on Bogoliubov theory (Lellouch et al 2017 Phys. Rev. X 7 021015) to a variety of resonantly-driven band models, from a simple shaken Wannier–Stark ladder to the more intriguing driven-induced Harper–Hofstadter model. In particular, we provide ab initio numerical and analytical predictions for the stability properties of these topical models. This work sheds light on general features that could guide current experiments to stable regimes of operation.

Modulational Instability of Dipolar Bose–Einstein Condensates in Optical Lattices with Three-Body Interactions**Supported by the National Natural Science Foundation of China under Grant No 11647017, and the Science Research Fund of Shaanxi University of Science and Technology under Grant No BJ16-03.

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 164Dy atoms with strong magnetic dipole–dipole interaction into an optical lattice.

Bloch oscillations of a Bose-Einstein condensate in a cavity-induced optical lattice

This article complements previous work on the nondestructive observation of Bloch oscillations of a Bose-Einstein condensate in an optical lattice formed inside a high-finesse optical cavity [H. Ke\ss{}ler et al., New J. Phys. 18, 102001 (2016)]. We present measurements showing that the observed Bloch frequency is independent of the atom number and hence the cooperative coupling strength, the intracavity lattice depth, and the detuning between the external pump light and the effective cavity resonance. We find that in agreement with theoretical predictions, despite the atom-cavity dynamics, the value of the Bloch frequency agrees with that expected in conventional optical lattices, where it solely depends on the sizes of the force and the lattice constant. We also show that Bloch oscillations are observed in a self-organized two-dimensional lattice, which is formed if, instead of axially pumping the cavity through one of its mirrors, the Bose-Einstein condensate is irradiated by an optical standing wave oriented perpendicularly with respect to the cavity axis. For this case, however, excessive decoherence prevents a meaningful quantitative assessment.