Bose-Einstein Condensates In Optical Lattices Research Articles

Chaotic control problem of BEC system based on Hartree–Fock mean field theory

Abstract Due to the difficulty of studying nonlinear quantum systems and the unique composition of Bose–Einstein condensate (BEC) systems, BECs face significant difficulties in solving dynamic analysis and chaotic control problems. Therefore, Hartree–Fock mean field theory is introduced to study the chaotic characteristics, control, and synchronization issues of BEC systems loaded on optical lattices. First, the stability and chaos of BECs in optical lattices were analyzed. Subsequently, constant shift method and activation control were introduced based on the Gross–Pitaevskii equation to achieve control and synchronization of the BEC system. Second, based on the Lyapunov exponent theory, offset parameters are added to BEC chaotic control to achieve control of particle density. Finally, based on the stability theory of linear systems, a control term is introduced to achieve variable analysis of the system’s drive–response system, ensuring that chaotic systems with different initial conditions can still achieve good synchronization and anti-synchronization control. The chaotic problem of BEC system was analyzed using numerical and theoretical methods in the experiment. The effect of adjusting the parameters of the BEC system under the constant shift method is significant. The system exhibits a chaotic state under the Lyapunov exponent, which is mainly concentrated between [3.4, 4.5], demonstrating good system stability. When the offset constant range is [4.21, 5.67], the maximum Lyapunov exponent value is below 0. In the problem of chaotic synchronization, adding activation control causes the system’s time series to exhibit anti-synchronization with spatiotemporal variable variation, while adding control terms leads the system to tend towards synchronization and anti-synchronization with time evolution. The analysis of chaotic control problems in BEC systems can provide reference value and theoretical basis for the dynamic research of quantum physics and related nonlinear systems.

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

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.

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.

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.

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.

Elementary excitation of spin-orbit coupled Bose-Einstein condensates in optical lattice

SynopsisThe phonon mode excitations of spin-orbit (SO) coupled Bose-Einstein condensates (BECs) trapped in an one-dimensional optical lattice are studied and the sound speed of the system is obtained analytically.

Anti-continuum approach on nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattice

This paper aims to analyze the stability of nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattice by anti-continuum approach. It is relatively convenient to employ the anti-continuum method for solving discrete nonlinear Schrödinger equation. This method has shown the ability to produce similar result of analysis of the system stability as produced by other methods. The dynamical stability of the system has been investigated within certain permissible range of parameters.

Dynamical phase diagram of Gaussian wave packets in optical lattices.

We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.

Kibble-Zurek dynamics in an array of coupled binary Bose condensates

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various systems from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs modes whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents, and , which give the static correlation-length critical exponent ν and the dynamic critical exponent z. Our approach provides an efficient way for the simultaneous determination of the critical exponents ν and z for a continuous phase transition.

Interactions and collisions of discrete breathers in two-species Bose-Einstein condensates in optical lattices.

The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of (87)Rb and (41)K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.

Modulational instability of a two-dimensional Bose-Einstein condensate in an optical lattice through a variational approach

We investigate the modulational instability of a two-dimensional Bose-Einstein condensate in a two-dimensional optical lattice using a time-dependent variational approach. Within this framework, we derive the ordinary differential equations for time evolution of the amplitude and phase of modulational perturbations. Analyzing these equations and the Hamiltonian of the system, we obtain the modulational instability criterion.

First principle explanation of phase transition for Bose-Einstein condensates in optical lattices

In this paper we consider Bose-Einstein condensates (BECs) in one-, two- and three-dimension lattice potentials. The key argument for the explanation of the transition from Superfluidity phase to Mott-Insulator phase is suggested to be the spontaneous symmetry breaking effect which occurs for critical values of the ratio between the on-site interaction term and the hopping matrix element. Such an effect can be directly seen in the Gross-Pitaevskii equation with double-well potentials and it also explains the different behavior between one-dimensional models and two/three-dimensional models.

Nonlinear phononics using atomically thin membranes.

Phononic crystals and acoustic metamaterials are used to tailor phonon and sound propagation properties by utilizing artificial, periodic structures. Analogous to photonic crystals, phononic band gaps can be created, which influence wave propagation and, more generally, allow engineering of the acoustic properties of a system. Beyond that, nonlinear phenomena in periodic structures have been extensively studied in photonic crystals and atomic Bose-Einstein condensates in optical lattices. However, creating nonlinear phononic crystals or nonlinear acoustic metamaterials remains challenging and only few examples have been demonstrated. Here, we show that atomically thin and periodically pinned membranes support coupled localized modes with nonlinear dynamics. The proposed system provides a platform for investigating nonlinear phononics.