Bose-Einstein Condensates In Optical Lattices Research Articles

Quantum Phase Transition and Engineering in Two-Component BEC in Optical Lattices

In this paper we review recent progress in studying quantum phase transitions in one- and two-component Bose–Einstein condensates (BEC) in optical lattices. These phase transitions involve the emergence and disappearance of quantum coherence over the whole optical lattice and of linear superposition of macroscopic quantum states. The latter may provide new means to engineer and manipulate novel macroscopic quantum states and novel coherent atomic beams for quantum information processing, quantum computing and other purposes.

Effective-mass analysis of Bose-Einstein condensates in optical lattices: Stabilization and levitation

We investigate the time evolution of a Bose-Einstein condensate in a periodic optical potential. Using an effective mass formalism, we study the equation of motion for the envelope function modulating the Bloch states of the lattice potential. In particular, we show how the negative effective-mass affects the dynamics of the condensate.

Out-of-gap Bose-Einstein solitons in optical lattices

We study the existence and the spectral and collisional properties of bright and dark solitons in a Bose-Einstein condensate (BEC) in optical lattices. Both types of these solitons are located on the background of a matter wave of finite amplitude with characteristic frequency lying outside the forbidden gap. Thus we term our solitons out-of-gap solitons. We discuss feasibility of practical preparation of the background wave to observe these solitons and make connections with recent experiments studying BEC in optical lattices. We prove that the dark out-of-gap solitons are robust against perturbations and numerically verify the possibility of their excitation using a phase imprinting technique.

Bose-Einstein condensates in optical lattices: Band-gap structure and solitons

We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.

Spatiotemporal dynamics of Bose-Einstein condensates in linear- and circular-chain optical lattices

We investigate the spatiotemporal dynamics of Bose-Einstein condensates in optical lattices that have a linear-or a circular-chain configuration with the tunneling couplings between nearest-neighbor lattice sites. A discrete nonlinear Schr\"odinger equation has been solved for various initial conditions and for a definite range of repulsive and attractive interatomic interactions. It is shown that the diversity of the spatiotemporal dynamics of the atomic population distribution such as a macroscopic self-trapping, bright and dark solitons, and symmetry breaking is derived from the positive and negative interatomic interactions. For the circular-chain configuration, two types of rotational modes are obtained as we introduce a definite relation for the initial phase conditions.

Quantum tunneling of Bose-Einstein condensates in optical lattices under gravity.

We investigate the quantum tunneling of Bose-Einstein condensates in optical lattices under gravity in the "Wannier-Stark localization" regime and "Landau-Zener tunneling" regime. Our results agree with experimental data [B. P. Anderson et al., Science 282, 1686 (1998); F. S. Cataliotti et al., Science 293, 843 (2001)]. We obtain the total decay rate which is valid over the entire range of temperatures, and show how it reduces to the appropriate results for the classical thermal activation at high temperatures, the thermally assisted tunneling at intermediate temperatures, and the pure quantum tunneling at low temperatures. We design an experimental protocol to observe this new phenomenon in further experiments.

Bloch waves and bloch bands of Bose-Einstein condensates in optical lattices

Bloch waves and Bloch bands of Bose-Einstein condensates in optical lattices are studied. We provide further evidence for the loop structure in the Bloch band, and compute the critical values of the mean-field interaction strength for the Landau instability and the dynamical instability.

Modulational instability in Bose-Einstein condensates in optical lattices

A self consistent theory of a cigar shaped Bose-Einstein condensate (BEC) periodically modulated by a laser beam is presented. We show, both theoretically and numerically, that modulational instability/stability is the mechanism by which wavefunctions of soliton type can be generated in cigar shaped BEC subject to a 1D optical lattice. The theory explains why bright solitons can exist in BEC with positive scattering length and why condensate with negative scattering length can be stable and give rise to dark solitary pulses.

Landau and dynamical instabilities of the superflow of Bose-Einstein condensates in optical lattices

The superfluidity of Bose-Einstein condensates in optical lattices are investigated. Apart from the usual Landau instability which occurs when a BEC flows faster than the speed of sound, the BEC can also suffer a dynamical instability, resulting in period doubling and other sorts of symmetry breaking of the system. Such an instability may play a crucial role in the dissipative motion of a trapped BEC in an optical lattice recently observed [1].

Bloch oscillations and Zener breakdown in an optical lattice

We study the dynamics of ultracold atoms in an optical lattice under constant bias. After recapitulating the ideas underlying Bloch oscillations and Zener's formula for interband transitions, the Bloch-Zener scenario is tested by means of accurate numerical solutions to the time-dependent Schr?dinger equation. It is shown how two shortcomings of the traditional Zener formula can be removed: the common weak-binding approximation can be circumvented by combining Kohn's insight into the structure of complex energy bands with the Dykhne-Davis-Pechukas description of transitions in terms of adiabatic excursions on analytically continued eigenvalue surfaces, and a usually neglected Stokes phenomenon comes into play when accounting for the finite width of the Brillouin zone. Treating Bose-Einstein condensates in optical lattices within the standard mean-field approximation at zero temperature, the ideal Bloch-Zener scenario turns out to be remarkably stable against the condensate's nonlinear self-interaction. Yet, under appropriate conditions a Bloch-oscillating Gross-Pitaevskii wavepacket reveals characteristic signatures of that nonlinearity, such as sudden phase jumps, slight shifts of the oscillation frequency or non-classical breathing modes. It is suggested that such experimentally detectable signatures will play an important role in future high-precision experiments aiming at the exploration of many-body dynamics in periodic potentials with condensates in optical lattices.

Bose-Einstein condensates in optical lattices: Spontaneous emission in the presence of photonic band gaps

An extended Bose-Einstein condensate (BEC) in an optical lattice provides a kind of periodic dielectric and causes band gaps to occur in the spectrum of light propagating through it. We examine the question whether these band gaps can modify the spontaneous emission rate of atoms excited from the BEC, and whether they can lead to a self-stabilization of the BEC against spontaneous emission. We find that self-stabilization is not possible for BECs with a density in the order of $10^{14}$ cm$^{-3}$. However, the corresponding non-Markovian behavior produces significant effects in the decay of excited atoms even for a homogeneous BEC interacting with a weak laser beam. These effects are caused by the occurrence of an avoided crossing in the photon (or rather polariton) spectrum. We also predict a new channel for spontaneous decay which arises from an interference between periodically excited atoms and periodic photon modes. This new channel should also occur in ordinary periodic dielectrics.

Photonic band gaps and defect states induced by excitations of Bose-Einstein condensates in optical lattices

We study the interaction of a Bose-Einstein condensate, which is confined in an optical lattice, with a largely detuned light field propagating through the condensate. If the condensate is in its ground state it acts as a periodic dielectric and gives rise to photonic band gaps at optical frequencies. The band structure of the combined system of condensed lattice-atoms and photons is studied by using the concept of polaritons. If elementary excitations of the condensate are present, they will produce defect states inside the photonic band gaps. The frequency of localized defect states is calculated using the Koster-Slater model.