Pulsating instability of a Bose-Einstein condensate in an optical lattice

We find numerically that in the limit of weak atom-atom interactions a Bose-Einstein condensate in an optical lattice may develop a pulsating dynamical instability in which the atoms nearly periodically form a peak in the occupation numbers of the lattice sites, and then return to the unstable initial state. Multiple peaks behaving similarly are also found. Simple arguments show that the pulsating instability is a remnant of integrability, and give a handle on the relevant physical scales.     

Low-acceleration instability of a Bose-Einstein condensate in an optical lattice

We study a Bose-Einstein condensate in a one-dimensional accelerated optical lattice using the mean-field version of the Bose-Hubbard model. Reminiscent of recent experiments [M. Cristiani et al., Opt. Express 12, 4 (2004)], we find a new type of an instability in this system that occurs in the limit when the acceleration is small.     

Klein tunneling of a quasirelativistic Bose-Einstein condensate in an optical lattice

A proof-of-principle experiment simulating effects predicted by relativistic wave equations with ultracold atoms in a bichromatic optical lattice that allows for a tailoring of the dispersion relation is reported. We observe the analog of Klein tunneling, the penetration of relativistic particles through a potential barrier without the exponential damping that is characteristic for nonrelativistic quantum tunneling. Both linear (relativistic) and quadratic (nonrelativistic) dispersion relations are investigated, and significant barrier transmission is observed only for the relativistic case.     

Phase diagram for a Bose-Einstein condensate moving in an optical lattice

The stability of superfluid currents in a system of ultracold bosons was studied using a moving optical lattice. Superfluid currents in a very weak lattice become unstable when their momentum exceeds 0.5 recoil momentum. Superfluidity vanishes already for zero momentum as the lattice deep reaches the Mott insulator (MI) phase transition. We study the phase diagram for the disappearance of superfluidity as a function of momentum and lattice depth between these two limits. Our phase boundary extrapolates to the critical lattice depth for the superfluid-to-MI transition with 2% precision. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed.     

Superfluid properties of a Bose-Einstein condensate in an optical lattice confined in a cavity

We study the effect of a one dimensional optical lattice in a cavity field with quantum properties on the superfluid dynamics of a Bose-Einstein condensate (BEC). In the cavity the influence of atomic backaction and the external driving pump become important and modify the optical potential. Due to the coupling between the condensate wavefunction and the cavity modes, the cavity light field develops a band structure. This study reveals that the pump and the cavity emerges as a new handle to control the superfluid properties of the BEC.     

Dynamical vortex phases in a Bose-Einstein condensate driven by a rotating optical lattice

We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. The onset of these different phases is described by the force balance of a driving force, a pinning force, and vortex-vortex interactions. In particular, when the optical lattice rotates faster than the condensate, an incommensurate effect leads to a vortex-liquid phase supported by the competition between the driving force and the dissipation.     

光格中旋量玻色-爱因斯坦凝聚的高阶非线性孤子激发

研究了一维光格中旋量玻色-爱因斯坦凝聚体的高阶非线性作用下的孤子激发,得出了用椭圆积分表示的明孤子解和特定参数条件下的暗孤子解析解,并求得了能量表达式.     

Creation of solitons and vortices by bragg reflection of Bose-Einstein condensates in an optical lattice

We study the dynamics of Bose-Einstein condensates in an optical lattice and harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semiclassical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection. For high atom densities, the first Bragg reflection generates a train of solitons and vortices, which destabilize the condensate and trigger explosive expansion. At lower densities, soliton and vortex formation requires multiple Bragg reflections, and damps the center-of-mass motion.     

变分法研究二维光晶格中玻色-爱因斯坦凝聚的调制不稳定性

利用含时变分法研究了二维光晶格中准二维玻色-爱因斯坦凝聚中的调制不稳定性. 在平均场近似下, 由准二维Gross-Pitaevskii方程出发, 利用变分法给出了调制波振幅和相位所满足的时间演化方程, 通过求解时间演化方程和能量分析法给出了发生调制不稳定性的条件, 决定于平面波振幅, 晶格强度, 调制波的波矢量和原子之间的两体相互作用.     

Self-organization of a Bose-Einstein condensate in an optical cavity

The spatial self-organization of a Bose-Einstein condensate (BEC) in a high-finesse linear optical cavity is discussed. The condensate atoms are laser-driven from the side and scatter photons into the cavity. Above a critical pump intensity the homogeneous condensate evolves into a stable pattern bound by the cavity field. The transition point is determined analytically from a mean-field theory. We calculate the lowest lying Bogoliubov excitations of the coupled BEC-cavity system and the quantum depletion due to the atom-field coupling.     

Controlling chaos in a Bose-Einstein condensate loaded into a moving optical lattice potential

The spatial structure of a Bose-Einstein condensate loaded into an optical lattice potential is investigated, and spatially chaotic distributions of the condensates are revealed. By means of changing of the s-wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s-wave scattering lengths only if the maximal Lyapunov exponent of the system is negative. The text was submitted by the authors in English.     

Imprinting vortices in a Bose-Einstein condensate using topological phases

Vortices were imprinted in a Bose-Einstein condensate using topological phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were transformed from a nonrotating state to one with quantized circulation by adiabatically inverting the magnetic bias field along the trap axis. Using surface wave spectroscopy, the axial angular momentum per particle of the vortex states was found to be consistent with 2 variant Planck's over 2pi or 4 variant Planck's over 2pi, depending on the hyperfine state of the condensate.     

Effect of the lattice alignment on Bloch oscillations of a Bose-Einstein condensate in a square optical lattice

We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study stability of these oscillations for non-vanishing interactions, which is shown to depend on an alignment of the force vector with respect to the lattice crystallographic axes. If the force is aligned along any of the axes, the mean field approach can be used to identify the stability conditions. On the contrary, for a misaligned force one has to employ the microscopic approach, which predicts periodic modulation of Bloch oscillations in the limit of a large forcing.     

Fano blockade by a bose-einstein condensate in an optical lattice

We study the transport of atoms across a localized Bose-Einstein condensate in a one-dimensional optical lattice. For atoms scattering off the condensate, we predict total reflection as well as full transmission for certain parameter values on the basis of an exactly solvable model. The findings of analytical and numerical calculations are interpreted by a tunable Fano-like resonance and may lead to interesting applications for blocking and filtering atom beams.     

Nucleation and growth of vortices in a rotating Bose-Einstein condensate

An analytic solution of the Gross-Pitaevskii equation for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The similarity of this behavior and mesoscopic superconductors is discussed.     

Coherence properties of a Bose-Einstein condensate in an optical superlattice

We study the effect of a one dimensional optical superlattice on the superfluid properties (superfluid fraction, number squeezing, dynamic structure factor) and the quasi-momentum distribution of the Mott-insulator. We show that due to the secondary lattice, there is a decrease in the superfluid fraction and the number fluctuation. The dynamic structure factor which can be measured by Bragg spectroscopy is also suppressed due to the addition of the secondary lattice. The visibility of the interference pattern (the quasi-momentum distribution) of the Mott-insulator is found to decrease due to the presence of the secondary lattice. Our results have important implications in atom interferometry and quantum computation in optical lattices.     

Ultraslow optical waveguiding in an atomic Bose-Einstein condensate

We investigate waveguiding of ultraslow light pulses in an atomic Bose-Einstein condensate. We show that under the conditions of off-resonant electromagnetically induced transparency, waveguiding with a few ultraslow modes can be realized. The number of modes that can be supported by the condensate can be controlled by means of experimentally accessible parameters. Propagation constants and the mode conditions are determined analytically using a Wentzel-Kramers-Brillouin analysis. Mode profiles are found numerically.     

Spatial chaos of trapped Bose-Einstein condensate in one-dimensional weak optical lattice potential

The spatially chaotic attractor in an elongated cloud of Bose-Einstein condensed atoms perturbed by a weak optical lattice potential is studied. The analytical insolvability and numerical incomputability of the atomic number density are revealed by a perturbed solution that illustrates the unpredictability of the deterministic chaos. Although this could lead the nonphysical explosion and unboundedness to the numerical solution, the theoretical analysis offers a criterion to avoid them. Moreover, the velocity field is investigated that exhibits the superfluid property of the chaotic system.     

Two-dimensional Bose-Einstein condensate in an optical surface trap

We report on the creation of a two-dimensional Bose-Einstein condensate of cesium atoms in a gravito-optical surface trap. The condensate is produced a few microm above a dielectric surface on an evanescent-wave atom mirror. After evaporative cooling by all-optical means, expansion measurements for the tightly confined vertical motion show energies well below the vibrational energy quantum. The presence of a condensate is observed in two independent ways by a magnetically induced collapse at negative scattering length and by measurements of the horizontal expansion.     

Quantum fluctuations and collective oscillations of a Bose-Einstein condensate in a 2D optical lattice

We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations. Using the hydrodynamic theory of superfluids, we calculate the corresponding shift of the collective frequencies of a harmonically trapped gas. We find that this correction can be of the order of a few percent and hence easily measurable in current experiments. The behavior of the quantum depletion of the condensate is also discussed.