Oscillations of a Bose-Einstein condensate in a rapidly contracting circular box

A Bose-Einstein condensate will evolve almost adiabatically if the number of atoms is large enough, even though the trap parameters may be changing rapidly. We demonstrate this by examining a Bose-Einstein condensate in a two-dimensional rapidly contracting circular box. We show that as a result of the contraction the condensate will oscillate about the instantaneous ground state. These oscillations will be small though when the number of atoms is large. Approximate analytic expressions are found for the evolving condensate wavefunction, both before and after the contraction has begun.     

A Rotating Bose-Einstein Condensation in a Toroidal Trap

We have studied the ground state configurations of a rotating Bose-Einstein condensation in a toroidal trap as the radius of the central Gaussian potential expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the
gaussian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.     

Consequence of superfluidity on the expansion of a rotating Bose-Einstein condensate

We propose an easily detectable signature of superfluidity in rotating, vortex-free gaseous Bose-Einstein condensates. We have studied the time evolution of the expansion of such a condensate after it is released from the confining trap. We find that if such a condensate is not initially rotating, then at some moment it will instantaneously achieve a circular cross section. If the condensate is initially rotating its irrotational flow and the conservation of angular momentum prevent the released condensate from attaining a circular cross section, since the instantaneous moment of inertia is then proportional to the asymmetry of this cross section.     

Tunneling control and localization for Bose-Einstein condensates in a frequency modulated optical lattice

The similarity between matter waves in periodic potential and solid-state physics processes has triggered the interest in quantum simulation using Bose-Fermi ultracold gases in optical lattices. The present work evidences the similarity between electrons moving under the application of oscillating electromagnetic fields and matter waves experiencing an optical lattice modulated by a frequency difference, equivalent to a spatially shaken periodic potential. We demonstrate that the tunneling properties of a Bose-Einstein condensate in shaken periodic potentials can be precisely controlled. We take additional crucial steps towards future applications of this method by proving that the strong shaking of the optical lattice preserves the coherence of the matter wavefunction and that the shaking parameters can be changed adiabatically, even in the presence of interactions. We induce reversibly the quantum phase transition to the Mott insulator in a driven periodic potential.     

Bessel型光晶格中自旋-轨道耦合极化激元凝聚的稳态结构

Bessel型光晶格是一种非空间周期性的柱对称的光晶格势场,其兼具无限深势阱和环状势阱的特征,在0阶Bessel光晶格势场中央形成深势阱,而在非0阶Beseel光晶格势场中能形成具有中央势垒的环状浅势阱.极化激元是一种半光半物质的准粒子,该准粒子甚至可以在室温条件下发生玻色-爱因斯坦凝聚相变,形成极化激元凝聚.另外,通过极化激元能级的腔诱导TE-TM分裂能在极化激元凝聚中实现足够强的自旋-轨道耦合作用.极化激元凝聚能在室温条件下实现,在其中又存在自旋-轨道耦合作用,其为量子物理的研究提供了全新的平台.本文把Bessel光晶格势场引入到极化激元凝聚系统,研究了存在自旋-轨道耦合作用下的旋量双组分极化激元凝聚系统的稳态结构.通过求解Gross-Pitaevskii方程给出了极化激元凝聚系统在实验室坐标系和旋转坐标系中极化激元凝聚系统的稳态结构,由于Bessel势场的引入,使得稳态结构更具有多样性.给出了实验室坐标系中在中央深势阱中存在的基础型高斯孤立子、多极孤立子和在环状浅势阱中存在环状孤立子和多极孤立子的稳态结构;给出了旋转坐标系中存在的涡旋环状孤立子,及其由于自旋-轨道相互作用引起的组...     

Vortex formation in a slowly rotating Bose-Einstein condensate confined in a harmonic-plus-Gaussian laser trap

Motivated by the recent experiment at ENS [V. Bretin, S. Stock, Y. Seurin and, J. Dalibard, Phys. Rev. Lett. 92, 050403 (2004)], we study a rotating (non-)interacting atomic Bose-Einstein condensate confined in a harmonic-plus-Gaussian laser trap potential. By adjusting the amplitude of the Gaussian laser potential, one can make quadratic-plus-quartic potential, purely quartic potential, and quartic-minus-quadratic potential. We show that an interacting Bose-Einstein condensate confined in a harmonic-plus-Gaussian laser trap breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We also show that by increasing the amplitude of the Gaussian laser trap, a vortex appears in a slowly rotating Bose-Einstein condensate. Moreover, one can also create a vortex in a slowly rotating non-interacting Bose-Einstein condensate confined in harmonic-plus-Gaussian laser potential.Received: 24 June 2004, Published online: 24 August 2004PACS: 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 05.30.Jp Boson systems     

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.     

Photon-photon gates in Bose-Einstein condensates

It has recently been shown that light can be stored in Bose-Einstein condensates for over a second. Here we propose a method for realizing a controlled phase gate between two stored photons. The photons are both stored in the ground state of the effective trapping potential inside the condensate. The collision-induced interaction is enhanced by adiabatically increasing the trapping frequency and by using a Feshbach resonance. A controlled phase shift of π can be achieved in 1 s or less.     

Dynamics of Bose-Einstein condensates in a one-dimensional optical lattice with double-well potential

We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π-mode self-trapping regime.     

Structural phase transitions of vortex matter in an optical lattice

We consider the vortex structure of a rapidly rotating trapped atomic Bose-Einstein condensate in the presence of a corotating periodic optical lattice potential. We observe a rich variety of structural phases which reflect the interplay of the vortex-vortex and vortex-lattice interactions. The lattice structure is very sensitive to the ratio of vortices to pinning sites and we observe structural phase transitions and domain formation as this ratio is varied.     

Coreless vortex formation in a spinor Bose-Einstein condensate

Coreless vortices were phase imprinted in a spinor Bose-Einstein condensate. The three-component order parameter of F=1 sodium condensates held in a Ioffe-Pritchard magnetic trap was manipulated by adiabatically reducing the magnetic bias field along the trap axis to zero. This distributed the condensate population across its three spin states and created a spin texture. Each spin state acquired a different phase winding which caused the spin components to separate radially.     

Black Holes in Bose–Einstein Condensates

It is shown that there exist both dynamically stable and unstable dilute-gas Bose–Einstein condensates that, in the hydrodynamic limit, exhibit a behavior completely analogous to that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models. We have also simulated the creation of a stable sonic black hole by solving the Gross–Pitaevskii equation numerically for a condensate subject to a trapping potential that is adiabatically deformed. A sonic black hole could in this way be created experimentally with state-of-the-art or planned technology.     

Dynamical instability of the XY spiral state of ferromagnetic condensates

We calculate the spectrum of collective excitations of the XY spiral state prepared adiabatically or suddenly from a uniform ferromagnetic F=1 condensate. For spiral wave vectors past a critical value, spin wave excitation energies become imaginary indicating a dynamical instability. We construct phase diagrams as functions of spiral wave vector and quadratic Zeeman energy.     

Adiabatical stability of density distributions under Vlasov dynamics

It is shown using Vlasov dynamics that the density distribution corresponding to a mean field Bose condensate in an external time dependent potential is adiabatically stable whereas density distributions corresponding to finite temperature are not. Received: 27 February 1998 / Revised: 20 April 1998 / Accepted: 23 April 1998     

Producing Bose-Einstein condensates using optical lattices

We relate the entropies of ensembles of atoms in optical lattices to atoms in simple traps. We then determine which ensembles of lattice-bound atoms will adiabatically transform into a Bose condensate. This shows a feasible approach to Bose condensation without evaporative cooling.     

Delocalizing transition of Bose-Einstein condensates in optical lattices

A Bose-Einstein condensate trapped in a two-dimensional optical lattice exhibits an abrupt transition manifested by the macroscopic wave function changing character from spatially localized to extended. Resulting from a bifurcation, this irreversible transition takes place as the interwell potential barrier is adiabatically decreased below a critical value. This is in sharp contrast to the corresponding one-dimensional case where such a bifurcation is absent and the extent of a localized mode is continuously tunable. We demonstrate how these phenomena can be experimentally explored.     

Robust exponential acceleration in time-dependent billiards

A class of nonrelativistic particle accelerators in which the majority of particles gain energy at an exponential rate is constructed. The class includes ergodic billiards with a piston that moves adiabatically and is removed adiabatically in a periodic fashion. The phenomenon is robust: deformations that keep the chaotic character of the billiard retain the exponential energy growth. The growth rate is found analytically and is, thus, controllable. Numerical simulations corroborate the analytic predictions with good precision. The acceleration mechanism has a natural thermodynamical interpretation and is applied to a hot dilute gas of repelling particles.     

Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas

We demonstrate a reversible conversion of a 6Li2 molecular Bose-Einstein condensate to a degenerate Fermi gas of atoms by adiabatically crossing a Feshbach resonance. By optical in situ imaging, we observe a smooth change of the cloud size in the crossover regime. On the Feshbach resonance, the ensemble is strongly interacting and the measured cloud size is 75(7)% of the one of a noninteracting zero-temperature Fermi gas. The high condensate fraction of more than 90% and the adiabatic crossover suggest our Fermi gas to be cold enough to form a superfluid.     

Dynamics of vortex dipoles in confined Bose-Einstein condensates

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.