Quasi-Nambu-Goldstone modes in Bose-Einstein condensates

We show that quasi-Nambu-Goldstone (NG) modes, which play prominent roles in high energy physics but have been elusive experimentally, can be realized with atomic Bose-Einstein condensates. The quasi-NG modes emerge when the symmetry of a ground state is larger than that of the Hamiltonian. When they appear, the conventional vacuum manifold should be enlarged. Consequently, topological defects that are stable within the conventional vacuum manifold become unstable and decay by emitting the quasi-NG modes. Contrary to conventional wisdom, however, we show that the topological defects are stabilized by quantum fluctuations that make the quasi-NG modes massive, thereby suppressing their emission.     

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.     

Bose-Einstein condensates in rotating lattices

Strongly interacting bosons in a two-dimensional rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order quantum phase transitions between states of different symmetries are observed at discrete rotation rates. For the square lattice we study, there are four possible ground-state symmetries.     

Spin-orbit-coupled dipolar Bose-Einstein condensates

We propose an experimental scheme to create spin-orbit coupling in spin-3 Cr atoms using Raman processes. By employing the linear Zeeman effect and optical Stark shift, two spin states within the ground electronic manifold are selected, which results in a pseudospin-1/2 model. We further study the ground state structures of a spin-orbit-coupled Cr condensate. We show that, in addition to the stripe structures induced by the spin-orbit coupling, the magnetic dipole-dipole interaction gives rise to the vortex phase, in which a spontaneous spin vortex is formed.     

Bose-Einstein condensates in strongly disordered traps

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semiquantitative analysis we find the size, shape, and excitation energy as a function of the disorder strength. For positive scattering length and sufficiently strong disorder the condensate decays into fragments each of the size of the Larkin length L. This state is stable over a large range of particle numbers. The frequency of the breathing mode scales as 1/L(2). For negative scattering length a condensate of size L may exist as a metastable state. These findings are generalized to anisotropic traps.     

Mesoscopic molecular ions in Bose-Einstein condensates

We study the possible formation of large (mesoscopic) molecular ions in an ultracold degenerate bosonic gas doped with charged particles (ions). We show that the polarization potentials produced by the ionic impurities are capable of capturing hundreds of atoms into loosely bound states. We describe the spontaneous formation of these hollow molecular ions via phonon emission and suggest an optical technique for coherent stimulated transitions of condensate atoms into a specific bound state. These results open up new possibilities for manipulating tightly confined ensembles.     

Uniting Bose-Einstein condensates in optical resonators

The relative phase of two initially independent Bose-Einstein condensates can be laser cooled to unite the two condensates by putting them into a ring cavity and coupling them with an internal Josephson junction. First, we show that this phase cooling process already appears within a semiclassical model. We calculate the stationary states, find regions of bistable behavior, and suggest a Ramsey-type experiment to measure the buildup of phase coherence between the condensates. We also study quantum effects and imperfections of the system.     

Three-dimensional solitons in two-component Bose-Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.     

Stable skyrmions in two-component Bose-Einstein condensates

We show that stable Skyrmions exist in two-component atomic Bose-Einstein condensates, in the regime of phase separation. Using full three-dimensional simulations we find the stable Skyrmions with topological charges Q = 1 and 2, and compute their properties. With reference to these computations we suggest the salient features of an experimental setup in which they might realized.     

Spin-orbit coupled spinor Bose-Einstein condensates

An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.     

Time reversal of Bose-Einstein condensates

Using Gross-Pitaevskii equation, we study the time reversibility of Bose-Einstein condensates (BEC) in kicked optical lattices, showing that in the regime of quantum chaos, the dynamics can be inverted from explosion to collapse. The accuracy of time reversal decreases with the increase of atom interactions in BEC, until it is completely lost. Surprisingly, quantum chaos helps to restore time reversibility. These predictions can be tested with existing experimental setups.     

Rydberg excitation of Bose-Einstein condensates

Rydberg atoms provide a wide range of possibilities to tailor interactions in a quantum gas. Here, we report on Rydberg excitation of Bose-Einstein condensed 87Rb atoms. The Rydberg fraction was investigated for various excitation times and temperatures above and below the condensation temperature. The excitation is locally blocked by the van der Waals interaction between Rydberg atoms to a density-dependent limit. Therefore, the abrupt change of the thermal atomic density distribution to the characteristic bimodal distribution upon condensation could be observed in the Rydberg fraction. The observed features are reproduced by a simulation based on local collective Rydberg excitations.     

Coherent decay of Bose-Einstein condensates

Atomic Bose-Einstein condensates are singular forms of matter with the coherence between constituent atoms as a defining characteristic. Although this viewpoint is increasingly validated through experimental findings, the mechanisms behind the observed losses are still understood with classical recombinant collision arguments between particles within the condensate itself. By incorporating a general interparticle interaction into the Hamiltonian, a coherent decay rate can be obtained, thus providing a direct link between the observed losses and the microscopic two-body parameters. Appearing in the lifetime, the interaction strength, lambda, is expressed as lambda=8 pia/(1-delta), where the small parameter delta is obtained from a fit to experimental loss data. Most importantly, the lowest order rate exhibits a novel density dependence (rho{3/2}) that can be identified in low temperature tests.     

Vortex-antivortex oscillation and tunneling in Bose-Einstein condensates

We study interacting condensates in anisotropic traps. Employing a two-level mean-field theory, which is valid provided the interaction energy is much smaller than ?ω_x and ?ω_y and the number of particles N is much larger than unity, we see that even a small interaction can drastically modify the dynamics of the system as predicted by García-Ripoll et al. [Phys. Rev. Lett. 87, 140403 (2001)]. In the present work, we supplement the discussion of the previous work and point out the important role of coupling between population difference and phase difference between two p states in the x and y directions. We also explore the stability of the vortex state for small systems with N ～ O(1), for which the mean-field theory is inapplicable. We performed the full quantum mechanical calculations using up to six single-particle states and showed that, when N is comparable to unity, quantum tunneling between the vortex and antivortex states can occur even though the interaction coefficient is so large that the vortex-antivortex oscillation is prohibited within the mean-field theory.     

Superposition solitons in two-component Bose-Einstein condensates

We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two-component Bose-Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic.     

Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates

Longitudinal confinement of dark solitons in quasi-one-dimensional Bose-Einstein condensates leads to sound emission and reabsorption. We perform quantitative studies of the dynamics of a soliton oscillating in a tight dimple trap, embedded in a weaker harmonic trap. The dimple depth provides a sensitive handle to control the soliton-sound interaction. In the limit of no reabsorption, the power radiated is found to be proportional to the soliton acceleration squared. An experiment is proposed to detect sound emission as a change in amplitude and frequency of soliton oscillations.     

Anti-control of chaos in Bose-Einstein condensates

The spatial structure of a Bose-Einstein Condensate (BEC) loaded into an optical lattice potential is investigated. We suggest a method for generating chaos in BEC by modulating periodic signals to convert the regular states into chaotic states. The maximal Lyapunov exponent is calculated as a function of modulation intensity and modulation frequency respectively, and the chaotic orbits associated with the positive Lyapunov exponents.