Excitations in a nonequilibrium Bose-Einstein condensate of exciton polaritons

We develop a mean-field theory of the dynamics of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied by means of a generalized Gross-Pitaevskii equation. A diffusive behavior of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry.     

Polarized nonequilibrium Bose-Einstein condensates of spinor exciton polaritons in a magnetic field

The effect of a magnetic field on a spinor exciton-polariton condensate has been investigated. A quenching of a polariton Zeeman splitting and an elliptical polarization of the condensate have been observed at low magnetic fields B<2 T. The effects are attributed to a competition between the magnetic field induced circular polarization buildup and the spin-anisotropic polariton-polariton interaction which favors a linear polarization. The sign of the circular polarization of the condensate emission at B<3 T is negative, suggesting that a dynamic condensation in the excited spin state rather than the ground spin state takes place in this magnetic field range. From about 2T on, the Zeeman splitting opens and from then on the slope of the circular polarization degree changes its sign. For magnetic fields larger than the 3 T, the upper spin state occupation is energetically suppressed and circularly polarized condensation takes place in the ground state.     

Spin dynamics of a vortical condensate of exciton polaritons in a GaAs microcavity

The temporal dynamics of a spinor exciton-polariton condensate in a high-quality anisotropic GaAs microcavity under pulsed resonant excitation with light possessing a nonzero orbital angular momentum is investigated. The phenomenon of spatial separation of the spin components of the polariton condensate upon pumping with a coherent superposition of two beams with opposite circular polarizations and orbital angular momenta is observed. The key factors for the observation of this effect are the lateral anisotropy of the microcavity that causes a splitting between the linear components of the polariton ground state and the occurrence of opposite orbital angular momenta for the two spin components of the condensate. The experimental results are in qualitative agreement with the theoretical model of the phenomenon developed in JETP Lett. 104, 827 (2016).     

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.     

STIRAP transport of Bose-Einstein condensate in triple-well trap

The irreversible transport of multi-component Bose-Einstein condensate (BEC) is investigated within the Stimulated Raman Adiabatic Passage (STIRAP) scheme. A general formalism for a single BEC in M-well trap is derived and analogy between multi-photon and tunneling processes is demonstrated. STIRAP transport of BEC in a cyclic triple-well trap is explored for various values of detuning and interaction between BEC atoms. It is shown that STIRAP provides a complete population transfer at zero detuning and interaction and persists at their modest values. The detuning is found not to be obligatory. The possibility of non-adiabatic transport with intuitive order of couplings is demonstrated. Evolution of the condensate phases and generation of dynamical and geometric phases are inspected. It is shown that STIRAP allows to generate the unconventional geometrical phase which is now of a keen interest in quantum computing.     

Exact transmission state of a Bose-Einstein condensate in a near-harmonic trap

We introduce a new confining potential which simulates preferably the realistic near-harmonic trap for a quasi-one-dimensional (1D) Bose-Einstein condensate (BEC). An exact transmission state of the BEC system is found and the corresponding spatial configurations, metastability, superfluidity and the transport properties are analyzed. Resonant transmission through the potential is predicted from the exact solution.     

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.     

Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap

We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, limited only by experimental factors such as drift and trap lifetime. The quantized rotation was initiated by transferring one unit variant Planck's over 2pi of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply connected, and was observed with a Bose-Einstein condensate fraction as small as 20%. We also created flow with two units of angular momentum and observed its splitting into two singly charged vortices when the trap geometry was changed from multiply to simply connected.     

Bose-Einstein condensate in a harmonic trap with an eccentric dimple potential

We investigate Bose-Einstein condensation of noninteracting gases in a harmonic trap with an offcenter dimple potential. We specifically consider the case of a tight and deep dimple potential, which is modeled by a point interaction. This point interaction is represented by a Dirac delta function. The atomic density, chemical potential, critical temperature and condensate fraction, and the role of the relative depth and the position of the dimple potential are analyzed by performing numerical calculations.     

Berry phase effect on the exciton transport and on the exciton Bose-Einstein condensate

With the exciton lifetime much extended in semiconductor quantum-well structures, the exciton transport and Bose-Einstein condensation have become a focus of research in recent years. We reveal a momentum-space gauge field in the exciton center-of-mass dynamics due to Berry phase effects. We predict a spin-dependent transport of the excitons analogous to the anomalous Hall and Nernst effects for electrons. We also predict spin-dependent circulation of a trapped exciton gas and instability in an exciton condensate in favor of vortex formation.     

Nonlinear Landau-Zener tunneling of Bose-Einstein condensate in a spatially magnetic modulated trap

We study tunneling of a Bose-Einstein condensates confined in a effective double-well potential (a single well with a spatially magnetic modulated scattering length, actually), called pseudo double-well trap, in which the interaction of atoms characterized by the s-wave scattering length a _s can be widely tuned with a magnetic-field Feshbach resonance. As a result, corresponding to different nonlinear parameters, the energy levels of the nonlinear Schrödinger equation can have complex structures in their dependence on the bias between the wells. We discuss the emergence of looped levels, which lead to a breakdown of adiabaticity that the Landau-Zener transition probability does not vanish even in the adiabatic limit. Moreover, we also find that the Landau-Zener tunneling in the pseudo trap show many striking properties distinguished from that of the real trap model (where the barrier is created by the external potential). Possible experimental observation in an opticallyinduced photonic lattices in a photorefractive material is suggested.     

Quasi-energy of single quantum particles and a Bose-Einstein condensate in a dynamical trap

The quasi-energy states have been found analytically for single quantum particles and an atomic Bose-Einstein condensate in a trap with periodically oscillating walls with a small modulation depth. A resonance is shown to exist as the modulation frequency approaches the difference of the frequencies corresponding to the levels in the unperturbed problem. Quasi-energy splitting and, accordingly, beats with a periodic population exchange between two levels in resonance have been found in the resonant case. Bistability of the response to trap size modulation, when the sustenance (depending on the initial conditions) of various quasi-energy states is possible under the same conditions, has been found for a Bose-Einstein condensate under resonance conditions.     

Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap

The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.     

Dynamic chaos and stability of a weakly open Bose-Einstein condensate in a double-well trap

We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.     

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     

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.     

Atomic condensate in an optical trap formed by a cavity mode

It has been shown that an optical trap for an atomic condensate formed by a mode of a ring cavity possesses specific properties. These properties are not featured by a trap formed by free beams and arise owing to quantum correlations (entanglement) between the localized atoms and the optical mode. In particular, there is an effect similar to an optomechanical phenomenon known as an “optical spring” (S. Martellucci et al., Bose–Einstein Condensates and Atom Lasers (Kluwer, Dordrecht, 2002)) and manifested by the emergence of an effective correction to the interaction between the localized atoms. The magnitude and sign of this correction can be controlled by varying the frequency of the source forming the trap.     

Chaos in a Bose-Einstein condensate

It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose-Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential.A formally exact solution of the time-dependent Gross-Pitaevskii equation is constructed,which describes the matter shock waves with chaotic or periodic amplitudes and phases.     

Oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

In this work, we study parametric excitations in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric excitations (oscillations of the BEC width). Regular oscillations disappear when one of the competing factors, i.e. the strength of harmonic trap or the strength of optical lattice, dominates. Parametric instabilities (chaotic dynamics) arise for large variations in the strength of the optical lattice.     

Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti et al. on atomic Josephson oscillation [Science 293, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement with the more recent experiment by Cataliotti et al. [New J. Phys. 5, 71 (2003)].Received: 20 March 2003, Published online: 30 July 2003PACS: 03.75.-b Matter waves - 03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations - 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow