Resonant five-body recombination in an ultracold gas of bosonic atoms

We combine theory and experiment to investigate five-body recombination in an ultracold gas of atomic cesium at negative scattering length. A refined theoretical model, in combination with extensive laboratory tunability of the interatomic interactions, enables the five-body resonant recombination rate to be calculated and measured. The position of the new observed recombination feature agrees with a recent theoretical prediction and supports the prediction of a family of universal cluster states at negative a that are tied to an Efimov trimer.

Phase-space analysis of bosonic spontaneous emission

We present phase-space techniques for the modelling of spontaneous emission in two-level bosonic atoms. The positive-P representation is shown to give a full and complete description within the limits of our model. The Wigner representation, even when truncated at second order, is shown to need a doubling of the phase-space to allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck equation and still fails to agree with the full quantum results of the positive-P representation. We show that quantum statistics and correlations between the ground and excited states affect the dynamics of the emission process, so that it is in general non-exponential. (c) 2005 Elsevier B.V. All rights reserved.

Temperature-driven collapse of a coherent binary mixture of condensates

We present a temperature- dependent Hartree- Fock- Bogoliubov- Popov theory to analyze the properties of the equilibrium states of an homogeneous mixture of bosonic atoms in two different hyperfine states and in the presence of an internal Josephson coupling. In our calculation we show that the bistable structure of the equilibrium states at zero temperature changes when we increase the temperature of the system. We investigate two mechanisms of the disappearance of bistability. In one, near the collapse of one of the equilibrium states, the acoustical branch becomes unstable and the gap of the optical branch goes to zero. In the other, there is no divergent behavior of the system and bistability disappears at a temperature in which the two equilibrium states merge at a zero- population fraction imbalance. When we further increase the temperature, this state remains as a unique equilibrium configuration.

Superchemistry: dynamics of coupled atomic and molecular Bose condensates

We analyze the dynamics of a dilute, trapped Bose-condensed atomic gas coupled to a diatomic molecular Bose gas by coherent Raman transitions. This system is shown to result in a new type of “superchemistry,” in which giant collective oscillations between the atomic and the molecular gas can occur. The phenomenon is caused by stimulated emission of bosonic atoms or molecules into their condensate phases.

Ordered structures in rotating ultracold Bose gases

Two-dimentional systems of trapped samples of few cold bosonic atoms submitted to strong rotation around the perpendicular axis may be realized in optical lattices and microtraps. We investigate theoretically the evolution of ground state structures of such systems as the rotational frequency Omega increases. Various kinds of ordered structures are observed. In some cases, hidden interference patterns exhibit themselves only in the pair correlation function; in some other cases explicit broken-symmetry structures appear that modulate the density. For N < 10 atoms, the standard scenario, valid for large sytems is absent, and is only gradually recovered as N increases. On the one hand, the Laughlin state in the strong rotational regime contains ordered structures much more similar to a Wigner molecule than to a fermionic quantum liquid. On the other hand, in the weak rotational regime, the possibility to obtain equilibrium states, whose density reveals an array of vortices, is restricted to the vicinity of some critical values of the rotational frequency Omega.

Transition to quantum turbulence in finite-size superfluids

A novel concept of quantum turbulence in finite size superfluids, such as trapped bosonic atoms, is discussed. We have used an atomic (87)Rb Bose-Einstein condensate (BEC) to study the emergence of this phenomenon. In our experiment, the transition to the quantum turbulent regime is characterized by a tangled vortex lines formation, controlled by the amplitude and time duration of the excitation produced by an external oscillating field. A simple model is suggested to account for the experimental observations. The transition from the non-turbulent to the turbulent regime is a rather gradual crossover. But it takes place in a sharp enough way, allowing for the definition of an effective critical line separating the regimes. Quantum turbulence emerging in a finite-size superfluid may be a new idea helpful for revealing important features associated to turbulence, a more general and broad phenomenon. [GRAPHICS] Amplitude versus elapsed time diagram of magnetically excited BEC superfluid, presenting the evolution from the non-turbulent regime, with well separated vortices, to the turbulent regimes, with tangled vortices (C) 2011 by Astro Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA

Mean-field description of a dynamical collapse of a fermionic condensate in a trapped boson-fermion mixture

We suggest a time-dependent dynamical mean-field-hydrodynamic model for the collapse of a trapped boson-fermion condensate and perform numerical simulation based on it to understand some aspects of the experiment by Modugno et al. [Science 297, 2240 (2002)] on the collapse of the fermionic condensate in the K-40-Rb-87 mixture. We show that the mean-field model explains the formation of a stationary boson-fermion condensate at zero temperature with relative sizes compatible with experiment. This model is also found to yield a faithful representation of the collapse dynamics in qualitative agreement with experiment. In particular we consider the collapse of the fermionic condensate associated with (a) an increase of the number of bosonic atoms as in the experiment and (b) an increase of the attractive boson-fermion interaction using a Feshbach resonance. Suggestion for experiments of fermionic collapse using a Feshbach resonance is made.

Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate

We use the time-dependent mean-field Cross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation managed bright soliton in a quasi-one dimensional Bose-Einstein condensate (BEC). Because of three-body recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a perturbation procedure that an alimentation of atoms from an external source to the BEC may compensate for the dissipation loss and lead to a dynamically-stabilized soliton. The result of the analytical perturbation method is in excellent agreement with mean-field numerics. It seems possible to obtain such a dynamically stabilized BEC soliton without dissipation in laboratory.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

Interacting Bose-Fermi mixtures in optical lattices

In this thesis, we investigate mixtures of quantum degenerate Bose and Fermi gases of neutral atoms in threedimensional optical lattices. Feshbach resonances allow to control interspecies interactions in these systems precisely, by preparing suitable combinations of internal atomic states and applying external magnetic fields. This way, the system behaviour can be tuned continuously from mutual transparency to strongly interacting correlated phases, up to the stability boundary.rnThe starting point for these investigations is the spin-polarized fermionic band insulator. The properties of this non-interacting system are fully determined by the Pauli exclusion principle for the occupation of states in the lattice. A striking demonstration of the latter can be found in the antibunching of the density-density correlation of atoms released from the lattice. If bosonic atoms are added to this system, isolated heteronuclear molecules can be formed on the lattice sites via radio-frequency stimulation. The efficiency of this process hints at a modification of the atom number distribution over the lattice caused by interspecies interaction.rnIn the following, we investigate systems with tunable interspecies interaction. To this end, a method is developed which allows to assess the various contributions to the system Hamiltonian both qualitatively and quantitatively by following the quantum phase diffusion of the bosonic matter wave.rnBesides a modification of occupation number statistics, these measurements show a significant renormalization of the bosonic Hubbard parameters. The final part of the thesis considers the implications of this renormalization effect on the many particle physics in the mixture. Here, we demonstrate how the quantum phase transition from a bosonic superfluid to a Mott insulator state is shifted towards considerably shallower lattices due to renormalization.

Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate

Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstrate that strongly entangled atomic beams may be produced which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures in direct analogy to the position and momentum correlations originally considered by EPR.

Matter-wave amplification and phase conjugation via stimulated dissociation of a molecular Bose-Einstein condensate

We propose a scheme for parametric amplification and phase conjugation of an atomic Bose-Einstein condensate (BEC) via stimulated dissociation of a BEC of molecular dimers consisting of bosonic atoms. This can potentially be realized via coherent Raman transitions or using a magnetic Feshbach resonance. We show that the interaction of a small incoming atomic BEC with a (stationary) molecular BEC can produce two counterpropagating atomic beams - an amplified atomic BEC and its phase-conjugate or "time-reversed" replica. The two beams can possess strong quantum correlation in the relative particle number, with squeezed number-difference fluctuations.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.