Th. Busch

Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates

We investigate dark-bright vector solitary wave solutions to the coupled nonlinear Schrödinger equations which describe an inhomogeneous two-species Bose-Einstein condensate. While these structures are well known in nonlinear fiber optics, we show that spatial inhomogeneity strongly affects their motion, stability, and interaction, and that current technology suffices for their creation and control in ultracold trapped gases. The effect of controllably different interparticle scattering lengths is examined, and stability against three-dimensional deformations is considered.

Motion of Dark Solitons in Trapped Bose-Einstein Condensates

We use a multiple time scale boundary layer theory to derive the equation of motion for a dark (or grey) soliton propagating through an effectively one-dimensional cloud of Bose-Einstein condensate, assuming only that the background density and velocity vary slowly on the soliton scale. We show that solitons can exhibit viscous or radiative acceleration (antidamping), which we estimate as slow but observable on experimental time scales.

STABILITY AND COLLECTIVE EXCITATIONS OF A TWO-COMPONENT BOSE-EINSTEIN CONDENSED GAS : A MOMENT APPROACH

The dynamics of a two-component dilute Bose gas of atoms at zero temperature is described in the mean field approximation by a two-component Gross-Pitaevskii Equation. We solve this equation assuming a Gaussian shape for the wavefunction, where the free parameters of the trial wavefunction are determined using a moment method. We derive equilibrium states and the phase diagrams for the stability for positive and negative s-wave scattering lengths, and obtain the low energy excitation frequencies corresponding to the collective motion of the two Bose condensates.

Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

Negative-mass hydrodynamics in a spin-orbit coupled Bose-Einstein condensate

A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features-shock waves, soliton trains, self-trapping, etc.-originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.

Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures

We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for a small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong. We investigate in detail how the correlations evolve between the limits. For balanced mixtures in the number of atoms in each species, the transition between the different limits involves sophisticated changes in the one- and two-body correlations. Particularly, we quantify the entanglement between the two components by means of the von Neumann entropy. We show that the limits equally exist when the number of atoms is increased for balanced mixtures. Also, the changes in the correlations along the transitions among these limits are qualitatively similar. We also show that, for imbalanced mixtures, the same limits with similar transitions exist. Finally, for strongly imbalanced systems, only two limits survive, i.e., a miscible limit and a phase-separated one, resembling those expected with a mean-field approach.

Shaping the evanescent field of optical nanofibers for cold atom trapping.

We investigate trapping geometries for cold, neutral atoms that can be created in the evanescent field of a tapered optical fibre by combining the fundamental mode with one of the next lowest possible modes, namely the HE(21) mode. Counter propagating red-detuned HE(21) modes are combined with a blue-detuned HE(11) fundamental mode to form a potential in the shape of four intertwined spirals. By changing the polarization from circular to linear in each of the two counter-propagating HE(21) modes simultaneously the 4-helix configuration can be transformed into a lattice configuration. The modification to the 4-helix configuration due to unwanted excitation of the the TE(01) and TM(01) modes is also discussed.

INHIBITION OF SPONTANEOUS EMISSION IN FERMI GASES

Fermi inhibition is a quantum-statistical analogue for the inhibition of spontaneous emission by an excited atom in a cavity. This is achieved when the relevant motional states are already occupied by a cloud of cold atoms in the internal ground state. We exhibit non-trivial effects at finite temperature and in anisotropic traps, and briefly consider a possible experimental realization.

Transverse mode of an atom laser

The transverse mode of an atom laser beam that is outcoupled from a Bose\char21{}Einstein condensate is investigated and is found to be strongly determined by the mean-field interaction of the laser beam with the condensate. For repulsive interactions, the condensate acts as a diverging lens for the outcoupled atoms, and transverse interference fringes in the atomic beam are predicted due to the coherent addition of amplitudes for atoms emitted from different regions in the condensate. This effect can be used to investigate the transverse coherence of an atom laser beam.

New spin squeezing and other entanglement tests for two mode systems of identical bosons

For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrization principle (SP) and conform to super-selection rules (SSR) that prohibit coherences between differing total particle numbers. Here we consider bi-partitite states for massive bosons, where both the system and sub-systems are modes (or sets of modes) and particle numbers for quantum states are determined from the mode occupancies. Defining non-entangled or separable states as those prepared via local operations (on the sub-systems) and classical communication processes, the sub-system density operators are also required to satisfy the SP and conform to the SSR, in contrast to some other approaches. Whilst in the presence of this additional constraint the previously obtained sufficiency criteria for entanglement, such as the sum of the and variances for the Schwinger spin components being less than half the mean boson number, and the strong correlation test of being greater than are still valid, new tests are obtained in our work. We show that the presence of spin squeezing in at least one of the spin components , and is a sufficient criterion for the presence of entanglement and a simple correlation test can be constructed of merely being greater than zero. We show that for the case of relative phase eigenstates, the new spin squeezing test for entanglement is satisfied (for the principle spin operators), whilst the test involving the sum of the and variances is not. However, another spin squeezing entanglement test for Bose–Einstein condensates involving the variance in being less than the sum of the squared mean values for and divided by the boson number was based on a concept of entanglement inconsistent with the SP, and here we present a revised treatment which again leads to spin squeezing as an entanglement test.