Session B31: BEC/Matter Wave Optics

New technique for ``non-destructively" imaging cold alkali atom clouds

In most cold atom experiments obtaining an image of the atomic cloud involves destroying the sample. Phase-contrast imaging can be used to get spatial density information with minimal perturbation of the sample, however, poor detection efficiency can greatly reduce the signal to noise ratio (S/N) obtained. We present a method which uses the ground state hyperfine structure and the $D_2$ cycling transition of alkali atoms to allow us to scatter many photons off each ``destroyed" atom, greatly compensating for optical detection losses. In our imaging technique, we transfer a small fraction (around 10\%) of the atoms from the $F=1$ hyperfine ground state to the $F=2$ ground state using a microwave or Raman pulse and then image those atoms with resonant probe light. The $F=2$ atoms leave the trap while the remaining $F=1$ atoms are not affected by the probe. The S/N is ultimately limited by statistical variation in the transfer fraction. This method works well even for optically thin atomic clouds. We use this partial transfer method to take multiple images of the same Bose-Einstein condensate.   

Quasiparticle Spectrum of 2-d Dirac Vortices in Optical Lattices

Bose-Einstein condensates (BEC's) in a honeycomb optical lattice are described by a nonlinear Dirac equaton (NLDE) in the long wavelength, mean field limit [1]. The bipartite structure of the lattice appears as pseudospin in the multi-component BEC with states above and below the Dirac point playing the roles of particles and antiparticles. Although much work has been done on NLDE's, the bulk of the literature deals with models with Poincare invariant nonlinearites. In contrast our equations break Poincare symmetry providing an opportunity to study phenomenological models in cosmology and particle physics where this symmetry is not manifest. We present the associated linear stability equations and apply them to the case of weak contact interactions to obtain the quasiparticle energies, states, and stabilities of vortex solutions of the mean field equations. We discuss future applications of our results to problems at the interface between condensed matter and particle physics. [1] L. H. Haddad and L. D. Carr, ``The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries,'' Physica D: Nonlinear Phenomena, v. 238, p. 1413 (2009). \underline {http://arxiv.org/pdf/0803.3039v1}   

Dark Soliton Dynamics In Bose-Einstein Condensates

In this talk, we will summarize some of the recent experimental activity on the dynamics of dark matter-wave solitons that has been enabled by the very controllable atomic physics setting of Bose-Einstein condensates, focusing especially on some of the most recent developments in quasi-1d settings. We will then illustrate how to connect these findings to numerical computations of one- and multi-soliton solutions and their linearization in appropriately tailored variants of the nonlinear Schrodinger equation which account for the transverse dimensions of the atomic clouds. We will motivate and compare numerical and experimental findings to simple particle-based theoretical models which capture the essential physics of the periodic oscillations observed in this system. Time permitting, we will generalize these considerations to finite-temperature condensates, as well as to multi-dimensional condensates and the precession of vortices within them.   

Gain-induced trapping of microcavity exciton polariton condensates

We have performed real and momentum space spectroscopy of exciton polariton condensates in a GaAs-based microcavity under non-resonant excitation with an intensity stabilized laser. An effective trapping mechanism is revealed, which is due to the stimulated scattering gain inside the finite excitation spot combined with the short lifetime. We observe several quantized modes without any externally applied potential, while the lowest state with macroscopic population shows Heisenberg-limited real and momentum space distributions. The experimental findings are qualitatively reproduced by an open dissipative Gross-Pitaevskii equation model including loss and gain terms.   

BEC manipulation with fictitious magnetic fields and Feshbach resonances

The interaction of Bose-Einstein condensate (BEC) atoms with counterpropagating laser beams can often be represented by fictitious magnetic fields [1]. These fictitious fields can be combined with ordinary magnetic fields to produce total fields whose amplitudes vary in space on the scale of the laser wavelength. When the strengths of such magnetic fields are positioned in the neighborhood of a Feshbach resonance, it can produce a spatial variation of the binary scattering length of the condensate atoms. We have studied how these fields can be used to engineer the shape and behavior of BEC's for typical experimental arrangements. We present results for $^{87}$Rb condensate shapes for BEC that can be formed when condensates are formed in the presence of spatially varying scattering lengths as well as the effects of turning on and off the fictitious magnetic fields in the presence of expanding condensates. All of the behaviors presented represent solutions of the time--independent and time--dependent Gross--Pitaevskii (GP) equation. Finally we comment briefly on cases where the GP equation breaks down.\\[4pt] [1] I. Deutsch and P. Jessen, {\bf 57}, 1972 (1998).   

Practical quantum metrology with Bose-Einstein condensates

We analyze in detail the recently proposed experiment [Boixo et al., Phys. Rev. Lett. {\bf 101}, 040403 (2008)] for achieving better than $1/N$ scaling in a quantum metrology protocol using a two mode Bose-Einstein condensate of $N$ atoms. There were several simplifying assumptions in the original proposal that made it easy to see how a scaling approaching $1/N^{3/2}$ may be obtained. We look at these assumptions in detail to see when they may be justified. We present numerical results that confirm our theoretical predictions for the effect of the spreading of the BEC wave function with increasing $N$ on the scaling. Numerical integration of the coupled Gross-Pitaevskii equations for the two mode BEC also shows that the assumption that the two modes share the same spatial wave function is justified for a length of time that is sufficient to run the metrology scheme.   

Two-colour plasma oscillations in a low-barrier BEC Josephson junction

The number and phase difference between the two wells of a Bose-Einstein condensate (BEC) in a double-well potential are often described by a two-mode model, which is applicable in the high-barrier limit for weakly coupled wells. We study the dynamics of a $^{87}$Rb BEC in a RF-dressed magnetic double well potential with a tunable barrier height, $V_b$. We prepare a number-imbalanced distribution and observe plasma-like oscillations of phase and number difference between the wells. When $\mu \la V_b$, where $\mu$ is the chemical potential, we find a two-frequency characteristic in these oscillations, a behaviour not predicted by the two-mode model. We compare our observations to full 3D time-dependent GPE simulations and present a simple model explaining the origin of this new phenomenon. Our study of these dynamics is important for understanding splitting experiments, in which a barrier is raised to divide a condensate.   

Dissipative Transport of a Bose-Einstein Condensate in an Optical Speckle Disorder Potential

We provide a theoretical model for understanding the hydrodynamic transport of Bose-Einstein condensates through optical-speckle disorder potentials. Analytic expressions are derived to describe the dissipative mechanism, in the limit that the depletion of the condensate induced by the speckle potential may be neglected. Comparison of our theoretical predictions, with the experimental data for large-amplitude dipole oscillations of the condensate, show striking qualitative agreement, allowing for precise quantification of the various time scales. Thus, the adeptness of our model, to correctly capture the essential physics of dissipation in such transport experiments, is established.   

Decoherence-free subspaces in BEC interferometry

We extend an approach originally developed to describe Bragg interferometry of Bose-Einstein condensates [1], to describe new interferometers based on quantum information concepts. This approach follows ideas recently introduced in neutron interferometry, such as the identification of decoherence free (DF) subspaces to reduce mechanical noise [2,3]. Using techniques that have been well calibrated by experiments in conventional BEC interferometry [1], we prototype extensions to standard Mach-Zehnder configurations, analogous to the four- and five-blade DF designs of neutron interferometry [2,3]. \\[4pt] [1] J. E. Simsarian, {\em et al.}, {\em Phys. Rev. Lett.} {\bf 85}, 2040 (2000) \newline [2] D. A. Pushin, M. Arif, and D. G. Cory, {\em Phys. Rev. A} {\bf 79}, 053635, (2009) \newline [3] ``A vibrational decoupled neutron interferometer,'' D. A. Pushin, {\em et al.} (preprint)   

Nonlinear wave-packet dynamics in a disordered medium

We develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as ``locked explosion'' and ``diffusive'' collapse. The equation can be applied to such distinct physical systems as laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered environment.   

Interferometry and Gravimetry with Spin-Orbit Coupled Condensates

We propose an implementation of an atom interferometer using a system of Bosons with an optically induced pseudo-spin-1/2 degree of freedom. The localized pseudo-spin degree of freedom allows for a trapped condensate to experience interference effects with out the need to for a system to travel large spatial path lengths. It is shown that a spatially varying Zeeman field will induce an energy splitting between the degrees of freedom that is dependent on gravity of the acceleration of the system. The effects of the many-body ground state are explored and a general procedure for observing inertial effects is given.   

Non-linear Structures in One and Two-mode BECs

In recent years, precise control of atoms in optical potentials has allowed initially coherent BECs to be split into multiple entities. The most famous example is the superfluid to Mott insulator transition, where phase coherence is completely lost between wells. We present results from a novel computational method which is able to break the spatial symmetry of a mean-field state in the presence of a barrier and give a full accounting of both non-linear effects and tunneling to access the superfluid and Mott insulator regimes as well as give, previously unknown, details of the transition between them. Our results include a new characterization of BEC atom interferometry experiments and an investigation of two-mode analogues of one-mode structures such as solitons and phase-driven oscillations.   

Reentrant stability of BEC standing wave patterns

We describe standing wave patterns induced by an attractive finite-ranged external potential that is placed inside a large Bose-Einstein condensate (BEC) [1]. As the potential depth increases, the time independent Gross-Pitaevskii equation develops solutions that have nodes in their wavefunction. We elucidate the nature of these standing wave BEC states and study their dynamical stability. One type of standing wave BEC solution is closely related to bound state solutions of the attractive potential; it can be dynamically stable in intervals of the potential well depth, implying that the standing wave BEC can evolve from a dynamically unstable to stable, and back to unstable status as the potential well is adiabatically deepened, a phenomenon that we refer to as ``reentrant dynamical stability.'' We numerically study the problem in a 2D BEC subject to a cylindrically symmetric square well, but our analysis reveals important general trends for 2D and 3D, independent of the symmetry of the potential. We also comment on long-range phase fluctuations that can be observed at the stability/instability transition points. \\[4pt] [1] R.M. Kalas, D. Solenov, and E. Timmermans, arXiv:0910.2711.   

Coherent manipulations of atomic wavefunctions in optical lattices

We report on the realization of dynamical control of transport for ultra-cold $^{88}$Sr atoms loaded in accelerated and amplitude-modulated optical lattices. Cold atoms trapped in vertical optical lattices give rise to localized states, the Wannier-Stark states. Delocalization can be recovered by introducing a resonant coupling among neighboring lattice sites. We demonstrated this by applying a modulation either to the phase or the amplitude of the lattice potential. Atomic samples loaded into modulated vertical optical-lattice potentials exhibit a resonant delocalization dynamics arising from intraband transitions among Wannier-Stark levels [1]. We demonstrate the coherent control of the spatial extent of atomic wavefunctions by reversibly stretching and shrinking the wavefunctions over a distance of more than one millimeter [2]. Furthermore we tailor the dispersion law of atomic traveling wave-packets and show the ability to reversibly switch between localization regime and tunneling one. From this a novel atom mirror in optical lattices is demonstrated by reversing the group velocity of the atoms. \\[4pt] [1] V. V. Ivanov \textit{et al.,} Phys. Rev. Lett. \textbf{100}, 043602 (2008) \\[0pt] [2] A. Alberti, V. V. Ivanov, G. M. Tino and G. Ferrari, Nature Physics \textbf{5}, 547 (2009)