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Physical Review A

Bragg diffraction of interacting Bose-Einstein condensates

Peng Zhang, Jian-Hua Wu, Xiao-Fei Zhang, Wu‐Ming Liu

Published Oct 27, 2010• 10 citations
Publisher

Abstract

We develop a theoretical model to investigate the Bragg diffraction of an elongated interacting Bose-Einstein condensate which is illuminated by a pair of laser beams. We find that the mean-field effect resulting from the atomic interaction plays an important role in modifying the atomic coherence. Our results show that both the repulsive and attractive interactions would dampen the momentum oscillation of the condensate; they establish surprisingly distinguishable equilibria for the atomic occupations among different diffraction orders. We also give an experimental proposal to observe this phenomenon.

DOI
10.1103/physreva.82.043628

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We develop a theoretical model to investigate the Bragg diffraction of an elongated interacting Bose-Einstein condensate which is illuminated by a pair of laser beams. We find that the mean-field effect resulting from the atomic interaction plays an important role in modifying the atomic coherence. Our results show that both the repulsive and attractive interactions would dampen the momentum oscillation of the condensate; they establish surprisingly distinguishable equilibria for the atomic occupations among different diffraction orders. We also give an experimental proposal to observe this phenomenon.
We present the results of an experiment on light scattering from an elongated Bose-Einstein condensate (BEC) interacting with a far-off-resonant pump laser. By collective atomic recoil lasing (CARL) a coherent superposition of two atomic wave packets with different momenta is created. Varying the intensity of a weak counterpropagating laser beam we observe the transition from the pure superradiant regime to the Bragg scattering regime, where Rabi oscillations in a two-level system are observed. The process is limited by the decoherence between the two atomic wave packets. In the superradiant regime the experiment gives evidence of a contribution to decoherence which depends on the initial velocity of the condensate. The system is described by the CARL-BEC model, which is a generalization of the Gross-Pitaevskii model to include the self-consistent evolution of the scattered field and a phase-diffusion decoherence process, which accounts for the observed damping.
The nature of Bose-Einstein condensation (BEC) in atomic vapours depends critically on the mean-field interaction of the atoms. When this interaction is attractive, the number of atoms in the condensate is limited. The interplay of this limit and the natural growth of the condensate during BEC leads to complicated dynamical behaviour. We develop a model for this behaviour based on the nonlinear Schrödinger equation and the quantum Boltzmann equation. The condensate occupation number is predicted to oscillate rapidly as the condensate alternately fills and collapses, and the oscillations are seen to persist for many cycles before the gas comes to equilibrium. Experimental evidence for these oscillations in the case of 7 Li is presented, along with details of the experimental apparatus and methods.
We have observed Bragg diffraction of a Bose-Einstein condensate of sodium atoms by a moving, periodic, optical potential. The coherent process of Bragg diffraction produced a splitting of the condensate with unidirectional momentum transfer. Using the momentum selectivity of the Bragg process, we separated a condensate component with a momentum width narrower than that of the original condensate. By repeatedly pulsing the optical potential while the atoms were trapped, we observed the trajectory of the split atomic wave packets in the confining magnetic potential.
We investigate the atomic diffraction of Bose-Einstein condensates in quantized light fields. Situations in which the light fields are in number states or coherent states are studied theoretically. Analytical derivation and numerical calculation are carried out to simulate the dynamics of the atomic motion. In the condition that atoms are scattered by light in the number states with imbalanced photon-number distribution, the atomic transitions between different momentum modes would sensitively depend on the transition order and the photon-number distribution. The number-state nature of the light fields modifies the period of atomic momentum oscillations and makes forward and backward atomic transitions unequal. For light fields in coherent states, whether or not the intensities of the light fields are balanced, the atomic diffraction is symmetric and independent of the transition order.
This thesis discusses a series of studies that investigate the effects of interaction – essentially the s-wave scattering – in the various properties of Bose-Einstein condensates (BEC). The phonon wavefunction in a BEC was measured using Bragg spectroscopy and compared with the well-known Bogoliubov theory. Phonons were first excited in a BEC of 3× 10 condensed Na atoms via small-angle two-photon Bragg scattering. Large angle Bragg scattering was then used to probe the momentum distribution. We found reasonable agreement with the theory. With the same technique of Bragg diffraction, we studied the four-wave mixing process for matter waves. The BEC was split into two strong source waves and a weak seed wave. The s-wave scattering coherently mixed pairs of atoms from the sources into the seed and its conjugate wave, creating a pair-correlated atomic beams with “squeezed” number difference. A Feshbach resonance was used to produce ultracold Na2 molecules with initial phase-space density in excess of 20. Starting from an atomic BEC, a magnetic field ramp shifted a bound state from above the threshold of the unbound continuum to below, creating a molecular population with almost zero center-of-mass motion. A reverse field ramp dissociated the cold molecules into free atom pairs carrying kinetic energy dependent on the ramp speed. This dependence provided a measure of the coupling strength between the bound state and the continuum. Condensates were loaded into optical lattices formed with retro-reflected single frequency lasers. Quantum phase transition from the superfluid state to Mott-insulator state was observed in a three dimensional lattice. The increased interaction and flattened dispersion relation led to strongly enhanced quantum depletion in the superfluid state. Thesis Supervisor: Wolfgang Ketterle Title: John D. MacAurthur Professor of Physics