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arXiv:1303.1137 · Physical Review A

Observation of transient momentum-space interference during scattering of a condensate from an optical barrier

R. Chang, Shreyas Potnis, Christopher W. Ellenor, M. Siercke, Alex Hayat, Aephraim M. Steinberg

Published Nov 26, 2013• 2 citations
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Abstract

Scattering theory traditionally deals with the asymptotic behavior of a system far removed from the actual scattering event. Here we present an experimental study of the one-dimensional scattering of a noninteracting condensate of ${}^{87}\mathrm{Rb}$ atoms from a potential barrier in the nonasymptotic regime for which the collision dynamics are still ongoing. We show that, for near-transparent barriers, there are two distinct transient scattering effects that arise and dramatically change the momentum distribution during the collision: a deceleration of wave-packet components in midcollision and an interference between incident and transmitted portions of the wave packet. Both effects lead to the re-distribution of momenta giving rise to a rich interference pattern that can be used to reconstruct the single-particle phase profile.

DOI
10.1103/physreva.88.053634

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Scattering theory traditionally deals with the asymptotic behavior of a system far removed from the actual scattering event. Here we present an experimental study of the one-dimensional scattering of a noninteracting condensate of 87Rb{}^{87}\mathrm{Rb}87Rb atoms from a potential barrier in the nonasymptotic regime for which the collision dynamics are still ongoing. We show that, for near-transparent barriers, there are two distinct transient scattering effects that arise and dramatically change the momentum distribution during the collision: a deceleration of wave-packet components in midcollision and an interference between incident and transmitted portions of the wave packet. Both effects lead to the re-distribution of momenta giving rise to a rich interference pattern that can be used to reconstruct the single-particle phase profile.
Bose-Einstein condensates of dilute gases provide a rich and versatile platform to study both single-particle and many-body quantum phenomena. This thesis describes several experiments using a Bose-Einstein condensate of Rb-87 as a model system to study novel matter-wave effects that traditionally arise in vastly different systems, yet are difficult to access. We study the scattering of a particle from a repulsive potential barrier in the non-asymptotic regime, for which the collision dynamics are on-going. Using a Bose-Einstein condensate interacting with a sharp repulsive potential, two distinct transient scattering effects are observed: one due to the momentary deceleration of particles atop the barrier, and one due to the abrupt discontinuity in phase written on the wavepacket in position-space, akin to quantum reflection. Both effects lead to a redistribution of momenta, resulting in a rich interference pattern that may be used to reconstruct the single-particle wavefunction. In a second experiment, we study the response of a particle in a periodic potential to an applied force. By abruptly applying an external force to a Bose-Einstein condensate in a one-dimensional optical lattice, we show that the initial response of a particle in a periodic potential is in fact characterized by the bare mass, and only over timescales long compared to that of interband dynamics is the usual effective mass an appropriate description. This breakdown of the effective mass description on fast timescales is difficult to observe in traditional solid state systems due to their large bandgaps and fast timescale of interband dynamics. Both these experiments make use of the condensate's long coherence length, and the ability to shape and modulate the external potential on timescales fast compared to the particle dynamics, allowing for observation of novel matter-wave effects.
Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.
We study the collision dynamics of two Bose-Einstein condensates with their dynamical wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective one-dimensional system, we identify regimes characterized by the relationship between inter- and intra-atomic interactions and the initial configuration of the system, akin to the equilibrium phase diagram of two interacting Bose condensates. We consider a dynamical setup in which two wave packets are initially at rest with a small separation about the center of an asymmetric harmonic trap. Upon release, we observe a rapid approach to dynamical equilibrium in the limits of very large and very small inter-particle repulsion, characterized by periodic transmission or reflection of the condensates as distinguishable units, whereas the intermediate, critical regime is characterized by extended transient dynamics, density fracturing, and dynamical mixing. We therefore have reason to believe that non-trivial behavior may exist during the collisions of Bose-Einstein condensates as a result of their non-linear interactions, and these effects may be observable in a suitable laboratory environment.
We study the collision dynamics of two Bose–Einstein condensates, with their dynamical wave functions modeled by a set of coupled, time-dependent Gross–Pitaevskii equations. In an effective one-dimensional system, we identify regimes characterized by the relationship between inter- and intra-atomic interactions and the initial configuration of the system, akin to the equilibrium phase diagram of two interacting Bose condensates. We consider a dynamical setup in which two wave packets are initially at rest, with a small separation about the center of an anisotropic harmonic trap. Upon release, we observe a rapid approach to dynamical equilibrium in the limits of very large and very small inter-particle repulsion, characterized by periodic transmission or reflection of the condensates as distinguishable units, whereas the intermediate, critical regime is characterized by extended transient dynamics, density fracturing, and dynamical mixing.
A new technique for the interferometric measurement of an atomic wavefunction is introduced theoretically, which is able to extract phase and amplitude information in a single measurement. I focus on the application of this technique to the single-particle wavefunction of a Bose condensed cloud of rubidium atoms. The technique differs from existing techniques mainly in its simplicity, as it requires only a single laser beam to be added to a typical Bose-Einstein condensation apparatus. A second novel aspect is the consideration of condensate collisions with an optical potential in the low-intensity limit where the potential barrier may be viewed as a phase mask. The technique is then demonstrated experimentally. A related effect, the transient enhancement of momentum during a collision, first predicted by JG Muga et al., has also been demonstrated. Finally, significant redesign and construction of an apparatus to produce condensates of 87Rb is documented. The main result of this work is the production of pure condensates of up to 150k atoms which can be repeated every 45s. A calibration technique is devised and demonstrated, whereby copies of the condensate are made, and the copies are used to reduce the centre-of-mass momentum uncertainty of the interacting cloud by a factor of five.
We investigate the nonlinear scattering dynamics in interacting atomic Bose-Einstein condensates under non-Hermitian dissipative conditions. We show that, by carefully engineering a momentum-dependent atomic loss profile, one can achieve matter-wave amplification through four-wave mixing in a quasi-one-dimensional nearly-free-space setup---a process that is forbidden in the counterpart Hermitian systems due to energy mismatch. Additionally, we show that similar effects lead to rich nonlinear dynamics in higher dimensions. Finally, we propose a physical realization for selectively tailoring the momentum-dependent atomic dissipation. Our strategy is based on a two-step process: (i) exciting atoms to narrow Rydberg or metastable excited states, and (ii) introducing loss through recoil; all while leaving the bulk condensate intact due to protection by quantum interference.