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arXiv:1307.0069 · Physical Review A

Observation of diffraction phases in matter-wave scattering

Xuguang Yue, Yueyang Zhai, Zhongkai Wang, Hongwei Xiong, Xuzong Chen, Xiaoji Zhou

Published Jul 3, 2013• 13 citations
arXivHTMLPDF

Abstract

We study the diffraction phase of different orders via the Dyson expansion series, for ultracold atomic gases scattered by a standing-wave pulse. As these diffraction phases are not observable in a single-pulse scattering process, a temporal Talbot-Lau interferometer consisting of two standing-wave pulses is demonstrated experimentally with a Bose-Einstein condensate to explore this physical effect. The role of the diffraction phases is clearly shown by the second standing-wave pulse in the relative population of different momentum states. Our experiments demonstrate obvious effects beyond the Raman-Nath method, while they agree well with our theory by including the diffraction phases. In particular, the observed asymmetry in the dependence of the relative population on the interval between two standing-wave pulses reflects the diffraction phase differences. The role of interatomic interaction in the Talbot-Lau interferometer is also discussed.

DOI
10.1103/physreva.88.013603

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We study the diffraction phase of different orders via the Dyson expansion series, for ultracold atomic gases scattered by a standing-wave pulse. As these diffraction phases are not observable in a single-pulse scattering process, a temporal Talbot-Lau interferometer consisting of two standing-wave pulses is demonstrated experimentally with a Bose-Einstein condensate to explore this physical effect. The role of the diffraction phases is clearly shown by the second standing-wave pulse in the relative population of different momentum states. Our experiments demonstrate obvious effects beyond the Raman-Nath method, while they agree well with our theory by including the diffraction phases. In particular, the observed asymmetry in the dependence of the relative population on the interval between two standing-wave pulses reflects the diffraction phase differences. The role of interatomic interaction in the Talbot-Lau interferometer is also discussed.
We study the effects of strong inter-particle interaction on diffraction of a Bose-Einstein condensate of ^6\mathrm{Li}_2 6 L i 2 molecules from a periodic potential created by pulses of a far detuned optical standing wave. For short pulses we observe the standard Kapitza-Dirac diffraction, with the contrast of the diffraction pattern strongly reduced for very large interactions due to interaction-dependent loss processes. For longer pulses diffraction shows the characteristic for matter waves impinging on an array of tubes and coherent channeling transport. We observe a slowing down of the time evolution governing the population of the momentum modes caused by the strong atom interaction. A simple physical explanation of that slowing down is the phase shift caused by the self-interaction of the forming matter wave patterns inside the standing light wave. Simple 1D mean field simulations qualitatively capture the phenomenon, however to quantitatively reproduce the experimental results the molecular scattering length has to be multiplied by factor of 4.2. In addition, two contributions to interaction-dependent degradation of the coherent diffraction patterns were identified: (i) in-trap loss of molecules during the lattice pulse, which involves dissociation of Feshbach molecules into free atoms, as confirmed by radio-frequency spectroscopy and (ii) collisions between different momentum modes during separation. This was confirmed by interferometrically recombining the diffracted momenta into the zero-momentum peak, which consequently removed the scattering background.
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We study several effects which lead to symmetry-broken momentum distributions of quantum gases released from optical lattices. In particular, we demonstrate that the interaction within the first milliseconds of the time-of-flight expansion can strongly alter the measurement of the initial atomic momentum distribution. For bosonic mixtures in state-dependent lattices, interspecies scattering processes lead to a symmetry breaking in momentum space. The underlying mechanism is identified to be diffraction of the matter wave from the total density lattice, which gives rise to a time-dependent interaction potential. Our findings are of fundamental relevance for the interpretation of time-of-flight measurements and for the study of exotic quantum phases such as the twisted superfluid. Beyond that, the observed matter-wave diffraction can also be used as an interferometric probe. In addition, we report on diffraction from the state-dependent standing light field, which leads to the same symmetry-broken momentum distributions, even for single component condensates.
In this thesis, we study the diffraction processes of a Bose-Einstein condensate of 87Rb atoms and outline our progress toward the realisation of an atom laser. The experiments are carried out with a condensate that is produced ‘all-optically’; this is covered in the first part of the thesis. For our diffraction processes, we expose the condensate to an intense, pulsed optical standing wave. We perform mean energy measurements and interpret our results with two different theories: one treating the condensed atoms as particles, the other focusing on the atoms’ wave properties. The first interpretation requires knowledge of the theoretical background of the atom-optics -kicked rotor (AOKR); in our experiments, we focus on the resonances in the early-time behaviour of the kicked atoms. The second interpretation retrieves an observation of the temporal Talbot effect—the atomic analogue to the optical Talbot effect. From this point of view, the full resonances represent the integer Talbot effect, whereas the early-time behaviour corresponds to the observation of the fractional Talbot effect. We find for both theoretical interpretations an excellent qualitative agreement between our experimental results and the results of our computer simulation of the AOKR. Furthermore, we outline our future work on the realisation of an atom laser as a tool for coherence measurements of the condensate via atom-counting statistics. In this context, the most current progress in our laboratory is given. We aim for a Bragg-scattering process of our condensate as a modified version of our prospective outcoupling technique for the atom laser; this process is modelled in a semi-classical approach, and our first experimental implementations are presented.
We have used an echo-type atom interferometer that manipulates laser-cooled atoms in a single ground state to investigate the effect of light scattering from pulsed and continuous-wave light. The interferometer uses two off-resonant standing-wave pulses applied at times t=0t=0t=0 and t=Tt=Tt=T to diffract and recombine momentum states separated by $2\ensuremath{\hbar}k$ at t=2Tt=2Tt=2T. Matter wave interference is associated with the formation of a density grating with period $\ensuremath{\lambda}/2$ in the vicinity of this echo time. The grating contrast is measured by recording the intensity of coherently backscattered light. The interferometer is perturbed by an additional pulse applied at $t=2T\ensuremath{-}\ensuremath{\delta}T$ or by continuous-wave background light. If the additional pulse is a standing wave, the momentum states interfering at t=2Tt=2Tt=2T are displaced and the grating contrast can be completely recovered due to constructive interference. In this case, the contrast shows a periodic modulation at the atomic recoil frequency as a function of $\ensuremath{\delta}T$. In a recent work, it was shown that the atomic recoil frequency can be measured easily and precisely when using coherence functions to model the signal shape. This paper provides an alternative description of the signal shape through an analytical calculation of echo formation in the presence of an additional standing-wave pulse. Using this treatment, it is possible to model the effects of spontaneous emission and spatial profile of the laser beam on the signal shape. Additionally, the theory predicts scaling laws as a function of the pulse area and the number of additional standing-wave pulses. These scaling laws are investigated experimentally and can be exploited to improve precision measurements of the atomic recoil frequency. We also show that coherence functions can be used to make a direct measurement of the populations of momentum states associated with the ground state under conditions where the Doppler-broadened velocity distribution of the sample is much larger than the recoil velocity. These measurements are consistent with Monte Carlo wave-function simulations. If the additional pulse is a traveling wave, we find that the grating contrast measured as a function of $\ensuremath{\delta}T$ can be modeled by a quasiperiodic coherence function as in previous experiments that utilized atomic beams. In this work, we investigate the dependence of the photon scattering rate on the intensity and detuning of the traveling wave. We also study the effects of perturbing the interferometer with continuous-wave light and find that the dependence of the photon scattering rate on the intensity and detuning of the perturbing field is consistent with expectations.
We study 87Rb Bose-Einstein condensation (BEC) loading into the pulse of the one-dimensional (1D) optical lattice experimentally. The lattice is turned on abruptly, held constant for a variable time, and then turned off abruptly. The measurement of the depth of the optical lattice is obtained by Kapitza-Dirac scattering. The temporal matter-wave-dispersion Talbot effect with 87Rb BEC is observed by applying a pair of pulsed standing waves (as pulsed phase gratings) with the separation of a variable delay.