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arXiv:physics/0408011 · Physical Review A

Splitting matter waves using an optimized standing-wave light-pulse sequence

Saijun Wu, Ying-Ju Wang, Quentin Diot, Mara Goff Prentiss

Published Apr 6, 2005• 98 citations
arXivHTMLPDF

Abstract

In a recent experiment (Wang et al., e-print cond-mat/0407689), it was observed that a sequence of two standing-wave square pulses can split a Bose-Einstein Condensate at rest into $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\hbar}\mathbf{k}$ diffraction orders with almost 100% efficiency. By truncating the Raman-Nath equations to a two-state model, we provide an intuitive picture that explains this double-square-pulse beam-splitter scheme. We further show it is possible to optimize a standing-wave multiple-square-pulse sequence to efficiently diffract an atom at rest to a symmetric superposition of $\ifmmode\pm\else\textpm\fi{}2n\ensuremath{\hbar}\mathbf{k}$ diffraction orders with $n>1$. The approach is considered to be qualitatively different from the traditional light-pulse schemes in the Bragg or the Raman-Nath region, and can be extended to more complex atomic optical elements that produce various tailored output momentum states from a cold atom source.

DOI
10.1103/physreva.71.043602

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We present a framework for designing optimal optical pulses for the matter-wave splitting of a Bose-Einstein Condensate (BEC) under the influence of experimental inhomogeneities, so that the sample is transferred from an initial rest position into a singular higher diffraction order. To represent the evolution of the population of atoms, the Schrödinger's equation is reinterpreted as a parameterized ensemble of dynamical units that are disparately impacted by the beam light-shift potential in a continuous manner. The derived infinite-dimensional coupled Raman-Nath equations are truncated to a finite system of diffraction levels, and we suppose that the parameter that defines the inhomogeneity in the control applied to the ensemble system is restricted to a compact interval. We first design baseline square pulse sequences for the excitation of BEC beam-splitter states following a previous study, subject to dynamic constraints for either a nominal system assuming no inhomogeneity or for several samples of the uncertain parameter. We then approximate the continuum state-space of the ensemble of dynamics using a spectral approach based on Legendre moments, which is truncated at a finite order. Control functions that steer the BEC system from an equivalent rest position to a desired final excitation are designed using a constrained optimal control approach developed for handling nonlinear dynamics. This representation results in a minimal dimension of the computational problem and is shown to be highly robust to inhomogeneity in comparison to the baseline approach. Our method accomplishes the BEC-splitting state transfer for each subsystem in the ensemble, and is promising for precise excitation in experimental settings where robustness to environmental and intrinsic noise is paramount.
Bose–Einstein condensate (BEC)-based atom interferometry exploits low temperatures and long coherence lengths to facilitate high-precision measurements. Progress in atom interferometry promises improvements in navigational devices like gyroscopes and accelerometers, as well as applications in fundamental physics such as accurate determination of physical constants. Previous work demonstrates that beam splitters and mirrors for coherent manipulation of dilute BEC momentum in atom interferometers can be implemented with sequences of non-resonant standing-wave light pulses. While previous work focuses on the optimization of the optical pulses’ amplitude and duration to produce high-order momentum states with high fidelity, we explore how varying the shape of the optical pulses affects optimal beam-splitter performance, as well as the effect of pulse shape on the sensitivity of optimized parameters in achieving high fidelity in high-momentum states. In simulations of two-pulse beam splitters utilizing optimized square, triangle, and sinc-squared pulse shapes applied to dilute BECs, we, in some cases, reduce parameter sensitivity by an order of magnitude while maintaining fidelity.
We study Kapitza-Dirac diffraction of a Bose-Einstein condensate from a standing light wave for a square pulse with variable pulse length but constant pulse area. We find that for sufficiently weak pulses, the usual analytical short-pulse prediction for the Raman-Nath regime continues to hold for longer times, albeit with a reduction of the apparent modulation depth of the standing wave. We quantitatively relate this effect to the Fourier width of the pulse, and draw analogies to the Rabi dynamics of a coupled two-state system. Our findings, combined with numerical modeling for stronger pulses, are of practical interest for the calibration of optical lattices in ultracold atomic systems.
Atom interferometers detect inertial effects with considerably larger sensitivity than that of traditional light wave interferometers. They uti- lize the relative small group velocity of coherent matter waves for more precise measurements, which is crucial for possible next-generation in- ertial navigation systems. In a hybrid optical dipole and magnetic trap system we generate Bose-Einstein condensates to be used as the source of matter waves for atom interferometry. We use tailored light pulse sequences to induce Kapitza-Dirac diffraction in the condensates, splitting them into multiple parts at discrete momentum orders. Nu- merical simulation and experimental realization is given for novel pulse sequences that splits ±4hk momentum orders.
We report the experimental realization of a multibeam atom laser. A single continuous atom laser is outcoupled from a Bose-Einstein condensate via an optical Raman transition. The atom laser is subsequently split into up to five atomic beams with slightly different momenta, resulting in multiple, nearly copropagating, coherent beams which could be of use in interferometric experiments. The splitting process itself is a realization of Bragg diffraction, driven by each of the optical Raman laser beams independently. This presents a significantly simpler implementation of an atomic beam splitter, one of the main elements of coherent atom optics.