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arXiv:2205.02416 · Journal of the Optical Society of America B

Characterizing ultra-narrow momentum of atoms by standing-wave light-pulse sequences

Shuyu Zhou, Chen Chen, Bowen Xu, Angang Liang, Ying Wang, Bin Wang

Published Oct 10, 2022• 3 citations
arXivHTMLPDF

Abstract

We propose a method to characterize the ultra-narrow momentum distribution of atomic gases by employing a standing-wave light-pulse sequences beam splitter. The mechanism of beam splitting is analyzed in detail, and the influence of a finite-width momentum distribution on the population of each diffraction order is given. The temperature of ultracold atomic gases can be calibrated by measuring the ratio of population in different diffraction orders after double standing-wave light pulses. We obtain analytical expressions for two typical cases, and demonstrate phase space evolution in the whole process by using the Wigner function. This method is valid for both classical atomic gas and Bose–Einstein condensates, and it is suited for temperature measurement on the space ultracold atomic physics platform, in which the ultra-narrow momentum distribution of atomic gas is of the order of 100 pK or even lower.

DOI
10.1364/josab.469158

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We propose a method to characterize the ultra-narrow momentum distribution of atomic gases by employing a standing-wave light-pulse sequences beam splitter. The mechanism of beam splitting is analyzed in detail, and the influence of a finite-width momentum distribution on the population of each diffraction order is given. The temperature of ultracold atomic gases can be calibrated by measuring the ratio of population in different diffraction orders after double standing-wave light pulses. We obtain analytical expressions for two typical cases, and demonstrate phase space evolution in the whole process by using the Wigner function. This method is valid for both classical atomic gas and Bose–Einstein condensates, and it is suited for temperature measurement on the space ultracold atomic physics platform, in which the ultra-narrow momentum distribution of atomic gas is of the order of 100 pK or even lower.
We experimentally verified our prior theoretical work [J. Opt. Soc. Am. B 39, 3012 (2022)] by employing matter-wave interference to measure the ultranarrow momentum width of an optically trapped Bose-Einstein condensate (BEC) in situ. Splitting the BEC wave packet into various diffraction orders through double stand-wave pulses, we calibrated the momentum width by fitting the oscillation curve of the population of the zero-momentum state. The observed interference fringes exhibited slight deviations from our simplified theory. We numerically calculated the Gross-Pitaevskii equation and utilized Wigner function to gain insight into the impact of the external trap potential and nonlinear term of BEC. We found that the discrepancy was caused by the combined effects of the mean-field interaction and spatial density modulation of BEC. This quantum thermometry is straightforward to apply and is especially well suited for temperature calibration in deep cooling experiments. For atomic samples at the pK level after deep cooling, interatomic interactions can be safely disregarded, enabling momentum-width calibration in a single shot.
In this thesis we investigate the diffraction of cold atomic gases by optical lattices. Of particular interest to atom interferometry is the implementation of a high momentum-transfer ``beam-splitter,'' which may be achieved by inducing quantum resonance in such an atomic gas. We use Monte Carlo simulations to investigate these quantum resonances in the regime where the gas receives laser pulses of finite duration, and demonstrate that an ϵ\epsilonϵ-pseudoclassical model for the dynamics of the gas atoms reproduces quantum resonant behavior for both zero-temperature and finite-temperature non-interacting gases. We show that this model agrees well with the fully quantum treatment of the system over a timescale set by the choice of experimental parameters. In similar setups, the depth of a laser lattice may be measured by exposing an atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the population found in each of the allowed momentum states. We present an analytic model for the time evolution of the atomic populations of the lowest momentum-states, which is sufficient for a weak lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices at zero and finite temperature. We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, leading to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a zero-temperature analytic formula describing such oscillations, extend it to include atoms with initial momenta detuned from our chosen initial value, and analyze the full finite-temperature response.
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>1n>1n>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.
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 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.
Precise knowledge of optical lattice depths is important for a number of areas of atomic physics, most notably in quantum simulation, atom interferometry, and for the accurate determination of transition matrix elements. In such experiments, lattice depths are often measured by exposing an ultracold atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the fraction of atoms found in each of the allowed momentum states by time-of-flight measurement, after some number of pulses. We present a full analytic model for the time evolution of the atomic populations of the lowest momentum states, which is sufficient for a ``weak'' lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices. Finally, we consider the situation where the initial gas is explicitly assumed to be at a finite temperature.