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arXiv:2101.07647 · Physical Review A

Aberrations in (3+1)-dimensional Bragg diffraction using pulsed Laguerre-Gaussian laser beams

Antje Neumann, Martina Gebbe, R. Walser

Published Apr 5, 2021• 5 citations
arXivHTMLPDF

Abstract

We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Laguerre-Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Laguerre-Gaussian laser beam envelope, studied with (3+1)-dimensional numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular, Gaussian, Blackman, and hyperbolic secant pulses. For the last, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the $\ensuremath{\pi}$-pulse time is explained from a renormalization of the simple Pendell\"osung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)-dimensional numerical simulations for pulsed Laguerre-Gaussian laser beams, as well as experimental data, and find very good agreement considering a mixture of Bose-Einstein condensate and thermal cloud.

DOI
10.1103/physreva.103.043306

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We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Laguerre-Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Laguerre-Gaussian laser beam envelope, studied with (3+1)-dimensional numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular, Gaussian, Blackman, and hyperbolic secant pulses. For the last, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the \ensuremathπ\ensuremath{\pi}\ensuremathπ-pulse time is explained from a renormalization of the simple Pendell"osung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)-dimensional numerical simulations for pulsed Laguerre-Gaussian laser beams, as well as experimental data, and find very good agreement considering a mixture of Bose-Einstein condensate and thermal cloud.
Atomic diffraction is the central concept of matter-wave interferometers, which provide the opportunity of high-precision rotation and acceleration sensing. Ultracold atoms are the ultimate quantum sensors for this purpose. Transferring photon momentum from two counterpropagating laser beams to atomic wavepackets prepares coherent superpositions in the momentum space, realising atomic beamsplitters and mirrors. Like classical optical systems, these matter-wave devices require exact specifications and ubiquitous imperfections need to be quantified. Therefore, in this thesis, the performance of (3+1)D atomic beamsplitters in the quasi-Bragg regime is studied numerically as well as analytically and is confirmed by experimental data [1]. Ideally, the incoming wavepacket can be split exactly into two parts or reflected perfectly with unit response, independent of its spatial and velocity distribution. However, the velocity selectivity of the Bragg diffraction, as well as losses into undesired diffraction orders in the quasi-Bragg regime, constitute aberrations, which cannot be neglected. The non-ideal behaviour due to spatial variations of the laser beam profiles and wavefront curvatures, regarding realistic Laguerre-Gaussian laser beams instead of ideal plane waves, reduces the diffraction efficiency and leads to rogue momentum components, just like misaligned lasers. In contrast, smooth temporal envelopes improve the beamsplitter performance. Different pulse shapes are taken into account, where some are amenable for closed analytical solutions. The realistic modelling and exhausting aberration studies characterises in detail atomic Bragg beamsplitters and demonstrate pathways for improvements, both required by challenging experiments. For hot ions in accelerator beams the atomic diffraction is used contrary to generate a velocity filter. Two counterpropagating far-detuned lasers transfer a narrow velocity class of ions from an initially broad distribution via a stimulated Raman transition between the ground states of a Λ-system. This colder subensemble prepares optimal initial conditions for precision collinear laser spectroscopy on fast ion beams. The efficiency of the filter is diminished by aberrations like the spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise. Spatial intensity variations of the ion and laser beams are considered, whereas wavefront curvature is negligible. A comprehensive master equation leads to conditions for the optimal frequency pair of lasers. The time-resolved population transfer characterises the filter performance and is evaluated numerically as well as analytically. Derived models match the numerical results, keeping the computational effort small. Taking into account the mentioned aberrations, the possible use of Raman transition as velocity filter for hot ions is demonstrated. Velocity classes with widths as low as 0.2 m/s can be transferred, achieving a significant population proportion from per mill to percent. Applying the analysis to current 40-Ca+ ion experiments, a sensitivity for measuring high ion acceleration voltages on the ppm level or below is substantiated.
The transition efficiency of atomic Bragg diffraction as mirrors and beam splitters in Bragg atom interferometers plays an essential role in impacting the fringe contrast and measurement sensitivity. This can be attributed to the properties of atomic sources, Bragg pulse shapes, the pulse duration, and the relative position deviation of the atoms and Bragg pulses. Here, we investigate the effect of the atomic source's diffusion and velocity width on the efficiency of Bragg diffraction of the moving cold atomic cloud. The transfer efficiency of Bragg mirrors and beam splitters are numerically simulated and experimentally measured, which are well consistent in comparison. We quantify these effects of atomic diffusion and velocity width and precisely compute how Bragg pulses' efficiencies vary as functions of these parameters. Our results and methodology allow us to optimize the Bragg pulses at different atomic sources and will help in the design of large momentum transfer mirrors and beam splitters in atom interferometry experiments.
Abstract Multi-photon Bragg diffraction is a powerful method for fast, coherent momentum transfer of atom waves. However, laser noise, Doppler detunings, and cloud expansion limit its efficiency in large momentum transfer (LMT) pulse sequences. We present simulation studies of robust Bragg pulses developed through numerical quantum optimal control. Optimized pulse performance under noise and cloud inhomogeneities is analyzed and compared to analogous Gaussian and adiabatic rapid passage pulses in simulated LMT Mach–Zehnder interferometry sequences. The optimized pulses maintain robust population transfer and phase response over a broader range of noise, resulting in superior contrast in LMT sequences with thermal atom clouds and intensity inhomogeneities. Large optimized LMT sequences use lower pulse area than Gaussian pulses, making them less susceptible to spontaneous emission loss. The optimized sequences maintain over five times better contrast with tens of ℏ k momentum separation and offer more improvement with greater LMT. Such pulses could allow operation of Bragg atom interferometers with unprecedented sensitivity, improved contrast, and hotter atom sources.
Bragg diffraction of an atomic wave packet in a retroreflective geometry with two counterpropagating optical lattices exhibits a light shift induced phase. We show that the temporal shape of the light pulse determines the behavior of this phase shift: In contrast to Raman diffraction, Bragg diffraction with Gaussian pulses leads to a significant suppression of the intrinsic phase shift due to a scaling with the third power of the inverse Doppler frequency. However, for box-shaped laser pulses, the corresponding shift is twice as large as for Raman diffraction. Our results are based on approximate but analytical expressions as well as a numerical integration of the corresponding Schr\"odinger equation.
We present an analytic theory of the diffraction of (matter) waves by a lattice in the ``quasi-Bragg" regime, by which we mean the transition region between the long-interaction Bragg and ``channeling'' regimes and the short-interaction Raman-Nath regime. The Schr\"odinger equation is solved by adiabatic expansion, using the conventional adiabatic approximation as a starting point, and reinserting the result into the Schr\"odinger equation to yield a second-order correction. Closed expressions for arbitrary pulse shapes and diffraction orders are obtained and the losses of the population to output states otherwise forbidden by the Bragg condition are derived. We consider the phase shift due to couplings of the desired output to these states that depends on the interaction strength and duration and show how these can be kept negligible by a choice of smooth (e.g., Gaussian) envelope functions even in situations that substantially violate the adiabaticity condition. We also give an efficient method for calculating the effective Rabi frequency (which is related to the eigenvalues of Mathieu functions) in the quasi-Bragg regime.
We report on the experimental study of a Bragg reflector for guided, propagating Bose-Einstein condensates. A one-dimensional attractive optical lattice of finite length created by red-detuned laser beams selectively reflects some velocity components of the incident matter wave packet. We find quantitative agreement between the experimental data and one-dimensional numerical simulations and show that the Gaussian envelope of the optical lattice has a major influence on the properties of the reflector. In particular, it gives rise to multiple reflections of the wave packet between two symmetric locations where Bragg reflection occurs. Our results are a further step towards integrated atom-optics setups for quasi-cw matter waves.