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arXiv:2203.07017 · Physical Review A

Bragg-diffraction-induced imperfections of the signal in retroreflective atom interferometers

Jens Jenewein, Sabrina Hartmann, Albert Roura, Enno Giese

Published Jun 16, 2022• 8 citations
arXivHTMLPDF

Abstract

We present a detailed study of the effects of imperfect atom-optical manipulation in Bragg-based light-pulse atom interferometers. Off-resonant higher-order diffraction leads to population loss, spurious interferometer paths, and diffraction phases. In a path-dependent formalism, we study numerically various effects and analyze the interference signal caused by an external phase or gravity. We compare first-order single and double Bragg diffraction in retroreflective setups. In double Bragg diffraction, phase imperfections lead to a beating due to three-path interference. Some effects of diffraction phases can be avoided by adding the population of the outer exit ports of double diffraction.

DOI
10.1103/physreva.105.063316

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We present a detailed study of the effects of imperfect atom-optical manipulation in Bragg-based light-pulse atom interferometers. Off-resonant higher-order diffraction leads to population loss, spurious interferometer paths, and diffraction phases. In a path-dependent formalism, we study numerically various effects and analyze the interference signal caused by an external phase or gravity. We compare first-order single and double Bragg diffraction in retroreflective setups. In double Bragg diffraction, phase imperfections lead to a beating due to three-path interference. Some effects of diffraction phases can be avoided by adding the population of the outer exit ports of double diffraction.
In a retroreflective scheme with an atom initially at rest, atomic Raman diffraction adopts some of the properties of Bragg diffraction due to additional couplings to off-resonant momenta. As a consequence, double Raman diffraction has to be performed in a Bragg-type regime, where the pulse duration is sufficiently long to suppress diffraction into spurious orders. Taking advantage of this regime, double Raman allows for resonant higher-order diffraction. We study theoretically the case of third-order diffraction and compare it to first order as well as a sequence of first-order Raman pulses giving rise to the same momentum transfer as the third-order pulse. Moreover, we demonstrate that interferometry is possible, and we investigate amplitude and contrast of a third-order double Raman Mach-Zehnder interferometer. In fact, third-order diffraction constitutes a competitive tool for the diffraction of ultracold atoms and interferometry based on large momentum transfer since it allows one to reduce the complexity of the experiment as well as the total duration of the diffraction process compared to a sequence, at the cost of higher pulse intensities.
The use of retroreflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called ``method of averaging,'' which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.
Spin squeezing in atomic ensembles enables atom interferometry with sensitivities below the shot-noise limit, but the associated entanglement is highly susceptible to loss, making imperfections in atom optics a central limitation. Bragg diffraction is an established technique for driving transitions between atomic momentum states and enables large-momentum transfer through higher-order diffraction while preserving the internal state. However, it is intrinsically limited by two competing mechanisms: Short light pulses induce parasitic diffraction into off-resonant orders beyond an effective two-level description, while long pulses face velocity selectivity. We derive analytical expressions in a second-quantized framework for the atom optics and phase uncertainty of a Mach-Zehnder interferometer including these effects. We demonstrate that sub-shot-noise scaling is achieved only in a regime of intermediate pulse duration. Furthermore, we show that deleterious effects of higher-order diffraction are partially mitigated by optimizing the input quantum state.
Imperfect Raman pulses can lead to the formation of multiple interfering paths and affect the output of an atom interferometer in high-precision measurement.We study the effect of the imperfect Raman pulses on the interferometric fringe contrast and the phase shift in the three-pulse atom interferometer by using the evolution operator method.Analytical expressions expanded to the second-order fluctuation of imperfect pulses are derived, in which the effect of coupling the imperfect pulses with laser detuning and pulse duration is also considered.The result indicates that the second-order fluctuation of imperfect pulses is dominant, however, it can be nearly ignored in the current requirements of atomic experiments.Even so, theoretical analysis is very necessary as it may be helpful in proposing some schemes to improve the interference efficiency for future high-precision measurements with atomic interferometry.
Light pulses have proven to be a powerful and versatile tool to implement beam splitters and mirrors for matter waves enabling atom interferometers. However, for high-precision measurements with such devices the specific realization is crucial and novel techniques might increase the sensitivity. To illustrate the diversity of light-pulse beam splitting and the subtle differences between the diffraction mechanisms, we study atomic Raman, Bragg, and the new method of double Bragg diffraction in a coherent way. Moreover, we introduce a versatile formalism to determine the interference signal of a Mach-Zehnder geometry and give an interpretation in terms of proper-time difference. In addition, we explore the feasibility of a specular mirror for atoms, which might lead to an interferometer testing the equivalence principle.
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.