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arXiv:1609.06344 · Physical Review A

Controlling the multiport nature of Bragg diffraction in atom interferometry

Richard H. Parker, C. X. Yu, Brian Estey, Weicheng Zhong, Eric Huang, Holger Müller

Published Nov 18, 2016• 34 citations
arXivHTMLPDF

Abstract

Bragg diffraction has been used in atom interferometers because it allows signal enhancement through multiphoton momentum transfer and suppression of systematics by not changing the internal state of atoms. Its multiport nature, however, can lead to parasitic interferometers, allows for intensity-dependent phase shifts in the primary interferometers, and distorts the ellipses used for phase extraction. We study and suppress these unwanted effects. Specifically, phase extraction by ellipse fitting and the resulting systematic phase shifts are calculated by Monte Carlo simulations. Phase shifts arising from the thermal motion of the atoms are controlled by spatial selection of atoms and an appropriate choice of Bragg intensity. In these simulations, we found that Gaussian Bragg pulse shapes yield the smallest systematic shifts. Parasitic interferometers are suppressed by a ``magic'' Bragg pulse duration. The sensitivity of the apparatus was improved by the addition of ac Stark shift compensation, which permits direct experimental study of sub-part-per-billion (ppb) systematics. This upgrade allows for a $310\ensuremath{\hbar}k$ momentum transfer, giving 6.6 Mrad measured in a Ramsey-Bord\'e interferometer.

DOI
10.1103/physreva.94.053618

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Bragg diffraction has been used in atom interferometers because it allows signal enhancement through multiphoton momentum transfer and suppression of systematics by not changing the internal state of atoms. Its multiport nature, however, can lead to parasitic interferometers, allows for intensity-dependent phase shifts in the primary interferometers, and distorts the ellipses used for phase extraction. We study and suppress these unwanted effects. Specifically, phase extraction by ellipse fitting and the resulting systematic phase shifts are calculated by Monte Carlo simulations. Phase shifts arising from the thermal motion of the atoms are controlled by spatial selection of atoms and an appropriate choice of Bragg intensity. In these simulations, we found that Gaussian Bragg pulse shapes yield the smallest systematic shifts. Parasitic interferometers are suppressed by a ``magic'' Bragg pulse duration. The sensitivity of the apparatus was improved by the addition of ac Stark shift compensation, which permits direct experimental study of sub-part-per-billion (ppb) systematics. This upgrade allows for a 310\ensuremathℏk310\ensuremath{\hbar}k310\ensuremathℏk momentum transfer, giving 6.6 Mrad measured in a Ramsey-Bord'e interferometer.
We experimentally and theoretically study Bragg diffraction as a tool for large-momentum transfer beam splitters in atom interferometry. A theoretical framework is developed to quantify the diffraction phase systematic caused by Bragg diffraction and experiments are performed to confirm these predictions using a Ramsey-Bord\\'e atom interferometer. We then develop methods to systematically cancel and reduce the diffraction phase systematic by carefully selecting Bragg diffraction parameters and utilizing Bloch oscillations. These techniques are then applied to an ongoing precision measurement of $h/m_\\text{Cs}$ for cesium, with the end goal of measuring the fine structure constant alpha\\alphaalpha. We demonstrate a high contrast simultaneous conjugate Ramsey-Bord\\'e interferometer using 5th order Bragg diffraction and 25 common mode Bloch oscillations which achieves 2.5times1062.5\\times 10^62.5times106 radians of phase. We also demonstrate an interferometer with a statistical uncertainty of deltaalpha/alpha=0.25\\delta \\alpha/\\alpha=0.25deltaalpha/alpha=0.25 ppb after 25 hours of integration time that has diffraction phase systematic error of around 1 ppb. Other sources of systematic uncertainty are also thoroughly explored and determined to better than 0.1 ppb. The techniques and theories developed in this thesis will hopefully help enable future precision measurements based on Bragg diffraction.
Velocity-selective Raman transitions are widely used in atom interferometers to prepare atomic ensembles with narrowly defined momentum distributions. However, differential light shifts between atomic energy levels generate velocity distributions that are correlated with the Raman beam intensity, and therefore with the position of the atoms within the laser beam. We show that these spatially inhomogeneous velocity distributions interact with detuning-dependent systematic effects in a Bragg diffraction-based simultaneous conjugate Ramsey-Bordé interferometer. These interactions can induce systematic phase shifts of order 10 milliradians in the interferometer phase. We further identify a "magic" detuning for velocity selection and show that operating at this detuning suppresses the systematic phase shift. Magic velocity selection eliminates systematic errors arising from correlations between atom velocity and position, facilitating high-resolution atom interferometry experiments targeting sub-part-per-billion accuracy.
Bragg diffraction of matter waves is an established technique used in the most accurate quantum sensors. It is also the method of choice to operate large-momentum-transfer, high-sensitivity atom interferometers. It suffers, however, from an intrinsic multi-path character. Optimal control theory (OCT) has recently led to an improved robustness of atom interferometers to a range of challenging environmental effects such as vibrations or platform accelerations. In this theoretical work, we apply OCT protocols to control the Bragg diffraction phase shifts, thereby enhancing the metrological accuracy of the interferometer. We show a minimization of the diffraction phase for realistic conditions of finite temperature of the incoming wavepacket in a multi-path, high-order Bragg interferometer in a Mach–Zehnder configuration. We study input states with different momentum widths and find that our approach mitigates diffraction phases below the microradian level in the case of 1% of the photon recoil, thereby eliminating one of the leading systematic effects in atom interferometry.
We report here on the realization of light-pulse atom interferometers with large-momentum-transfer atom optics based on a sequence of Bragg transitions. We demonstrate momentum splitting up to 200 photon recoils in an ultracold atom interferometer. We highlight a new mechanism of destructive interference of the losses leading to a sizable efficiency enhancement of the beam splitters. We perform a comprehensive study of parasitic interferometers due to the inherent multiport feature of the quasi-Bragg pulses. Finally, we experimentally verify the phase shift enhancement and characterize the interferometer visibility loss.
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.
We present up to 24-photon Bragg diffraction as a beam splitter in light-pulse atom interferometers to achieve the largest splitting in momentum space so far. Relative to the 2-photon processes used in the most sensitive present interferometers, these large momentum transfer beam splitters increase the phase shift 12-fold for Mach-Zehnder (MZ) and 144-fold for Ramsey-Bordé (RB) geometries. We achieve a high visibility of the interference fringes (up to 52% for MZ or 36% for RB) and long pulse separation times that are possible only in atomic fountain setups. As the atom's internal state is not changed, important systematic effects can cancel.