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arXiv:2002.10785 · Physical Review A

Limitations for field-enhanced atom interferometry

D. Comparat

Published Feb 14, 2020• 7 citations
arXivHTMLPDF

Abstract

We discuss the possibility to enhance the sensitivity of optical interferometric devices by increasing their open area using an external field gradient that acts differently on the two arms of the interferometers. The use of a combined electric and magnetic field cancels nonlinear terms that dephase the interferometer. This is possible using well-defined (typically with $n\ensuremath{\sim}20$ Rydberg) states, a magnetic field of a few Tesla, and an electric field gradient of $\ensuremath{\sim}10\phantom{\rule{0.28em}{0ex}}\mathrm{V}/{\mathrm{cm}}^{2}$. However, this allows for interaction times only on the order of tens of microseconds, leading to a reachable accuracy of only 1 or 2 orders of magnitude higher than standard light-pulse atom interferometers. Furthermore, the control of fields and states and three-dimensional (3D) trajectories puts severe limits to the reachable accuracy. This idea is therefore not suitable for precision measurement but might eventually be used for gravity or neutrality in antimatter studies.

DOI
10.1103/physreva.101.023606

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We discuss the possibility to enhance the sensitivity of optical interferometric devices by increasing their open area using an external field gradient that acts differently on the two arms of the interferometers. The use of a combined electric and magnetic field cancels nonlinear terms that dephase the interferometer. This is possible using well-defined (typically with n\ensuremath∼20n\ensuremath{\sim}20n\ensuremath∼20 Rydberg) states, a magnetic field of a few Tesla, and an electric field gradient of \ensuremath∼10V/cm2\ensuremath{\sim}10\phantom{\rule{0.28em}{0ex}}\mathrm{V}/{\mathrm{cm}}^{2}\ensuremath∼10V/cm2. However, this allows for interaction times only on the order of tens of microseconds, leading to a reachable accuracy of only 1 or 2 orders of magnitude higher than standard light-pulse atom interferometers. Furthermore, the control of fields and states and three-dimensional (3D) trajectories puts severe limits to the reachable accuracy. This idea is therefore not suitable for precision measurement but might eventually be used for gravity or neutrality in antimatter studies.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultracold atoms can be precisely manipulated at the quantum level and can be held for very long times in traps; they would therefore be an ideal setting for interferometry. In this paper, we discuss how the nonlinearities from atom–atom interactions, on the one hand, allow us to efficiently produce squeezed states for enhanced readout and, on the other hand, result in phase diffusion that limits the phase accumulation time. We find that low-dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom–atom interactions. Even for time sequences generated by optimal control, the achievable minimal detectable interaction energy Δ E min is of the order of 10 −4 μ, where μ is the chemical potential of the Bose–Einstein condensate (BEC) in the trap. From these we have to conclude that for more precise measurements with atom interferometers, more sophisticated strategies, or turning off the interaction-induced dephasing during the phase accumulation stage, will be necessary.
The basic physical principles behind atom interferometers based on optical pulses of light are summarized. This method of atom interferometry is based on measurements in the time and frequency domain and is an inherently precise measurement technique. After a brief discussion of some of the important technical requirements for good fringe accuracy and visibility, we describe an interferometer that has measured the acceleration of an atom due to gravity with a resolution better than one part in 1010. We project that the absolute accuracy of our measurement will be of the order of a few parts in 109. We also describe an interferometer experiment that measures the recoil energy shift of an atom when it absorbs a photon. When combined with the value of the Rydberg constant and the mass ratios MCs/mp and mp/me, one can obtain a value for α, the fine structure constant. Currently, we have an experimental resolution Δα/α ∼ 10-8 after two hours of integration time and are studying the systematic effects that affect the measurement.
To increase the measured phase of an atom interferometer and improve its sensitivity, researchers attempt to increase the enclosed space-time area using two methods: creating larger separations between the interferometer arms and having longer evolution times. However, increasing the evolution time reduces the bandwidth that can be sampled, whereas decreasing the evolution time worsens the sensitivity. In this paper, we attempt to address this by proposing a setup for high-bandwidth applications, with improved overall sensitivity. This is realized by accelerating and holding the atoms using optical dipole traps. We find that accelerations of up to 103–105{10}^{3}\text{--}{10}^{5}103–105 m/s2{\mathrm{m/s}}^{2}m/s2 can be achieved using acousto-optic deflectors to move the traps. By comparing the sensitivity of our approach to acceleration as a baseline to traditional atom interferometry, we find a substantial improvement to the state of the art. In the limit of appropriate beam and optics stabilization, sensitivities approaching ${10}^{\ensuremath{-}14}$ (m/s2{\mathrm{m/s}}^{2}m/s2)/Hz\sqrt{\mathrm{Hz}}Hz​ may be achievable at 1 Hz, while detection at 1 kHz with a sensitivity an order of magnitude better than traditional free-fall atom interferometers is possible with today's systems.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many elds of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long measurement times and precise readout. Ultra cold atoms can be precisely manipulated at the quantum level, held for very long times in traps, and would therefore be an ideal setting for interferometry. In this paper we discuss how the non-linearities from atom-atom interactions on one hand allow to efficiently produce squeezed states for enhanced readout, but on the other hand result in phase diffusion which limits the phase accumulation time. We find that low dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom-atom interactions. Even for time sequences generated by optimal control the achievable minimal detectable interaction energy ∆Emin is on the order of 10−4µ, where µ is the chemical potential of the BEC in the trap. From there we have to conclude that for more precise measurements with atom interferometers more sophisticated strategies, or turning off the interaction induced dephasing during the phase accumulation stage, will be necessary. PACS numbers: 37.25.+k,03.75.-b,37.10.Gh,02.60.Pn
The mirrors and beamsplitters of atom interferometers often suffer from inhomogeneities in coupling strength and effective detuning because different atoms see different laser intensities, Zeeman and Doppler shifts and are in different Zeeman sub-states. This limits the fringe visibility for a simple interferometer, which falls off rapidly if extra mirrors are added, for example to increase the interferometer area. In practice, one usually therefore filters the atomic velocities/sub-states, thus losing signal, and/or restricting operation to small-area interferometers with low sensitivity. The problem is familiar in the field of NMR, where, instead of using simple pi or pi/2 pulses, the phase and potentially amplitude are modulated during the pulse so as to make the result robust to the inhomogeneities encountered. Despite the similarities with NMR systems, the numbers, correlations and performance measures for atom interferometry are different. We have used optimal control theory to obtain robust high fidelity mirror pulses for atom interferometry. Importantly, while the designs are found by computational simulation, we can validate them experimentally, with remarkably good agreement. We have addressed the optimization of individual mirror pulses, but the eventual aim is to optimize the interferometer as a whole: errors introduced in one pulse can be compensated at a later stage, for example. Our pulses yield high contrast without the need to filter the atomic sample and maintain this even in the case of extended pulse sequences, thus making it possible to achieve significantly larger interferometer areas than with simple pi pulses.