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Optical and Quantum Sensing and Precision Metrology II

Measuring AC Zeeman shifts using a trapped cold atom interferometer on chip

B. Wirtschafter, Soizic Hello, Christoph Ira Westbrook, Matthieu Dupont-Nivet

Published Mar 19, 2025• 0 citations
Publisher

Abstract

Atom chip based interferometry holds signicant promise for embedded precise measurements of time, accelerations, rotations, and magnetic fields. It can enable compact sensors for various carriers like planes, boats, and drones, making it advantageous for navigation applications. When measuring acceleration with a cold atom interferometer, it is necessary to separate the two states during the interferometry sequence. Microwave dressed potentials generated from CPWs within a magnetic trap are one approach to achieve such on-chip manipulation. Two specic challenges arise in this process. First, the microwave field emitted by a waveguide introduces an AC Zeeman shifts, leading to a bias phase in the interferometer output. Precise determination of this bias is necessary for accurate parameter readout. Second, positioning the atom trap accurately between the two waveguides is crucial to obtain the necessary symmetry during separation; otherwise, the contrast of the interferometer is signicantly reduced. To address these challenges, we present a method for measuring AC Zeeman shifts using Ramsey interferometry.

DOI
10.1117/12.3039019

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Atom chip based interferometry holds signicant promise for embedded precise measurements of time, accelerations, rotations, and magnetic fields. It can enable compact sensors for various carriers like planes, boats, and drones, making it advantageous for navigation applications. When measuring acceleration with a cold atom interferometer, it is necessary to separate the two states during the interferometry sequence. Microwave dressed potentials generated from CPWs within a magnetic trap are one approach to achieve such on-chip manipulation. Two specic challenges arise in this process. First, the microwave field emitted by a waveguide introduces an AC Zeeman shifts, leading to a bias phase in the interferometer output. Precise determination of this bias is necessary for accurate parameter readout. Second, positioning the atom trap accurately between the two waveguides is crucial to obtain the necessary symmetry during separation; otherwise, the contrast of the interferometer is signicantly reduced. To address these challenges, we present a method for measuring AC Zeeman shifts using Ramsey interferometry.
We present an on-chip cold atom inertial sensor based on a Ramsey sequence configured to measure acceleration. Cold atom interferometers are of great interest due to their excellent stability and sensitivity to inertial effects. Atom chips enable a drastic size reduction of the sensor by trapping atoms during the whole measurement. During the interferometry sequence, we create a superposition of two atomic states and spatially split them, rendering the device sensitive to acceleration. We give the current noise budget at Allan deviation first point for our on-chip accelerometer.
Summary form only given. Atom chips [1] have shown to be very successful for trapping and manipulating cold atoms. Atom interferometry in the vicinity of an atom chip has been recently achieved by coherently splitting a Bose-Einstein condensate with radiofrequency [2] and microwave [3] dressing. However, some limitations on the precision of the phase measurement occur in this case due to the phase diffusion process resulting from mean field interactions in the Bose-Einstein condensate.In this communication, we will discuss the possibility of using a thermal (i.e. non-condensed) ensemble of ultra-cold atoms trapped on an atom chip in order to create a trapped-atom interferometer with much weaker atomic interactions. In such a scheme (which can be seen as the atomic equivalent of a white light interferometer in optics), the coherence time will strongly depend on the level of symmetry that can be achieved between the potentials forming the two arms of the interferometer. For example, in a simple model of two harmonic potentials, it can be shown that a slight relative frequency difference Δω/ω can be associated with a limitation on the coherence time T given by the following expression: T≈ 2π1ίω kΘ Δω where Θ is the temperature of the atomic ensemble and k the Boltzmann constant (the latter expression being valid only for kΘ >> ! ω). For example, a relative asymmetry of 10-3 will result, for a temperature of about 1μK, to a limitation on the coherence time of 40ms, which favourably compares to what has been achieved experimentally with Bose-Einstein condensates [2]. We will then discuss how we plan to achieve, with the on-going experiment at Thales TRT [4], a splitting of the atomic cloud with the highest possible level of symmetry. The basic idea is to use internal state labelling on the so-called “clock states” of the 87Rb atom and microwave dressing [3] with two independent coplanar waveguides, each waveguide being preferentially resonant with one of the two internal states involved in the process. This way, we expect to have quasi-independent control over the two arms of the interferometer and thus to be able to achieve a coherent splitting as much symmetrical as possible.We will finally discuss the potential applications of this technique in terms of acceleration and gravity measurement with cold atoms on a chip, which could be of great interest in the future if combined, for example, with high bandwidth microelectromechanical sensors.
We present a toolbox of microstrip building blocks for microwave atom chips geared towards trapped atom interferometry. Transverse trapping potentials based on the AC Zeeman (ACZ) effect can be formed from the combined microwave magnetic near fields of a pair or a triplet of parallel microstrip transmission lines. Axial confinement can be provided by a microwave lattice (standing wave) along the microstrip traces. Microwave fields provide additional parameters for dynamically adjusting ACZ potentials: detuning of the applied frequency to select atomic transitions and local polarization controlled by the relative phase in multiple microwave currents. Multiple ACZ traps and potentials, operating at different frequencies, can be targeted to different spin states simultaneously, thus enabling spin-specific manipulation of atoms and spin-dependent trapped atom interferometry.
Ultracold atom experiments use a gas of neutral atoms with temperatures less than 100 µK above absolute zero and offer unmatched experimental control of quantum states and coherence, which has allowed ultracold atom-based measurements to be some of the most precise to date. While ultracold atom experiments can control almost all atomic degrees of freedom, spin-dependent trapping and spatial manipulation has remained difficult if not inaccessible. We are developing a method of spin-dependent trapping and spatial manipulation for ultracold neutral atoms using the AC Zeeman force produced by a microwave magnetic near-field gradient generated by an atom chip. We measure the AC Zeeman force on ultracold rubidium atoms by observing its effect on the motion of atoms in free-fall and on those confined in a trap. We have studied the force as a function of microwave frequency detuning from a hyperfine transition at 6.8 GHz at several magnetic field strengths and have observed its characteristic bipolar and resonant features predicted by two-level dressed atom theory. We find that the force is several times the strength of gravity in our setup, and that it can be targeted to a specific hyperfine transition while leaving other hyperfine states and transitions relatively unaffected. We find that our measurements are reasonably consistent with parameter-free theoretical predictions.
Atom optics has been a highly active field of research with many scientific breakthroughs over the past two decades, largely due to successful advances in laser technology, microfabrication techniques, and the development of laser cooling and trapping of neutral atoms. This dissertation details several atom optics experiments with the motivation to develop tools and techniques for precision atom wave interferometry. It provides background information about atom optics and the fundamentals behind laser cooling and trapping, including basic techniques for cold gas thermometry and absorptive detection of atoms. A brief overview of magnetic trapping and guiding in tight wire-based traps is also provided before the experimental details are presented. ❧ We developed a novel laser source of 780 nm light using frequency-doubled 1560 nm fiber amplifier. This laser system provided up to a Watt of tunable frequency stabilized light for two Rb laser cooling and trapping experiments. One system generates Bose-Einstein condensates in an optical trap while the second is based on atom chip magnetic traps. The atom chip system, detailed in this thesis, was designed and built to develop the tools necessary for transport and loading large numbers of cold atoms and explore the potential for guided atom interferometry. Techniques and results from this experiment are presented, including an efficient magnetic transport and loading method to deliver cold atom to atom chip traps. We also developed a modeling tool for the magnetic fields formed by coiled wire geometries, as well as planar wire patterns. These models helped us design traps and determine adiabatic transportation of cold atoms between macro-scale traps and micro-traps formed on atom chips. Having achieved near unity transfer efficiency, we demonstrated that this approach promises to be a consistent method for loading large numbers of atoms into micro-traps. Furthermore, we discuss an in situ imaging technique to investigate magnetic field contours of the traps and the dynamics of atoms within those confining potentials. We also controlled the propagation along the atom chip guides by accelerating atoms with longitudinal magnetic gradients, and investigated an atom focusing scheme. ❧ While the atom chip wire guides perform a role analogous to optical fibers guiding light waves, ""free space"" cold atoms offer great opportunity for precision interferometry. We describe a second on-going atom optics experiment that measures gravity gradients using a pair of atom fountain interferometers separated by one meter. We have demonstrated Gravity Gradiometer resolution down to 4x10⁻⁹ g/m using a 40 kg test mass. The atomic physics subsystem is described in detail, including the vacuum, cold atom source, optics, magnetic coils and shields, and vibration isolation and compensation. The system is designed to be a compact, robust, transportable instrument, taking strides towards future gravity gradient measurements in the field. In the realm of space applications, there has been interest for micro-gravity science experiments aboard the International Space Station, along with instrument development for gravity mapping of Earth and planetary bodies with satellite-based instruments. Furthermore, there are ground-based applications for gravity imaging of local density distributions, precision measurement of gravity, as well as proposals for redefining the kilogram, detecting gravitational waves and determining the Gravitational constant.
Spin-specific trapping and mechanical control of ultracold atoms is difficult with current techniques, but offers the possibility of exploring new physics systems, such as spin-dependent trapped atom interferometers, as well as quantum gates, 1D many-body spin gases, and novel cooling schemes. Microwave near-field potentials based on the AC Zeeman effect provide a mechanism for such spin-specific control of atoms: in principle, independent potentials can be targeted to different spin states simultaneously. A broadband microwave atom chip can be used to generate both AC Zeeman trapping potentials and a microwave lattice for long distance trap positioning. We present recent experimental results on the successful trapping of ultracold rubidium atoms in an AC Zeeman atom chip trap using RF intra-hyperfine manifold transitions. Notably, these traps suppress the potential roughness encountered in traditional micro-magnetic chip traps.