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arXiv:2012.07792

Doppler Compensated Cavity For Atom Interferometry

Rustin Nourshargh, Sam Hedges, Mehdi Langlois, Kai Bongs, Michael Holynski

Published Dec 14, 2020• 0 citations
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Abstract

We propose and demonstrate a scheme to enable Doppler compensation within optical cavities for atom interferometry at significantly increased mode diameters. This has the potential to overcome the primary limitations in cavity enhancement for atom interferometry, circumventing the cavity linewidth limit and enabling mode filtering, power enhancement, and a large beam diameter simultaneously. This approach combines a magnified linear cavity with an intracavity Pockels cell. The Pockels cell introduces a voltage tunable birefringence allowing the cavity mode frequencies to track the Raman lasers as they scan to compensate for gravitationally induced Doppler shifts, removing the dominant limitation of current cavity enhanced systems. A cavity is built to this geometry and shown to simultaneously realize the capability required for Doppler compensation, with a 5.04~mm $1/e^{2}$ diameter beam waist and an enhancement factor of $>$5x at a finesse of 35. Furthermore, this has a tunable Gouy phase, allowing the suppression of higher order spatial modes and the avoidance of regions of instability. This approach can therefore enable enhanced contrast and longer atom interferometry times while also enabling the key features of cavity enhanced atom interferometry, power enhancement and the reduction of aberrations. This is relevant to future reductions in the optical power requirement of quantum technology, or in providing enhanced performance for atom interferometers targeting fundamental science.

DOI
10.48550/arxiv.2012.07792

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We propose and demonstrate a scheme to enable Doppler compensation within optical cavities for atom interferometry at significantly increased mode diameters. This has the potential to overcome the primary limitations in cavity enhancement for atom interferometry, circumventing the cavity linewidth limit and enabling mode filtering, power enhancement, and a large beam diameter simultaneously. This approach combines a magnified linear cavity with an intracavity Pockels cell. The Pockels cell introduces a voltage tunable birefringence allowing the cavity mode frequencies to track the Raman lasers as they scan to compensate for gravitationally induced Doppler shifts, removing the dominant limitation of current cavity enhanced systems. A cavity is built to this geometry and shown to simultaneously realize the capability required for Doppler compensation, with a 5.04~mm 1/e21/e^{2}1/e2 diameter beam waist and an enhancement factor of >>>5x at a finesse of 35. Furthermore, this has a tunable Gouy phase, allowing the suppression of higher order spatial modes and the avoidance of regions of instability. This approach can therefore enable enhanced contrast and longer atom interferometry times while also enabling the key features of cavity enhanced atom interferometry, power enhancement and the reduction of aberrations. This is relevant to future reductions in the optical power requirement of quantum technology, or in providing enhanced performance for atom interferometers targeting fundamental science.
We propose and demonstrate a scheme for Doppler compensated optical cavity enhancement of atom interferometers at significantly increased mode diameters. This overcomes the primary limitations in cavity enhancement for atom interferometry, circumventing the cavity linewidth limit and enabling spatial mode filtering, power enhancement, and a large beam diameter simultaneously. This approach combines a magnified linear cavity with an intracavity Pockels cell. The Pockels cell induces a voltage-controlled birefringence allowing the cavity mode frequencies to follow the Raman lasers as they track gravitationally induced Doppler shifts, removing the dominant limitation of current cavity enhanced systems. A cavity is built to this geometry and shown to simultaneously realise Doppler compensation, a 5.8 ± 0.15 mm1/ e 2 diameter beam waist and an enhancement factor of >5× at a finesse of 35. Tuneable Gouy phase enables the suppression of higher order spatial modes and the avoidance of regions of instability. Atom interferometers will see increased contrast at extended interferometry times along with power enhancement and the reduction of optical aberrations. This is relevant to power constrained applications in quantum technology, alongside the absolute performance requirements of fundamental science.
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Summary form only given. The development of atom interferometry in the last few decades has led to high precision measurements of inertial effects and tests of fundamental physics [1]. New methods for higher sensitivity atom interferometers (AIs) are being explored, in particular the interrogation of atoms with optical cavities. The benefits of optical cavities would be higher optical power allowing large momentum transfer beam splitters, and possibly cleaner and controlled phase profiles [2]. However high sensitivity AIs require long interrogation times, which, combined with cold atom cloud expansion, bring the challenges of large centimetric waists in cavities. We propose an optical resonator composed of a convergent lens with two flat mirrors at its focal planes as shown on figure 1 [3]. When perfectly aligned any input field can be resonating inside. Especially, when a Gaussian beam, with waist w0' on the first mirror, is inputted to the cavity, the lens conjugates it to the second mirror with waist w0= λf/πw0'. This cavity is marginally stable and exhibits a half degenerate behaviour: all modes resonate at the same frequencies, odd and even modes being separated by half a free spectral range. Thus it does not have strong mode cleaning properties but it is able to magnify any input field. When misaligned, this cavity goes out of its degenerate behaviour and the circulating field begins to degrade due to mode filtering. A numerical study of the cavity behaviour, using an ABCD transfer matrix formalism, showed that typical controllable misalignments of a few micrometres would not be critical for atom interrogation. Further degradations due to surface defects and tilts are being investigated.
Optical cavities can enhance atom-light coupling in atom interferometry, but free-fall geometries require large transverse modes. Marginally stable resonators provide such modes, yet aberrations and alignment imperfections turn their near-degenerate response into detuning-dependent transverse ring modes, strongly limiting the usable interaction volume under static excitation. Here, we turn this limitation into a resource. By chirping the interrogation frequency across the cavity resonance while dynamically shaping the input amplitude, we map laser detuning onto the transverse position and scan the cavity-enhanced coupling across the atomic cloud. In a cavity-enhanced Bragg diffraction experiment with 87^{87}87Rb atoms, this produces a nearly uniform effective interaction region of about 15 mm and increases the transfer efficiency from about 5% to 28%. We also demonstrate phase-coherent operation of a three-pulse atom interferometer using chirped cavity-enhanced Bragg pulses. These results establish scanning-cavity interrogation as a route to large-area, cavity-enhanced atom interferometry.
Abstract Large-scale atom interferometers promise unrivaled strain sensitivity to mid-band gravitational waves, and will probe a new parameter space in the search for ultra-light scalar dark matter. These proposals require gradiometry with kilometer-scale baselines, a momentum separation above 104ℏk between interferometer arms, and optical transitions to long-lived clock states to reach the target sensitivities. Prohibitively high optical power and wavefront flatness requirements have thus far limited the maximum achievable momentum splitting. Here we propose a scheme for optical cavity enhanced atom interferometry, using circulating, spatially resolved pulses, and intracavity frequency modulation to meet these requirements. We present parameters for the realization of 20 kW circulating pulses in a 1 km interferometer enabling 104ℏk splitting on the 698 nm clock transition in 87Sr. This scheme addresses the presently insurmountable laser power requirements and is feasible in the context of a kilometer-scale atom interferometer facility.
Atom interferometers employing optical cavities to enhance the beam splitter pulses promise significant advances in science and technology, notably for future gravitational wave detectors. Long cavities, on the scale of hundreds of meters, have been proposed in experiments aiming to observe gravitational waves with frequencies below 1 Hz, where laser interferometers, such as LIGO, have poor sensitivity. Alternatively, short cavities have also been proposed for enhancing the sensitivity of more portable atom interferometers. We explore the fundamental limitations of two-mirror cavities for atomic beam splitting, and establish upper bounds on the temperature of the atomic ensemble as a function of cavity length and three design parameters: the cavity ggg factor, the bandwidth, and the optical suppression factor of the first and second order spatial modes. A lower bound to the cavity bandwidth is found which avoids elongation of the interaction time and maximizes power enhancement. An upper limit to cavity length is found for symmetric two-mirror cavities, restricting the practicality of long baseline detectors. For shorter cavities, an upper limit on the beam size was derived from the geometrical stability of the cavity. These findings aim to aid the design of current and future cavity-assisted atom interferometers.