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A half-degenerate optical resonator for cold-atom interferometry

Sapam Ranjita Chanu, N. Mielec, Arnaud Landragin, Rémi Geiger

Published May 28, 2018• 0 citations
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Abstract

We present the analysis of a half degenerate optical resonator consisting of a lens located between two plane mirrors. This resonator was designed to support a large waist (cm) Gaussian beam for applications to precision inertial measurements based on large momentum transfer atom interferometry. We investigate the spatial profile of the resonating beam, and the optical gain for different beam size, and the influence of misalignments on the degeneracy of the cavity. FFT simulations show that aberrations and surface imperfections of the optics are the main contributors to spatial inhomogeneities of the resonating beam, which supports our experimental results. We also report the stability of this resonator locked to an ultra-stable optical reference.

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We present the analysis of a half degenerate optical resonator consisting of a lens located between two plane mirrors. This resonator was designed to support a large waist (cm) Gaussian beam for applications to precision inertial measurements based on large momentum transfer atom interferometry. We investigate the spatial profile of the resonating beam, and the optical gain for different beam size, and the influence of misalignments on the degeneracy of the cavity. FFT simulations show that aberrations and surface imperfections of the optics are the main contributors to spatial inhomogeneities of the resonating beam, which supports our experimental results. We also report the stability of this resonator locked to an ultra-stable optical reference.
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.
Abstract We propose a marginally stable optical resonator suitable for atom interferometry. The resonator geometry is based on two flat mirrors at the focal planes of a lens that produces the large beam waist required to coherently manipulate cold atomic ensembles. Optical gains of about 100 are achievable using optics with part-per-thousand losses. The resulting power build-up will allow for enhanced coherent manipulation of the atomic wavepackets such as large separation beamsplitters. We study the effect of longitudinal misalignments and assess the robustness of the resonator in terms of intensity and phase profiles of the intra-cavity field. We also study how to implement atom interferometry based on large momentum transfer Bragg diffraction in such a cavity.
The development of atom interferometry in the last few decades has led to high precision measurements of inertial effects and tests of fundamental physics. New methods for higher sensitivity atom interferometers (AIs) are being explored, particularly the interrogation of atoms with optical cavities [1]. Its benefits would be higher optical power allowing large momentum transfer beam splitters, and possibly cleaner and controlled phase profiles. However high sensitivity AIs require long interrogation times, which combined with cold atom expansion, bring the challenges of large waists in cavities.
Optical cavities are an enabling technology of modern quantum science: From their essential role in the operation of lasers to applications as flywheels in atomic clocks and interaction-enhancing components in quantum optics experiments, developing a quantitative understanding of the mode shapes and energies of optical cavities has been crucial for the growth of the field. Nonetheless, the standard treatment using paraxial quadratic optics fails to capture the influence of optical aberrations present in modern cavities with high finesse, small waist, and/or many degenerate modes. In this work, we compute the mode spectrum of optical resonators, allowing for both nonparaxial beam propagation and beyond-quadratic mirrors and lenses. Generalizing prior works, we develop a complete theory of resonator aberrations, including intracavity lenses, nonplanar geometries, and arbitrary mirror forms. Harnessing these tools, we reconcile the near absence of aberration in the work of Schine et al. [N. Schine et al., Nature (London) 534, 671 (2016)] with the strongly evident aberrations in the seemingly similar cavity of Clark et al. [L. W. Clark et al., Nature (London) 582, 41 (2020)]. We further validate our approach by comparison to a family of nonplanar lens cavities realized in the laboratory, finding good quantitative agreement. This work opens prospects for cavities with smaller waists and more degenerate modes.
We present a novel atom interferometer configuration that combines large momentum transfer with the enhancement of an optical resonator for the purpose of measuring gravitational strain in the horizontal directions. Using Bragg diffraction and taking advantage of the optical gain provided by the resonator, we achieve momentum transfer up to 8ℏk with mW level optical power in a cm-sized resonating waist. Importantly, our experiment uses an original resonator design that allows for a large resonating beam waist and eliminates the need to trap atoms in cavity modes. We demonstrate inertial sensitivity in the horizontal direction by measuring the change in tilt of our resonator. This result paves the way for future hybrid atom or optical gravitational wave detectors. Furthermore, the versatility of our method extends to a wide range of measurement geometries and atomic sources, opening up new avenues for the realization of highly sensitive inertial atom sensors.
One of the main residual limitations of inertial sensors based on atom interferometry stems from laser beam distortions, which cause parasitic phase shifts and non-homogeneous matter-light couplings. Here we present numerical simulations, accompanied by analytical calculations, which quantify the impact of these effects in a cold atom gradiometer. We demonstrate that the propagation of interferometric laser beam aberrations, combined with initial asymmetry and significant time-of-flight expansion of the the two atomic sources, limit the common-mode rejection of phase noise in a differential configuration. The resulting deviations in gravitational acceleration and its gradient are within reach of current experimental devices. Our study allows us to evaluate the surface quality requirements for retroreflective optics in cold-atom gradiometers of various baselines, and can be extended to other sensors based on different interferometer geometries.