Viability of rotation sensing using phonon interferometry in Bose-Einstein condensates
Charles Woffinden, Andrew J. Groszek, Guillaume Gauthier, Bradley Mommers, M. W. J. Bromley, Simon A. Haine, Halina H. Rubinsztein-Dunlop, Matthew J. Davis, Tyler W. Neely, Mark A. Baker
We demonstrate the use of a ring-shaped Bose-Einstein condensate as a rotation sensor by measuring the interference between two counter-propagating phonon modes imprinted azimuthally around the ring. We observe rapid decay of the excitations, quantified by quality factors of at most Q ≈ 27. We numerically model our experiment using the c-field methodology, allowing us to estimate the parameters that maximise the performance of our sensor. We explore the damping mechanisms underlying the observed phonon decay, and identify two distinct Landau scattering processes that each dominate at different driving amplitudes and temperatures. Our simulations reveal that Q is limited by strong damping of phonons even in the zero temperature limit. We perform an experimental proof-of-principle rotation measurement using persistent currents imprinted around the ring. We demonstrate a rotation sensitivity of up to \Delta \Omega ≈ 0.3 rad s^{-1} Δ Ω ≈ 0.3 r a d s − 1 from a single image, with a theoretically achievable value of \Delta \Omega ≈ 0.04 rad s^{-1} Δ Ω ≈ 0.04 r a d s − 1 in the atomic shot-noise limit. This is a significant improvement over the shot-noise-limited \Delta \Omega ≈ 1 rad s^{-1} Δ Ω ≈ 1 r a d s − 1 sensitivity obtained by Marti et al. [Phys. Rev. A 91, 013602 (2015)] for a similar setup.
We demonstrate the use of a ring-shaped Bose-Einstein condensate as a rotation sensor by measuring the interference between two counter-propagating phonon modes imprinted azimuthally around the ring. We observe rapid decay of the excitations, quantified by quality factors of at most Q ≈ 27. We numerically model our experiment using the c-field methodology, allowing us to estimate the parameters that maximise the performance of our sensor. We explore the damping mechanisms underlying the observed phonon decay, and identify two distinct Landau scattering processes that each dominate at different driving amplitudes and temperatures. Our simulations reveal that Q is limited by strong damping of phonons even in the zero temperature limit. We perform an experimental proof-of-principle rotation measurement using persistent currents imprinted around the ring. We demonstrate a rotation sensitivity of up to \Delta \Omega ≈ 0.3 rad s^{-1} Δ Ω ≈ 0.3 r a d s − 1 from a single image, with a theoretically achievable value of \Delta \Omega ≈ 0.04 rad s^{-1} Δ Ω ≈ 0.04 r a d s − 1 in the atomic shot-noise limit. This is a significant improvement over the shot-noise-limited \Delta \Omega ≈ 1 rad s^{-1} Δ Ω ≈ 1 r a d s − 1 sensitivity obtained by Marti et al. [Phys. Rev. A 91, 013602 (2015)] for a similar setup.
Atomic superfluids formed using Bose-Einstein condensates (BECs) in a ring trap are currently investigated in the context of superfluid hydrodynamics, quantum sensing, and matter-wave interferometry. The characterization of the rotational properties of such superfluids is important, but can presently only be performed by using optical absorption imaging, which completely destroys the condensate. Recent studies have proposed coupling the ring BEC to optical cavity modes carrying orbital angular momentum to make minimally destructive measurements of the condensate rotation. The sensitivity of these proposals, however, is bounded below by the standard quantum limit set by the combination of laser shot noise and radiation pressure noise. In this work we provide a theoretical framework that exploits the fact that the interaction between the scattered modes of the condensate and the light reduces to effective optomechanical equations of motion. We present a detailed theoretical analysis to demonstrate that the use of squeezed light and backaction evasion techniques allows the angular momentum of the condensate to be sensed with noise well below the standard quantum limit. Our proposal is relevant to atomtronics, quantum sensing, and quantum information.
The precision of most compact inertial sensing schemes using trapped- and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counterpropagating sound waves within the condensate and use in situ absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of $\ensuremath{\sim}\text{rad}\phantom{\rule{0.16em}{0ex}}{\text{s}}^{\ensuremath{-}1}/\sqrt{\text{Hz}}$, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at the high densities and small volumes of trapped Bose-Einstein condensed gases.
Recently, a method has been proposed to detect the rotation of a ring Bose-Einstein condensate, , in real-time, and with minimal destruction by using a cavity driven with optical fields carrying orbital angular momentum []. This method is sensitive to the magnitude of the condensate winding number but not its sign. In the present work, we consider simulations of the rotation of the angular lattice formed by the optical fields and show that the resulting cavity transmission spectra are sensitive to the sign of the condensate winding number. We demonstrate the minimally destructive technique on persistent current rotational eigenstates, counter-rotating superpositions, and a soliton singly or in collision with a second soliton. Conversely, we also investigate the sensitivity of the ring condensate, given knowledge of its winding number, to the rotation of the optical lattice. This characterizes the effectiveness of the optomechanical configuration as a laboratory rotation sensor. Our results are important to studies of rotating ring condensates used in atomtronics, superfluid hydrodynamics, simulation of topological defects and cosmological theories, interferometry using matter-wave solitons, and optomechanical sensing. Published by the American Physical Society 2024
We present numerical simulations of the cavity optomechanical detection of persistent currents and bright solitons in an atomic Bose-Einstein condensate confined in a ring trap. This paper describes a technique that measures condensate rotation , in real time, and with minimal destruction, in contrast to currently used methods, all of which destroy the condensate completely. For weakly repulsive interatomic interactions, the analysis of persistent currents extends our previous few-mode treatment of the condensate [P. Kumar ] to a stochastic Gross-Pitaevskii simulation. For weakly attractive atomic interactions, we present the first analysis of optomechanical detection of matter-wave soliton motion. We provide optical cavity transmission spectra containing signatures of the condensate rotation, sensitivity as a function of the system response frequency, and atomic density profiles quantifying the effect of the measurement backaction on the condensate. We treat the atoms at a mean-field level and the optical field classically, account for damping and noise in both degrees of freedom, and investigate the linear as well as nonlinear response of the configuration. Our results are consequential for the characterization of rotating matter waves in studies of atomtronics, superfluid hydrodynamics, and matter-wave soliton interferometry. Published by the American Physical Society 2024
Atom interferometers provide exquisite measurements of the properties of noninertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring-shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent noninteracting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.
A quantum device for measuring two-body interactions, scalar magnetic fields and rotations is proposed using a Bose–Einstein condensate (BEC) in a ring trap. We consider an imbalanced superposition of orbital angular momentum modes with opposite winding numbers for which a rotating minimal atomic density line appears. We derive an analytical model relating the angular frequency of the minimal density line rotation to the strength of the nonlinear atom–atom interactions and the difference between the populations of the counter-propagating modes. Additionally, we propose a full experimental protocol based on direct fluorescence imaging of the BEC that allows to measure all the quantities involved in the analytical model and use the system for sensing purposes.