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arXiv:1601.02549 · Physical Review Letters

Interacting Atomic Interferometry for Rotation Sensing Approaching the Heisenberg Limit

Stephen Ragole, Jacob M. Taylor

Published Nov 11, 2016• 28 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.117.203002

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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.
We theoretically investigate supercurrents of ultracold atoms in angularly ac-shaken ring lattices subjected to external rotation. Our results demonstrate how these supercurrents can be harnessed for the development of high-precision atomtronic angular accelerometers. Using both analytical and numerical approaches within the Bose-Hubbard model framework, we demonstrate that a significant net atomic current arises when the lattice driving frequency is tuned to an integer fraction of the Bloch frequency, while the current averages to nearly zero away from such a resonance. In the single-particle regime, the resonance width scales inversely with the averaging time, thereby setting a fundamental Fourier-limited bound on the measurement's sensitivity. Strikingly, our numerical simulations demonstrate that this Fourier limit - a fundamental barrier in the non-interacting system - can be surpassed by introducing weak interactions between atoms. In the interacting regime, the sensitivity surpasses the Fourier-limited scaling with the averaging time, achieving an improvement of at least two orders of magnitude over the single-particle scenario, and exceeding the performance of previously proposed ultracold-atom-based angular accelerometers. These findings pave the way for developing new atomic-current-based inertial sensors with interaction-enhanced sensitivity.
The Sagnac interferometry has widely been used to measure rotation frequency. Beyond the conventional single-particle scheme, we propose a multiparticle scheme via Bose condensed atoms. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring via a state-dependent rotating potential, and then the atoms are recombined for interference via Ramsey pulses. The phase accumulation time is determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are entangled. By implementing parity measurement, the ultimate measurement precision can be saturated, and the achieved measurement precisions approach the Heisenberg limit. Our results provide a promising way to exploit many-body quantum entanglement in precision rotation sensing.
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.
Quantum Sensors, like atom interferometers (AI), can be employed for high-precision measurements of inertial forces, including their application as gravimeters, gradiometers, accelerometers, and gyroscopes. Their measurement principle relies on ultracold atoms that are prepared in quantum-mechanical superposition states in external degrees of freedom. These states can be prepared by a momentum transfer of a Raman laser. Then the superposition state senses the effect of an inertial force, which induce a corresponding relative phase. The phase is read out by a final coupling which converts the interferometric phase into a atom number difference between the two states. The difference provides an estimate of the interferometric phase and the corresponding quantity of interest. The quantum mechanical noise of the atomic ensemble cause a fundamental uncertainty of this estimation, which I analyze for generic AIs. For small atomic densities, the quantum phase noise of the ensemble limits the interferometric sensitivity. For large densities, quantum number fluctuations generate density fluctuations, which generates phase noise. I show that these two competing effects result in an optimal atom number with a maximal interferometer resolution. Squeezed atomic samples allow for a reduction of the quantum noise of one quantity at the expense of an increased noise along of a conjugate quantity. Phase and number are such quantities which obey to a variant of Heisenberg’s uncertainty principle. Neither phase nor number squeezing can improve the maximal interferometer resolution. As one main result of this thesis, I show how an optimal squeezing in between number and phase squeezing, allows for a fundamental improvement. I evaluate possible experimental paths to implement the proposed protocol. Concepts for a squeezing-enhanced operation of external-degree AIs have not yet been demonstrated. I propose and implement an atomic gravimeter, which is designed to accept spin-squeezed atomic states as input states. The interferometer is designed such that the interferometer couplings are performed in spin space, while the phase accumulation is performed in momentum states. For this interferometer, the squeezed input can be directly obtained from spin dynamics in spinor Bose-Einstein condensates. The main noise contributions in the experiment are analyzed, which results in a factor of 84 above the relevant quantum limit, preventing a squeezing enhancement so far. I outline a suppression of the main noise source, uncontrolled AC Stark shift on the squeezed mode and propose future important applications, including test of spontaneous collapse theories and an improvement of large-scale, high-precision gradiometers.
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 study the ultimate quantum limit of rotation sensing with a few strongly interacting bosons confined in a quasi-one-dimensional ring trap with two weak links. It is demonstrated that a self-consistent many-body solution of the problem is required to correctly predict the ultimate sensitivity of this strongly correlated many-body gyroscope to rotation. For both small rotation velocities and small particle numbers, the many-body quantum Fisher information becomes maximal for large interaction couplings, showing the potential of strongly interacting miniaturized many-body sensors to precisely estimate slow rotations with high spatial resolution.