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arXiv:1210.0033 · Physical Review A

Collective excitation interferometry with a toroidal Bose-Einstein condensate

G. Edward Marti, Ryan Olf, Dan Stamper-Kurn

Published Jan 5, 2015• 77 citations
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Abstract

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.

DOI
10.1103/physreva.91.013602

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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∼rads\ensuremath−1/Hz\ensuremath{\sim}\text{rad}\phantom{\rule{0.16em}{0ex}}{\text{s}}^{\ensuremath{-}1}/\sqrt{\text{Hz}}\ensuremath∼rads\ensuremath−1/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.
Compact inertial sensing schemes using trapped- and guided-atom interferometers have been unable to achieve high precision because of uncontrolled phase errors caused by trapping potentials and interactions. Here, we demonstrate an atom-shot-noise limited acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotations. Our system operates at 104−10610^4 - 10^6104−106 times higher density and in a volume 10910^9109 times smaller than free-falling atom interferometers.
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.
Interferometric measurements with matter waves are established techniques for sensitive gravimetry, rotation sensing, and measurement of surface interactions, but compact interferometers will require techniques based on trapped geometries. In a step towards the realisation of matter wave interferometers in toroidal geometries, we produce a large, smooth ring trap for Bose–Einstein condensates using rapidly scanned time-averaged dipole potentials. The trap potential is smoothed by using the atom distribution as input to an optical intensity correction algorithm. Smooth rings with a diameter up to 300 μ m are demonstrated. We experimentally observe and simulate the dispersion of condensed atoms in the resulting potential, with good agreement serving as an indication of trap smoothness. Under time of flight expansion we observe low energy excitations in the ring, which serves to constrain the lower frequency limit of the scanned potential technique. The resulting ring potential will have applications as a waveguide for atom interferometry and studies of superfluidity.
An atom interferometer using Bose-Einstein condensates has been implemented and is used to measure the dynamic polarizability of 87Rb. An off-resonant standing-wave laser beam is used to manipulate the motion of atomic wavepackets in order to implement splitting and reflection operations. It is demonstrated that these operations can be performed with near unity fidelity. Interferometer times of up to 72 ms as well as arm separations of up to 0.42 mm are achieved experimentally. The primary limitation for guided-wave atom interferometers with a large arm separation is found to be the effect of the confining potential along the waveguide axis. Such a potential causes a spatially varying phase shift on the wavepackets as they propagate in the interferometer. Different parts of the cloud therefore interfere with different phases, leading to a reduction of the interferometer contrast. A model of the phase shifts on the wavepackets agrees well with the experimental data. In a different scheme in which the wavepackets oscillate freely in the confining potential, these phase shifts completely cancel. Interference is observed at times up to 0.9 s in this case, but with a fluctuating overall phase of the output, which is attributed to mechanical instabilities. Finally, the dynamic polarizability of 87Rb is measured. A well-calibrated laser beam is applied to one atomic packet and not the other, inducing a differential phase shift. This technique requires relatively low laser intensity and works for arbitrary optical frequencies. For offresonant light, the ac polarizability is obtained with a statistical accuracy of 3% and a calibration uncertainty of 6%. On resonance, the dispersion-shaped behavior of the Stark shift is observed, but with a broadened linewidth that is attributed to multiple and collective light scattering effects. The resulting nonlinearity may prove useful for the production and control of squeezed quantum states. In general, this work also demonstrates the applicability of condensate interferometry to practical measurements.
We study two different subjects related to ultra-cold Bose gases. First we study the influence of the trap and the background pressure on particle loss and temperature change for trapped atom clouds. We find the number of particles to exponentially decrease over time due to the imperfect vacuum, while the rate of temperature change differs between a magnetic trap and a far off resonance optical trap. Secondly, we study the properties of a standing sound wave induced in a Bose-Einstein condensate. Phase contrast imaging is used to image the condensate in order to observe the density profile as a function of time. We find that there is coupling between the standing wave and other collective modes. There is a clear relation between the frequencies of these collective modes, and also between the frequencies of these modes and the frequency used to induce the modes. We also find that the amplitude of the standing wave decays over time.
Abstract The coherent manipulation of a quantum wave is at the core of quantum sensing. For instance, atom interferometers require linear splitting and recombination processes to map the accumulated phase shift into a measurable population signal. Although Bose Einstein condensates (BECs) are the archetype of coherent matter waves, their manipulation between trapped spatial modes has been limited by the strong interparticle collisions. Here, we overcome this problem by using BECs with tunable interaction trapped in an innovative array of double-well potentials and exploiting quantum tunneling to realize linear beam splitting. We operate several Mach-Zehnder interferometers in parallel, canceling common-mode potential instabilities by a differential analysis, thus demonstrating a trapped-atom gradiometer. Furthermore, by applying a spin-echo protocol, we suppress additional decoherence sources and approach unprecedented coherence times of one second. Our interferometer will find applications in precision measurements of forces with a high spatial resolution and in linear manipulation of quantum entangled states for sensing with sub shot-noise sensitivity.