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arXiv:1701.02154 · Physical Review Letters

Spin-Orbit-Coupled Interferometry with Ring-Trapped Bose-Einstein Condensates

J. L. Helm, T. P. Billam, Ana Rakonjac, Simon L. Cornish, S. A. Gardiner

Published Feb 6, 2018• 27 citations
arXivHTMLPDF

Abstract

We propose a method of atom interferometry using a spinor Bose-Einstein condensate with a time-varying magnetic field acting as a coherent beam splitter. Our protocol creates long-lived superpositional counterflow states, which are of fundamental interest and can be made sensitive to both the Sagnac effect and magnetic fields on the sub-μG scale. We split a ring-trapped condensate, initially in the m_{f}=0 hyperfine state, into superpositions of internal m_{f}=±1 states and condensate superflow, which are spin-orbit coupled. After interrogation, the relative phase accumulation can be inferred from a population transfer to the m_{f}=±1 states. The counterflow generation protocol is adiabatically deterministic and does not rely on coupling to additional optical fields or mechanical stirring techniques. Our protocol can maximize the classical Fisher information for any rotation, magnetic field, or interrogation time and so has the maximum sensitivity available to uncorrelated particles. Precision can increase with the interrogation time and so is limited only by the lifetime of the condensate.

DOI
10.1103/physrevlett.120.063201

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We propose a method of atom interferometry using a spinor Bose-Einstein condensate with a time-varying magnetic field acting as a coherent beam splitter. Our protocol creates long-lived superpositional counterflow states, which are of fundamental interest and can be made sensitive to both the Sagnac effect and magnetic fields on the sub-μG scale. We split a ring-trapped condensate, initially in the m_{f}=0 hyperfine state, into superpositions of internal m_{f}=±1 states and condensate superflow, which are spin-orbit coupled. After interrogation, the relative phase accumulation can be inferred from a population transfer to the m_{f}=±1 states. The counterflow generation protocol is adiabatically deterministic and does not rely on coupling to additional optical fields or mechanical stirring techniques. Our protocol can maximize the classical Fisher information for any rotation, magnetic field, or interrogation time and so has the maximum sensitivity available to uncorrelated particles. Precision can increase with the interrogation time and so is limited only by the lifetime of the condensate.
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.
Sagnac interferometers with massive particles promise unique advantages in achieving high-precision measurements of rotation rates over their optical counterparts. Recent proposals and experiments are exploring nonballistic Sagnac interferometers where trapped atoms are transported along a closed path. This is achieved by using superpositions of internal quantum states and their control with state-dependent potentials. We address emergent questions regarding the dynamical behavior of Bose-Einstein condensates in such an interferometer and its impact on rotation sensitivity. We investigate complex dependencies on atomic interactions as well as trap geometries, rotation rates, and speed of operation. We find that temporal transport profiles obtained from a simple optimization strategy for noninteracting particles remain surprisingly robust also in the presence of interactions over a large range of realistic parameters. High sensitivities can be achieved for short interrogation times far from the adiabatic regime. This highlights a route to building fast and robust guided-ring Sagnac interferometers with fully trapped atoms.
Atom interferometry with high visibility is of high demand for precision measurements. Here, a parallel multicomponent interferometer is achieved by preparing a spin-2 Bose-Einstein condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms confined in a hybrid magneto-optical trap. After the preparation of a spinor Bose-Einstein condensate with spin degrees of freedom entangled, we observe four spatial interference patterns in each run of measurements corresponding to four hyperfine states we mainly populate in the experiment. The atomic populations in different Zeeman sublevels are made controllably using magnetic-field-pulse induced Majorana transitions. The spatial separation of atom cloud in different hyperfine states is reached by Stern-Gerlach momentum splitting. The high visibility of the interference fringes is reached by designing a proper overlap of the interfering wave packets. Due to uncontrollable phase accumulation in Majorana transitions, the phase of each individual spin is found to be subjected to unreproducible shift in multiple experimental runs. However, the relative phase across different spins is stable, paving a way towards noise-resilient multicomponent parallel interferometers.
Abstract Free space atom-interferometry traditionally suffers from the large distances that atoms have to fall in order to achieve long interaction times. Trapped atom interferometry is emerging as a powerful way of achieving long interaction times in a reduced experimental volume. Here, we demonstrate bi-chromatic adiabatic magnetic shell traps as a novel tool for matterwave interferometry. We dress the magnetic hyperfine states of the F = 1 and F = 2 Rubidium 87 Bose–Einstein Condensates thus creating two independently controllable shell traps of which we use the ∣ F = 1 , m ¯ F = − 1 〉 and ∣ F = 2 , m ¯ F = 1 〉 adiabatic states. Using microwave pulses, we put atoms originally loaded into one of the two shell-traps into a superposition between the two shell traps. Since the two traps can be manipulated independently, their position and vertical curvature can be matched, thus creating a good starting point for an atom interferometer. This interferometer can be sensitive to spatially varying electric or magnetic fields, which could be DC or RF magnetic fields or microwaves. We demonstrate that the trap-matching afforded by the independent control of the shell traps allows for a tenfold increase in coherence times when compared to adiabatic potentials created by a single RF-frequency. For large-radius shells the atoms are confined to a 2D surface enabling highly sensitive imaging matterwave interferometers.
We report the experimental realization of a versatile ring trap for ultracold atoms. The ring geometry is created by the time-averaged adiabatic potential resulting from the application of an oscillating magnetic bias field to a rf-dressed quadrupole trap. Lifetimes for a Bose-Einstein condensate in the ring exceed 11s11\mathrm{s}11s and the ring radius was continuously varied from $50 \ensuremath{\mu}\text{m}$ to $262 \ensuremath{\mu}\text{m}$. An efficient method of loading the ring from a conventional time-averaged orbiting potential trap is presented together with a rotation scheme which introduces angular momentum into the system. The ring presents an opportunity to study the superfluid properties of a condensate in a multiply connected geometry and also has applications for matter-wave interferometry.