Abstract
We present a protocol for rotation measurement via matter-wave Sagnac interferometry using trapped ions. The ion trap based interferometer encloses a large area in a compact apparatus through repeated round-trips in a Sagnac geometry. We show how a uniform magnetic field can be used to close the interferometer over a large dynamic range in rotation speed and measurement bandwidth without contrast loss. Since this technique does not require the ions to be confined in the Lamb–Dicke regime, Doppler laser cooling should be sufficient to reach a sensitivity of .
Highlights
E 2 = mc2 2 us criThe Sagnac effect can be used to measure the rotational velocity Ω of a reference frame by observing the phase shift of an interferometer in that frame whose paths enclose an area A perpendicular to any component of Ω
E = hωoptical, whereas for atoms of rest mass m moving at non-relativistic speeds (p mc), E = mc2
Some of the drawbacks of this, as compared to an optical gyroscope, are that Ṅ is smaller, and the free-flight atom trajectories enclose the interferometer area A only once. The latter constraint has meant that increasing A has necessarily involved increasing the physical size of the apparatus, which can be undesirable for some applications
Summary
The Sagnac effect can be used to measure the rotational velocity Ω of a reference frame by observing the phase shift of an interferometer in that frame whose paths enclose an area A perpendicular to any component of Ω (see, e.g. [1] for a review). Some of the drawbacks of this, as compared to an optical gyroscope, are that Ṅ is smaller, and the free-flight atom trajectories enclose the interferometer area A only once. The latter constraint has meant that increasing A has necessarily involved increasing the physical size of the apparatus, which can be undesirable for some applications. Much like an optical gyroscope, this allows atomic trajectories to repeatedly enclose the same physical area, thereby accumulating Sagnac phase continuously for a time that is not limited by a ballistic flight trajectory. The harmonic trapping potential makes the area enclosed independent of the initial ion velocity, eliminating a source of scale factor instability found in free space atom interferometers. These factors, coupled with the extremely long coherence times of trapped ions, give the trapped ion interferometer the potential to enclose a large effective area in a small apparatus with high stability
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