Sagnac effect in a chain of mesoscopic quantum rings

Abstract

The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential 10^{10} enhancement of the rotational phase shift in comparison to optical Sagnac gyroscopes. Here we analyze ballistic transport of matter waves in a one dimensional chain of N coherently coupled quantum rings in the presence of a rotation of angular frequency, \Omega. We show that the transmission probability, T, exhibits zero transmission stop gaps as a function of the rotation rate interspersed with regions of rapidly oscillating finite transmission. With increasing N, the transition from zero transmission to the oscillatory regime becomes an increasingly sharp function of \Omega with a slope \partialT/\partial \Omega N^2. The steepness of this slope dramatically enhances the response to rotations in comparison to conventional single ring interferometers such as the Mach-Zehnder and leads to a phase sensitivity well below the standard quantum limit

Entanglement-enhanced atomic gyroscope

“…Several proposals have already been made to use these squeezed, and other entangled atomic states, such as maximally entangled "NOON" (|N, 0 > +|0, N >) states, to make general phase measurements with sub-shot-noise sensitivities [11][12][13][14][15][16][17]. It has also been shown that uncorrelated atoms can also achieve sub-shot-noise sensitivities of rotational phase shifts [18] by using a chain of matter wave interferometers or a chain of gyroscopes.…”

Effect of input–output coupling on the sensitivity of coupled resonator optical waveguide gyroscopes

“…4. A similar quadratic dependence has been predicted for the sensitivity of an atom gyroscope consisting of a chain of coupled ring-shaped atom interferometers, and it is due to the slope of the Chebyshev polynomials u J x at the limits x → 1, which correspond to the transmission band edges [20]. This sensitivity, which is linear in the rotation Ω, is in contrast to the maximum sensitivity indicated in [8], S max 4πωR 2 ∕c 2 N 1∕κ, from which it was argued that a CROW gyro was no more sensitive than a RFOG with enclosed area N 1πR 2 .…”

“…Furthermore, we can simplify the unit cell translation matrix T U LHM U RHM via the Chebyshev polynomials of the second kind, u J x [20]:…”

A SQUID Analog with a Bose-Einstein Condensate

“…The atom SQUID interaction region can be compact, so it will be interesting to compare its rotation-sensing performance with the current state of the art, the atom optics-based gyroscope [25]. The painted potential technique also allows for the creation of more complex circuit geometries, such as networks of rings [26], and the system could also be used to study instability mechanisms leading to vortex formation when a BEC flows through a constriction [27]. It may be possible to apply the technology demonstrated here to recent proposals [28][29][30][31][32][33] to create macroscopic quantum superpositions of different flow states in an atom SQUID.…”