Quantum Rotation Sensing with Dual Sagnac Interferometers in an Atom-Optical Waveguide

Abstract

Sensitive and accurate rotation sensing is a critical requirement for applications such as inertial navigation [1], north-finding [2], geophysical analysis [3], and tests of general relativity [4]. One effective technique used for rotation sensing is Sagnac interferometry, in which a wave is split, traverses two paths that enclose an area, and then recombined. The resulting interference signal depends on the rotation rate of the system and the area enclosed by the paths [5]. Optical Sagnac interferometers are an important component in present-day navigation systems [6], but suffer from limited sensitivity and stability. Interferometers using matter waves are intrinsically more sensitive and have demonstrated superior gyroscope performance [7-9], but the benefits have not been large enough to offset the substantial increase in apparatus size and complexity that atomic systems require. It has long been hoped that these problems might be overcome using atoms confined in a guiding potential or trap, as opposed to atoms falling in free space [10][11][12]. This allows the atoms to be supported against gravity, so a long measurement time can be achieved without requiring a large drop distance. The guiding potential can also be used to control the trajectory of the atoms, causing them to move in a circular loop that provides the optimum enclosed area for a given linear size [13]. Here we use such an approach to demonstrate a rotation measurement with Earth-rate sensitivity.A small number of trapped-atom Sagnac interferometers have been demonstrated in the past [14-18], but none have been used to make a quantitative rotation measurement. The largest enclosed areas have been achieved using a linear interferometer that is translated along a direction perpendicular to the interferometer axis [19], but this approach may not be well-suited for inertial measurements in a moving vehicle. Here, we demonstrate a true two-dimensional interferometer configuration in which atoms travel in circular trajectories through a static confining potential. We obtain an effective enclosed area of 0.50 mm 2 , compared to areas of 0.20 mm 2 reported by Wu et al.[15] and 0.35 mm 2 recently obtained by the Los Alamos group [18]. Our approach is readily scalable to weaker traps and multiple orbits by the atoms, making larger areas feasible.Another key advance is the use of dual counterpropagating interferometer measurements. Here, two Sagnac interferometers are implemented at the same time in the same trap, with atoms travelling at opposite velocities over the same paths. This technique was developed for free space interferometers [8], and allows the common-mode rejection of interferometric phases from accelerations, laser noise, background fields, and other effects that can mask the rotation signal. The Sagnac effect itself is differential and can be extracted by comparing the two individual measurements. This technique is likely to be essential for any practical rotation-sensing system, but has not previously been demonstrated in a trapped-atom s...

Effect of trap symmetry and atom-atom interactions on a trapped-atom interferometer with internal state labeling

“…In the case with spatial separation, to reuse the previous results we suppose that a ↑↓ = 0 and a ↑↑ = a ↓↓ = a (we consider rubidium 87). More precisely, a ↑↓ is not zero but we suppose that the spatial separation between the two spin states is enough to neglect the wave function overlap (10). Thus Eqs.…”

“…Trapped cold atom interferometers play an important role in the realization of sensing devices such as atomic clocks [1,2], accelerometers [3,4,[6][7][8], gyroscopes [9,10], and magnetometers [11,12]. In such devices, as compared for example with interferometers using free-falling atoms, the confinement typically results in higher atom densities, hence stronger atom-atom interactions [13,14].…”

Multi-loop atomic Sagnac interferometry

“…Multiple loops were created in ring traps employing quantum degenerate gases for different purposes including the investigation of superconductive flows 15 , 16 . Exploiting them for guided atomic Sagnac interferometers in optical or magnetic traps remains an experimental challenge 17 – 20 .

Figure 2 Space-time diagram and pulse timings of a multi-loop interferometer.

…”

Robust inertial sensing with point-source atom interferometry for interferograms spanning a partial period

“…Analogous to the Sagnac phase shift in a laser gyroscope, in a rotating frame, an atom interferometer experiences a Sagnac phase shift proportional to the inner product of the rotation vector and the Sagnac area [4]. For guided-wave atom interferometers, the matter-wave trajectories follow the guide geometry, and the Sagnac area is fixed [5,6]. For free-space atom interferometers, the Sagnac area depends on atoms' initial velocity, and there are different approaches to handle this degree of freedom.…”