Sagnac Interferometry with a Single Atomic Clock

Abstract

We theoretically discuss an implementation of a Sagnac interferometer with cold atoms. In contrast to currently existing schemes our protocol does not rely on any free propagation of atoms. Instead it is based on superpositions of fully confined atoms and state-dependent transport along a closed path. Using Ramsey sequences for an atomic clock, the accumulated Sagnac phase is encoded in the resulting population imbalance between two internal (clock) states. Using minimal models for the above protocol we analytically quantify limitations arising from atomic dynamics and finite temperature. We discuss an actual implementation of the interferometer with adiabatic radio-frequency potentials that is inherently robust against common mode noise as well as phase noise from the reference oscillator.PACS numbers: 07.60. Ly, 03.75.Dg The Sagnac effect enables interferometric measurements of rotation with high precision [1]. For example, the large Wettzell laser gyroscope achieves a theoretical resolution of 10. Interferometers based on matterwaves instead of light promise resolution enhancement by orders of magnitude that scales with particle mass [3], see [4] for a recent review. Despite the immense challenges in achieving similar particle flux and interferometer areas as with photons, atomic gyroscopes [5,6] have reached performance levels that should enable applications in fundamental physics, geodesy, seismology, or inertial navigation. Atom interferometers [7] have been demonstrated with record sensitivities below 10 −9 rad/ √ s [8, 9] outperforming commercial navigation sensors by orders of magnitude. Recent experiments aim at geodetic [10] and navigational applications combining multi-axis measurements of acceleration and rotation [11,12]. Since free falling atoms require large apparatus size, ring shaped traps and guided interferometers have been proposed [13][14][15][16] and demonstrated [17][18][19][20][21][22] for a variety of geometries and levels of sophistication, e.g., using soliton dynamics in Bose-Einstein condensates to enhance sensitivity by non-linear interactions or to prevent wavepacket dispersion [23][24][25].So far, the paradigm for matter wave Sagnac interferometry relies on DeBroglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a propertime difference experienced by two observers moving in opposite directions along closed paths and has indeed been measured with atomic clocks flown around Earth [26]. Inspired by this, we investigate an interferometer comprised of a single atomic clock. It uses the acquired phase shift between atoms in two different internal clock (spin) states that are each fully confined in atom traps but separately displaced. This approach offers a high degree of control over atomic motion, removing velocity dependent effects and phase front and interferometric stability requirements of laser beams. It improves con- Figure 1: Experimental sequence depicted in an inertial frame. Starting wit...

Dispersive detection of radio-frequency-dressed states

“…Species-and state-dependent control becomes possible in some scenarios [8,11], because the trap defining rf polarization component depends on the atomic g factor. Such control provides prospects for quantum simulations of many-body physics as well as atom interferometers without any free propagation [12].…”

“…Dispersive light-matter interaction at a very low technical noise level resulting from operation at radio frequencies is a prerequisite for quantum-non-demolition (QND) measurements in a range of vapor cell experiments with very large atom numbers (n ≈ 10 12 ) and consequently low relative quantum noise, including spin squeezing [13], deterministic quantum memory [14], and teleportation [15]. Such QND measurements also play * Corresponding author: thomas.fernholz@nottingham.ac.uk a role in atom interferometry where it is desirable to lower the quantum projection noise [16] inherent to any atomic magnetometer [17], clock [18], or interferometer [19] by using spin squeezed states [20,21] or other nonclassical states [22] as inputs.…”

Mean-Field Dynamics and Fisher Information in Matter Wave Interferometry

“…If we restrict ourselves to measurements of the population of each spin state, then F C ¼ P j¼þ1;−1 P [29], who depart from the notion of freely propagating matter waves, and consider two spin components j þ 1i and j − 1i, where the trapping potential for each component can be manipulated independently. The two spin components are transported around a closed loop in opposite directions via a time-dependent trapping potential, and then recombined via a microwave coupling pulse at time T such that the state of the system at the final time t f is ψ AE1 ðθ; t f Þ ¼ ð1= ffiffi ffi 2 p Þ½ψ AE1 ðθ; TÞ − iψ ∓1 ðθ; TÞ.…”

“…For example, there have been several recent proposals for atomic gyroscopes based on interference of Bose condensed atoms (BECs) confined in toroidal geometries, or "ring traps" [26][27][28][29][30][31]. The analysis of these schemes has largely been concerned with the complex multimode dynamics of the order-parameter ψðr; tÞ, which displays rich mean-field dynamics due to the interatomic interactions.…”

Rotation sensing with trapped ions

“…While interferometers with enclosed area have been demonstrated with clouds of trapped neutral atoms [2,3], maintaining the coherence across the ensemble needed for a gyroscope has proved difficult, and alternative ideas have been proposed [4,5]. We describe a combination of laser-driven spindependent momentum kicks in one direction with ion trap voltage changes along an orthogonal direction that perform interferometry with trapped ions in a Sagnac (as opposed to Mach-Zehnder) configuration.…”