# A Synchronous Spin-Exchange Optically Pumped NMR-Gyroscope
## 1 Introduction  
Spin-exchange pumped NMR gyroscopes [1; 2; 3; 4; 5; 6] use the precession of spin-polarized nuclei to measure rotation. A vapor cell contains one or more isotopes of noble gas atoms and an alkali-metal vapor. The alkali-metal vapor is optically pumped using circularly polarized near-infrared laser light. Spin-exchange collisions between the polarized alkali-metal and noble gas atoms polarize the noble gas nuclei. When subject to a magnetic (or \"bias\") field, the polarized species undergo Larmor precession. By simultaneously measuring the Larmor precession of each entity, magnetic field correlations can be removed, thereby increasing sensitivity to non-magnetic spin-dependent phenomena, such as inertial rotation.  
The precession of a polarized gas about a constant bias field constitutes an inertial reference frame, i.e., the gas has (ideally) no way of knowing whether or not its container is rotating. If the precession of the polarized gas is measured relative to a fixed point in the laboratory frame, such as with a pick-up coil, then rotation of the pick-up coil about the bias field will change the measured rate of precession of the polarized gas.  
The application of polarized gases as inertial sensors is promising because of their low intrinsic noise, miniaturize-ability, low power consumption, insensitivity to acceleration, and intrinsic scaling from experimental observable to rotation that is independent of experimental parameters [7; 8]. Interest in novel navigation systems which operate in global positioning system (GPS) denied environments has increased as of late. To date, the United States, Russia, China, and India have successfully demonstrated the capability to destroy their own satellites [9]. Such capability could potentially be used to remove GPS satellites. Other GPS denied environments include subterraneanand submarine travel. One obstacle to harnessing geothermal energy resources is the limited \"in-hole\" navigation of horizontal drilling rigs. The future development of autonomous vehicles also relies on robust navigation, including in GPS denied environments. NMR gyroscopes will likely first be used to provide long-term corrections to another miniaturized gyroscope whose short term noise performance is superior but whose long term drift is inferior to the NMR gyroscope. A proof-of-concept experiment along these lines was recently performed using a classical and quantum accelerometer [10].  
Important sources of systematic errors in spin-exchange pumped NMR gyroscopes are longitudinal (i.e., parallel to the bias field) spin-exchange fields produced by polarized alkali-metal atoms or noble gas nuclei [1; 3; 11]. Such longitudinal spin-exchange fields are not identical for all noble gas species, and therefore cannot be removed in the same way as classical magnetic field correlations. Longitudinal spin-exchange fields are well suppressed by synchronous spin-exchange optical pumping [1; 12], wherein the alkali-metal vapor is optically pumped transverse to a low duty cycle pulsed bias field. Each bias field pulse produces 2\(\pi\) precession of the alkali-metal atoms such that, despite having a gyromagnetic ratio in excess of 10\({}^{3}\)x that of the noble gas nuclei, the alkali-metal atoms can effectively co-precess with the noble gas nuclei.  
This manuscript describes a \({}^{131}\)Xe-\({}^{129}\)Xe synchronous spin-exchange optically pumped NMR gyroscope which uses modulation of the alkali-metal (\({}^{85}\)Rb) polarization to drive both Xe isotopes' NMR simultaneously. The Rb is also used as an embedded magnetometer to detect the Xe precession. Compared to our recent work [1; 2] describing NMR excitation by modulating the bias field, polarization modulation (PM) further suppresses the influence of time-averaged longitudinal Rb spin-exchange fields [12] by moving such fields from DC to AC. We study how modulation of the embedded Rb magnetometer causes signal mixing on our detection which leads to an effective change in scale factor [13].