We demonstrate a transversely polarized spin-exchange pumped noble gas comagnetometer which suppresses systematic errors from longitudinal polarization. Rb atoms as well as 131 Xe and 129 Xe nuclei are simultaneously polarized perpendicular to a pulsed bias field. Both Xe isotopes' nuclear magnetic resonance conditions are simultaneously satisfied by frequency modulation of the pulse repetition rate. The Rb atoms detect the Xe precession. We highlight the importance of magnetometer phase shifts when performing comagnetometry. For detection of non-magnetic spin-dependent interactions the sensing bandwidth is 1 Hz, the white-noise level is 7 µHz / √ Hz, and the bias instability is ≈ 1 µHz.Spin-exchange (SE) pumped comagnetometers [1, 2] utilize co-located ensembles of spin-polarized alkali-metal atoms and noble gas nuclei [3] to suppress magnetic field noise. Such devices have been used to place upper bounds on spin-mass couplings [4,5], Lorentz violations [6-10], and atomic electric dipole moments [11][12][13], and for the measurement of inertial rotation [2,[14][15][16]. The fundamental uncertainty of a SE pumped comagnetometer's measure of inertial rotation scales favorably with sensor size compared to alternative technologies [17].Longitudinal SE fields are important sources of systematic uncertainty in devices which utilize the embedded alkali-metal atoms for high SNR detection. Consider an ensemble of two noble gas species (a and b) which are spin-exchange optically pumped (SEOP) in a common magnetic field B z and are each subject to some spin-dependent interaction X. The Larmor resonance frequency of isotope a can be written as [2,[18][19][20]]where γ is the gyromagnetic ratio, S and K are the respective alkali-metal and noble gas polarizations, z subscripts refer to the longitudinal components (i.e., parallel to the bias field direction), and b i j is the SE coefficient characterizing the influence of j's polarization on i. With knowledge of ρ = γ a /γ b , simultaneous measurement of Ω a and Ω b allows B z to be suppressed while sensitivity to X a z and X b z is retained [21]. In this paper we demonstrate a SE pumped 131 Xe-129 Xe comagnetometer which suppresses time-averaged S z and K z such thatwhere the superscripts a and b refer to 129 Xe and 131 Xe, respectively, and ρ = 3.373417(38) [22]. The comagnetometer relies on a dual-species version of synchronous SEOP [23], wherein noble gas nuclei are continuously polarized transverse to a frequency modulated pulsed bias field. We demonstrate that the correlation between the frequency of precession of 131 Xe and 129 Xe is sufficient FIG. 1: Schematic of apparatus. Field shim coils are not shown. The green trace depicts the frequency modulated bias field pulses.to resolve 7 µHz / √ Hz of white frequency noise with a low frequency field noise suppression of > 10 3 . We also demonstrate the influence of alkali-metal magnetometer phase shifts on the field noise suppression of the comagnetometer.A schematic of the experimental setup is shown in Fig. 1. 85 Rb atoms...