Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate.

We measure the dispersion relation, gap, and magnetic moment of a magnon in the ferromagnetic F = 1 spinor Bose-Einstein condensate of (87)Rb. From the dispersion relation we measure an average effective mass 1.033(2)(stat)(10)(sys) times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. The measured mass is higher than theoretical predictions of mean-field and beyond-mean-field Beliaev theory for a bulk spinor Bose gas with s-wave contact interactions. We observe a magnon energy gap of h × 2.5(1)(stat)(2)(sys) Hz, which is consistent with the predicted effect of magnetic dipole-dipole interactions. These dipolar interactions may also account for the high magnon mass. The effective magnetic moment of -1.04(2)(stat)(8)(sys) times the atomic magnetic moment is consistent with mean-field theory.

Temperature Sensitivity of 14N-V and 15N-V Ground-State Manifolds.

We measure electron- and nuclear-spin transition frequencies in the ground state of nitrogen-vacancy (N-V) centers in diamond for two nitrogen isotopes (14N-V and 15N-V) over temperatures ranging from 77 to 400 K. Measurements are performed using Ramsey interferometry and direct optical readout of the nuclear and electron spins. We extract coupling parameters Q (for 14N-V), D, A‖, A⊥, and γe/γn, and their temperature dependences for both isotopes. The temperature dependences of the nuclear-spin transitions within the ms=0 spin manifold near room temperature are found to be 0.52(1) ppm/K for 14N-V(|mI = -1⟩ ↔ |mI = +1⟩) and -1.1(1) ppm/K for 15N-V(|mI = -1/2⟩ ↔ |mI = +1/2⟩). An isotopic shift in the zero-field splitting parameter D between 14N-V and 15N-V is measured to be ~ 120 kHz. Residual transverse magnetic fields are observed to shift the nuclear-spin transition frequencies, especially for 15N-V. We have precisely determined the set of parameters relevant for the development of nuclear-spin-based diamond quantum sensors with greatly reduced sensitivity to environmental factors.

Demonstration of diamond nuclear spin gyroscope.

We demonstrate the operation of a rotation sensor based on the nitrogen-14 (14N) nuclear spins intrinsic to nitrogen-vacancy (NV) color centers in diamond. The sensor uses optical polarization and readout of the nuclei and a radio-frequency double-quantum pulse protocol that monitors 14N nuclear spin precession. This measurement protocol suppresses the sensitivity to temperature variations in the 14N quadrupole splitting, and it does not require microwave pulses resonant with the NV electron spin transitions. The device was tested on a rotation platform and demonstrated a sensitivity of 4.7°/s (13 mHz/Hz), with a bias stability of 0.4 °/s (1.1 mHz).