Spin dephasing as a probe of mode temperature, motional state distributions, and heating rates in a two-dimensional ion crystal

We employ spin-dependent optical dipole forces to characterize the transverse center-of-mass (COM) motional mode of a two-dimensional Wigner crystal of hundreds of Be-9(+). By comparing the measured spin dephasing produced by the spin-dependent force with the predictions of a semiclassical dephasing model, we obtain absolute mode temperatures in excellent agreement with both the Doppler laser cooling limit and measurements obtained from a previously published technique [B. C. Sawyer et al., Phys. Rev. Lett. 108, 213003 ( 2012)]. Furthermore, the structure of the dephasing histograms allows for discrimination between initial thermal and coherent states of motion. We also apply the techniques discussed here to measure the ambient-heating rate of the COM mode of a 2D Coulomb crystal in a Penning trap. This measurement places an upper limit on the anomalous single-ion heating rate due to electric field noise from the trap electrode surfaces of d (n) over bar /dt similar to 5 s(- 1) for our trap at a frequency of 795 kHz, where (n) over bar is the mean occupation of quantized COM motion in the axial harmonic well.