Feasibility analysis of a proposed test of quantum gravity via optical magnetometry in xenon

We present an analysis of the sensitivity limits of a proposed experimental search for quantum gravity, using an approach based on optical magnetometry in the noble gas isotope ${}^{129}\mathrm{Xe}$. The analysis relies on a general uncertainty principle model that is consistent with most formulations of quantum gravity theory, where the canonical uncertainty relations are modified by a leading-order correction term that is linear in momentum. In turn, this correction modifies the magnetic moment of the spin-polarized ${}^{129}\mathrm{Xe}$ atoms that are immersed in a magnetic field in the proposed experiment, which results in a velocity-dependent variation of their Larmor frequency, that is detected via two-photon laser spectroscopy. The thermal distribution of atomic velocities, in conjunction with the Doppler effect, is used to scan the interrogating laser over different atomic velocities and search for a corresponding variation in their Larmor frequencies. We show that the existing bounds on the leading-order quantum gravity correction can be improved by ${10}^7$ with existing technology, where another factor of ${10}^2$ is possible with near-future technical capabilities.

Figure 1

(a) The partial energy-level diagram of ${}^{129}\mathrm{Xe}$. A circularly polarized ultraviolet laser drives spin-selective two-photon excitation in hyperpolarized ${}^{129}\mathrm{Xe}$ atoms, where the excited state emits infrared light via radiative decay. The nuclear spin of the atoms precesses around an applied magnetic field, which is perpendicular to the laser propagation direction. Correspondingly, the ground-state population coherently oscillates between the two magnetic sublevels, resulting in oscillation of the emitted infrared fluorescence. The latter is detected for extraction of the precession (Larmor) frequency. (b) Illustration of the proposed experiment. (c) Tuning the laser to different frequencies in the Doppler-broadened profile of the two-photon transition corresponds to different atom velocities, which in turn are associated with different QG shifts of the Lamor frequency.

Figure 2

Minimum detectable QG correction coefficient, ${\alpha }_{0,\min }$, as a function of laser frequency, ${\omega }_l$, for different values of laser power, ${\omega }_l$, and number of measurements, $N_m$. Four examples are shown with a combination of two values for $P_l$ (1 and $100\mathrm{W}$) and two values for $N_m$ (1 and 2190). The latter correspond to total measurement times, $N_m{T}_m$, of $4.7\mathrm{h}$ and $1\mathrm{yr}$, respectively. The optimal laser frequency, ${\omega }_{l,\mathrm{opt}}={\omega }_{\text{Xe}}+0.85\mathrm{\Delta }{\omega }_D$, is identified by a black vertical line.

Figure 3

The minimum values of the QG correction coefficient ${\alpha }_{0,\min }$ at the optimal laser frequency ${\omega }_{l,\mathrm{opt}}$ (blue), the corresponding optimized fractional sensitivity $S_{\min }$ at ${\omega }_l={\omega }_{l,\text{opt}}$ (purple), and the optimized fractional sensitivity on two-photon resonance, $S_{\min }$ at ${\omega }_l={\omega }_{\text{Xe}}$ (green). Notable time scales of 1 day (solid), 1 week (dashed), and 1 month (dot-dashed) are indicated in orange.