Nuclear quadrupole resonances in compact vapor cells: The crossover between the NMR and the nuclear quadrupole resonance interaction regimes

We present an experimental study that maps the transformation of nuclear quadrupole resonances (NQRs) from the pure nuclear quadrupole regime to the quadrupole-perturbed Zeeman regime. The transformation presents an interesting quantum-mechanical problem since the quantization axis changes from being aligned along the axis of the electric-field gradient tensor to being aligned along the magnetic field. The large nuclear quadrupole shifts present in our system enable us to study this regime with relatively high resolution. We achieve large nuclear quadrupole shifts for $I=3∕2$ ${}^{131}\mathrm{Xe}$ by using a cube-shaped $1{\mathrm{mm}}^3$ vapor cell with walls of different materials. The enhancement of the NQR shift from the cell wall materials is an observation that opens up an additional adjustable parameter to tune and enhance the nuclear quadrupole interactions in vapor cells. As a confirmation that the interesting and complex spectra that we observe are indeed expected, we compare our data to numerical calculations and find excellent agreement.

Figure 1

(Color online) (a) The apparatus. The $1{\mathrm{mm}}^3$ cell is roughly centered on an orthogonal three axis set of magnetic coils. A laser beam of maximum power $3\mathrm{mW}$ enters the cell. The transmitted power is detected by a photodiode. (b) The coordinate system: The $\widehat{z}$ axis coincides with the light propagation direction, $\widehat{k}$. The magnetic field direction is in the $\widehat{y}\text{−}\widehat{z}$ plane rotated by an angle $\phi$ from the $\widehat{z}$ axis.

Figure 2

Examples of experimental data. (a) A free-induction decay. The signal is proportional to the amplitude of the modulation of the photodiode signal caused by the Rb precession and is presented in volts. The magnetic field during the probe phase was $275\mathrm{nT}$, and $\phi$ was $\sim 70°$. Beating from the ${}^{131}\mathrm{Xe}$ triplet is seen in the inset, which shows the residuals from a fit of a damped sine wave to the data. (b) The Fourier transform of the data in (a). Here the signal is presented as a power spectral density in the units of root-mean-squared volts in a $1\mathrm{Hz}$ bandwidth. The inset is a plot of the NQR splitting versus $\cos \phi$. The solid symbols are data collected at $300\mathrm{mW}∕{\mathrm{cm}}^2$, and the open symbols are data collected at $60\mathrm{mW}∕{\mathrm{cm}}^2$. For the low (high) power data, the Rb field was $0.12\mu \mathrm{T}$ $\left(0.19\mu \mathrm{T}\right)$. For comparison, the applied field was $\sim 0.8\mu \mathrm{T}$. There is more distortion in the parabolic shape of the curve for the low power data—particularly when the applied field was orthogonal to the light propagation direction where the approximation that $B_{\mathrm{Rb}}\parallel \widehat{k}$ would not hold as well. The dashed line is a fit to the high-power data, which gives a value of $\Delta {\Omega }_0∕2\pi =0.39\left(1\right)\mathrm{Hz}$. Our value for $\Delta {\Omega }_0$ is $\sim 43\%$ larger than the largest value reported by Wu et al. [14].

Figure 3

(Color online) Spectra versus applied field for $\phi =22°$ (a) and $\phi =39°$ (b). The grey lines represent the six frequency differences between the four nuclear sublevels computed numerically (see text). The black lines mark the ${}^{129}\mathrm{Xe}$ transition versus field. Each vertical line represents a different frequency spectrum acquired at the specific magnetic field that it intersects on the horizontal axis. The symbol size is proportional to the signal amplitude, and the same amplitude scale was used for both angles of $\phi$. The laser intensity was $300\mathrm{mW}∕{\mathrm{cm}}^2$ and $B_{\mathrm{Rb}}$ was $0.19\mu \mathrm{T}$. The inset in (a) shows the ${}^{131}\mathrm{Xe}$ nuclear energy levels in the low-field NQR regime. Since the energies of the nuclear sublevels go as $m^2$ at zero magnetic field [1], the $\mid +3∕2⟩$ and $\mid -3∕2⟩$ states are degenerate at zero field, as are the $\mid +1∕2⟩$ and $\mid -1∕2⟩$ states. The inset in (b) shows the nuclear energy levels in the high-field NMR regime.

Figure 4

(Color online) A single spectrum collected with $28\mathrm{nT}$ and $\phi =39°$, which corresponds to the second spectrum from the left-hand side in Fig. 3. The predicted transition frequencies are also shown for reference. The signal has the units of root-mean-squared amplitude for a $32.768\mathrm{s}$ averaging time. Given that the $T_2$ time is about $5\text{seconds}$, we compromised on signal amplitude to achieve improved frequency resolution.