Hyperfine frequency shift and Zeeman relaxation in alkali-metal-vapor cells with antirelaxation alkene coating

An alkene-based antirelaxation coating for alkali-metal vapor cells exhibiting Zeeman relaxation times up to 77 s was recently identified by Balabas et al. The long relaxation times, two orders of magnitude longer than in paraffin- (alkane-) coated cells, motivate revisiting the question of what the mechanism is underlying wall-collision-induced relaxation and renew interest in applications of alkali-metal vapor cells to secondary frequency standards. We measure the width and frequency shift of the ground-state hyperfine $m{}_F=0\to m{}_F^{\prime }=0$ transition (clock resonance) in vapor cells with ${}^{85}$Rb and ${}^{87}$Rb atoms, with an alkene antirelaxation coating. We find that the frequency shift is slightly larger than for paraffin-coated cells and that the Zeeman linewidth scales linearly with the hyperfine frequency shift.

Figure 1

Apparatus: the alkene-coated cell is placed inside a four-layer mu-metal shield. A one-loop microwave antenna is positioned next to the cell. The orthogonal 3-axis coils and three gradient coils along the same axes induce an $\sim$3.6 mG bias magnetic field to resolve the Zeeman components of the hyperfine resonance. The magnetic-field axis is slightly tilted with respect to the axial symmetry to achieve optimum clock-resonance contrast. A synthesizer provides a fixed microwave source set 5 MHz above the hyperfine transition and is mixed with the output of a function generator whose frequency is swept through a 2 kHz span about a 5 MHz center frequency. A circulator directs the mixed output to the first one-loop microwave antenna and directs the return signal to a spectral analyzer (S.A.). The second one-loop antenna (when connected to the S.A.) serves to monitor the microwave power next to the cell. The inner-shield temperature stabilization is realized with two electric heaters consisting of quad-twisted nonmagnetic wire coiled in two solenoids parallel to the main axial symmetry and supplemented with a water heating and cooling system. The light beam from a distributed feedback (DFB) laser, is resonant with the rubidium (Rb) ${\text{D}}_1$ line, and is nearly linearly polarized, with approximately 5$\%$ circularity for optimum resonance contrast. Also for maximum contrast, the optical frequency is locked to the blue-detuned side of the peaks of $F=2\to F^{\prime }=1$ (${}^{87}$Rb) and $F=3\to F^{\prime }=2$ (${}^{85}$Rb), using a dichroic atomic vapor laser lock (DAVLL) [37]. Stability of the laser optical frequency is monitored with a reference (noncoated) cell and a Fabry-Pérot cavity. A photodiode registers the light transmission through the cell, and the signal is amplified, sampled, and recorded with a digital acquisition system (DAQ). [Note: the apparatus is a multipurpose platform (Chapters 5 and 6 of Ref. [38] show the complete range of configurations) designed to be used separately or in conjunction with a field-able multipurpose magnetometer platform (Chapter 4 of Ref. [38]), to investigate areas of atomic magnetometry and secondary frequency standards.]

Figure 2

Upper panel shows the eleven Zeeman components of the hyperfine resonance in ${}^{85}\mathrm{Rb}$ resolved with a $\sim$3.6-mG-bias magnetic field. The relative intensities of the peaks depend on the relative orientation of the pump-light beam, the bias magnetic and microwave fields, the pump-light detuning, and the pump-light polarization. Under typical conditions the optical resonant absorption through the alkali-metal vapor is $\sim$25$\%$ and increases by 1$\%$ to 5$\%$ on the hyperfine resonances. Lower panel shows the Zeeman sublevels for the hyperfine ground states $\mathit{F}=2$ and $\mathit{F}=3$ for ${}^{85}\mathrm{Rb}$, and the corresponding Zeeman components of the hyperfine transition.

Figure 3

Example of how the $m_F=0\to m_F^{\prime }=0$ hyperfine transition ([0-0] - clock resonance) width and frequency shift are extracted. Panel (a) shows the scan of a ${}^{87}$Rb clock resonance at large optical (10.7 $\mu$W) and microwave powers. The data are fit to a Lorentzian. The difference between the data and the wings of the fit may be attributed to imperfections in the measurement (see Sec. 6). The induced error in determining the resonance center frequency is within the margin of measurement error. To mitigate timing jitter the center frequency is measured from both the marker-step and from the beginning of the scan. In this example the clock-resonance unscaled (Sec. 5) full width at half maximum (FWHM) and unscaled frequency shift, relative to the hyperfine frequency for atoms in free space, are 104 and $-206$ Hz (average of the measurement referenced to the marker-step and of the measurement from the start of the scan), respectively. Panels (b)(1) and (b)(2) show the extraction of the clock-resonance width and frequency shift by extrapolation to zero light power (each data point represents an extrapolation to zero microwave power). The example shown is for the alkene-coated, 2-inch-long, 1-inch-diameter, cylindrical cell filled with isotopically enriched ${}^{87}$Rb [see Table (row 7) and Fig. 4].

Figure 4

Panels (a), (b), and (c) show the data for the C-30 coated cell and for the deuterated-paraffin-coated cell as circles and squares respectively. The vertical dotted lines serve to guide the eye. Panel (a) shows the dependence of the scaled linewidth on the scaled-frequency shift of the hyperfine clock-resonance. The data are scaled (Sec. 5) to a 1 inch spherical cell at 25 ${}^{\circ }$C and to the hyperfine frequency of the ${}^{85}$Rb species. The oval shapes serve to group cells with similar characteristics. The solid oval shows the alkene-coated cells with Zeeman polarization (longitudinal) relaxation times $T_1$ (Sec. 5) ranging between 3 to 53 s. The hashed oval shows the paraffin coated cells [14]. The dashed lines are the simulated adiabatic, spin exchange, and sum of both contributions to the hyperfine-resonance linewidth. For panels (b) and (c), the time between wall collisions is given in $\mu$s for each cell. Typical error bar magnitudes are given in Fig. 3. The two horizontal segments join ${}^{85}$Rb and ${}^{87}$Rb data in the cells with rubidium in isotopic abundance. Note the different vertical-axis scales in (b) and (c). Panel (b) shows the dependence of Zeeman transverse relaxation rate 1/$T_2$ on scaled-frequency shift of the hyperfine resonance for the three paraffin-coated cells of Ref. [14] for which $T_2$ was measured. The data points for the Zeeman longitudinal relaxation rate $1/T_1$, for the alkene C-30 and deuterated-paraffin coated cells, are added to panel (b) for reference only. The light slanted dashed line in panel (b) is the replica of the $1/T_1$ linear fit (darker dashed line) in panel (c). Panel (c) shows the dependence of Zeeman longitudinal relaxation rate ($1/T_1$) on scaled frequency-shift of the hyperfine resonance in the four alkene-coated cells in the present work. $T_1$ is indicated next to each alkene-coated cell in panel (c). The alkane C-30 and deuterated-paraffin-coated-cell data do not follow the same linear dependence observed in the alkene C20-24-coated cells and are not part of the linear fit in panel (c).