Electric-field-induced change of the alkali-metal vapor density in paraffin-coated cells

Alkali-metal vapor cells with antirelaxation coating (especially paraffin-coated cells) have been a central tool in optical pumping and atomic spectroscopy experiments for 50 years. We have discovered a dramatic change of the alkali-metal vapor density in a paraffin-coated cell upon application of an electric field to the cell. A systematic experimental characterization of the phenomenon is carried out for electric fields ranging in strength from 0–8 kV/cm for paraffin-coated cells containing rubidium and cells containing cesium. The typical response of the vapor density to a rapid (duration $\lesssim 100\text{ms}$) change in electric field of sufficient magnitude includes (a) a rapid (duration of $\lesssim 100\text{ms}$) and significant increase in alkali-metal vapor density followed by (b) a less rapid (duration of $\sim 1\text{s}$) and significant decrease in vapor density (below the equilibrium vapor density), and then (c) a slow (duration of $\sim 100\text{s}$) recovery of the vapor density to its equilibrium value. Measurements conducted after the alkali-metal vapor density has returned to its equilibrium value indicate minimal change (at the level of $\lesssim 10\%$) in the relaxation rate of atomic polarization. Experiments suggest that the phenomenon is related to an electric-field-induced modification of the paraffin coating.

Figure 1

Schematic of setup for experiments with cesium atoms contained in paraffin-coated cells at California State University–East Bay (CSU-EB). HV—high voltage output of power supply, NDF—neutral density filter, IF—interference filter, PD—photodiode.

Figure 2

Design of high voltage electrode assembly for the experiment. Cylindrical box is made of copper, rounded edges are used on surfaces near the high voltage electrode to minimize possibility of discharge. Insulating support for the high voltage plate is manufactured from G10 plastic.

Figure 3

(Color online) Cesium density as a function of time (upper plot, data points connected with line) with electric field of 4 kV/cm magnitude applied (lower plot). The polarity of the electric field is switched at $t=100\text{s}$. Dashed line indicates average equilibrium density $n_0$ prior to field reversal. Temperature of the cell and stem are $\approx 20°\text{C}$. Density data acquired every 5 s, extracted from a fit to the Cs $D_2$ absorption spectrum. Data acquisition is too slow to show the detailed dynamics of the rapid increase and decrease in vapor density as the polarity is switched, although subsequent experiments at RRI using a different method of data acquisition are able to investigate these dynamics. Fluctuations in the value of $n$ are due to frequency jitter of the VCSEL during scans through the absorption spectrum, which degrades the quality of the fits.

Figure 4

(Color online) Cesium density as a function of time (upper plots in each graph) with electric field of 1, 2, 3, and 4 kV/cm magnitude applied, polarity switched every 250 s (lower plots in each graph). The cell temperature was $20°\text{C}$.

Figure 5

(Color online) Average maximum decrease in Cs vapor density $\left(\Delta n\right)$ when field polarity is switched as a function of electric-field magnitude for different cell temperatures. Electric-field magnitude starts at zero and is increased sequentially in steps of 1 kV/cm. There was a 30 min delay between changes in field magnitude, and data at different temperatures were taken on different days.

Figure 6

(Color online) Average maximum fractional decrease in Cs vapor density $\left(\Delta n/n_0\right)$ when field polarity is switched as a function of electric-field magnitude for the case where the electric-field magnitude is successively increased (filled circles) and the case where the electric-field magnitude is successively decreased (hollow circles). Data taken at $T=20°\text{C}$, with a 30 min delay between changes in field magnitude.

Figure 7

(Color online) Cesium density as a function of time (upper plots in each graph). Applied electric field is shown in the lower plots in each graph. Temperature of cell is $\approx 21°\text{C}$. In this experiment, the electric-field polarity was switched at $\left|\vec{E}\right|=5\text{kV}/\text{cm}$, and then the electric field was turned off for various intervals. After this delay the field polarity was switched several times at $\left|\vec{E}\right|=2\text{kV}/\text{cm}$.

Figure 8

(Color online) Schematic diagram indicating the side view of the experimental arrangement for the Rb measurements. The insulating material is Teflon and all screws are Nylon. The beam path through the cell is indicated by the bold line. The stem of the cell is located at the far side of the cell in this view and is roughly parallel to the electric-field plates.

Figure 9

(Color online) Upper plot shows the time-dependent Rb vapor density in a paraffin-coated cell upon the sudden application of a 4.4 kV/cm electric field across it at time $t=0\text{s}$ and sudden switching off of the field at $t=300\text{s}$. The middle plot shows the data from the upper plot for the time-dependent Rb density during the turning on of the 4.4 kV/cm field with an expanded time scale, and the lower plot shows the vapor density during the turning off of the field with an expanded time scale. The dashed horizontal lines represent the equilibrium vapor density in the cell at zero field. The time interval between successive data points is $\sim 130\text{ms}$. The rise time of the high voltage power supply for the electric field is $\sim 70\text{ms}$ and the fall time is $\sim 170\text{ms}$, comparable with the data acquisition rate. The vapor density is calculated from the raw data by taking the natural log of the fractional light transmission signal and comparing with a calculation assuming linear absorption. The absolute density level is accurate to within a factor of 2, whereas the relative density level is accurate at the few percent level.

Figure 10

Increase (upper plot) and decrease (lower plot) in the Rb vapor density in a paraffin-coated cell during the burst and drop of Rb vapor density, respectively, after the electric field is turned on as a function of applied electric-field magnitude. Note that the vertical scales of the two plots are different by a factor of 50. At approximately 1.6 kV/cm a threshold for the effect is observed. Note that two data points, one at $\approx 2.1\text{kV}/\text{cm}$ and the other at $\approx 6.0\text{kV}/\text{cm}$ lie outside the trend, and these outliers did not reproduce in subsequent experiments. These outliers are characteristic of the repeatability of the measurements.

Figure 11

Increase (upper plot) and decrease (lower plot) in the Rb vapor density in a paraffin-coated cell during the burst and drop of Rb vapor density, respectively, after the electric field is turned off as a function of applied electric-field magnitude. The threshold for electric-field-induced Rb vapor density changes is at $\sim 2.3\text{kV}/\text{cm}$, below which no effect is seen and above this value a steady increase is observed. Note that the burst amplitude for the field turning off is significantly smaller than that for the field turning on (Fig. 10, upper plot), and to clearly observe the threshold an inset with expanded vertical scale is included in the upper plot. The amplitudes of the drop in Rb density is within a factor of 2 of those observed for the turning on of the electric field throughout the data, and at high field magnitudes they are nearly equal.

Figure 12

(Color online) Relaxation rate of ${}^{85}\text{R}\text{b}$ polarization in paraffin-coated cell with electric fields of various magnitudes on and off. Relaxation rate is based on the width of nonlinear magneto-optical rotation resonances. Data are acquired after switching electric field and waiting for vapor density to reach equilibrium $\left(\approx 100\text{s}\right)$. Inset shows typical NMOR resonance data used to extract the relaxation rate ${\gamma }_{\text{rel}}$ from a fit of the data to Eq. (1).

Figure 13

(Color online) Shift of the zero-field nonlinear magneto-optical rotation resonance for ${}^{85}\text{R}\text{b}$ $F=3\to F^{\prime }$ components of the $D_2$ line with electric fields of various magnitudes applied to the paraffin-coated cell. Data are acquired after switching electric field and waiting for vapor density to reach equilibrium $\left(\approx 100\text{s}\right)$.

Figure 14

(Color online) Dots are experimental data for Cs vapor density in paraffin-coated cell upon switching of electric field polarity at time $t=500\text{s}$, shown previously in Fig. 3. Solid line shows numerical solution of rate equations for $n\left(t\right)$ with the following parameters: ${\rho }_0=2\times {10}^{-6}$, ${\delta }_a=100$, ${\gamma }_{d0}=2\times {10}^{-4}{\text{s}}^{-1}$, ${\delta }_d=1000$, ${\tau }_a=2\text{s}$, ${\tau }_d=0.5\text{s}$, $\xi =0.25{\text{cm}}^3/\text{s}$, $\Gamma =5\times {10}^{-4}{\text{s}}^{-1}$, cell volume $V=85{\text{cm}}^3$, coating surface area $A=85{\text{cm}}^2$. Parameters are in rough agreement with those from Refs. [22, 35] where applicable.

Figure 15

Results of model calculation for parameters of Fig. 14 for the number of atoms in the coating $N_c\left(t\right)$. Upper plot has same time scale as Fig. 14, lower plot shows same results over a longer time scale to observe recovery of $N_c$ to its equilibrium value. Note that the vertical scale does not begin at zero, and in fact there is less than a 5% change in $N_c$ caused by the electric field.