Relaxation of atomic polarization in paraffin-coated cesium vapor cells

The relaxation of atomic polarization in buffer-gas-free, paraffin-coated cesium vapor cells is studied using a variation on Franzen’s technique of “relaxation in the dark” [Franzen, Phys. Rev. 115 850 (1959)]. In the present experiment, narrow-band, circularly polarized pump light, resonant with the Cs D2 transition, orients atoms along a longitudinal magnetic field, and time-dependent optical rotation of linearly polarized probe light is measured to determine the relaxation rates of the atomic orientation of a particular hyperfine level. The change in relaxation rates during light-induced atomic desorption (LIAD) is studied. No significant change in the spin relaxation rate during LIAD is found beyond that expected from the faster rate of spin-exchange collisions due to the increase in Cs density.

Figure 1

Light frequency detuning $\Delta$ dependence of optical rotation (lower plot) near an atomic resonance (occurring at $\Delta =0$). The optical rotation is caused by a difference in the amplitudes of the real parts of the complex indices of refraction (upper plot) for left- and right-circularly polarized light ($n_{+}$ and $n_{-}$, respectively). The rotation angle is proportional to the difference $n_{-}-n_{+}$, since it arises due to the difference in phase velocities between the circular components of the linearly polarized light. For this plot, the magnetic field $B=0$, and a Lorentzian model of line broadening is employed, where the width is $\Gamma$. Plots are intended only to illustrate the spectral dependences, amplitudes are arbitrary.

Figure 2

Light frequency detuning $\Delta$ dependence of optical rotation (lower plot) caused by splitting of the resonance frequencies for left- and right-circularly polarized light due to Zeeman shifts of sublevels in a magnetic field $B=\Gamma ∕\left(2g{\mu }_0\right)$ ($\Gamma$ is the width of the resonance, where we use a Lorentzian model of line broadening, $g$ is the Landé factor, and ${\mu }_0$ is the Bohr magneton). Upper plot shows the dependence of the real parts of the complex indices of refraction for left- and right-circularly polarized light in the presence of a longitudinal magnetic field. The optical rotation is proportional to the difference $n_{-}-n_{+}$. Plots are intended only to illustrate the spectral dependences, amplitudes are arbitrary.

Figure 3

Schematic diagram of the experimental setup. PBS—polarizing beamsplitting cube, PD1(2)—photodiodes for light detection in polarimeter, and DAVLL—Dichroic Atomic Vapor Laser Lock (described in text and shown in Fig. 4).

Figure 4

Schematic of Dichroic Atomic Vapor Laser Locking (DAVLL) system described in text. PD-photodiodes, BS-polarizing beamsplitting cube, P-polarizer, and $\lambda ∕4$-quarter-wave plate. Detailed description can be found in Ref. 37. Light from the diode laser passes through a linear polarizer before passing through an uncoated Cs cell at room temperature ($\approx 21°\mathrm{C}$—corresponding to around one absorption length for the center of the $F=4\to F^{\prime }$ hyperfine component of the D2 transition). The cell is immersed in a magnetic field ($\sim 200\mathrm{G}$, applied along the direction of light propagation) that splits the Zeeman components of the Doppler-broadened Cs absorption spectrum. An analyzer (that can be continuously tuned from a circular to a linear analyzer) at the output measures the resulting change in the light polarization properties. The output of the analyzer functions as the error signal for the electronic feedback system.

Figure 5

Comparison of frequency stability of a Newport model 2010 external cavity diode laser (central $\text{wavelength}=852\mathrm{nm}$, tuned near the $F=4\to F^{\prime }$ hyperfine component of the D2 line) with and without use of the DAVLL system [37]. Laser frequency is measured by saturated absorption spectroscopy using an uncoated Cs vapor cell in an auxiliary setup. The saturated absorption spectrum is power-broadened to allow tracking of the laser detuning over the wide frequency range shown in the plot.

Figure 6

(Color online) Upper plot shows typical data for the time-dependent component of optical rotation of the linearly polarized probe light after the circularly polarized pump light is blocked. There is clear evidence of two oppositely signed contributions to optical rotation that relax at different rates, shown in the lower plot. Cell temperature $21°\mathrm{C}$, Cs $\text{density}=1.7\times {10}^{10}\text{atoms}∕{\mathrm{cm}}^3$, pump light $\text{power}=4\mathrm{mW}$, probe light $\text{power}=3\mu \mathrm{W}$, and $\mid \vec{B}\mid \approx 2\mathrm{G}$. Data taken with cell A (Table ). Diode laser is tuned about $400\mathrm{MHz}$ to the low frequency side from the center of the $F=4\to F^{\prime }$ hyperfine component of the Cs D2 absorption line, where the amplitudes of the two contributions are large (see Fig. 10). Lower plot shows the two oppositely signed contributions to the optical rotation signal and their exponential decay (extracted from the fit to the data shown in the upper plot).

Figure 7

Relaxation rates ${\gamma }_s$ (open circles) and ${\gamma }_f$ (closed circles) as a function of probe light power (upper plot) and pump light power (lower plot). Dashed lines represent the average values of the relaxation rates for the light powers where all other data is acquired (pump $\text{power}\approx 4\mathrm{mW}$, probe $\text{power}\approx 3\mu \mathrm{W}$). Data taken with cell B (Table ). Diode laser is tuned about $400\mathrm{MHz}$ to the low frequency side from the center of the $F=4\to F^{\prime }$ hyperfine component of the Cs D2 absorption line (see Fig. 10), cell temperature $\approx 21°\mathrm{C}$, Cs $\text{density}=8\times {10}^9\text{atoms}∕{\mathrm{cm}}^3$, $\mid \vec{B}\mid \approx 10\mathrm{G}$. Data points reflect the average of data for several measurements. Light power was changed by inserting various neutral density filters into the beam paths. Above probe light powers of $\sim 8\mu \mathrm{W}$, evidence of optical pumping is seen as the relaxation rates are clearly affected. All other measurements reported in this work are taken with probe-light powers around $3\mu \mathrm{W}$.

Figure 8

Magnetic-field dependence of the relaxation rates ${\gamma }_s$ (open circles) and ${\gamma }_f$ (closed circles). Data taken with cell B (Table ). Laser frequency detuned $\approx 400\mathrm{MHz}$ to the high-frequency wing of the $F=4\to F^{\prime }$ hyperfine component of the Cs D2 absorption line (where the amplitudes of the time-dependent signals are large, see Fig. 10). Pump light $\text{power}=4\mathrm{mW}$, probe light $\text{power}=3\mu \mathrm{W}$, and Cs $\text{density}=8\times {10}^9\text{atoms}∕{\mathrm{cm}}^3$.

Figure 9

Magnetic-field dependence of the amplitudes of time-dependent optical rotation ${\alpha }_s$ and ${\alpha }_f$ [see Eq. (7)], same conditions as in Fig. 8. Open circles correspond to ${\alpha }_s$, closed circles correspond to ${\alpha }_f$.

Figure 10

Dependence of the relaxation rates (upper plot) and amplitudes of optical rotation (middle plot) on detuning from resonance. Zero detuning corresponds to the center of the $F=4\to F^{\prime }$ hyperfine component of the Cs D2 absorption line. Pump light $\text{power}=4\mathrm{mW}$, probe light $\text{power}=3\mu \mathrm{W}$, Cs $\text{density}=8\times {10}^9\text{atoms}∕{\mathrm{cm}}^3$, and $\mid \vec{B}\mid =10\mathrm{G}$. Open circles correspond to the slower rate ${\gamma }_s$ and the corresponding rotation amplitude ${\alpha }_s$, closed circles correspond to the faster rate ${\gamma }_f$ and the corresponding rotation amplitude ${\alpha }_f$ [see Eq. (7)]. Data taken with cell B (Table ). Lower plot shows the transmission spectrum for the low-power probe light in the absence of pump light and magnetic field.

Figure 11

Relaxation rates (${\gamma }_f$ and ${\gamma }_s$) as the temperature of cells A and B (Table ) is changed, plotted with respect to the Cs density. Cell A’s temperature was varied from $\approx 24.3°\mathrm{C}\text{to}\approx 30°\mathrm{C}$, while cell B’s temperature was varied from $\approx 22.4°\mathrm{C}\text{to}\approx 27.6°\mathrm{C}$. A single linear fit describes the fast rates for both cells (solid line), separate linear fits are carried out for the slow rates (dashed lines). Laser frequency is detuned $\approx 400\mathrm{MHz}$ to the high-frequency wing of the $F=4\to F^{\prime }$ hyperfine component of the Cs D2 absorption line (where the amplitudes of the time-dependent signals are large, see Fig. 10), pump light $\text{power}=4\mathrm{mW}$, probe light $\text{power}=3\mu \mathrm{W}$, and $\mid \vec{B}\mid =10\mathrm{G}$. It is apparent that there is some systematic deviation of the fast relaxation rate data from the linear trend (most of the data for ${\gamma }_f$ at Cs densities between $\left(20\text{and}30\right)\times {10}^9{\mathrm{cm}}^{-3}$ fall below the linear fit, while most of the data for Cs densities $>30\times {10}^9{\mathrm{cm}}^{-3}$ falls above the linear fit). The spread of these systematic deviations is on the order of the run-to-run reproducibility of the data, so at present we do not ascribe it any particular significance.

Figure 12

Upper plot shows relaxation rates as a function of time when the cell is exposed to off-resonant light that causes desorption of Cs atoms from the paraffin coating (LIAD, see Ref. 23). Open circles correspond to the slower rate ${\gamma }_s$, closed circles correspond to the faster rate ${\gamma }_f$ [see Eq. (7)]. Lower plot shows the change in Cs density when the cell is exposed to the desorbing light. Desorbing light at $514\mathrm{nm}$ has intensity $\approx 7\mathrm{mW}∕{\mathrm{cm}}^2$, and is activated at $t=100\mathrm{s}$ and turned off at $t=380\mathrm{s}$. Laser frequency is detuned $\approx 400\mathrm{MHz}$ to the high-frequency wing of the $F=4\to F^{\prime }$ hyperfine component of the Cs D2 absorption line (where the amplitudes of the time-dependent signals are large, see Fig. 10), pump light $\text{power}=4\mathrm{mW}$, probe light $\text{power}=3\mu \mathrm{W}$, $\mid \vec{B}\mid =10\mathrm{G}$, and cell $\text{temperature}=20°\mathrm{C}$.

Figure 13

(Color online) Fast rate as a function of Cs density, where in one case the Cs density is changed by heating the cell, and in the other case the Cs density is changed by using off-resonant light to desorb atoms from the paraffin coating (LIAD). The factor of 4 difference in the slopes is evidence of extra relaxation induced when the cell is heated. The slope obtained using LIAD to control the density is consistent with that expected from $\mathrm{Cs}\mathrm{Cs}$ spin-exchange relaxation. All data are taken with cell A (Table ). Cell conditions described in previous figure captions (Fig. 12 for LIAD and Fig. 11 for heating).

Figure 14

Comparison of theoretical prediction of relaxation-in-the-dark rates based on Eq. (8) where for the spin-exchange rate ${\gamma }_{\mathit{se}}=n{\sigma }_{\mathit{se}}{v}_{\mathrm{rel}}$ we employ ${\sigma }_{\mathit{se}}=2\times {10}^{-14}{\mathrm{cm}}^2$ determined by previous measurements [2], and we determine that ${\gamma }_{\mathit{er}}=9.0\left(1\right){\mathrm{s}}^{-1}$ and ${\gamma }_u=1.2\left(1\right){\mathrm{s}}^{-1}$ from fitting the data. LIAD is used to change the Cs vapor density in this case, all data are taken with cell A (Table ), cell conditions described in the caption of Fig. 12.