Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells

Transcription

1 PHYSICAL REVIEW A VOLUME 59, NUMBER 3 MARCH 1999 Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer Joseph Henry Laboratory, Physics Department, Princeton University, Princeton, New Jersey Received 11 November 1997; revised manuscript received 12 June 1998 We report on some unusual magnetic-resonance phenomena of optically pumped Rb vapor in high-pressure gas cells. When Rb-Rb spin exchange is the fastest spin-relaxation rate, we observe a considerable narrowing of the magnetic-resonance linewidths with increasing pump-laser power. The experimentally measured Rb magnetic-resonance linewidths are in excellent agreement with a theoretical model, which includes the processes of Rb-He and Rb-Xe spin destruction, Rb-Rb spin exchange, and Rb optical pumping. S X PACS number s : Bx, Cy, Jz I. INTRODUCTION Hyperpolarized 3 He or 129 Xe are noble gases for which the nuclear-spin polarization has been increased from the normal, thermal-equilibrium values of a few parts per million to several tens of percent by optical pumping. Hyperpolarized gases are being used for an increasing number of applications, ranging from polarizers for neutrons to medical imaging 1 6. Two types of optical pumping have proven to be useful for producing hyperpolarized gases: 1 direct pumping of metastable 3 S 1 He atoms with 1080-nm resonance light, followed by spin exchange with ground-state He atoms 7,8 ; and 2 spin-exchange of 3 He and 129 Xe with optically pumped alkali-metal atoms 9, which is the subject of this paper. In spin-exchange optical pumping the absorption cells are operated at quite high temperatures to increase the numberdensity of the alkali-metal atoms, which speeds up the spin exchange between the spin-polarized alkali-metal atoms and the noble-gas nuclei. Hyperpolarized 129 Xe, can be most efficiently polarized if it is present at the level of a few percent in a multiatmosphere 4 He carrier gas, which pressure broadens the absorption line of the alkali-metal atoms and makes it possible to absorb most of the light of a broadband laser. For similar reasons, 3 He is also pumped at multiatmosphere pressures. At these high temperatures and pressures, the equilibrium spin polarization produced in the alkali-metal atoms is expected to be very well characterized by a spin temperature, whether the spin-exchange rate between alkalimetal atoms is large or small with respect to the opticalpumping rate or the various spin-destruction rates of the system 10. Because of the practical importance of spinexchange pumping, we have carried out extensive experiments to characterize fully the physics at high pressures and high temperatures. The spin-destruction rates of the system are most conveniently measured by observing and analyzing relaxation in the dark, a method pioneered by Franzen 11 and Bouchiat and Grossetête 12. The transient signals from relaxation in the dark are not very sensitive to the spin-conserving spinexchange rate between alkali-metal atoms. However, optical pumping and spin-exchange rates can be precisely studied while the atoms are being pumped by measuring the resonant frequencies and widths of the radio frequency rf magnetic resonance transitions. The resonance frequencies are shifted by absorption of light, as first shown by Barrat and Cohen- Tannoudji 13, and the linewidths are determined in a complicated way by optical pumping and by collisional processes. While investigating the magnetic-resonance linewidths in high-temperature, high-pressure cells, we noticed a very striking phenomenon, light narrowing of the widths of the most prominent magnetic resonance lines. The term light narrowing denotes a substantial narrowing of the magneticresonance linewidth with increasing pump-laser power. We know of only one prior study of a somewhat similar lightnarrowing phenomenon by Bhaskar et al. 14. In that case, the magnetic field was so low that the resonant frequencies differed by much less than the linewidths, and the observed linewidth was nearly completely determined by rf-power broadening, magnified by the ratio T 1 /T 2 of the longitudinal relaxation time T 1 to the transverse relaxation time T 2, in accordance with the Bloch formula. Increasing the opticalpumping rate shortens the effective value of T 1 while having little effect on T 2, thereby decreasing the rf-power broadening. The light narrowing which is the subject of this paper occurs even in the limit of vanishing rf power; it is characteristic of larger magnetic fields, where the individual magnetic resonances are well resolved by quadratic splitting, and it represents a substantial suppression of the spinexchange contribution to the linewidth for high spin polarization. As we outlined below, a quantitative analysis of the light narrowing allows us to obtain precise data on the opticalpumping and spin-exchange rates, and it provides a useful check on spin-destruction rates, which are obtained more conveniently from experiments on relaxation in the dark. Our quantitative studies of the light narrowing confirm the observation of Young et al. 15 that the distribution of atoms between the magnetic sublevels of the alkali-metal atoms is very well described by a spin temperature. The basic theory of light narrowing and light shift is reviewed in Sec. II. The experimental procedures are outlined in Sec. III, and a comparison of experimental results with theory is presented in Sec. IV /99/59 3 / /$15.00 PRA The American Physical Society

2 PRA 59 LIGHT NARROWING OF RUDIBIUM MAGNETIC II. THEORY A. Optical pumping and light shift The real and virtual absorption of nearly resonant light can pump atoms out of the ground state and also shift the energy of the sublevels 13. These two effects can be described by an effective Hamiltonian operator H (i /2) E, where the light absorption part broadens the magnetic resonance linewidth, as discussed in more detail in the next sections, and the light-shift part E v s S acts like a fictitious magnetic field proportional to the mean photon spin s and interacting with the electron spin S 13,16,17. As shown in Ref. 10, when the opticalabsorption line has a Lorentzian profile, which is very close to the experimentally observed profile for Rb in He, the broadening and the shift of the magnetic-resonance transitions due to optical pumping can be described by a complex optical-pumping rate R R i v, which is given by R R i v r e cf d a /2 i a, where r e is the classical electron radius, c is the speed of light, and f defines the oscillator strength of the corresponding optical transition ( f 1 3 for the D1 line of Rb, and a and a are the optical transition frequency and linewidth. The flux of photons in the frequency interval to d is d. In the case of a Gaussian laser profile the evaluation of the integral in Eq. 1 leads to R 2 ln 2 r 3 ef l hc l A wi l. 2 Here l, l, and I l are the Gaussian linewidth full width at half maximum FWHM, wavelength, and power of the pump laser. A is an effective area of the pump beam in the cell. The complex overlap function w 18 is given by w w iw exp ln 2 r is 2 erfc ln 2 r is. 3 The relative detuning is s 2( l a )/ l, where a and l are the atomic transition frequency and laser frequency. The relative atomic linewidth is r a / l. For the experimental results shown later it is convenient to write the opticalpumping rate R as R I l, with the optical-pumping rate constant 2 ln 2r ef 3 l w r,s hc l A cm2 nm J 1 4 w r,s l A. 5 The coefficient cm 2 nm/j is calculated for l 800 nm. Equations 1 5 will be the basis for a comparison with the experimental results. We note that for our experimental conditions the light shift due to real transitions 13 is more then one order of magnitude smaller than the light shift due to virtual transitions 10, and will be therefore neglected. B. Total linewidth and the light-narrowing phenomena In high-pressure cells of the type used for spin-exchange optical pumping, the occupation probability of a spin sublevel of azimuthal quantum number m is very nearly proportional to exp( m), where is the spin-temperature parameter 19. For the spin-temperature distribution the mean electron spin S z can be used to define a polarization P 2 S z tanh( /2). The magnitude of the polarization is determined by a balance between the optical-pumping rate R, which creates polarization, and the spin-relaxation rates which destroy polarization. As described in Ref. 10, itis useful to distinguish between electron-spin-relaxation interactions which fluctuate rapidly with respect to the hyperfine frequency of the ground state (S-damping interactions, with rate 1/T sd ), and interactions which fluctuate slowly with respect to the hyperfine frequency of the ground state (F-damping interactions, with rate 1/T fd ). It can be shown that under steady-state conditions of spin-exchange optical pumping, and with a negligible F-damping rate 1/T fd, the polarization P is given by 10 RT sd P s z. 6 1 RT sd The origin of 1/T sd is collisions between Rb atoms and buffer-gas atoms, or binary collisions between two Rb atoms, for which some of the spin-angular momentum is converted to translational angular momentum of the pair of colliding atoms. The mean longitudinal photon spin is s z. For left circularly polarized light, s z 1, for right circularly polarized light, s z 1, and for linearly polarized light, s z 0. One way to determine the spin-temperature distribution and the linewidth of individual Zeeman transitions of the Rb ground state is to measure the radio-frequency spectrum of the optically pumped atoms. In all the linewidth measurements shown in this paper the applied magnetic field B 0 is large enough that the resonant frequencies f,m 1 E f,m E f,m 1 are well resolved from each other. The mean azimuthal quantum number m m 1 2 defines a m 1 Rb ground-state Zeeman transition inside one hyperfine multiplet with quantum number f. For 85 Rb (I 5 2 ) f a 3 orf b 2. A weak magnetic field B 1 cos t oscillating along the x axis creates a coherence 13 between two consecutive Zeeman states f,m and f,m 1. The radio-frequency radiation leads to a transverse electron-spin polarization S, which rotates at a frequency. It can be shown that 10 S P g s B B 1 8 I 2 m Q m a 2 4m 2 am 2 am 2 am xcos t y sin t am xsin t y cos t m Q m b 2 4m 2 bm 2 2 bm xcos t bm y sin t bm xsin t y cos t, where ( I 2I 1; a 2a 1; b 2b 1), and fm and fm are the frequency and linewidth of a specific transi- 7

3 2080 APPELT, BARANGA, YOUNG, AND HAPPER PRA 59 tion with quantum numbers f and m. We denote unit vectors along the x and y axes by x and y. For small radio-frequency field amplitudes B 1, S is proportional to B 1 and to the population differences between the coupled sublevels fm PQ m with e m I m 2P 1 P I m 1 P Q m. 8 Z I 1 P [I] 1 P [I] The factors Q m are the probabilities that the nucleus will have the azimuthal quantum number m. The parts of S due to coherences in the multiplets f a and f b rotate in opposite directions about the magnetic field. In order to monitor S we applied a circular polarized probe laser beam propagating perpendicular to the static magnetic field B 0 as specified in Ref. 15, and we measured the modulated light absorption with a photodetector. The Rb radiofrequency spectrum is obtained by sweeping the magnetic field B 0 and keeping the radio frequency constant. For 85 Rb the expected spectrum consists of ten Lorentzian resonance peaks at the frequencies fm, with amplitudes proportional to Q m ( f 2 4m 2) and the widths fm. The width of each individual transition fm is given by 10 fm 1 T ex 1 T sd R 3 I 2 1 4m 2 4 I 2 P T ex Rs z m I 1 a f f 2 4m 2 4 I 2 1 Q m T fd T ex, where is the isotopic fraction of 85 Rb ( for 85 Rb in natural abundance, and 1/T ex is the rate for Rb-Rb spin exchange irrespective of the isotope. For the special case of the transition f 3,m 5 2 in 85 Rb, the linewidth 3,5/2 can be expressed as 3,5/ T sd 6T fd 6 R 1 T ex 7 5P P 1 P 5 1 P 6 1 P Equations 10 and 6 are used in this paper to analyze experimental results. They depend on three physical processes which destroy coherence and determine the linewidth. First, the S-damping rate T sd 1 is the randomization rate of the electron spin due to binary atomic collisions or van der Waals molecules with very short collisionally limited lifetimes. These collisions can occur between two alkalimetal atoms or between an alkali-metal atom and a buffergas atom. The second rate constant T fd 1 is the F-damping rate, and describes the destruction of coherence due to Zeeman transitions inside one hyperfine multiplet. This F damping occurs because of the formation of Rb-buffer-gas van der Waals molecules with short collisionally limited lifetimes. The contribution from T 1 fd is negligible for Rb-He collisions, but perhaps noticeable in the case of Rb-Xe collisions. Walker, Anderson, and Kadlicek showed that some fraction of Rb-Rb collisions may also lead to F damping 20. The third term in Eq. 10 is the optical-pumping rate R I l of Eq. 4. This term describes the damping of the rotating magnetization S due to the absorption of photons. The last term in Eq. 10 describes the line broadening due to Rb-Rb spin exchange. The spin-exchange rate constant T 1 ex Rb v is proportional to the Rb number density Rb and to the rate coefficient v for Rb-Rb collisions ( cm 2 ) 21,22. Note that the term in the square brackets in Eq. 10, the slowing-down factor, depends on the electron-spin polarization P. Increasing the light intensity will increase the optical-pumping rate R and will also increase the spin polarization P in accordance with Eq. 6. From the form of Eq. 10 we see that increasing the light intensity will broaden the linewidth light broaden because of the term proportional to the optical-pumping rate R, and will narrow the linewidth light narrow because of the term proportional of the spin-exchange rate T 1 ex, since the slowing-down factor for spin exchange diminishes with increasing polarization P. For sufficiently rapid spin exchange, the light narrowing will exceed the light broadening. The light narrowing of the spin-exchange contribution of Eq. 10 comes from the conservation of angular momentum. The coherence 3,3 3,2, whose damping is given by Eq. 10, represents a component F of transverse spin, which must be conserved in a collision. For low polarization, there are few constraints on where the transverse spin is deposited after the collision, so there will be appreciable excitation of coherences f,m f,m 1 for all f, f, and m. The amount of the initial coherence 3,3 3,2 regenerated after the collision is relatively small, since the transverse spin is shared by many coherences. However, for high polarization, the creation of appreciable coherences with m 5 2 would not conserve the large longitudinal spin, so the collisions regenerate nearly the same coherence that was initially present and there is little damping. One can readily verify from Eq. 9 that in the limit P 1 and 1 the spin-exchange damping of the highestspin coherence a,a a,a 1 vanishes. We include also into our considerations the broadening of the linewidth due to radio frequency irradiation and to magnetic-field inhomogeneities. From the Bloch equations one can show that the total linewidth FWHM is given by 1 m 2 fm a 2 fm B 2 1 C, 11 where C describes a constant background broadening due to static magnetic-field inhomogeneities and due to optical pumping of the probe-laser beam. The broadening due to radio-frequency irradiation is given by the second term in the square root of Eq. 11, where a fm is a coefficient which depends in a complicated way on f and m, but which is of order B /( I ). Equations 10 and 11 will be used to explain our experimental linewidth measurements. For most of our experimental conditions fm C,a fm B 1, so that the broadening due to magnetic-field inhomogeneity, optical

4 PRA 59 LIGHT NARROWING OF RUDIBIUM MAGNETIC FIG. 1. Sketch of the experimental setup used for the measurements of the light shift and the linewidths of the 85 Rb Zeeman transitions. PD: photodetector, ND filters: neutral density filters. pumping of the probe laser, and rf irradiation are small contributions to the total measured linewidths. III. EXPERIMENT The experimental setup is shown in Fig. 1. For investigating the Rb linewidths we made two different high-pressure Rb optical-pumping cells, both glass spheres with an inner diameter of 2 cm: a He cell, which contains 13.5 atm at 20 C of 3 He buffer gas and 0.08 atm of N 2, and a Xe cell containing 8 atm of 4 He, 0.08 atm of N 2, and atm of Xe. Both cells contained a few milligrams of natural Rb metal and were placed in a hot air oven to maintain a defined Rb number density. For the light-shift measurements and the temperature dependence of the linewidth we used a cylindrical Xe cell with a 2.4-cm inner diameter and a length of 6 cm containing 7.6 atm of 4 He, 0.08 atm of N 2 and 0.1 atm of Xe. The temperature range used in our measurements was between 100 and 140 C. For optical pumping we used either an Opto Power Corp. B015 fiber-optic-coupled diode laser, emitting 9Wofunpolarized laser power at the Rb D 1 line 795 nm, or an Opto Power Corp. 150 Watt CW water-cooled stack of 10 Al x Ga 1 x As/GaAs laser diode arrays not shown in Fig. 1. The spectral linewidth was approximately 2.1-nm FWHM for the fiber-optic-coupled laserdiode array and 4-nm FWHM for the high-power laser-diode array. Due to difficulties of collimation of the divergent beam of the high-power laser-diode stack, we obtained a maximum power of 20 W in front of the cell. For the fiber-optic-coupled laser-diode array, the laser beam was shaped to a nearly parallel beam with the desired diameter by using a beam expander. After passing a polarizing cube and a /4 waveplate circular polarizer we measured 4Wof 95% circular polarized pumping light at the front window of the oven. We estimated that a maximum power of 3 W of pumping light entered into the cell. A series of neutraldensity filters was used to vary the pump-laser power. The pumping beam is parallel to a uniform static magnetic field B 0 31 G, which is produced by a pair of 1.5-m-diameter Helmholtz coils. The field of 31 G corresponds to a Zeemantransition frequency of 14.4 MHz for the ground state of 85 Rb atoms. A radio-frequency modulating field of mG amplitude, applied perpendicular to B 0, was produced by a pair of 12-cm-diameter Helmholtz coils concentric with the x axis, mounted on either side of the oven. The coils were driven by a 40-db rf amplifier coupled to a digital function generator. Radio-frequency current was applied to the coils and tuned to the Bohr condition for transitions between the Zeeman sublevels f,m and f,m 1. As described by Eq. 7, the rf field generated transverse magnetization rotating in synchronism with the rf. For detection of the rotating magnetization we applied perpendicular to the static magnetic field a circularly polarized Ti:sapphire laser probe beam at 795 nm. The intensity of this beam was 1 mw or less, and the beam diameter was reduced with an iris from 3 mm to less than 1 mm. This was done in order to minimize the broadening of the linewidths due to inhomogeneous optical pumping of the probe laser and due to residual magnetic-field inhomogeneities along the probe-beam diameter. The transmitted intensity of the probe beam, which is modulated by the rotating Rb magnetization, was monitored by a fast photodiode operated in the photoconductive mode. The signal was monitored by a lock-in amplifier with the rf frequency as reference, and recorded by a digital LeCroy oscilloscope. When the magnitude of the magnetic field B 0 was swept through the Rb resonances, the transmitted probe beam exhibited resonances corresponding to the 85 Rb Zeeman transitions. By calibrating the rate of the magnetic-field sweep, the linewidths and line positions of the different Zeeman transitions could be determined. The atomic linewidth of 85 Rb in the high-pressure cells (0.27 nm for 7.6 atm of 4 He), as well as the total gas pressure and the 85 Rb number density, have been measured by scanning the Ti:sapphire probe-beam frequency over the resonance at nm with no circular polarizer, and monitoring the transmission 23. IV. RESULTS A. Spectral profile of the pump laser The spectrum of the circularly polarized fiber-opticscoupled diode laser beam transmitted through the Rb vapor in the He high-pressure cell was measured by an Optical Multichannel Analyzer OMA. The OMA spectral resolution is 0.03 nm, and the Rb atomic linewidth in an 8-atm 3 He optical-pumping cell is 0.29 nm. Figure 2 shows the results of these OMA measurements, taken at four different temperatures. At T 80 C the top trace in Fig. 2 there is practically no absorption due to the low Rb number density in the cell. Consequently this trace reflects the spectral profile of the pump laser, showing a slightly asymmetric Gaussian-like profile with 2.1-nm FWHM. As the temperature increases the line center is attenuated by the increased density of Rb atoms. For these measurements we tuned the maximum of the laser spectral profile to the Rb D 1 atomic transition. At T 185 C the Rb vapor is optically so thick that nearly 63% of the pumping light is absorbed.

5 2082 APPELT, BARANGA, YOUNG, AND HAPPER PRA 59 FIG. 2. Transmitted intensity vs wavelength of the fiber-opticscoupled diode laser array, which is used as the pump laser in our experiments. The trace at T 80 C shows the slightly asymmetric profile of the pump laser which we approximate with a Gaussian profile of width FWHM l 2.1 nm. With increasing temperature the center of the profile is attenuated, indicating the increasing absorption of the laser light by Rb in the high-pressure He cell. FIG. 3. a Light shift of the transition f 3,m 5 2 of 85 Rb as a function of pump-laser wavelength in the cylindrical Xe cell see text. The circles correspond to measured values and the solid line is v /(2 6). The imaginary part of v of Eq. 1 is evaluated with Eqs. 2 and 3 using the measured values l 2.1 nm for the Gaussian width of the pump laser, a 0.27 nm for the atomic linewidth, and 5 W/ cm 2 for the laser power density. b 85 Rb linewidth FWHM in Hz of the transition f 3,m 5 2 vs the pumplaser wavelength in the cylindrical Xe cell see text. The circles are the measured values, and the solid line is R/(6 ) in accordance with Eq. 10, with R I l and given by Eq. 5. B. Optical-pumping rate and light-shift effects Although light shifts due to virtual transitions have long been understood 13,16, their close connection to the optical-pumping rate R, as outlined by Eqs. 1 5, and their ease of measurement make them a valuable consistency check. As discussed in Sec. II A, the effect of optical pumping on the ground state of Rb atoms can be described by a complex optical-pumping rate R R i v. The width of the Zeeman resonance lines is proportional to the opticalpumping rate R and the shift of the resonance frequencies of the lines the light shift due to virtual transitions, since the shift due to real transitions is negligible is v /(6 2 ). Here we present experimental results for the case where the laser linewidth 2.1 nm is much broader than the atomic linewidth 0.27 nm. Figure 3 a shows the experimental results of the light shift for the 85 Rb transition, f 3,m 5 2, as a function of the laser wavelength. Figure 3 b shows the measured linewidth for m 5 2 versus the laser wavelength. These measurements have been done with a cylindrical Xe cell, at T 100 C, and a magnetic field B 0 31 G. At this temperature the Rb-Rb spin-exchange rate is smaller than the optical-pumping rate, and the Rb-Xe spindestruction rate. The pump beam in the cell was collimated to a diameter of 8 mm, and the power deposited in the cell was 2.5 W. The wavelength of the diode-pump laser was varied by changing the applied current. The wavelength and the laser power have been calibrated as a function of the applied current. The measured values for linewidths and light shift have been normalized to the value of the laser power at resonance, making use of the measured, nearly linear dependence of laser power on detuning. The frequency of the f 3,m 5 2 transition was measured for different pump-laser wavelengths. When the laser was tuned to maximum overlap with the atomic absorption line [s 0 in Eq. 3, the light shift was taken to be zero. The Zeeman resonance frequency 14.4 MHz for this condition was taken as a reference frequency. As shown in Fig. 3 a, the maximum measured frequency shifts are 4 khz and the relative maxima are separated by 2.1 nm, which corresponds to the linewidth FWHM of the pump laser. The width of the f 3,m 5 2 transition, in the limit where the transverse spin-relaxation rate due to optical pumping is small compared to other Rb spin-relaxation processes, was 7000 Hz. This value was determined by systematically reducing the optical pumping power leaving all other experimental variables fixed until no further change was observed in the measured width. In the limit of vanishing opticalpumping power, the width is mainly due to spin destruction by Rb-Xe collisions this cell contained 0.1 atm of Xe at 20 C), Rb-Rb spin exchange, and a small constant offset C, as described by Eqs. 10 and 11. Subtracting this 7000-Hz limiting value from the total measured linewidth, we determined the linewidth contributions due to optical pumping and displayed these values in Fig. 3 b. The two solid lines in Fig. 3 correspond to the model given by Eqs. 1 3 multiplied by the slowing down factor which is 1 6 for the case of 85 Rb), and with the three parameters mentioned above: atomic linewidth 0.27 nm, laser linewidth 2.1 nm and laser-power density (2.5 W/0.5 cm 2 ). The light shift in frequency units v /(2 6) is displayed in Fig. 3 a, and the line broadening R/( 6) is shown in Fig. 3 b. The slight difference between theory and experimental results can be ascribed to deviations from the Gaussian spectral profile assumed for the pump laser see Fig. 2. Because of the self-consistency of the measured light shifts and light-induced line broadenings

6 PRA 59 LIGHT NARROWING OF RUDIBIUM MAGNETIC FIG. 4. Temperature dependence of the 85 Rb linewidth FWHM for the transition f 3,m 5 2. The filled open circles represent measured values with 20 W of pumping power in front back of the cell, and the squares correspond to a measurement at 1.5 W laser power in front of the cell. The solid lines are drawn to guide the eyes. with each other and with Eqs. 1 3, one can have some confidence that the effects of optical pumping are accounted for correctly by the theoretical model on which our analysis is based. C. Rb linewidth vs temperature Figure 4 shows the 85 Rb linewidth 3,5/2 / FWHM of the transition f 3,m 5 2 versus the temperature of the cylindrical Xe cell. The applied magnetic field was B 0 31 G. The high-power diode laser stack fully illuminated the cell volume. The values for the linewidth have been obtained for two different pump-laser power conditions. The dots in Fig. 4 correspond to a 20-W pump-laser power measured in front of the oven window, the solid circles are linewidths measured in front of the cell, and the open circles are linewidths measured at the back of the cell, after the pump beam has passed through most of the vapor. The squares correspond to a 1.5-W pump-laser power. While the circles show a linewidth decreasing with temperature, the linewidth represented by the squares increases slightly with temperature from 6 khz at T 60 C to 7 khz at T 100 C. Two different relaxation mechanisms are responsible for this behavior. At low laser power there is a negligible line broadening due to optical pumping, and the width is dominated mainly by Rb-Xe collisions and by Rb-Rb spin-exchange collisions see Eq. 10. The spin-exchange relaxation increases with the Rb number density i.e., temperature, which in Fig. 4 squares is the main reason for the slight increase of the linewidth with temperature. At high laser power 20 W the dominant relaxation mechanism is optical pumping. The decrease of the linewidth with increasing temperature can be explained by the absorption of the pump-laser intensity before the linewidth measurement position in the cell. This reduces the relaxation due to optical pumping at the end of the cell. D. Rb linewidth vs pump-laser power 1. Light-narrowing phenomena At conditions where Rb-Rb spin-exchange processes dominate over all other line-broadening mechanisms, an un- FIG. 5. Two magnetic-field scans for the transition f 3,m 5 2 of 85 Rb for two different pump-laser power intensities. The temperature of the He cell was 140 C, and the cell was fully illuminated. The upper trace, taken at I l 0.08 W, is 2.5 times broader than the lower trace (I l 1.55 W), demonstrating the lightnarrowing phenomenon. usual narrowing of the linewidth with increasing pump-laser intensity is expected see Eq. 10. Figure 5 is an example of the light-narrowing effect. The figure shows two Lorentzianline profiles of the transition f 3,m 5 2 of 85 Rb, as measured in the He cell for the two different pump-laser powers I l 0.08 and 1.55 W. Note that the pump-laser power in the upper trace, is almost 20 times smaller than in the lower trace but the linewidth is 2.5 times broader. As already mentioned in Sec. II, the nature of this light-narrowing effect is due to a suppression of the Rb-Rb spin-exchange broadening mecha- FIG. 6. a Linewidth of the transition f 3, m 5 2 of 85 Rb vs pump-laser power. All experimental data shown are measured for the He cell at three different temperatures T 100 C circles, 130 C squares, and 140 C triangles. A strong light-narrowing effect occurs at higher temperatures. The solid lines correspond to the theory of Eqs. 6, 10, and 11. b Light narrowing of 85 Rb for the spherical Xe cell see text. The solid lines, representing the theory of Eqs. 6, 10, and 11, are in good agreement with the experimental observed linewidths.

7 2084 APPELT, BARANGA, YOUNG, AND HAPPER PRA 59 nism through optical pumping and not to a reduction of the rf-broadening contribution see Bhaskar et al Comparison of the experimental results with the theory Figure 6 shows the results of the measured 85 Rb linewidth FWHM of the first transition (m 5 2 ) as a function of the pump-laser power. Figure 6 a displays the measurements for the He cell, and Fig. 6 b shows the results for the spherical Xe cell containing atm Xe at 20 C). Let us first discuss the results for T 100 C circles, where the Rb-Rb spin exchange is not the dominant contribution to the total linewidth. As the measurements indicate, the linewidth above I l 1 W is proportional to the pump-laser power. This is described in Eq. 10 by the term linear in the laser power I l /6. At very low laser power the linewidth converges to a constant value, which is 1 khz in the He cell and 2.7 khz in the Xe cell. In the case of the He cell this constant value consists mainly in the Rb-Rb spin-exchange rate and the constant offset C ( 400 Hz in our case. In the case of the Xe cell, the Rb-Xe spin-destruction rate and the Rb-Rb spin-exchange rate are the dominant contributions. At higher temperatures the Rb-Rb spin-exchange rate becomes the dominant broadening mechanism and, according to the last term of Eq. 10, one expects a strong dependence of the linewidth on the Rb polarization and on the laser power. This is most pronounced for T 140 C in Fig. 6 a triangles. The linewidth drops from 8.5 khz at 0.08-W laser power to 3.5 khz at 1.55-W laser power. A slight light-narrowing effect at T 120 C in the Xe cell is shown in Fig. 6 b squares. The solid lines in Fig. 6 are not the best fits to the experimental values, but are the results of model calculations, based on Eqs. 6, 10, and 11, with the following parameters: T 1 sd 8000 s 1 1 for the Xe cell and T sd 410 s 1 (510 and 560 s 1 ) at T 100 C (130 and 140 C) for the He cell 22 ; 7000 J 1 has been estimated from laser power and beam area measurements in 1 these experiments Eq. 5 ; the spin-exchange rates T ex are 4900 s 1 (17 000, , and s 1 ) for T 100 C, (120,130, and 140 C). V. CONCLUSIONS We have shown the effects of broadband laser-optical pumping on the linewidth and line position of Rb Zeeman transitions in high-pressure optical-pumping cells. Furthermore, we demonstrated that the width of the Rb magneticresonance transitions is fully determined by only three parameters: the optical-pumping rate, the Rb buffer-gas spindestruction rate, and the Rb-Rb spin-exchange rate. At high temperatures, where the Rb-Rb spin-exchange rate is dominant, we observed light-narrowing effects, which is caused by the suppression of the spin-exchange broadening at highspin polarization. ACKNOWLEDGMENTS This work was supported by the AFOSR and the Defense Advanced Research Project Agency, with assistance from the Princeton cyclotron group, funded by the NSF. 1 M. S. Albert, G. D. Cates, B. Driehuys, W. Happer, B. Saam, C. S. Springer, and A. Wishnia, Nature London 370, G. Navon, Y.-Q. Song, T. Rõõm, S. Appelt, R. E. Taylor, and A. Pines, Science 271, T. Rõõm, S. Appelt, R. Seydoux, E. L. Hahn, and A. Pines, Phys. Rev. B 55, T. E. Chupp et al., Phys. Rev. Lett. 72, ; R.E. Stoner et al., ibid. 77, P. L. Anthony et al. Phys. Rev. Lett. 71, S. Appelt, G. Waeckerle, and M. Mehring, Phys. Lett. A 204, ; Phys. Rev. Lett. 72, G. Eckert, et al., Nucl. Instrum. Methods Phys. Res. Sect. A 320, P. J. Nacher and M. Leduc, J. Phys. France 46, T. G. Walker and W. Happer, Rev. Mod. Phys. 69, S. Appelt, A. Ben-Amar Baranga, C. J. Erickson, M. V. Romalis, A. R. Young, and W. Happer, Phys. Rev. A 58, W. Franzen, Phys. Rev. 115, M. A. Bouchiat and F. Grossetête, J. Phys. France 27, J. P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22, N. D. Bhaskar, J. Camparo, W. Happer, and A. Sharma, Phys. Rev. A 23, A. R. Young, S. Appelt, A. Ben-Amar Baranga, C. Erickson, and W. Happer, Appl. Phys. Lett. 70, A. Kastler, J. Opt. Soc. Am. 53, W. Happer and B. S. Mathur, Phys. Rev. 163, Handbook of Mathematical Functions, edited by M. Abramowitz and I. E. Stegun, Natl. Bur. Stand. U. S., Appl. Math. Ser. No. 55 U.S. GPO, Washington, DC, 1964, pp L. Wilmer Anderson, Francis M. Pipkin, and James C. Baird, Phys. Rev. 116, T. G. Walker, W. A. Anderson, and S. Kadlicek, Phys. Rev. Lett. 80, T. J. Killian, Phys. Rev. 27, A. Ben-Amar Baranga, S. Appelt, M. V. Romalis, C. J. Erickson, A. R. Young, G. D. Cates, and W. Happer, Phys. Rev. Lett. 80, M. V. Romalis, E. Miron, and G. D. Gates, Phys. Rev. A 56,