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Measurement of g-factors in neon by quantum beat spectroscopy
Volume 30, number 2
OPTICS COMMUNICATIONS
August 1979
MEASUREMENT OF g-FACTORS IN NEON BY QUANTUM BEAT SPECTROSCOPY J.R. BRANDENBERGER
Department of Physics, Lawrence University, Appleton, Wisconsin54911, USA Received 8 May 1979
Laser-driven quantum beat spectroscopy has been used to measure Land6 g-factors in two states of the 2p s (2 P1/2) 3p manifold of neon. Transient lineshape data, captured by a simple photographic averagingtechnique, permit determination of the g-factors to a precision of 0.2%. The results are in good agreement with previous measurements, but the agreement with theory is less certain.
Quantum beat spectroscopy provides an elegant method for measuring fine, hyperfine, Stark, and Zeeman splittings in atoms and molecules [1 ]. In the Zeeman case where one measures Land6 g-factors, the quantum beat method complements high field techniques because quantum beat g-factors are determined in low magnetic fields where the Zeeman Hamiltonian is simple. The beat method has another important feature: laser excitation can be employed without introducing ac Stark shifts because the beat signal is monitored only after the laser field is turned off. Most quantum beat measurements reported to date have involved atoms with long-lived states, beam or vapor targets, accuracies at the 1% level, and the use of transient digitizers and signal averagers to capture the data [2]. By way of contrast, this paper reports on laserdriven Zeeman quantum beat measurements involving short-lived states in neon; the target atoms in this work are located in an rf-discharge; a simple but semi-precise mode of photographic data capture is employed, and the technique is pushed to the 0.2% level. Land6 g-factors provide a useful bridge between theory and experiment because calculated g-factors depend sensitively on coupling schemes and subtle effects, while experimental g-factors are easy to measure. The simplest Zeeman quantum beat (ZQB) experiments require only a pair of split Zeeman sublevels IJ, m j> = I 1, +1 ) coupled to a lower IJ, m j) = 10, 0) state. Under the proper choice of experimental conditions, a laser pulse creates the coherent superposition
(I 1,+ 1)e/~°÷t + I 1, - 1 ) e / t ° - t ) e -t/2r. This state proceeds to decay, but owing to the slight difference w = co+ - c o in the Bohr frequencies, the fluorescence exhibits interference beats in the form
I(t) =A e-t/r[1 ÷B cos(~ot + ~)] ,
(1)
where B = B(T, r, tp) is the modulation depth parameter which depends on the beat period T, the excited state lifetime r, and the pulse length tp. When tp is much less than T, the modulation depth approaches unity. The present work involvesg-factors in the 2P2 and 2P5 states (Paschen notation) of the 2p 5 (2P1/3) 3p manifold of neon. Since both are short-lived J = 1 states (16.6 and 18.7 nsec respectively), and since both are easily excited from the lower-lying l s 3 J = 0 metastable level, they satisfy the conditions enumerated above. Thus eq. (1) should describe the fluorescence from these states, and the modulation depth parameter should approach unity for short laser pulses. The choice of these states for this work was prompted by the fact that their g-factors were determined recently to 0.04% by optical pumping [3]. Hence they provide ideal test cases for the simple ZQB method employed here. The experimental layout is conventional. Neon gas at 0.4 Torr, sealed in a 1 cm X 1 cm X 4 cm quartz cuvette of high optical quality, is excited by a weak 100 MHz rf continuous-wave oscillator to produce the ls 3 metastables. Laser pulses of 7 ns (fwhm) duration 181
Volume 30, number 2
OPTICS COMMUNICATIONS
and about 1.5 GHz (fwhm) spectral width from a 20 pps N2-pumped dye laser excite the metastables to the 2P2 or 2P5 state depending on whether the laser is tuned to 616.36 nm or 626.65 nm respectively. The dye laser employs a 2400 £/mm holographic grating used at grazing incidence [4] ; its coherent output is highly polarized, but we use an external polarizer to reduce the superfluorescence in the laser beam. Peak power of the fraction of the laser beam incident on the neon cell is about 200 W. Amplitude instability of the dye laser is about 5%, and spectral jitter is about 1.5 GHz, comparable to the Doppler width of the neon lines of interest here. The neon cuvette is centered in a pair of 20 cm diameter Helmholtz coils whose calibration and inhomogeneity are determined by NMR in the vicinity of I00 G. Since all ZQB measurements are performed in fields on the order of 20 G, and since no magnetic materials are located within a meter or more of the coils, it is possible to make -+0.1% relative field measurements by monitoring the field current with a 0.05% precision, thermally-stabilized resistance standard. Both the direction and polarization of the incident light pulses are perpendicular to the magnetic field. Neon fluorescence arising from the rf as well as the laser excitation is monitored in the direction of the magnetic field. This light is analyzed (the analyzer's axis is normal to the incident polarization so as to suppress reflected light), narrowband filtered, and finally gathered by a 6 mm dia × 1 m long fibre optic which leads to a remote RCA 4840 photomultiplier wired for fast response. The output of the photomultiplier is connected to the 5 0 ~ input of a 350 MHz Tektronix 485 oscilloscope. A sinusoidal reference signal, arbitrarily chosen to be 95.0000(2) MHz, is simultaneously displayed on the scope screen via the instrument's second channel. Quantum beat lineshape data are usually captured by transient digitizers and signal averagers. Although this method has obvious advantages, the instrumentation is expensive, especially where short rise-times are required (as in the present work). For this reason and for the sake of simplicity, lineshape data for the present work were captured directly from the screen of the oscilloscope. A high quality single lens reflex camera with a 55 mm, f[2 lens and an additional closeup lens are used to photograph the scope's screen. The beam intensity and graticule illumination controls are 182
August 1979
set so that a 10 sec time exposure of ASA 400 film with an f/2.8 aperture setting photographically averages about 200 laser shots. Prints measuring 12 cm X 17 cm on high contrast paper provide a permanent simultaneous record of the averaged lineshapes and reference signals. Using the graticule lines recorded directly on the photographs, we separately digitize the ZQB and reference signals into data sets consisting of 40 points each. Adjacent points in the resulting discrete lineshapes are separated by 2 ns. Both lineshapes are analyzed by non-linear least-squares fitting programs. The processing of the 95.0000 MHz reference signal provides a precise temporal calibration of the image of the graticule on each photograph; the results of this fit are then used in the fitting of the ZQB lineshape. Possible lineshape distortions, especially those along the time axis due to imperfect CRT optics, have been investigated. By simultaneous display of two identical 95.0000 MHz reference traces at various positions on the scope screen, distortion gradients are measured and found to be small. Once these gradients are known, the positions of the reference and ZQB signals are carefully maintained at the same locations on the scope screen, so that the inferred beat frequencies can be corrected for the small scope distortions. Camera distortions, if present, are immaterial because the digitizations are based on the image of the scope's graticule. The ZQB lineshape data are least-squares fitted with the function that appears in eq. (1) except that a sixth floating parameter representing an arbitrary baseline is also included. The output of the fitting program provides the best overall values for the original amplitude, lifetime, modulation depth, beat frequency, phase angle, and baseline for each data set. A total of 60 separate ZQB lineshapes acquired at six different values of magnetic field (-+ 17.81 G, +21.38 G, and +24.96 G) have been processed. The fits are good, especially at low neon target densities where the incidence of multiple scattering is minimized. For a typical fit, the rms residual is 1% of the original amplitude of the quantum beat lineshape. Three of the six floating parameters returned by the fit are of interest. Values for the modulation depth parameter, B, vary from 0.2 to 0.5 in reasonable agreement with the results of lineshape simulations that take into account realistic values of T, r, and the shape
Volume 30, number 2
OPTICS COMMUNICATIONS
Table 1 Experimental and theoretical g-factors in the 2p2 and 2ps states of the 2p 5 (2P1/2) 3p manifold of neon. The uncertainties of +-0.002 in the present work are largely systematic. State
gexp (this work)
gexp (Giacobino)
gtheory (Liberman)
2p2 2ps
1.337 (2) 0.994 (2)
1.3397 (6) 0.9932 (4)
1.346 0.985
of the laser pulse. Inferred 2P2 and 2P5 lifetimes, on the other hand, tend to be 20% to 30% too long except at low target densities. A t the minimum possible target density, however, the inferred lifetime o f the 2P5 state is 19(1) ns, in good agreement with the theoretical value of 18.7 ns [5]. We assume that the longer lifetimes at the higher target densities arise from light trapping due to multiple scattering. The dimensions o f the cell and the pressure o f the neon gas are such as to minimize coUisional broadening effects. The most important fitted parameter is the beat frequency w from which one extracts the g-factor via g = h w / [ J H . Since the fits described above yielded 60 values o f 6Oexp distributed over six values ofHexp, we perform a linear least-squares fit of Wex p to Hex p to determine the best overall values for the g-factors for the two states. The results of these latter fits are shown in table 1 along with the more accurate, optical pumping results o f Giacobino [3] and the theoretical values o f Liberman [6]. The experimental uncertainties o f +0.002 stem almost entirely from systematic uncertainties (+0.001 in the field determinations and -+0.001 in scope distortion effects are the dominant contributions); the random uncertainty is an order o f magnitude smaller than the systematic uncertainty in the present work.
August 1979
The acceptable agreement between the present work and that o f Giacobino suggests that the simple, photographic method o f data gathering employed here can, when performed with care, yield results that are reliable at the 0.2% level. Unfortunately Liberman attaches no uncertainties to his calculated g-factors, and hence little can be said about the apparent discrepancy between theory and experiment for these particular states. The author is pleased to acknowledge the assistance of R.A. Peterson and J.E. Gastineau. This work was supported b y Research Corporation, the National Science Foundation (Grant SPI77-25895), and Lawrence University.
References [1 ] For a review article and numerous references on quantum beat spectroscopy, see the treatment by S. Haroche, in: High resolution laser spectroscopy, Vol. 13 in the Topics of Applied Physics series, ed. K. Shimoda, (Springer-Verlag, Berlin 1976). For more recent work see M.P. Silverman, S. Ha.roche and M. Gross, Phys. Rev. A 18 (1978) 1507; H. Lundberg and S. Svanberg, Optics Comm. 27 (1978) 235. [2] For notable exceptions, see P. Schenck, R. Hilborn and H. Metcalf, Phys. Rev. Lett. 31 (1973) 189; P. Lebow, F. Raab and H. Metcalf, Phys. Rev. Lett. 42 (1979) 85. [3] E. Giacobino, J. Physique 38 (1977) 1377. [4] M.G. Littman and H. Metcalf, Appl. Opt. 17 (1978) 2224; M.G. Littman, Optics Lett. 3 (1978) 138; I. Shoshan and U.P. Oppenheim, Optics Comm. 25 (1978) 375. [6] W.L. Wiese, M.W. Smith and B.M. Glennon, Atomic transition probabilities, NSRDS-NBS 4 Vol. I (U.S. Gov. Printing Office, Washington 1966). [7] S. Liberman, Physica 69 (1973) 598.
183
OPTICS COMMUNICATIONS
August 1979
MEASUREMENT OF g-FACTORS IN NEON BY QUANTUM BEAT SPECTROSCOPY J.R. BRANDENBERGER
Department of Physics, Lawrence University, Appleton, Wisconsin54911, USA Received 8 May 1979
Laser-driven quantum beat spectroscopy has been used to measure Land6 g-factors in two states of the 2p s (2 P1/2) 3p manifold of neon. Transient lineshape data, captured by a simple photographic averagingtechnique, permit determination of the g-factors to a precision of 0.2%. The results are in good agreement with previous measurements, but the agreement with theory is less certain.
Quantum beat spectroscopy provides an elegant method for measuring fine, hyperfine, Stark, and Zeeman splittings in atoms and molecules [1 ]. In the Zeeman case where one measures Land6 g-factors, the quantum beat method complements high field techniques because quantum beat g-factors are determined in low magnetic fields where the Zeeman Hamiltonian is simple. The beat method has another important feature: laser excitation can be employed without introducing ac Stark shifts because the beat signal is monitored only after the laser field is turned off. Most quantum beat measurements reported to date have involved atoms with long-lived states, beam or vapor targets, accuracies at the 1% level, and the use of transient digitizers and signal averagers to capture the data [2]. By way of contrast, this paper reports on laserdriven Zeeman quantum beat measurements involving short-lived states in neon; the target atoms in this work are located in an rf-discharge; a simple but semi-precise mode of photographic data capture is employed, and the technique is pushed to the 0.2% level. Land6 g-factors provide a useful bridge between theory and experiment because calculated g-factors depend sensitively on coupling schemes and subtle effects, while experimental g-factors are easy to measure. The simplest Zeeman quantum beat (ZQB) experiments require only a pair of split Zeeman sublevels IJ, m j> = I 1, +1 ) coupled to a lower IJ, m j) = 10, 0) state. Under the proper choice of experimental conditions, a laser pulse creates the coherent superposition
(I 1,+ 1)e/~°÷t + I 1, - 1 ) e / t ° - t ) e -t/2r. This state proceeds to decay, but owing to the slight difference w = co+ - c o in the Bohr frequencies, the fluorescence exhibits interference beats in the form
I(t) =A e-t/r[1 ÷B cos(~ot + ~)] ,
(1)
where B = B(T, r, tp) is the modulation depth parameter which depends on the beat period T, the excited state lifetime r, and the pulse length tp. When tp is much less than T, the modulation depth approaches unity. The present work involvesg-factors in the 2P2 and 2P5 states (Paschen notation) of the 2p 5 (2P1/3) 3p manifold of neon. Since both are short-lived J = 1 states (16.6 and 18.7 nsec respectively), and since both are easily excited from the lower-lying l s 3 J = 0 metastable level, they satisfy the conditions enumerated above. Thus eq. (1) should describe the fluorescence from these states, and the modulation depth parameter should approach unity for short laser pulses. The choice of these states for this work was prompted by the fact that their g-factors were determined recently to 0.04% by optical pumping [3]. Hence they provide ideal test cases for the simple ZQB method employed here. The experimental layout is conventional. Neon gas at 0.4 Torr, sealed in a 1 cm X 1 cm X 4 cm quartz cuvette of high optical quality, is excited by a weak 100 MHz rf continuous-wave oscillator to produce the ls 3 metastables. Laser pulses of 7 ns (fwhm) duration 181
Volume 30, number 2
OPTICS COMMUNICATIONS
and about 1.5 GHz (fwhm) spectral width from a 20 pps N2-pumped dye laser excite the metastables to the 2P2 or 2P5 state depending on whether the laser is tuned to 616.36 nm or 626.65 nm respectively. The dye laser employs a 2400 £/mm holographic grating used at grazing incidence [4] ; its coherent output is highly polarized, but we use an external polarizer to reduce the superfluorescence in the laser beam. Peak power of the fraction of the laser beam incident on the neon cell is about 200 W. Amplitude instability of the dye laser is about 5%, and spectral jitter is about 1.5 GHz, comparable to the Doppler width of the neon lines of interest here. The neon cuvette is centered in a pair of 20 cm diameter Helmholtz coils whose calibration and inhomogeneity are determined by NMR in the vicinity of I00 G. Since all ZQB measurements are performed in fields on the order of 20 G, and since no magnetic materials are located within a meter or more of the coils, it is possible to make -+0.1% relative field measurements by monitoring the field current with a 0.05% precision, thermally-stabilized resistance standard. Both the direction and polarization of the incident light pulses are perpendicular to the magnetic field. Neon fluorescence arising from the rf as well as the laser excitation is monitored in the direction of the magnetic field. This light is analyzed (the analyzer's axis is normal to the incident polarization so as to suppress reflected light), narrowband filtered, and finally gathered by a 6 mm dia × 1 m long fibre optic which leads to a remote RCA 4840 photomultiplier wired for fast response. The output of the photomultiplier is connected to the 5 0 ~ input of a 350 MHz Tektronix 485 oscilloscope. A sinusoidal reference signal, arbitrarily chosen to be 95.0000(2) MHz, is simultaneously displayed on the scope screen via the instrument's second channel. Quantum beat lineshape data are usually captured by transient digitizers and signal averagers. Although this method has obvious advantages, the instrumentation is expensive, especially where short rise-times are required (as in the present work). For this reason and for the sake of simplicity, lineshape data for the present work were captured directly from the screen of the oscilloscope. A high quality single lens reflex camera with a 55 mm, f[2 lens and an additional closeup lens are used to photograph the scope's screen. The beam intensity and graticule illumination controls are 182
August 1979
set so that a 10 sec time exposure of ASA 400 film with an f/2.8 aperture setting photographically averages about 200 laser shots. Prints measuring 12 cm X 17 cm on high contrast paper provide a permanent simultaneous record of the averaged lineshapes and reference signals. Using the graticule lines recorded directly on the photographs, we separately digitize the ZQB and reference signals into data sets consisting of 40 points each. Adjacent points in the resulting discrete lineshapes are separated by 2 ns. Both lineshapes are analyzed by non-linear least-squares fitting programs. The processing of the 95.0000 MHz reference signal provides a precise temporal calibration of the image of the graticule on each photograph; the results of this fit are then used in the fitting of the ZQB lineshape. Possible lineshape distortions, especially those along the time axis due to imperfect CRT optics, have been investigated. By simultaneous display of two identical 95.0000 MHz reference traces at various positions on the scope screen, distortion gradients are measured and found to be small. Once these gradients are known, the positions of the reference and ZQB signals are carefully maintained at the same locations on the scope screen, so that the inferred beat frequencies can be corrected for the small scope distortions. Camera distortions, if present, are immaterial because the digitizations are based on the image of the scope's graticule. The ZQB lineshape data are least-squares fitted with the function that appears in eq. (1) except that a sixth floating parameter representing an arbitrary baseline is also included. The output of the fitting program provides the best overall values for the original amplitude, lifetime, modulation depth, beat frequency, phase angle, and baseline for each data set. A total of 60 separate ZQB lineshapes acquired at six different values of magnetic field (-+ 17.81 G, +21.38 G, and +24.96 G) have been processed. The fits are good, especially at low neon target densities where the incidence of multiple scattering is minimized. For a typical fit, the rms residual is 1% of the original amplitude of the quantum beat lineshape. Three of the six floating parameters returned by the fit are of interest. Values for the modulation depth parameter, B, vary from 0.2 to 0.5 in reasonable agreement with the results of lineshape simulations that take into account realistic values of T, r, and the shape
Volume 30, number 2
OPTICS COMMUNICATIONS
Table 1 Experimental and theoretical g-factors in the 2p2 and 2ps states of the 2p 5 (2P1/2) 3p manifold of neon. The uncertainties of +-0.002 in the present work are largely systematic. State
gexp (this work)
gexp (Giacobino)
gtheory (Liberman)
2p2 2ps
1.337 (2) 0.994 (2)
1.3397 (6) 0.9932 (4)
1.346 0.985
of the laser pulse. Inferred 2P2 and 2P5 lifetimes, on the other hand, tend to be 20% to 30% too long except at low target densities. A t the minimum possible target density, however, the inferred lifetime o f the 2P5 state is 19(1) ns, in good agreement with the theoretical value of 18.7 ns [5]. We assume that the longer lifetimes at the higher target densities arise from light trapping due to multiple scattering. The dimensions o f the cell and the pressure o f the neon gas are such as to minimize coUisional broadening effects. The most important fitted parameter is the beat frequency w from which one extracts the g-factor via g = h w / [ J H . Since the fits described above yielded 60 values o f 6Oexp distributed over six values ofHexp, we perform a linear least-squares fit of Wex p to Hex p to determine the best overall values for the g-factors for the two states. The results of these latter fits are shown in table 1 along with the more accurate, optical pumping results o f Giacobino [3] and the theoretical values o f Liberman [6]. The experimental uncertainties o f +0.002 stem almost entirely from systematic uncertainties (+0.001 in the field determinations and -+0.001 in scope distortion effects are the dominant contributions); the random uncertainty is an order o f magnitude smaller than the systematic uncertainty in the present work.
August 1979
The acceptable agreement between the present work and that o f Giacobino suggests that the simple, photographic method o f data gathering employed here can, when performed with care, yield results that are reliable at the 0.2% level. Unfortunately Liberman attaches no uncertainties to his calculated g-factors, and hence little can be said about the apparent discrepancy between theory and experiment for these particular states. The author is pleased to acknowledge the assistance of R.A. Peterson and J.E. Gastineau. This work was supported b y Research Corporation, the National Science Foundation (Grant SPI77-25895), and Lawrence University.
References [1 ] For a review article and numerous references on quantum beat spectroscopy, see the treatment by S. Haroche, in: High resolution laser spectroscopy, Vol. 13 in the Topics of Applied Physics series, ed. K. Shimoda, (Springer-Verlag, Berlin 1976). For more recent work see M.P. Silverman, S. Ha.roche and M. Gross, Phys. Rev. A 18 (1978) 1507; H. Lundberg and S. Svanberg, Optics Comm. 27 (1978) 235. [2] For notable exceptions, see P. Schenck, R. Hilborn and H. Metcalf, Phys. Rev. Lett. 31 (1973) 189; P. Lebow, F. Raab and H. Metcalf, Phys. Rev. Lett. 42 (1979) 85. [3] E. Giacobino, J. Physique 38 (1977) 1377. [4] M.G. Littman and H. Metcalf, Appl. Opt. 17 (1978) 2224; M.G. Littman, Optics Lett. 3 (1978) 138; I. Shoshan and U.P. Oppenheim, Optics Comm. 25 (1978) 375. [6] W.L. Wiese, M.W. Smith and B.M. Glennon, Atomic transition probabilities, NSRDS-NBS 4 Vol. I (U.S. Gov. Printing Office, Washington 1966). [7] S. Liberman, Physica 69 (1973) 598.
183