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High resolution polarization spectroscopy of the 557 nm transition of Krl
Volume 26, number 1
OPTICS COMMUNICATIONS
July 1978
HIGH RESOLUTION POLARIZATION SPECTROSCOPY OF THE 557 nm TRANSITION OF KrI *
H. GERHARDT, T. HUHLE, J. NEUKAMMER and P.J. WEST Institut far A tom- uncl FestkOrperphysik, Freie Universitiit Berlin, Berlin, Germany
Received 30 March 1978
A high resolution polarization experiment performed on the ls 5 -2p3 transition in even krypton isotopes is described. A least square analysis of the data shows a good agreement with existing theoretical calculations.
Laser polarization spectroscopy is a new nonlinear spectroscopic method [ 1] which offers advantages in sensitivity and resolution. It makes use of the polarization dependence of the nonlinear interaction between two light beams in a gas. A polarized saturating beam is used to orient or align a selected group of atoms by optical pumping. These atoms can then be sensitively detected through their effects on the polarization of a probe laser beam. In favorable cases polarization spectroscopy has a signal-to-noise (S/N) ratio 1000 times that of saturated absorption spectroscopy. This letter reports a polarization experiment on the 557 nm line ( l s s - 2 P 3 ) of natural krypton isotopes. The measurements are compared with existing theoretical calculations and, in addition, the results are discussed with respect to related saturated absorption experiments [2]. The experimental set-up is nearly the same in both techniques. The metastable ls 5 level of krypton was populated by a rf-discharge in a resonance cell at a gas pressure of 200 mbar. The polarizers were used directly as entrance and exit windows of the cell to avoid the possible depolarization effects of additional glass plates. The saturating beam from a high resolution dye laser spectrometer [3] was circularly polarized. The light of the probe beam transmitted through the polarizers was detected by a photomultiplier via a grating spectrometer. In fig. 1a a polarization spectrum of krypton is shown. The data points represent a signal analyzer scan * Work supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 161.
58
I
I
I
I
50 00 (a)
2600
200
z LLJ
:
f
(b)
~_ 0.07
5
_oo,U [|
Kr[78 Kr80 Kr82 Kr84 Kr86 9/2--11/2 r83
I,
I
I,I
t,
160 320 480 BEATFREQUENCY (MHz) Fig. 1. (a). Polarization spectrum of all even natural krypton components (data points). (b) First derivative of (a). The solid lines represent a least square fit to the data points.
covering all components of even natural Kr isotopes. Only one hyperfine transition of 83Kr can be seen in this selected part of the spectrum. The frequency of the dye laser was swept in steps of 250 kHz by con-
Volume 26, number 1
OPTICS COMMUNICATIONS
trolling a He-Ne offset locking system with a frequency synthesizer. For simplification several steps are represented by each data point in fig. 1. The crossing angle between the two polarizers was adjusted to 80 mrad to yield the best S/N ratio. A dispersion shaped waveform will always be obtained if the analyzer is slightly rotated from the perpendicular position. However, depending on the natural abundance of the observed isotopes, the pure dispersion signal can be superimposed by a more or less strong Lorentzian component. A non-negligible Lorentzian part for instance is easily seen in the case of 84Kr. Another more sensitive high resolution scan of the 78Kr and 80Kr components is displayed in fig. 2a. It is obvious that the dispersion waveform dominates for the low abundant components. Because of the complex form of the polarization spectrum, the precise resonance positions of the individual isotopes can be determined only by fitting the
(a)
50.00
26.00
>
E
2.00
•
Z 0 14J
0.07
~ (b)
i-
3~
0.03
- 0.01
Kr78 iL
&v =102.3 141MHz
KrS0 LI
I
I
I
I
0
40
80
120
BEATFREQUENCY (MHz)
Fig. 2 (a), (b). High resolution polarization spectrum and first derivative of Kr 78 and 80 components. The solid linea are least square fits to the data points. The isotope shift is given in the actual frequency.
July 1978
data with an appropriate theoretical expression. This problem can easily be solved digitally. Furthermore'a test of the theoretical description of the polarization spectroscopy is possible. The signal intensity at the detector for this experiment is given by [1 ] I=I 0
~+02+
~ + - -
?
'
(1)
I 0 is the unattenuated probe power, ~ the finite extinction ratio of the analyzers, 0 is the rotation angle from the perpendicular position of the polarizers, Ki = 2 ( E - E i ) / F is the laser detuning, F is the linewidth at fwhm, E the energy of the dye laser beam, and E i the energy position of the resonance center of isotope i. The parameter s i describes the intensity difference between the counter-rotating probe components and is linearly dependent on the atomic concentration. In the case of 0 ~ 0 only a Lorentzian signal is detected, but the signal intensity is not proportional to the abundance ratio. For 0 >>s i a dispersion shaped waveform will be detected. The solid lines in figs. 1a and 2a represent the result of the least squares fit of eq. (1) to the data points. The measured spectra are in excellent agreement with the theory. Especially no deviation from the theoretical curves can be seen far outside the line centers. During the fitting procedure all line positions E i, all parameters si of the lines, the angle 0 and intensity I 0 were varied to get the optimal parameter set for the absolute minimized theoretical function. From the fit the amplitudes of the lorentzian- and dispersion part : of the 84Kr component (0/s84 ~ 1)were determined to be 1:2 and of the 78Kr component (0/s78 >> 1) to be 1 : 100. Therefore the measurement of the less abundant components can be well described by a dispersion curve given by the second term ofeq. (1). The influence of the lorentzian and dispersion signals on the waveform of the spectrum is better illustrated by the first derivative of the polarization spectrum which is displayed in figs. lb and 2b. Again, the solid lines represent a fit of the data points. In addition further evidence for the quality of the fit is demonstrated. The waveform of the low abundant components is symmetrical, whereas the 84Kr component shows a large asymmetry. The differentiated spectrum has the advantage of giving a better resolution than the original spectrum. The linewidth of 7 MHz (fwhm) is half the width of the integrated signal. The observed line59
Volume 26, number 1
OPTICS COMMUNICATIONS
x30
Kr 78
Kr 8(
Kr 82
Kr84
Kr 86
Kr 83 912 ~11/2
I
I
1
I
1
I V-
300 MHz
I
4
Fig. 3. Polarization spectrum of even krypton components with almost crossed polarizers (0 ~ 0.3 mrad).
July 1978
width, however, is still larger than the natural linewidth of 5 MHz. This is caused by the finite crossing angle of the two oppositely directed beams. The constant background of the differential spectrum indicates that the Doppler background, due to thermal collisions and characteristic of saturated absorption spectra, does not exist. Following theoretical calculations one should expect the optimum S/N ratio for 0 ---x/~-. An extinction ratio of ~ = 10 -7, appropriate for the polarizers used here, yields 0 ~ 0.3 mrad. In fig. 3a polarization spectrum obtained with a comparable crossing angle is displayed. The spectrum represents a recorder scan. No fitting procedure was applied. Again, a negligible background signal is recorded. In contrast to figs. 1 and 2, the intensity ratio of the lines deviates strongly from the abundance ratio. The 78Kr component is not as well resolved as in the case 0 >> x/~. The discrepancy can be explained by considering the source of noise. For the theoretical value only laser intensity fluctuations are considered. A main source of noise in the experiment is backscattering from the saturation beam. This backscattered light interferes with the probe beam and causes interference patterns which change strongly in intensity when the laser is tuned across the lines. Therefore an angle 0 >>x/~yields a better S/N ratio. The optimum angle depends on the specific experimental set-up.
KrS0 Kr 82 Kr 80 Kr78 l T i
Kr86 ~ ~ l Kr 83 9/2-11/2
300MHz
i
Kr83 9/2~11/2
Kr 78 I
l
300MHz
I
Fig. 4. Saturation spectrum of even natural krypton isotopes. The right spectrum is an amplified (× 10) version.
60
Volume 26, number l
OPTICS COMMUNICATIONS
For a comparison of the spectra obtained by polarization spectroscopy, a saturated absorption spectrum of all natural krypton isotopes is shown in fig. 4. Two recorder scans over all even Kr components are displayed. The right spectrum is an amplified (X 10) version. In contrast with the polarization spectrum, the saturation spectrum shows a broad and intense background due to thermal collisions. This background makes it difficult to resolve weak line components which are separated by less than the Doppler width. The background can be reduced [4] by addition of quenching atoms, but that reduces the overall signal. Polarization spectroscopy is not sensitive to thermal collisions because thus tend to reduce the initial alignment. A further advantage of polarization spectroscopy is the better signal-to-noise ratio. The sensitivity of the polarization spectroscopy method is shown by the resolution of the 78Kr isotope with an abundancy of only 0.35%. The 78Kr component is clearly resolved even in the natural isotope mixture. In this experiment an improvement by the factor of 10 was achieved for the resolution of the 78Kr component compared to the saturation spectrum. The isotope shift of the 78Kr and 80Kr isotopes was measured earlier [2] in a saturation experiment to be Av78 = 111.8(15)MI-Iz. There was a discrepancy between our earlier result and the result of Av78 =
July 1978
99.9(9) MHz obtained by Br6chignac [5] who also employed saturation spectroscopy. In that experiment enriched samples were used and the Doppler background was reduced by addition of xenon as quenching gas. Our polarization experiment yields a value of ArT08 = 102.3(4) MHz, in fair agreement with the result of ref. [5] although the error bars still do not overlap. The uncertainty of 400 kHz is given by the mean standard deviation of several runs. The deviation of the earlier value is caused mainly by the poor signalto-background ratio of the saturation experiment in pure natural krypton samples. All other results of the polarization experiment are comparable with the resuits of the saturation experiment.
References [I] C. Wieman and T.W. H~nsch, Phys. Rev. Letters 36 (1976) 1170. [2] H. Gerhardt, R. Wenz and E. Matthias, Phys. Letters 61A (1977) 377. [3] H. Gerhardt and A. Timmermann, Opt. Comm. 21 (1977) 343. [4] C. Brdchignac, R. Vetter and P.R. Berman, J. Phys. B 10 (1977) 3443. [5] C. Brdchignac, J. Phys. B 10 (1977) 2105.
61
OPTICS COMMUNICATIONS
July 1978
HIGH RESOLUTION POLARIZATION SPECTROSCOPY OF THE 557 nm TRANSITION OF KrI *
H. GERHARDT, T. HUHLE, J. NEUKAMMER and P.J. WEST Institut far A tom- uncl FestkOrperphysik, Freie Universitiit Berlin, Berlin, Germany
Received 30 March 1978
A high resolution polarization experiment performed on the ls 5 -2p3 transition in even krypton isotopes is described. A least square analysis of the data shows a good agreement with existing theoretical calculations.
Laser polarization spectroscopy is a new nonlinear spectroscopic method [ 1] which offers advantages in sensitivity and resolution. It makes use of the polarization dependence of the nonlinear interaction between two light beams in a gas. A polarized saturating beam is used to orient or align a selected group of atoms by optical pumping. These atoms can then be sensitively detected through their effects on the polarization of a probe laser beam. In favorable cases polarization spectroscopy has a signal-to-noise (S/N) ratio 1000 times that of saturated absorption spectroscopy. This letter reports a polarization experiment on the 557 nm line ( l s s - 2 P 3 ) of natural krypton isotopes. The measurements are compared with existing theoretical calculations and, in addition, the results are discussed with respect to related saturated absorption experiments [2]. The experimental set-up is nearly the same in both techniques. The metastable ls 5 level of krypton was populated by a rf-discharge in a resonance cell at a gas pressure of 200 mbar. The polarizers were used directly as entrance and exit windows of the cell to avoid the possible depolarization effects of additional glass plates. The saturating beam from a high resolution dye laser spectrometer [3] was circularly polarized. The light of the probe beam transmitted through the polarizers was detected by a photomultiplier via a grating spectrometer. In fig. 1a a polarization spectrum of krypton is shown. The data points represent a signal analyzer scan * Work supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 161.
58
I
I
I
I
50 00 (a)
2600
200
z LLJ
:
f
(b)
~_ 0.07
5
_oo,U [|
Kr[78 Kr80 Kr82 Kr84 Kr86 9/2--11/2 r83
I,
I
I,I
t,
160 320 480 BEATFREQUENCY (MHz) Fig. 1. (a). Polarization spectrum of all even natural krypton components (data points). (b) First derivative of (a). The solid lines represent a least square fit to the data points.
covering all components of even natural Kr isotopes. Only one hyperfine transition of 83Kr can be seen in this selected part of the spectrum. The frequency of the dye laser was swept in steps of 250 kHz by con-
Volume 26, number 1
OPTICS COMMUNICATIONS
trolling a He-Ne offset locking system with a frequency synthesizer. For simplification several steps are represented by each data point in fig. 1. The crossing angle between the two polarizers was adjusted to 80 mrad to yield the best S/N ratio. A dispersion shaped waveform will always be obtained if the analyzer is slightly rotated from the perpendicular position. However, depending on the natural abundance of the observed isotopes, the pure dispersion signal can be superimposed by a more or less strong Lorentzian component. A non-negligible Lorentzian part for instance is easily seen in the case of 84Kr. Another more sensitive high resolution scan of the 78Kr and 80Kr components is displayed in fig. 2a. It is obvious that the dispersion waveform dominates for the low abundant components. Because of the complex form of the polarization spectrum, the precise resonance positions of the individual isotopes can be determined only by fitting the
(a)
50.00
26.00
>
E
2.00
•
Z 0 14J
0.07
~ (b)
i-
3~
0.03
- 0.01
Kr78 iL
&v =102.3 141MHz
KrS0 LI
I
I
I
I
0
40
80
120
BEATFREQUENCY (MHz)
Fig. 2 (a), (b). High resolution polarization spectrum and first derivative of Kr 78 and 80 components. The solid linea are least square fits to the data points. The isotope shift is given in the actual frequency.
July 1978
data with an appropriate theoretical expression. This problem can easily be solved digitally. Furthermore'a test of the theoretical description of the polarization spectroscopy is possible. The signal intensity at the detector for this experiment is given by [1 ] I=I 0
~+02+
~ + - -
?
'
(1)
I 0 is the unattenuated probe power, ~ the finite extinction ratio of the analyzers, 0 is the rotation angle from the perpendicular position of the polarizers, Ki = 2 ( E - E i ) / F is the laser detuning, F is the linewidth at fwhm, E the energy of the dye laser beam, and E i the energy position of the resonance center of isotope i. The parameter s i describes the intensity difference between the counter-rotating probe components and is linearly dependent on the atomic concentration. In the case of 0 ~ 0 only a Lorentzian signal is detected, but the signal intensity is not proportional to the abundance ratio. For 0 >>s i a dispersion shaped waveform will be detected. The solid lines in figs. 1a and 2a represent the result of the least squares fit of eq. (1) to the data points. The measured spectra are in excellent agreement with the theory. Especially no deviation from the theoretical curves can be seen far outside the line centers. During the fitting procedure all line positions E i, all parameters si of the lines, the angle 0 and intensity I 0 were varied to get the optimal parameter set for the absolute minimized theoretical function. From the fit the amplitudes of the lorentzian- and dispersion part : of the 84Kr component (0/s84 ~ 1)were determined to be 1:2 and of the 78Kr component (0/s78 >> 1) to be 1 : 100. Therefore the measurement of the less abundant components can be well described by a dispersion curve given by the second term ofeq. (1). The influence of the lorentzian and dispersion signals on the waveform of the spectrum is better illustrated by the first derivative of the polarization spectrum which is displayed in figs. lb and 2b. Again, the solid lines represent a fit of the data points. In addition further evidence for the quality of the fit is demonstrated. The waveform of the low abundant components is symmetrical, whereas the 84Kr component shows a large asymmetry. The differentiated spectrum has the advantage of giving a better resolution than the original spectrum. The linewidth of 7 MHz (fwhm) is half the width of the integrated signal. The observed line59
Volume 26, number 1
OPTICS COMMUNICATIONS
x30
Kr 78
Kr 8(
Kr 82
Kr84
Kr 86
Kr 83 912 ~11/2
I
I
1
I
1
I V-
300 MHz
I
4
Fig. 3. Polarization spectrum of even krypton components with almost crossed polarizers (0 ~ 0.3 mrad).
July 1978
width, however, is still larger than the natural linewidth of 5 MHz. This is caused by the finite crossing angle of the two oppositely directed beams. The constant background of the differential spectrum indicates that the Doppler background, due to thermal collisions and characteristic of saturated absorption spectra, does not exist. Following theoretical calculations one should expect the optimum S/N ratio for 0 ---x/~-. An extinction ratio of ~ = 10 -7, appropriate for the polarizers used here, yields 0 ~ 0.3 mrad. In fig. 3a polarization spectrum obtained with a comparable crossing angle is displayed. The spectrum represents a recorder scan. No fitting procedure was applied. Again, a negligible background signal is recorded. In contrast to figs. 1 and 2, the intensity ratio of the lines deviates strongly from the abundance ratio. The 78Kr component is not as well resolved as in the case 0 >> x/~. The discrepancy can be explained by considering the source of noise. For the theoretical value only laser intensity fluctuations are considered. A main source of noise in the experiment is backscattering from the saturation beam. This backscattered light interferes with the probe beam and causes interference patterns which change strongly in intensity when the laser is tuned across the lines. Therefore an angle 0 >>x/~yields a better S/N ratio. The optimum angle depends on the specific experimental set-up.
KrS0 Kr 82 Kr 80 Kr78 l T i
Kr86 ~ ~ l Kr 83 9/2-11/2
300MHz
i
Kr83 9/2~11/2
Kr 78 I
l
300MHz
I
Fig. 4. Saturation spectrum of even natural krypton isotopes. The right spectrum is an amplified (× 10) version.
60
Volume 26, number l
OPTICS COMMUNICATIONS
For a comparison of the spectra obtained by polarization spectroscopy, a saturated absorption spectrum of all natural krypton isotopes is shown in fig. 4. Two recorder scans over all even Kr components are displayed. The right spectrum is an amplified (X 10) version. In contrast with the polarization spectrum, the saturation spectrum shows a broad and intense background due to thermal collisions. This background makes it difficult to resolve weak line components which are separated by less than the Doppler width. The background can be reduced [4] by addition of quenching atoms, but that reduces the overall signal. Polarization spectroscopy is not sensitive to thermal collisions because thus tend to reduce the initial alignment. A further advantage of polarization spectroscopy is the better signal-to-noise ratio. The sensitivity of the polarization spectroscopy method is shown by the resolution of the 78Kr isotope with an abundancy of only 0.35%. The 78Kr component is clearly resolved even in the natural isotope mixture. In this experiment an improvement by the factor of 10 was achieved for the resolution of the 78Kr component compared to the saturation spectrum. The isotope shift of the 78Kr and 80Kr isotopes was measured earlier [2] in a saturation experiment to be Av78 = 111.8(15)MI-Iz. There was a discrepancy between our earlier result and the result of Av78 =
July 1978
99.9(9) MHz obtained by Br6chignac [5] who also employed saturation spectroscopy. In that experiment enriched samples were used and the Doppler background was reduced by addition of xenon as quenching gas. Our polarization experiment yields a value of ArT08 = 102.3(4) MHz, in fair agreement with the result of ref. [5] although the error bars still do not overlap. The uncertainty of 400 kHz is given by the mean standard deviation of several runs. The deviation of the earlier value is caused mainly by the poor signalto-background ratio of the saturation experiment in pure natural krypton samples. All other results of the polarization experiment are comparable with the resuits of the saturation experiment.
References [I] C. Wieman and T.W. H~nsch, Phys. Rev. Letters 36 (1976) 1170. [2] H. Gerhardt, R. Wenz and E. Matthias, Phys. Letters 61A (1977) 377. [3] H. Gerhardt and A. Timmermann, Opt. Comm. 21 (1977) 343. [4] C. Brdchignac, R. Vetter and P.R. Berman, J. Phys. B 10 (1977) 3443. [5] C. Brdchignac, J. Phys. B 10 (1977) 2105.
61