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Hyperfine structure in 21Ne using laser-induced absorption line narrowing
Voitune Ih, number
3
March
OPTICS COMMUNICATIONS
HYPERFINE STRUCTURE IN 21Ne USING LASER-INDUCED
1976
ABSORPTION LINE NARROWING
C. DELSART and J.-C. KELLER Lahoratvire Aimi C’ottou, C.h’.R.S. II. BCtiment 50.5, 9140.5 - OrsaJa, France Received
3 December
1975
llsing Absorption Line Narrowing (A.L.N.) in three-level atomic systems in interaction with two quasi-resonant singlemode lasers, we have measured the magnetic and electric hyperfine constants of the 1 SJ, 1 ss. 2~~ and 2p4 levels ot ’ 211\ic,
1. Introduction
Absorption Line Narrowing (also called “cross-saturated absorption”) in a Doppler-broadened threelevel system in interaction with two quasi-resonant single-mode lasers has been recently observed in neon [I]. A first application to isotope shift measurements has demonstrated the possibility to use this method for Doppler free spectroscopy. In this paper, we report hyperfine structure measurements in I1 Ne using the same technique for a much more complicated spectroscopic case. Fig. 1. Ilnergy level diagram and characteristics
trf the laser
fields.
2. The A.L.N. effect The system under study is a three-level atomic system interacting with two laser beams propagating either in the same direction or in two opposite directions (fig. 1). The first laser (saturating beam) selectively interacts with those atoms, over a narrow axial velocity range corresponding to the homogeneous width. which are Doppler shifted into resonance. The second laser probes the resulting velocity selection, allowing thus Doppler free spectroscopy. In our case the probing beam has a fixed frequency, R,, and the frequency. Cl,, of the saturating beam is tuned over the Doppler profile of the (1 + 2) transition. Monitoring the transmission of the probing beam a2 through the cell versus Sz, , resonances are observed at a frequency
(E = +1 or ~ I according to whether the laser beams propagate in the same direction or in two opposite directions). If the atomic lines w, and w2 exhibit hyperfine structures, a resonance should be observed for each three-level system corresponding to allowed transitions. The separation between the resonance frequencies due to a pair (i,j) of these cascades is:
Volume
16, number
OPTICS COMMUNICATIONS
3
The shape and width of the resonances can easily be calculated if the laser powers are low. A third-order theory gives in the case w1 > w2 and for a negligible population difference between levels 2 and 3, lorentzian shaped resonances with a specified width (at very low pressure) Y=Yl +eY2 $(Y2
+ Y3L
where ri is the inverse lifetime of level i [ 131.
3. Application to hyperfiie
structures
For the [2s2 + 2p4 + ls4] and [2s2 + 2p4 -+ Is51 three-level systems of 21Ne (nuclear spin 4) each level exhibits a hyperfine splitting and one obtains many allowed cascades (18 possible cascades in the first case and 21 in the second case). Each of these cascades is characterized by the values F3, F2 and F1 of the total angular momentum of the hyperfine sublevels involved. The position of the resonance for a given cascadeF3+F2+F1 is: R,(F,
+F2 + F1) = RR(21Ne) + Q,B,
+ I$K,A, _
Ol
E-
- fK,A, - Q,B,l
[&A3 +Q3B3 -
iK2A2
-
Q2B217 (1)
*2
Ai and Bi are respectively the magnetic and electric hyperfine structure constants of level i, Ki=Fi(F,+l)-J&$+1)-I(Z+l), 3 K,(K,+l) - Z(I+l)J(J+l) Qi =
U(U-
l)Ji(Ui-1)
’
S22,(21Ne) is the resonance frequency for the unobservable cascade which would be given by the system without hyperfine splittings (A. = Bi = 0, i = 1, 2, 3). In a sample containing also i ONe for instance: a1,(21Ne) -
E
- S1,(20Ne) = [ti1(21Ne)-
w1(20Ne)]
u$[02(21Ne) - w2(20Ne)].
March
and the second bracket is the corresponding shift for the w2 transition.
4. Experimental hyperfiie
1976
isotope
spectra
The experimental arrangement is almost the same as in our previous paper [l] ; the only differences are in the use of prisms to mix the two beams and of avalanche photodiodes as detectors at 1.15 p. The laser a2 iaa 1.15 p He-Ne laser and the laser s2 I is a dye laser [2] operating at 6096 A or at 5945 A; they are linearly polarized with the same polarization axis. The frequency calibration and control of the dye laser is obtained by the use of a “sigmameter” [3]. In our particular experiment the useful tuning range of the dye laser is about 4.5 GHz. The observed resonance widths are about 75 MHz and 100 MHz respectively for E = + 1 and E = - 1; these values are larger than the expected ones. Collisions and also laser light power are mainly responsible for the broadening of the resonances; the experimental study of both effects is on progress. We have used two different neon samples. The abundances of 21Ne, 22Ne and 20Ne were respectively 91%, 5.7% and 3.3% in one case and 94%, 4.8% and 1.2% in the other case. Typical spectra are shown in figs. 2 and 3. Similar spectra have been previously obtained for the (2s~ + 2p4 -+ 1~~) cascade using laser induced fluorescence line narrowing techniques [4]. The use of the A.L.N. method results in an enhancement of the signal-tonoise ratio and in an increase of the resolution. Many resonances can be clearly seen on the spectra; those corresponding to the even isotopes were easily identified by adding some 2oNe or 22Ne to the sample and also by comparison with spectra obtained with a natural neon mixture [ 11. The well resolved hyperfine components were identified using the previously calculated values of A and B [5]. They are indicated in figs. 2 and 3 where they are labelled as ordered triplets (F,,Fz> Fr). As already mentioned in [I] the intensity pattern in our A.L.N. experiment is strongly dependent on the absorption of the saturating beam R, and is not yet clearly understood.
In formula (2) the first bracket is the isotope shift (21Ne-20Ne) as usually defined for the w, transition 389
Volu~nc 16, number 3 c
2ON.Z
Table I
=Ne
A( lss) = -261.2 .A(ls4) =. 460 A(2pq)= --308.6 A&) = -744
D
I3 -
E
-
D
-
FGi-l
5. Data analysis From the measured positions of the clearly identified components, using eq. (l), one can obtain 3 1 independent linear relations fulfilled by the set of spec-
I= Cl
G
--
n D
_
E ^
-.
._--
I
J ..
-7 c
, 1000 MHz
L=
%e
, d
G H A
E
K
E
l:ig. 3. llyperfine spectra for the cascade 2~ + 2pJ + A = (;. :, ;,, B = (3, 3. 3). C = (3. 2, $)> 1) = (1.1, ;). L_= (4, f, j), 1: = (3.3, ;,, G = (f, ;, :), H = (;,i, :,. I= ($,f.+)..l =(t,1,3,.1<=(~,~,?).L=(~,3,~,.
390
L
I ss.
I t * i
2.3 4 1.5 3
B(lss) B(ls4) B(2p4) B(2s2)
= = = =
11s + 33+ 451 29 i
IO 8 6 2
troscopic parameters involved in the structures. These parameters are the A and B values of the four levels (2~2, 2p4, 1s4 and ls5) and also the values of a,(21 ) for each of the recordings shown in figs. 2 and 3 (12 parameters). For a light element such as neon, the isotopic shift is purely due to the mass effect and then the (21Ne 20Ne) shift for a line can easily be deduced from the ( 22Ne-20Ne) shift for the same line [6]. This has been verified experimentally [6.7] and is in agreement with ab initio evaluations of the field isotopic effect in neon [8]. Making use of this assumption one can easily deduce in our A.L.N. spectra the position of C2,(2tNe) from the positions of the even isotope resonances. This can be done for three of the experimental recordings and gives thus three other linear relations to be fulfilled by the parameters. A least mean square calculation was then performed, using the 34 available linear equations, to determine the 12 parameters. The values obtained (in MHz) for the A and B parameters are given in table 1 The r.1n.s. value of the difference Au between measured and calculated positions (for 34 equations and 12 free parameters) is:
Ao = n
E
March 1976
OPTlCS COMMUNICATIONS
c
I
(Ar#(34-
12) = 13 MHz.
This value is close to the experimental uncertainties in the positions of the components (-15 MHz) which are mainly due to frequency drift of the I. 15 I-(laser during an experiment and to imperfections in the visible laser scanning. The quoted error in the A and R values corresponds to an increase of 5% of the r.m.s. value when the parameter is fixed to its limit value. the other parameters being free. All these A and n values had been previously measured either by atomic beam magnetic resonance (level ls5) [9], or by conventional high resolution optical spectroscopy (levels 2s2. 2p4, 1s4) [6, IO], or by level crossing (level 2p4j 11 l] , or by laser- atomic beam spectroscopy (level 7,~~) [I’_].
Volume
16, number
3
OPTICS COMMUNICATIONS
The values obtained by the A.L.N. method are in good agreement with these measurements as well as with previously calculated values [S] , except for a small discrepancy in the experimental (B(2s2) value. The precision of the measurement is of course not as good as in the magnetic resonance method and as in the level crossing method. However with a higher precision in the frequency calibration of the visible laser and a better control of the infrared laser frequency it should be possible to take advantage of the great number of observed resonances to reach a precision comparable to that of the level crossing method.
6. Conclusion When dealing with hyperfine structures in an A.L.N. experiment the main problem is the identification of the observed resonances. As long as this problem can be solved (i.e. for low J value cascades or if an estimation of the hyperfine constants is available) one can use the method to determine hyperfine structure constants with a reasonably good accuracy. The problem of the interpretation of the observed relative intensities of the various hyperfine cascades in our particular
March
1976
experimental conditions (high absorption of the visible laser beams, degenerate levels perturbed by polarized laser beams, etc.) would be interesting to study if one wanted to extend the method to other complicated spectroscopic problems.
References [l] C. Delsart and J.-C. Keller, Opt. Commun. 15 (1975) 91. [2] S. Liberman and J. Pinard, Appl. Phys. Lett. 24 (1974) 142. [3] P. Juncar and J. Pinard, Opt. Commun. 14 (1975) 438. [4] T.W. Ducas, M.S. Feld, L.W. Ryan, M. Skribanowitz and A. Javan, Phys. Rev. 5 (1972) 1036. [S] S. Liberman, Physica 69 (1973) 598. [6] R.-J. Champeau and J.-C. Keller, J. Phys. B, Atom. Molec. Phys. 6 (1973) L 76. [ 71 E. Giacobino et al., to be publ. in Phys. Rev. (Dec. 1975). [8] J.-C. Keller, Thesis de 3rd cycle, Lab. Aimd Cotton, Orsay (1972). [9] G.M. Grosof, P. Buck, W. Lichten and 1.1. Rabi, Phys. Rev. Lett. 1 (1958) 214. [lo] R.-J. Champeau, J.-C. Keller, 0. Robaux and J. Verges, J. Phys. B, Atom. Molec. Phys. 7 (1974) L 163. [ 111 b. Giacobino, J. de Physique Lettres 36 (1975) L 65. [ 121 R.-J. Champeau and J.C. Keller, J. de Physique Lettres 36 (1975) L 161. [13] T. Hansch and P. Toschek, Z. Phys. 236 (1970) 213.
391
3
March
OPTICS COMMUNICATIONS
HYPERFINE STRUCTURE IN 21Ne USING LASER-INDUCED
1976
ABSORPTION LINE NARROWING
C. DELSART and J.-C. KELLER Lahoratvire Aimi C’ottou, C.h’.R.S. II. BCtiment 50.5, 9140.5 - OrsaJa, France Received
3 December
1975
llsing Absorption Line Narrowing (A.L.N.) in three-level atomic systems in interaction with two quasi-resonant singlemode lasers, we have measured the magnetic and electric hyperfine constants of the 1 SJ, 1 ss. 2~~ and 2p4 levels ot ’ 211\ic,
1. Introduction
Absorption Line Narrowing (also called “cross-saturated absorption”) in a Doppler-broadened threelevel system in interaction with two quasi-resonant single-mode lasers has been recently observed in neon [I]. A first application to isotope shift measurements has demonstrated the possibility to use this method for Doppler free spectroscopy. In this paper, we report hyperfine structure measurements in I1 Ne using the same technique for a much more complicated spectroscopic case. Fig. 1. Ilnergy level diagram and characteristics
trf the laser
fields.
2. The A.L.N. effect The system under study is a three-level atomic system interacting with two laser beams propagating either in the same direction or in two opposite directions (fig. 1). The first laser (saturating beam) selectively interacts with those atoms, over a narrow axial velocity range corresponding to the homogeneous width. which are Doppler shifted into resonance. The second laser probes the resulting velocity selection, allowing thus Doppler free spectroscopy. In our case the probing beam has a fixed frequency, R,, and the frequency. Cl,, of the saturating beam is tuned over the Doppler profile of the (1 + 2) transition. Monitoring the transmission of the probing beam a2 through the cell versus Sz, , resonances are observed at a frequency
(E = +1 or ~ I according to whether the laser beams propagate in the same direction or in two opposite directions). If the atomic lines w, and w2 exhibit hyperfine structures, a resonance should be observed for each three-level system corresponding to allowed transitions. The separation between the resonance frequencies due to a pair (i,j) of these cascades is:
Volume
16, number
OPTICS COMMUNICATIONS
3
The shape and width of the resonances can easily be calculated if the laser powers are low. A third-order theory gives in the case w1 > w2 and for a negligible population difference between levels 2 and 3, lorentzian shaped resonances with a specified width (at very low pressure) Y=Yl +eY2 $(Y2
+ Y3L
where ri is the inverse lifetime of level i [ 131.
3. Application to hyperfiie
structures
For the [2s2 + 2p4 + ls4] and [2s2 + 2p4 -+ Is51 three-level systems of 21Ne (nuclear spin 4) each level exhibits a hyperfine splitting and one obtains many allowed cascades (18 possible cascades in the first case and 21 in the second case). Each of these cascades is characterized by the values F3, F2 and F1 of the total angular momentum of the hyperfine sublevels involved. The position of the resonance for a given cascadeF3+F2+F1 is: R,(F,
+F2 + F1) = RR(21Ne) + Q,B,
+ I$K,A, _
Ol
E-
- fK,A, - Q,B,l
[&A3 +Q3B3 -
iK2A2
-
Q2B217 (1)
*2
Ai and Bi are respectively the magnetic and electric hyperfine structure constants of level i, Ki=Fi(F,+l)-J&$+1)-I(Z+l), 3 K,(K,+l) - Z(I+l)J(J+l) Qi =
U(U-
l)Ji(Ui-1)
’
S22,(21Ne) is the resonance frequency for the unobservable cascade which would be given by the system without hyperfine splittings (A. = Bi = 0, i = 1, 2, 3). In a sample containing also i ONe for instance: a1,(21Ne) -
E
- S1,(20Ne) = [ti1(21Ne)-
w1(20Ne)]
u$[02(21Ne) - w2(20Ne)].
March
and the second bracket is the corresponding shift for the w2 transition.
4. Experimental hyperfiie
1976
isotope
spectra
The experimental arrangement is almost the same as in our previous paper [l] ; the only differences are in the use of prisms to mix the two beams and of avalanche photodiodes as detectors at 1.15 p. The laser a2 iaa 1.15 p He-Ne laser and the laser s2 I is a dye laser [2] operating at 6096 A or at 5945 A; they are linearly polarized with the same polarization axis. The frequency calibration and control of the dye laser is obtained by the use of a “sigmameter” [3]. In our particular experiment the useful tuning range of the dye laser is about 4.5 GHz. The observed resonance widths are about 75 MHz and 100 MHz respectively for E = + 1 and E = - 1; these values are larger than the expected ones. Collisions and also laser light power are mainly responsible for the broadening of the resonances; the experimental study of both effects is on progress. We have used two different neon samples. The abundances of 21Ne, 22Ne and 20Ne were respectively 91%, 5.7% and 3.3% in one case and 94%, 4.8% and 1.2% in the other case. Typical spectra are shown in figs. 2 and 3. Similar spectra have been previously obtained for the (2s~ + 2p4 -+ 1~~) cascade using laser induced fluorescence line narrowing techniques [4]. The use of the A.L.N. method results in an enhancement of the signal-tonoise ratio and in an increase of the resolution. Many resonances can be clearly seen on the spectra; those corresponding to the even isotopes were easily identified by adding some 2oNe or 22Ne to the sample and also by comparison with spectra obtained with a natural neon mixture [ 11. The well resolved hyperfine components were identified using the previously calculated values of A and B [5]. They are indicated in figs. 2 and 3 where they are labelled as ordered triplets (F,,Fz> Fr). As already mentioned in [I] the intensity pattern in our A.L.N. experiment is strongly dependent on the absorption of the saturating beam R, and is not yet clearly understood.
In formula (2) the first bracket is the isotope shift (21Ne-20Ne) as usually defined for the w, transition 389
Volu~nc 16, number 3 c
2ON.Z
Table I
=Ne
A( lss) = -261.2 .A(ls4) =. 460 A(2pq)= --308.6 A&) = -744
D
I3 -
E
-
D
-
FGi-l
5. Data analysis From the measured positions of the clearly identified components, using eq. (l), one can obtain 3 1 independent linear relations fulfilled by the set of spec-
I= Cl
G
--
n D
_
E ^
-.
._--
I
J ..
-7 c
, 1000 MHz
L=
%e
, d
G H A
E
K
E
l:ig. 3. llyperfine spectra for the cascade 2~ + 2pJ + A = (;. :, ;,, B = (3, 3. 3). C = (3. 2, $)> 1) = (1.1, ;). L_= (4, f, j), 1: = (3.3, ;,, G = (f, ;, :), H = (;,i, :,. I= ($,f.+)..l =(t,1,3,.1<=(~,~,?).L=(~,3,~,.
390
L
I ss.
I t * i
2.3 4 1.5 3
B(lss) B(ls4) B(2p4) B(2s2)
= = = =
11s + 33+ 451 29 i
IO 8 6 2
troscopic parameters involved in the structures. These parameters are the A and B values of the four levels (2~2, 2p4, 1s4 and ls5) and also the values of a,(21 ) for each of the recordings shown in figs. 2 and 3 (12 parameters). For a light element such as neon, the isotopic shift is purely due to the mass effect and then the (21Ne 20Ne) shift for a line can easily be deduced from the ( 22Ne-20Ne) shift for the same line [6]. This has been verified experimentally [6.7] and is in agreement with ab initio evaluations of the field isotopic effect in neon [8]. Making use of this assumption one can easily deduce in our A.L.N. spectra the position of C2,(2tNe) from the positions of the even isotope resonances. This can be done for three of the experimental recordings and gives thus three other linear relations to be fulfilled by the parameters. A least mean square calculation was then performed, using the 34 available linear equations, to determine the 12 parameters. The values obtained (in MHz) for the A and B parameters are given in table 1 The r.1n.s. value of the difference Au between measured and calculated positions (for 34 equations and 12 free parameters) is:
Ao = n
E
March 1976
OPTlCS COMMUNICATIONS
c
I
(Ar#(34-
12) = 13 MHz.
This value is close to the experimental uncertainties in the positions of the components (-15 MHz) which are mainly due to frequency drift of the I. 15 I-(laser during an experiment and to imperfections in the visible laser scanning. The quoted error in the A and R values corresponds to an increase of 5% of the r.m.s. value when the parameter is fixed to its limit value. the other parameters being free. All these A and n values had been previously measured either by atomic beam magnetic resonance (level ls5) [9], or by conventional high resolution optical spectroscopy (levels 2s2. 2p4, 1s4) [6, IO], or by level crossing (level 2p4j 11 l] , or by laser- atomic beam spectroscopy (level 7,~~) [I’_].
Volume
16, number
3
OPTICS COMMUNICATIONS
The values obtained by the A.L.N. method are in good agreement with these measurements as well as with previously calculated values [S] , except for a small discrepancy in the experimental (B(2s2) value. The precision of the measurement is of course not as good as in the magnetic resonance method and as in the level crossing method. However with a higher precision in the frequency calibration of the visible laser and a better control of the infrared laser frequency it should be possible to take advantage of the great number of observed resonances to reach a precision comparable to that of the level crossing method.
6. Conclusion When dealing with hyperfine structures in an A.L.N. experiment the main problem is the identification of the observed resonances. As long as this problem can be solved (i.e. for low J value cascades or if an estimation of the hyperfine constants is available) one can use the method to determine hyperfine structure constants with a reasonably good accuracy. The problem of the interpretation of the observed relative intensities of the various hyperfine cascades in our particular
March
1976
experimental conditions (high absorption of the visible laser beams, degenerate levels perturbed by polarized laser beams, etc.) would be interesting to study if one wanted to extend the method to other complicated spectroscopic problems.
References [l] C. Delsart and J.-C. Keller, Opt. Commun. 15 (1975) 91. [2] S. Liberman and J. Pinard, Appl. Phys. Lett. 24 (1974) 142. [3] P. Juncar and J. Pinard, Opt. Commun. 14 (1975) 438. [4] T.W. Ducas, M.S. Feld, L.W. Ryan, M. Skribanowitz and A. Javan, Phys. Rev. 5 (1972) 1036. [S] S. Liberman, Physica 69 (1973) 598. [6] R.-J. Champeau and J.-C. Keller, J. Phys. B, Atom. Molec. Phys. 6 (1973) L 76. [ 71 E. Giacobino et al., to be publ. in Phys. Rev. (Dec. 1975). [8] J.-C. Keller, Thesis de 3rd cycle, Lab. Aimd Cotton, Orsay (1972). [9] G.M. Grosof, P. Buck, W. Lichten and 1.1. Rabi, Phys. Rev. Lett. 1 (1958) 214. [lo] R.-J. Champeau, J.-C. Keller, 0. Robaux and J. Verges, J. Phys. B, Atom. Molec. Phys. 7 (1974) L 163. [ 111 b. Giacobino, J. de Physique Lettres 36 (1975) L 65. [ 121 R.-J. Champeau and J.C. Keller, J. de Physique Lettres 36 (1975) L 161. [13] T. Hansch and P. Toschek, Z. Phys. 236 (1970) 213.
391