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4He optical pumping with polarization modulated light
Volume 81, number 6
OPTICS COMMUNICATIONS
15 March 1991
4He optical pumping with polarization modulated light H. Gilles, B. Cheron and J. Hamel Laboratoire de Spectroscopic Atomique (URA 19) ISMRA, Boulevard Mar~chal Juin, F. 14050 Caen Cedex, France
Received 6 August 1990
In optical pumping experiments using a laser, beam polarization can be changed easily with the help of an electro-optic device. High frequency modulation ofa LNA laser beam polarization has been used to pump 4He (23St) metastable atoms. New resonances, never observed before, have been studied theoretically and experimentally, and application to high sensitivity magnetometers is suggested.
1. Introduction Thirty years ago, optical pumping was subject to many publications. In 1972, Happer published an interesting general review o f theoretical and experimental optical pumping works [ 1 ]. Many applications are possible, in particular, the pumping o f (23S1) metastable helium atoms is used in the construction o f high sensitivity magnetometers [ 2 ], as a source o f polarized electrons [ 3 ], to prepare polarized 3He nuclei [4] and to polarize ions via Penning collisions [ 5 ]. The recent development of IR lasers tuned at 2 = 1.083 lim permits now original new experiments. Recently, we obtained interesting results in 4He optical pumping with an intensity modulated laser using an acousto-optic modulator ( A O M ) at a frequency close to the Larmor frequency o f metastable He atoms [ 6 ]. In the present paper we describe new optical pumping effects obtained when the A O M is replaced by an electro-optic modulator (EOM). This device works like a birefringent plate in which the phase shift between the two neutral axes is modulated by an applied voltage. Then, the intensity o f the light transmitted through the EOM remains constant but the polarization is modulated. This resulting polarization is rather complex because the ellipticity o f the radiation changes at the frequency o f the voltage. For example, in the case o f "large modulation rates", the polarization periodically changes from linear to circular polarization. This polariza-
tion modulation technique is then different from early works in which the electric field rotates [ 7,8 ].
2. Experimental set-up The experimental arrangement represented on fig. 1 is nearly the same as that described in ref. [ 6 ]. A spherical pyrex cell ( ~ = 4 c m ) filled with 4He at a pressure o f i.5 Torr and submitted to a weak H F discharge is placed inside a magnetic shield to avoid laboratory magnetic perturbations. A pair o f Helm-
t p L ~#'~1,--~ I] I'q lJ
• o,,,~f,,,-'~~ ...................... ',,_,,i~"7 4,',:,,
F:q .
Fig. 1. Experimental set-up. L: LNA tunable laser, P: linear polarizer, EOM: electro-optic modulator, C: Helium cell, b: Helmhoitz coils, S: magnetic shield, PD 1, PD2: photodetectors, D: signal amplifier, dc and ac are respectively the mean value and the modulated part of the detected signal, GI: dc power supply, G2: function generator, A: lock-in amplifier, R: chart recorder.
0030-4018/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
369
Volume 81, number 6
OPTICS COMMUNICATIONS
holtz coils provides the static magnetic field B. The pumping light comes out of a LNA diode-pumped laser tuned on the Do (23S~-23po) 4He line at 2 = 1.0829 ttm. The laser beam is linearly polarized before reaching the EOM, then it propagates into the helium cell and a Ge photodiode detects the transmitted light. The EOM is electrically biased with a dc power supply and a hf function generator provides the modulation voltage at angular frequency A. The amplitude of the dc or ac component of the photoelectric signal is recorded as a function of the magnetic field B. We consider here two particular configurations: magnetic field B parallel (Bn) or perpendicular (B±) to the laser beam propagation direction.
15 March 1991
e = ( 1/v/2) [ux+exp(iA#)uy],
(3)
with A ¢ = a + b cos(~t); a and b may be set at any value with the electro-optic modulator command device. The polarization vector is then expanded in Fourier series restricted to the first three terms exp (iA#) = e x p ( i a ) × [Jo +2iJ~ c o s ( Q t ) - 2 J 2 cos(2•t) ] ,
(4)
where Jn---Jn(b), is the nth order Bessel function of the phase parameter b. (Apqk)p is then calculated using the formalism described in ref. [ 11 ]. We also assume that the radiative damping constant Fe of the 23po state is much greater than the mean pumping rate 1/TD, so that pO is negligible and pO can be considered as constant. We look for a general solution:
3. Theory pkq= We first recall the well known equations of optical pumping [9,10] using the irreducible tensorial operator representation of the density matrices p and pe of a system of 4He atoms in the 23S, metastable state and 23po state respectively. The evolution of the standard components pk and p k is given by dpkq/ dt = - iqtopkq 1
Fp~+ A&o*qo F~
o
"JI- ~ p (~Oqk)p -I- ~7~PeoA0$q0 , 0 dp,o/dt =
0 -r~poo
(x/~/Tp) (AP°)v,
( 1)
(2)
where to is the Larmor angular frequency in the magnetic field B, F the relaxation constant of the metastable level (we assume a unique constant), A is the creation rate of the metastable atoms by the discharge. ( l / Tv) (Ap~) p is the pumping term where Tp is the pumping time. l/Tp is proportional to the power density of the beam, which is assumed here to be low enough in order to avoid absorption saturation. However, l / Tp may be of the same order as the relaxation constant F, so that light broadening may occur. We neglect light shift. The last term in (1) represents the repopulation by spontaneous emission from the upper level 23po with Fo the radiation damping constant (Fe___107 s - l ). In configuration (B~), the electric field takes the following form 370
~ n~
~n)pkqexp(inQt) "
(5)
-oo
For a given angular frequency ~, resonance occurs when n~-- qto. If £2:~ F, the different resonances are well isolated and can be studied separately. The resonances are monitored by measuring the absorption of the pumping beam by the cell. The He vapor is supposed to be optically thin. Main resonances are observed at to=~2 and to=~2/2 and appear on the modulation of the transmitted beam at null, ~2 and 2~2 frequencies. For example, in configuration (Bll), modulations at 0, ~ and 2 ~ frequencies exhibit resonance at to=~2/2 and are expressed in lowest order in l/Tp as 1
So( II, t 2 / 2 ) = _gEj2 sin2a 1 + ( X _ 2 u ) 2 , Sa(ll,/2/2) = g 2 j I ×
(6)
sin 2a 2
(Jo - J 2 ) cos 12t+ (Jo +J2) ( X - 2u) sin K2t 1 -st-( X - 2 u ) 2 (7)
a m ( II, K2/2) = _ g 2 j 2 sin2a X
cos 212t+ ( X - 2 u ) sin 2~2t 1+ ( X _ 2 u ) 2 ,
(8)
where g = 1/TvF, X=~2/F, u = t a / F . Resonances at to = 12 are also expected in this con-
Volume 81, number 6
OPTICS COMMUNICATIONS
figuration. In configuration (B+) the main resonances are expected at to=O, on the modulations at null and 2 0 frequencies. Modulation at 2 0 is expressed as
S2a( _1_,O) 3
--8g
phase
15 March 1991 quadrature
_g2j21 (cos 20t+ (X-u) k
sin 2Ot 1+ (X--u) 2
2] cos2Ot+3(X-u) sin2Ot'~ [l+(X_u)2l[l+4(X_u)2] ,]
[1-2(X-u)
•
(9) At low optical power (q << 1 ), the second term in the large brackets may be neglected.
4. Experimental results Resonances with significant amplitudes are observed under the following conditions: - Configuration (B,): resonances at t o = O / 2 and to = O. The amplitude of the modulations at 0, O, 2 0 are dependent of the constant phase shift a. - Configuration ( B l ) : resonances at t o = O (no signal at to= O / 2 ) . The amplitude of the modulation is negligible at O and practically independent of the constant phase shift a at 20. These observations are in agreement with the predictions. We have analysed some of the resonances with more details. (i) Longitudinalpumping (configuration (Bm): fig. 2 shows resonances observed when the magnetic field is scanned around the value corresponding to a Larmor frequency to = O/2. The resonances are detected at null frequency (a) and at O (b) and 2 0 (c) frequencies where the amplitudes are analysed in-phase and in-quadrature with the modulation of the pumping beam. The phase constant a is n / 4 and the phase parameter b is rt/2. We see that the signal to noise ratio increases from null to 2 0 frequency. As expected from relation (8), the amplitudes of the 2 0 modulation either in-phase or in-quadrature are nearly equal. For the O modulation, relation (7) predicts that the relative amplitude of the in-phase and in-quadrature resonances are strongly dependent of the phase parameter b. Fig. 3 represents the ratio S/A of the amplitudes in-phase and in-quadrature versus b ( × : experimental, full line: calcu-
Fig. 2. Amplitude oftbe modulations of the transmitted beam at null (a), 12 (b) and 212 (c) frequencies versus magnetic field. Resonances are observed at l.armor frequency to=t2/2. Beam propagationdirection parallelto the magneticfield, constantphase shift a = 7t/4 and phase parameter b = n/2.
lated). As predicted, the in-phase signal vanishes for b = 1.84 rad. Finally, taking into account the responsitivity of the electronics, the relative values of the in-phase amplitudes at 0, O, 2 0 frequencies are in reasonable agreement with the predictions given by relations (6), (7), (8). The amplitude of the 2 0 modulation versus phase shift a is represented on fig. 4. A very good agreement is found with theoretical predictions (function "sin2a '' plotted in full line). Similarly, fair agreement is observed between experiment and theory for the amplitude of the O modulation versus a on fig. 5. (ii) Transversalpumping(configuration (B±): fig. 6 shows the amplitude of the modulation at 2 0 versus magnetic field and for two values of the optical power. Resonances are observed at Larmor frequency to=O. The power density is close to 3 roW/ cm 2 in fig. 6a and 14 m W / c m 2 in fig. 6b. Large light broadening is seen on fig. 6b and in addition, the inphase curve exhibits a reversal: this is in agreement with the theory (relation ( 9 ) ) .
371
Volume 81, number 6
OPTICS COMMUNICATIONS
15 March 1991
u I
I
I
tO0
8O
n
E 4O
2O
0
-1.0
-0.5
I
I
I
I
0
0.5
1.0
1.5
2.0
p h a s e shift a (rad)
Fig. 3. Ratio S/A between the in-phase and in-quadrature amplitude modulation at # frequency versus phase parameter/7. Resonances are observed at Larmor frequency to=~/2. Beam propagation direction parallel to the magnetic field and constant phase shift afx/4. ( ×: experimental, solid line: calculated).
1.2 x
1.0
x
0,8 o
0.6
x
x
w
0.4
0.2
0 0.3
0.8
1.3
1.8
2.3
phase parameter b (rad)
Fig. 4. Relative amplitude in-phase at frequency 2£2 of the resonance at Larmor frequency o~=~/2 versus constant phase shift a. The beam is parallel to the magnetic field and the phase parameter b is set at ~/2. Solid line is theoretical. 372
Volume 81, number 6
OPTICS COMMUNICATIONS
100
~
l
15 March 1991
i
l
1
50
(10 @ @
7o
___=
0
n
E
x ._._...~.-
~
-50
-1 O0
-1.0
I
I
I
I
I
-0.5
0
0.5
1.0
1,5
2,0
phase shift a (rad)
Fig. 5. Relative amplitude in-phase ( X ) and in-quadrature ( o ) at frequency ~2 of the resonance at Larmor frequency t o = g / 2 versus constant phase shift a. The beam is parallel to the magnetic field and the phase parameter is set at 7t/2. Solid lines are theoretical.
5. Conclusion phase
nolse f ~
quadrature
~ e
/
Our study of optical pumping with polarization modulated light gives original results, never published before, to our knowledge. The comparison with the developed theoretical model is fairly good. In view of the excellent signal to noise ratio and the possibility to detect resonances in longitudinal as well as in transversal configurations, this new method may be very useful in high sensitivity magnetometry. The obtained performances must be now compared with other methods such as magnetic resonance and intensity modulated optical pumping.
References lmG
Fig. 6. Amplitude of the modulation at frequency 2M versus magnetic feld and for two values of the optical power. Resonances are observed at Larmor frequency t a f t , beam perpendicular to the magnetic field, constant phase shift a-- lt/4 and phase parameter b f x / 2 . The power density is close to 3 mW/cm 2 in (a) and 14 mW/cm 2 in (b).
[ 1 ] W. Happer, Rev. Mod. Phys. 44 (1972) 169. [21 M. Leduc and J, Hamel, Revue Scientifique et Technique de la D6fense. France, 4 (1989) 31. [3] G.H. Rutherford, J.M. Ratliff, J.G. Lynn, F.B. Dunning and G.K. Waiters, Rev. Sci. Inst., submitted. [4] D.S. Betts and M. Leduc, Ann. Phys. Fr. 11 (1986) 227. [ 5 ] J. Hamel and J.P. Barrat, J. de Phys. 39 (1978) 500.
373
Volume 81, number 6
OPTICS COMMUNICATIONS
[6]A. Cassimi, B. Cheron and J. Hamel, J. Physique, to be published. [7] E.B. Aleksandrov, Opt. Spectroc. 19 (1965) 252. [8] J. Dupoint-Roc and C. Cohen-Tannoudji, C.R. Acad. Sc. Paris, B267 (1968) 1275.
374
15 March 1991
[9] C. Cohen-Tannoudji, Ann. Phys. 7 (1962) 423. [ 10] J.P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22 ( 1961 ) 359, 443. [ 11 ] J.P. Faroux, Thesis Paris (1969) (unpublished; microfilm no AO 3807, CNRS, 15 Quai Anatole France, 75007 Paris).
OPTICS COMMUNICATIONS
15 March 1991
4He optical pumping with polarization modulated light H. Gilles, B. Cheron and J. Hamel Laboratoire de Spectroscopic Atomique (URA 19) ISMRA, Boulevard Mar~chal Juin, F. 14050 Caen Cedex, France
Received 6 August 1990
In optical pumping experiments using a laser, beam polarization can be changed easily with the help of an electro-optic device. High frequency modulation ofa LNA laser beam polarization has been used to pump 4He (23St) metastable atoms. New resonances, never observed before, have been studied theoretically and experimentally, and application to high sensitivity magnetometers is suggested.
1. Introduction Thirty years ago, optical pumping was subject to many publications. In 1972, Happer published an interesting general review o f theoretical and experimental optical pumping works [ 1 ]. Many applications are possible, in particular, the pumping o f (23S1) metastable helium atoms is used in the construction o f high sensitivity magnetometers [ 2 ], as a source o f polarized electrons [ 3 ], to prepare polarized 3He nuclei [4] and to polarize ions via Penning collisions [ 5 ]. The recent development of IR lasers tuned at 2 = 1.083 lim permits now original new experiments. Recently, we obtained interesting results in 4He optical pumping with an intensity modulated laser using an acousto-optic modulator ( A O M ) at a frequency close to the Larmor frequency o f metastable He atoms [ 6 ]. In the present paper we describe new optical pumping effects obtained when the A O M is replaced by an electro-optic modulator (EOM). This device works like a birefringent plate in which the phase shift between the two neutral axes is modulated by an applied voltage. Then, the intensity o f the light transmitted through the EOM remains constant but the polarization is modulated. This resulting polarization is rather complex because the ellipticity o f the radiation changes at the frequency o f the voltage. For example, in the case o f "large modulation rates", the polarization periodically changes from linear to circular polarization. This polariza-
tion modulation technique is then different from early works in which the electric field rotates [ 7,8 ].
2. Experimental set-up The experimental arrangement represented on fig. 1 is nearly the same as that described in ref. [ 6 ]. A spherical pyrex cell ( ~ = 4 c m ) filled with 4He at a pressure o f i.5 Torr and submitted to a weak H F discharge is placed inside a magnetic shield to avoid laboratory magnetic perturbations. A pair o f Helm-
t p L ~#'~1,--~ I] I'q lJ
• o,,,~f,,,-'~~ ...................... ',,_,,i~"7 4,',:,,
F:q .
Fig. 1. Experimental set-up. L: LNA tunable laser, P: linear polarizer, EOM: electro-optic modulator, C: Helium cell, b: Helmhoitz coils, S: magnetic shield, PD 1, PD2: photodetectors, D: signal amplifier, dc and ac are respectively the mean value and the modulated part of the detected signal, GI: dc power supply, G2: function generator, A: lock-in amplifier, R: chart recorder.
0030-4018/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
369
Volume 81, number 6
OPTICS COMMUNICATIONS
holtz coils provides the static magnetic field B. The pumping light comes out of a LNA diode-pumped laser tuned on the Do (23S~-23po) 4He line at 2 = 1.0829 ttm. The laser beam is linearly polarized before reaching the EOM, then it propagates into the helium cell and a Ge photodiode detects the transmitted light. The EOM is electrically biased with a dc power supply and a hf function generator provides the modulation voltage at angular frequency A. The amplitude of the dc or ac component of the photoelectric signal is recorded as a function of the magnetic field B. We consider here two particular configurations: magnetic field B parallel (Bn) or perpendicular (B±) to the laser beam propagation direction.
15 March 1991
e = ( 1/v/2) [ux+exp(iA#)uy],
(3)
with A ¢ = a + b cos(~t); a and b may be set at any value with the electro-optic modulator command device. The polarization vector is then expanded in Fourier series restricted to the first three terms exp (iA#) = e x p ( i a ) × [Jo +2iJ~ c o s ( Q t ) - 2 J 2 cos(2•t) ] ,
(4)
where Jn---Jn(b), is the nth order Bessel function of the phase parameter b. (Apqk)p is then calculated using the formalism described in ref. [ 11 ]. We also assume that the radiative damping constant Fe of the 23po state is much greater than the mean pumping rate 1/TD, so that pO is negligible and pO can be considered as constant. We look for a general solution:
3. Theory pkq= We first recall the well known equations of optical pumping [9,10] using the irreducible tensorial operator representation of the density matrices p and pe of a system of 4He atoms in the 23S, metastable state and 23po state respectively. The evolution of the standard components pk and p k is given by dpkq/ dt = - iqtopkq 1
Fp~+ A&o*qo F~
o
"JI- ~ p (~Oqk)p -I- ~7~PeoA0$q0 , 0 dp,o/dt =
0 -r~poo
(x/~/Tp) (AP°)v,
( 1)
(2)
where to is the Larmor angular frequency in the magnetic field B, F the relaxation constant of the metastable level (we assume a unique constant), A is the creation rate of the metastable atoms by the discharge. ( l / Tv) (Ap~) p is the pumping term where Tp is the pumping time. l/Tp is proportional to the power density of the beam, which is assumed here to be low enough in order to avoid absorption saturation. However, l / Tp may be of the same order as the relaxation constant F, so that light broadening may occur. We neglect light shift. The last term in (1) represents the repopulation by spontaneous emission from the upper level 23po with Fo the radiation damping constant (Fe___107 s - l ). In configuration (B~), the electric field takes the following form 370
~ n~
~n)pkqexp(inQt) "
(5)
-oo
For a given angular frequency ~, resonance occurs when n~-- qto. If £2:~ F, the different resonances are well isolated and can be studied separately. The resonances are monitored by measuring the absorption of the pumping beam by the cell. The He vapor is supposed to be optically thin. Main resonances are observed at to=~2 and to=~2/2 and appear on the modulation of the transmitted beam at null, ~2 and 2~2 frequencies. For example, in configuration (Bll), modulations at 0, ~ and 2 ~ frequencies exhibit resonance at to=~2/2 and are expressed in lowest order in l/Tp as 1
So( II, t 2 / 2 ) = _gEj2 sin2a 1 + ( X _ 2 u ) 2 , Sa(ll,/2/2) = g 2 j I ×
(6)
sin 2a 2
(Jo - J 2 ) cos 12t+ (Jo +J2) ( X - 2u) sin K2t 1 -st-( X - 2 u ) 2 (7)
a m ( II, K2/2) = _ g 2 j 2 sin2a X
cos 212t+ ( X - 2 u ) sin 2~2t 1+ ( X _ 2 u ) 2 ,
(8)
where g = 1/TvF, X=~2/F, u = t a / F . Resonances at to = 12 are also expected in this con-
Volume 81, number 6
OPTICS COMMUNICATIONS
figuration. In configuration (B+) the main resonances are expected at to=O, on the modulations at null and 2 0 frequencies. Modulation at 2 0 is expressed as
S2a( _1_,O) 3
--8g
phase
15 March 1991 quadrature
_g2j21 (cos 20t+ (X-u) k
sin 2Ot 1+ (X--u) 2
2] cos2Ot+3(X-u) sin2Ot'~ [l+(X_u)2l[l+4(X_u)2] ,]
[1-2(X-u)
•
(9) At low optical power (q << 1 ), the second term in the large brackets may be neglected.
4. Experimental results Resonances with significant amplitudes are observed under the following conditions: - Configuration (B,): resonances at t o = O / 2 and to = O. The amplitude of the modulations at 0, O, 2 0 are dependent of the constant phase shift a. - Configuration ( B l ) : resonances at t o = O (no signal at to= O / 2 ) . The amplitude of the modulation is negligible at O and practically independent of the constant phase shift a at 20. These observations are in agreement with the predictions. We have analysed some of the resonances with more details. (i) Longitudinalpumping (configuration (Bm): fig. 2 shows resonances observed when the magnetic field is scanned around the value corresponding to a Larmor frequency to = O/2. The resonances are detected at null frequency (a) and at O (b) and 2 0 (c) frequencies where the amplitudes are analysed in-phase and in-quadrature with the modulation of the pumping beam. The phase constant a is n / 4 and the phase parameter b is rt/2. We see that the signal to noise ratio increases from null to 2 0 frequency. As expected from relation (8), the amplitudes of the 2 0 modulation either in-phase or in-quadrature are nearly equal. For the O modulation, relation (7) predicts that the relative amplitude of the in-phase and in-quadrature resonances are strongly dependent of the phase parameter b. Fig. 3 represents the ratio S/A of the amplitudes in-phase and in-quadrature versus b ( × : experimental, full line: calcu-
Fig. 2. Amplitude oftbe modulations of the transmitted beam at null (a), 12 (b) and 212 (c) frequencies versus magnetic field. Resonances are observed at l.armor frequency to=t2/2. Beam propagationdirection parallelto the magneticfield, constantphase shift a = 7t/4 and phase parameter b = n/2.
lated). As predicted, the in-phase signal vanishes for b = 1.84 rad. Finally, taking into account the responsitivity of the electronics, the relative values of the in-phase amplitudes at 0, O, 2 0 frequencies are in reasonable agreement with the predictions given by relations (6), (7), (8). The amplitude of the 2 0 modulation versus phase shift a is represented on fig. 4. A very good agreement is found with theoretical predictions (function "sin2a '' plotted in full line). Similarly, fair agreement is observed between experiment and theory for the amplitude of the O modulation versus a on fig. 5. (ii) Transversalpumping(configuration (B±): fig. 6 shows the amplitude of the modulation at 2 0 versus magnetic field and for two values of the optical power. Resonances are observed at Larmor frequency to=O. The power density is close to 3 roW/ cm 2 in fig. 6a and 14 m W / c m 2 in fig. 6b. Large light broadening is seen on fig. 6b and in addition, the inphase curve exhibits a reversal: this is in agreement with the theory (relation ( 9 ) ) .
371
Volume 81, number 6
OPTICS COMMUNICATIONS
15 March 1991
u I
I
I
tO0
8O
n
E 4O
2O
0
-1.0
-0.5
I
I
I
I
0
0.5
1.0
1.5
2.0
p h a s e shift a (rad)
Fig. 3. Ratio S/A between the in-phase and in-quadrature amplitude modulation at # frequency versus phase parameter/7. Resonances are observed at Larmor frequency to=~/2. Beam propagation direction parallel to the magnetic field and constant phase shift afx/4. ( ×: experimental, solid line: calculated).
1.2 x
1.0
x
0,8 o
0.6
x
x
w
0.4
0.2
0 0.3
0.8
1.3
1.8
2.3
phase parameter b (rad)
Fig. 4. Relative amplitude in-phase at frequency 2£2 of the resonance at Larmor frequency o~=~/2 versus constant phase shift a. The beam is parallel to the magnetic field and the phase parameter b is set at ~/2. Solid line is theoretical. 372
Volume 81, number 6
OPTICS COMMUNICATIONS
100
~
l
15 March 1991
i
l
1
50
(10 @ @
7o
___=
0
n
E
x ._._...~.-
~
-50
-1 O0
-1.0
I
I
I
I
I
-0.5
0
0.5
1.0
1,5
2,0
phase shift a (rad)
Fig. 5. Relative amplitude in-phase ( X ) and in-quadrature ( o ) at frequency ~2 of the resonance at Larmor frequency t o = g / 2 versus constant phase shift a. The beam is parallel to the magnetic field and the phase parameter is set at 7t/2. Solid lines are theoretical.
5. Conclusion phase
nolse f ~
quadrature
~ e
/
Our study of optical pumping with polarization modulated light gives original results, never published before, to our knowledge. The comparison with the developed theoretical model is fairly good. In view of the excellent signal to noise ratio and the possibility to detect resonances in longitudinal as well as in transversal configurations, this new method may be very useful in high sensitivity magnetometry. The obtained performances must be now compared with other methods such as magnetic resonance and intensity modulated optical pumping.
References lmG
Fig. 6. Amplitude of the modulation at frequency 2M versus magnetic feld and for two values of the optical power. Resonances are observed at Larmor frequency t a f t , beam perpendicular to the magnetic field, constant phase shift a-- lt/4 and phase parameter b f x / 2 . The power density is close to 3 mW/cm 2 in (a) and 14 mW/cm 2 in (b).
[ 1 ] W. Happer, Rev. Mod. Phys. 44 (1972) 169. [21 M. Leduc and J, Hamel, Revue Scientifique et Technique de la D6fense. France, 4 (1989) 31. [3] G.H. Rutherford, J.M. Ratliff, J.G. Lynn, F.B. Dunning and G.K. Waiters, Rev. Sci. Inst., submitted. [4] D.S. Betts and M. Leduc, Ann. Phys. Fr. 11 (1986) 227. [ 5 ] J. Hamel and J.P. Barrat, J. de Phys. 39 (1978) 500.
373
Volume 81, number 6
OPTICS COMMUNICATIONS
[6]A. Cassimi, B. Cheron and J. Hamel, J. Physique, to be published. [7] E.B. Aleksandrov, Opt. Spectroc. 19 (1965) 252. [8] J. Dupoint-Roc and C. Cohen-Tannoudji, C.R. Acad. Sc. Paris, B267 (1968) 1275.
374
15 March 1991
[9] C. Cohen-Tannoudji, Ann. Phys. 7 (1962) 423. [ 10] J.P. Barrat and C. Cohen-Tannoudji, J. Phys. Radium 22 ( 1961 ) 359, 443. [ 11 ] J.P. Faroux, Thesis Paris (1969) (unpublished; microfilm no AO 3807, CNRS, 15 Quai Anatole France, 75007 Paris).