- Email: [email protected]
High buffer gas pressure perturbation of coherent population trapping in sodium vapors
2 November
1998
PHYSICS
LETTERS A
Physics Letters A 248 ( 1998) 80-85
High buffer gas pressure perturbation of coherent population trapping in sodium vapors J.H. Xu ‘, G. AIzettaa~b-’ a ScudaNormale Superiore and INFM. Piazza dei Cavalieri 7. 56126 PBa, Italy h Dipartimento di Fisica. Urriversitri di Pisu, Piazza Dante 1, 56126 Piss. It&
Received 20 May 1998; revised manuscript received 10 August 1998; accepted for publication Communicated
17 August
1998
by B. Fricke
Abstract We report an experimental investigation of coherent population trapping in specially selected Zeeman levels of the sodium atom, performed under high buffer gas pressure in a polydimethyisiloxane coated cell at room temperature. The results show that coherent population trapping will not be completely destroyed when the buffer gas pressure reaches 1100 Torr for He and 1000, 800, and 500 Torr, for Ne, Ar and Kr, respectively. Buffer gases with heavier mass play a larger destructive role for the coherent popuIation trapping. The line width of the dark resonance is reduced with buffer gas pressure. The behavior of the dark resonances on increasing buffer gas is discussed and possible applications are pointed out. @ 1998 Elsevier Science R.V. PAC.% 32.7O.C~; 32.80.Wr Kqwords: Coherent population
1.
trapping;
Velocity-changing
collisions;
Introduction
Recently, much attention has been given to the study of the coherent population trapping (CPT) of alkali atoms in a superposition state. This was mainly stimulated by many interesting applications based on this effect. Examples for such applications are laser cooling on the coherent state resulting in a tem~rature lower than the recoil limit [ 11, development of a nontraditional laser without population inversion [2,3], laser isotope separation [ 41, and enhancement of the index of refraction [ 51, etc. Many studies on the CPT have been pe~ormed in absence of collisions between atoms and buffer gases, such as in an atomic beam or ’ E-mail: hua~cmp.sns.it.
Optical pumping
in a cell under high vacuum. However, very few papers [ 61 considered the influence of buffer gas on the coherent population trapping effect. Actually, it is inteiesting to investigate CPT in the presence of high pressure buffer gases in order to understand better the perturbations of CPT caused by the buffer gases. This would, in turn, help us to develop new applications, for example, the enhancement of light propagation under collision dominated circumstances. In the present work we show how one can take advantage of optical pumping effects to increase the atomic population in proper selected Zeeman levels for an enhancement of caherent population trapping. It is well known [ ‘71 that optical pumping cannot only create but also maintain a nonequilibrium population in different magnetic sublevels of the ground state.
0375-9601/98/$ - see front matter @ 1998 Elsevier Science B.V. All rights reserved PII SO375-9601(98)00647-l
J.H. Xu, G. Aketta/Phwics
Since collisions with a diamagnetic gas do not change the atomic spin orientation in the ground states, they can be used to maintain a nonequilibrium distribution in some specific Zeeman levels. When the Zeeman levels of the ground state (IF = 2, M,G = -2); IF = 1, M,c = - 1) ) are selected, atomic population in these levels can be increased by buffer gas enhanced optical pumping effects, and thus the dark resonance, particularly at high pressure, is more pronounced. For sodium atoms, experiments are traditionally performed in a glass cell or a heat pipe oven with high temperature in order to produce an adequate atomic vapor density. In the present work, the experiment was performed at room temperature, that is, different from the traditional method. Thanks to the photoatomic effect [ 81, sodium vapors with high density and low velocity can be prepared in a polydimethylsiloxane (PDMS) coated cell at room or even much lower temperature. The last point to be mentioned is the coherent light source preparation. In a A configuration, two coherent radiation sources are needed for the CPT preparation. Usually, an acousto-optical modulator is used to create the second, frequency shifted light beam [ 91. That two first order sidebands are created from a single laser frequency by an electro-optical modulator is another way [ lo] for preparation of CPT by twophoton excitation. More simple, we used here just a commercial multimode (CR599) dye laser. Two coherent light frequencies were created using an intracavity mode selection method. We found this is a very reliable method satisfying the experimental requirements for observing CPT. Generally speaking, the way to produce CPT of sodium atoms in a three level A configuration is to apply two electromagnetic fields whose energy difference equals the difference between the two separated, low-lying electronic states. When this relative resonance is fulfilled, one finds that the transition probability between one of the superposition states of the two ground levels and the upper state becomes zero, i.e. a dark state is created. Even though the other superposition state is interacting with the upper excited state, all atoms can be accumulated in the dark state after several cycles of optical pumping. Under low magnetic fields, it is possible to select only one pair of Zeeman levels in the ground state for forming a A system. In our case, we used IF = 2. MF = -2)
------
Letters A 248 (1998) 80-85 MF=
-2
F=?
F=l
81
-1
I
2
---
F=2
F=l
0
L_-
Fig. I. Zeeman structure of sodium D I line. The pair (IF = ?,M,c = -2);IF = 1.k’~ = -1)) in the ground state is selected for coherent population trapping in a A configuration.
and IF = 1, M,c = -1) in the ground state as the pair of levels for CPT. One can see clearly from Fig. I that optical pumping can greatly enhance the population of this pair which is involved in the trapping state. In consequence, population trapping should not be destroyed too much due to the combination of collisional dephasing and increased optical pumping with increasing buffer gas pressure. In contrast, if other levels like IF = 2, MF = -1) and IF = 1. MF = 0) are selected, the population of these levels is decreased due to optical pumping. The consequence is evident that the trapping effect should be also decreased by optical pumping with increasing buffer gas pressure.
2. Experimental
results
The experimental setup for observing the dark resonance, similar to that of the first experimental observation [ 111, is shown schematically in Fig. 2. Sodium is contained in a glass cell coated with PDMS, connected directly to a vacuum system and to gas reservoirs, in order to study the perturbation of CPT by buffer gases at various pressures. The sodium vapor was prepared by the photo-atomic effect, instead of evaporation of sodium metal by thermal heating. The details of the preparation of the coated cell can be found elsewhere [ 121. The density of sodium vapour at room temperature can thus be up to 10” cmp3, produced by desorption with an extra laser at 514 nm, 200 mW. A gradient magnetic field Hh’ was applied to produce a weak Zeeman splitting of the sodium ground levels, in order to match the coherent resonance in a tiny range along the axis direction. Thus the phe-
82
J.H. Xu, G, Alzetta/F%ysics
Letters A 243 11998) 80-85
GAS FILLING
Fig. 2. Experimental setup for observation of the dark resonances at room temperature. C: PDMS coated celi containing sodium atoms connected to a vacuum system for buffer gases filling; H,: gradient magnetic held; H,,,: modulated magnetic field; laser beam tuned to the sodium DI line with (I- polarization: FP: Fabry-Perot interferometer; SA: spectrum analyzer to monitor the beat frequency: L: lens; MM: monochromator; DS: digitizing oscilloscope; and PL: plotter.
Fig. 3. Laser mode distribution in a multimode dye laser (the upper trace ); and laser mode selected by an intracavity etaion with a mode spacing of 6 x AZ! (the lower trace). Two adjacent modes were used for the coherent population trapping experiment.
----yx__
280
nomenon of transparency induced by CPT takes place in this tiny zone. An amplitude modulated magnetic field E&,,with a few G was used to scan the Zeeman splitting. This produces a scan of the position of the dark resonance along the magnetic field direction. A multimode dye laser was tuned to the Dt line of the sodium atom; (+- polarization was created by means of a h/4 plate. The axial mode spacing Ai\v of the laser with a cavity length d of 54 cm is c/2d = 277.7 MHz. An intracavity mode selection technique was used to create the frequencies needed for two photon excitation, by inserting an etalon into the laser cavity. Carefully adjusting the etalon, three strong modes spaced by 6 x Av, oscillating inside the gain profile, were obtained. These modes monitored by a FuboPer& interferometer are shown in Fig. 3. Modes occurring between the three strong modes were completely suppressed by mode competitions. The laser beam was tilted about 10 degree with respect to the magnetic field. The magnetic field axis was taken as the quantization axis. With respect to this axis all kinds of polarization (cr+ , CT-, T) are possible. Thus the beat frequency of 1665 MHz (6 x Av) can exactly match the specially selected resonance between the level IF = 2, MF = -2) in the 32Pr,2 excited state and the levels (/F = ~,MF = -2);lF = ~,MF = -I)) in the 3’St/a ground state of sodium at the magnetic field of 54 G. By modulating the weak magnetic field at 1.5 Hz, the black line is scanned along the direction of the magnetic field. The modulated black line signal was detected by a photomultiplier via a monochroma-
*I_.-.--
,
/._-“._._._-.-_‘-
._.^
i
20
Magnetic field
Fig. 4. A typical dark resonance of buffer gas.
spectrum
measured
in absence
tor, whose slit was set parallel to the black line which is orthogonal to the magnetic field direction. The signal was collected and averaged by a digitizing oscilloscope, and printed on a IBM colour plotter. We paid special attention to the behavior of CPT at high buffer gas pressure. The experiment was carried out up to the disappearance of the black line when increasing the buffer gas pressure. The laser intensity used for the experiment is 170 mW with a beam diameter of 1.5 mm. A typical dark resonance signal measured in absence of buffer gas is shown in Fig. 4. We define a contrast C to evaluate the dark resonance strength, c = LX, - Iti” I max + Li” ’
(1)
where Imnx and Z,,, are the maximum and minimum fluorescence intensity measured, respectively, at one side of the black line and inside the black line. The
J.H. Xu. G. Abettu/Physics
Letters A 248 (1998)
1.4 He Ne Ar Kr
n l
80-VA.
g
z g 5 0
’
.
60-
.
.
i
.
A .
.
40-
.
.
A .
0
,
.
1.0.
I 200
. ..I
b 0.6.
.
l
.
l
. 400
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.
. *
0
.1
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.
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1.2
80-85
. I 600
*
I 800
’
. . I 1000
.
0.4 -
.
I 1200
0.2’1 0
I 20
I 40
I 60
P (Torr) Fig. 5. Dependence of the normalized dark resonance strengths on the pressure of various buffer gases.
contrast C is normalized to 1, when no buffer gas is present. The dark resonance strengths at different buffer gas pressures were thus evaluated and shown in Fig. 5. It was found that the dark resonance strength gets less pronounced with increasing buffer gas pressure but it can eventually survive up to a dramatic high value of buffer gas pressure: 1100 Torr of He. We also investigated the pressure dependence of the dark resonance intensity for other buffer gases: Ne, Ar and Kr at the same experimental conditions. We found that they cause a similar decay tendency but the limit pressure decreases from 1100 Torr of He to 1000 Torr of Ne, to 800 Tot-r of Ar and to 500 Torr of Kr, when increasing the mass of the buffer gas atoms. Moreover, the line width of the dark resonance gets narrower with increasing pressure of the buffer gas. The line width was calibrated [ 111 using Zeeman resonances produced by a weak radio frequency field at about 40 MHz. Results obtained with He as buffer gas are shown in Fig. 6. It is demonstrated that the line width of the dark resonance is reduced by buffer gas from 1.3 MHz to 0.4 MHz, when the pressure increases from 10e4 to 100 Torr.
3. Discussion The present experimental results show an evidence that the strength of dark resonance decreases very slowly when increasing the pressure, for all the buffer gases used. Consequently, the coherent dark state can be preserved at very high pressure of buffer gas. More-
.
. I 80
1
, 100
I 120
I 140
I 160
P (Torr) Fig. 6. The line width of the dark resonance reduced as a function of the pressure of helium gas.
over, buffer gas with heavier mass can more effective destroy the dark resonance. We are going to discuss these results in more detail. The destruction of the dark resonance due to buffer gas is reasonable because collisions dephase the coherence. But the decrease is surprisingly insensitive to the buffer gas pressure. This may be mainly caused by: (a) optical pumping increases the population of the levels involved in forming the coherent population trapping state; (b) velocity changing collisions (VCCs) increases the population of the levels involved in the two photon resonance. We should emphasize that the CPT configuration we selected is different from the one of Ref. [ 91. In our case, the Zeeman level pair (]F=~,MF=-2);lF=l,M~=-1))oftheground state is chosen for the dark resonance preparation. The population of this pair is increased by optical pumping effects which are enhanced by increasing the buffer gas pressure. Consequently, the coherent population trapping is then enhanced by the pressure enhanced optical pumping. On the other hand, the collisions induce a dephasing which decreases the coherent trapping present contemporaneously in the system. Therefore, the consequence is that the dark resonance is destroyed with increasing buffer gas pressure, but very slowly. In contrast, if another level pair, for example (IF = ~,MF = -1);IF = ~,MF = -l)), of the ground state is chosen for the dark resonance preparation, the population in these levels is decreased by optical pumping. As a result, the dark resonance is dramatically destroyed by the increase of optical pumping with increasing buffer gas, in addition to the col-
84
J.H. Xu. G. AIzettcr/Physics
lisional dephasing. This effect has been observed in Ref. [ 91 where the dark resonance is very sensitive to the presence of buffer gas. The dark resonance is completely destroyed at only 10 Torr of helium. Therefore it is so important to choose proper Zeeman levels allowing optical pumping effects to increase the population of the levels involved in CPT. In the case of velocity selective excitation using single mode laser light, only one velocity group of atoms can be in resonance. Therefore, only a small quantity of atoms can take part in the interaction process. Mostly the unexcited atoms can be considered as a reservoir. If the collision rate is smaller than the decay rate of the excitation, fresh atoms can easily transit into the interaction region and be excited. In case of two-photon excitation, these atoms can be trapped on the dark state. When the collision rate is larger than the decay rate, a dual phenomenon occurs: fresh atoms may require a higher number of collisions to enter the interaction region, resulting in a destruction of the coherent trapping process: on the other hand, the VCCs may eventually allow CPT to survive due to the following: In the presence of large density of buffer gas, the VCCs process for sodium is Na(3p,c,)+M~Na(3p,ul)+M,
(2)
where ~1~is the component of velocity along the laser direction initially selected by laser excitation and US is the final velocity component after collision, and M is the collision partner. Because of the VCCs, all velocity groups of atoms in the above case can experience resonances, a reservoir is then not longer present in the system. Therefore, all velocity groups of atoms can be trapped to the dark state even in the presence of high buffer gas pressure. On the other hand, the VCCs depends very much on the mass of the colliding partner M. The heavier M, the more the amount of the atomic momentum changes along the laser beam direction. Higher collision numbers are needed to enter into the resonance for heavier buffer gases. Therefore, the dark resonance is destroyed more efficiently with heavier buffer gases than with light buffer gases, as shown in Fig. 5. This explanation is also supported by a hole burning experiment [ 131, showing that the redistribution of atomic velocities in a heavier buffer gas is less efficient than in a light buffer gas. Collisions with buffer gas atoms may not affect the
Letters A 248 (1998) 80-85
coherence between the Zeeman levels of the ground state from the interaction potential point of view, since the nuclear spin orientation involving the trap state is not significantly affected by the interaction potential between the two colliding partners [ 141. The experimental results showing that CPT still exists at high pressure of buffer gas are well consistent with the above explanations. Our results show that the line width of the dark resonance depends very much on the buffer gas pressure. The line width narrows sharply with the pressure of buffer gas in the range of lop4 to 60 Torr, and then tends slightly to a broadening at higher pressure. In absence of buffer gas the line width is mainly determined by the time-of-flight broadening. With increasing the buffer gas pressure, the time-of-flight can be prolonged by a reduction of the mean free path. The line width gets then narrower with increasing buffer gas pressure. The collisional narrowing of a line width can be traced back to the pioneer work of Dicke [ 151. On the other hand, the line width becomes also broadened due to the collisional broadening. Therefore, a balance between narrowing and broadening takes place at certain pressures. The collisional broadening will overcome the Dicke narrowing if the pressure is increased further. The present experimental result shown in Fig. 6 is in a good agreement with this explanation.
4. Summary An experiment aimed to study high buffer gas pressure perturbation of coherent population trapping in sodium vapors has been performed in a PDMS coated cell at room temperature. Two adjacent modes from a modulated three mode laser beam have been used as a light source for the establishment of CPT, derived by means of an intracavity mode selection technique in a commercial cw multimode dye laser. Specific Zeeman levels (IF = 2, MF = -2); IF = I, MF = - 1)) have been selected for preparing the coherent trapping effect. The purpose is evident that the population in these levels can be increased by optical pumping. We predict that the same results should be obtained if the symmetric pair (IF = 2, MF = 2); IF = 1, MF = I)) is chosen. The existence of the trapping effect even at a pressure over one atmosphere for helium confirms that optical pumping and velocity changing collisions
J.H. Xu. G. Alzettu/Plrysics
play key roles in preserving the CPT in presence of high buffer gas pressure. Heavier buffer gases can more efficiently destroy the dark resonance than light buffer gases. A pressure induced line width narrowing of the dark resonance is caused by collisions which prolongs the time atoms need to cross the laser beam. The present work can be applied to study not only the optical pumping induced but also the collision induced coherence transfer among different A systems. In a high magnetic field, the whole dark resonance spectra of the sodium atom have been obtained [ 161. When the optical pumping alters the population in different Zeeman levels of the ground state, the coherent trapping among the all dark resonances will be changed with changing buffer gas pressure. The dark lines intensity should also change if the collision induced coherence transfers population from one to another very close dark line. Since in case of the dark resonance the atomic medium has very small absorption and since CPT can resist at high pressure of buffer gas, the present study may have applications to open a window permitting light transmission in high pressure circumstances, for example, to some particular cases where absorption is a serious problem at a very long propagation length.
Acknowledgement This work was supported by the Italian Institute of Physics of Condensed matter (INFM). The authors wish to thank R. Bernheim for the critical reading of the manuscript. They also gratefully acknowledge the interest and encouragement of F. Bassani.
Letter.? A 2JR (1998) 80-85
85
References A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste. C. Cohen-Tannoudji, Phys. Rev. Lett. 61 ( 1988) 826; E. Korsunsky, D. Kosachiov. B Matisov, Yu. Rozhdestvensky. L. Windholz. C. Neureiter. Phys. Rev. A 48 (1993) 1419. O.A. Kocharovskaya, Ya.1. Khanin, Zh. Eksp. Teor. Fiz. 90 (1986) 1610. S.E. Harris, Phys. Rev. Lett. 62 (1989) 1033. A. Kasapi, Phys. Rev. Lett. 77 (1996) 1035. M. 0. Scully, Phys. Rev. Lett. 67 ( 1991 ) 1855. J.H. Xu. Ph.D. thesis, Scuola Normale Superiore, Piss, Italy (1994); D.E. Nikonov. U.W. Rather, M.O. Scully, S.Y. Zhu, ES. Fry, X. Li. G.G. Padmabandu, M. Fleischhauer, Quantum Opt. 6 (1994) 245; S. Ezekiel et al., J. Lightwave Technol. I3 ( 1995) 1189; S. Brandt. A. Nagel, R. Wynands,D. Meschde Phys. Rev. A 56 (1997) R1063. R.A. Bernheim, Optical Pumping - An Introduction (Benjamin, New York, 1965); W. Happer, Rev. Mod. Phys. 44 (1972) 169. J.H. Xu, A. Gozzini, F. Mango, G. Alzetta, R. Bemheim. Phys. Rev. A 54 ( 1996) 3146. G.G. Padmabandu, X. Li, C. Su. ES. Fry, D.E. Nikonov, S.Y. Zhu. G.M. Meyer, M.O. Scully, Quantum Opt. 6 (1994) 261. W. Maichen, F. Renzoni, 1. Mazets, E. Korsunsky. L. Windholz, Phys. Rev. A 53 ( 1996) 3444. G. Alzetta. A. Gozzini, L. Moi, G. Orriols, II Nuovo Cimento 36 (1976) 9. A. Gozzini, F. Mango, J.H. Xu, F. Maccarroni, G. Alzetta. R. Bernheim, 11 Nuovo Cimento ISD (1993) 709. F. Renzoni. L. Windholz, J.H. Xu, M. Elbel, Phys. Lett A 227 (1997) 357. E.R. Eliel, M.C. de Lignie. Laser Spectroscopy IX, M.S. Feld, J.E. Thomas, A. Mooradian, eds. (Academic Press, New York. 1989) p. 23. R.H. Dicke. Phys. Rev 89 (1953) 472. R. Holler, F. Renzoni, L. Windholz, J.H. Xu. J. Opt. Sot. Am. B 14 (1997) 2221.
1998
PHYSICS
LETTERS A
Physics Letters A 248 ( 1998) 80-85
High buffer gas pressure perturbation of coherent population trapping in sodium vapors J.H. Xu ‘, G. AIzettaa~b-’ a ScudaNormale Superiore and INFM. Piazza dei Cavalieri 7. 56126 PBa, Italy h Dipartimento di Fisica. Urriversitri di Pisu, Piazza Dante 1, 56126 Piss. It&
Received 20 May 1998; revised manuscript received 10 August 1998; accepted for publication Communicated
17 August
1998
by B. Fricke
Abstract We report an experimental investigation of coherent population trapping in specially selected Zeeman levels of the sodium atom, performed under high buffer gas pressure in a polydimethyisiloxane coated cell at room temperature. The results show that coherent population trapping will not be completely destroyed when the buffer gas pressure reaches 1100 Torr for He and 1000, 800, and 500 Torr, for Ne, Ar and Kr, respectively. Buffer gases with heavier mass play a larger destructive role for the coherent popuIation trapping. The line width of the dark resonance is reduced with buffer gas pressure. The behavior of the dark resonances on increasing buffer gas is discussed and possible applications are pointed out. @ 1998 Elsevier Science R.V. PAC.% 32.7O.C~; 32.80.Wr Kqwords: Coherent population
1.
trapping;
Velocity-changing
collisions;
Introduction
Recently, much attention has been given to the study of the coherent population trapping (CPT) of alkali atoms in a superposition state. This was mainly stimulated by many interesting applications based on this effect. Examples for such applications are laser cooling on the coherent state resulting in a tem~rature lower than the recoil limit [ 11, development of a nontraditional laser without population inversion [2,3], laser isotope separation [ 41, and enhancement of the index of refraction [ 51, etc. Many studies on the CPT have been pe~ormed in absence of collisions between atoms and buffer gases, such as in an atomic beam or ’ E-mail: hua~cmp.sns.it.
Optical pumping
in a cell under high vacuum. However, very few papers [ 61 considered the influence of buffer gas on the coherent population trapping effect. Actually, it is inteiesting to investigate CPT in the presence of high pressure buffer gases in order to understand better the perturbations of CPT caused by the buffer gases. This would, in turn, help us to develop new applications, for example, the enhancement of light propagation under collision dominated circumstances. In the present work we show how one can take advantage of optical pumping effects to increase the atomic population in proper selected Zeeman levels for an enhancement of caherent population trapping. It is well known [ ‘71 that optical pumping cannot only create but also maintain a nonequilibrium population in different magnetic sublevels of the ground state.
0375-9601/98/$ - see front matter @ 1998 Elsevier Science B.V. All rights reserved PII SO375-9601(98)00647-l
J.H. Xu, G. Aketta/Phwics
Since collisions with a diamagnetic gas do not change the atomic spin orientation in the ground states, they can be used to maintain a nonequilibrium distribution in some specific Zeeman levels. When the Zeeman levels of the ground state (IF = 2, M,G = -2); IF = 1, M,c = - 1) ) are selected, atomic population in these levels can be increased by buffer gas enhanced optical pumping effects, and thus the dark resonance, particularly at high pressure, is more pronounced. For sodium atoms, experiments are traditionally performed in a glass cell or a heat pipe oven with high temperature in order to produce an adequate atomic vapor density. In the present work, the experiment was performed at room temperature, that is, different from the traditional method. Thanks to the photoatomic effect [ 81, sodium vapors with high density and low velocity can be prepared in a polydimethylsiloxane (PDMS) coated cell at room or even much lower temperature. The last point to be mentioned is the coherent light source preparation. In a A configuration, two coherent radiation sources are needed for the CPT preparation. Usually, an acousto-optical modulator is used to create the second, frequency shifted light beam [ 91. That two first order sidebands are created from a single laser frequency by an electro-optical modulator is another way [ lo] for preparation of CPT by twophoton excitation. More simple, we used here just a commercial multimode (CR599) dye laser. Two coherent light frequencies were created using an intracavity mode selection method. We found this is a very reliable method satisfying the experimental requirements for observing CPT. Generally speaking, the way to produce CPT of sodium atoms in a three level A configuration is to apply two electromagnetic fields whose energy difference equals the difference between the two separated, low-lying electronic states. When this relative resonance is fulfilled, one finds that the transition probability between one of the superposition states of the two ground levels and the upper state becomes zero, i.e. a dark state is created. Even though the other superposition state is interacting with the upper excited state, all atoms can be accumulated in the dark state after several cycles of optical pumping. Under low magnetic fields, it is possible to select only one pair of Zeeman levels in the ground state for forming a A system. In our case, we used IF = 2. MF = -2)
------
Letters A 248 (1998) 80-85 MF=
-2
F=?
F=l
81
-1
I
2
---
F=2
F=l
0
L_-
Fig. I. Zeeman structure of sodium D I line. The pair (IF = ?,M,c = -2);IF = 1.k’~ = -1)) in the ground state is selected for coherent population trapping in a A configuration.
and IF = 1, M,c = -1) in the ground state as the pair of levels for CPT. One can see clearly from Fig. I that optical pumping can greatly enhance the population of this pair which is involved in the trapping state. In consequence, population trapping should not be destroyed too much due to the combination of collisional dephasing and increased optical pumping with increasing buffer gas pressure. In contrast, if other levels like IF = 2, MF = -1) and IF = 1. MF = 0) are selected, the population of these levels is decreased due to optical pumping. The consequence is evident that the trapping effect should be also decreased by optical pumping with increasing buffer gas pressure.
2. Experimental
results
The experimental setup for observing the dark resonance, similar to that of the first experimental observation [ 111, is shown schematically in Fig. 2. Sodium is contained in a glass cell coated with PDMS, connected directly to a vacuum system and to gas reservoirs, in order to study the perturbation of CPT by buffer gases at various pressures. The sodium vapor was prepared by the photo-atomic effect, instead of evaporation of sodium metal by thermal heating. The details of the preparation of the coated cell can be found elsewhere [ 121. The density of sodium vapour at room temperature can thus be up to 10” cmp3, produced by desorption with an extra laser at 514 nm, 200 mW. A gradient magnetic field Hh’ was applied to produce a weak Zeeman splitting of the sodium ground levels, in order to match the coherent resonance in a tiny range along the axis direction. Thus the phe-
82
J.H. Xu, G, Alzetta/F%ysics
Letters A 243 11998) 80-85
GAS FILLING
Fig. 2. Experimental setup for observation of the dark resonances at room temperature. C: PDMS coated celi containing sodium atoms connected to a vacuum system for buffer gases filling; H,: gradient magnetic held; H,,,: modulated magnetic field; laser beam tuned to the sodium DI line with (I- polarization: FP: Fabry-Perot interferometer; SA: spectrum analyzer to monitor the beat frequency: L: lens; MM: monochromator; DS: digitizing oscilloscope; and PL: plotter.
Fig. 3. Laser mode distribution in a multimode dye laser (the upper trace ); and laser mode selected by an intracavity etaion with a mode spacing of 6 x AZ! (the lower trace). Two adjacent modes were used for the coherent population trapping experiment.
----yx__
280
nomenon of transparency induced by CPT takes place in this tiny zone. An amplitude modulated magnetic field E&,,with a few G was used to scan the Zeeman splitting. This produces a scan of the position of the dark resonance along the magnetic field direction. A multimode dye laser was tuned to the Dt line of the sodium atom; (+- polarization was created by means of a h/4 plate. The axial mode spacing Ai\v of the laser with a cavity length d of 54 cm is c/2d = 277.7 MHz. An intracavity mode selection technique was used to create the frequencies needed for two photon excitation, by inserting an etalon into the laser cavity. Carefully adjusting the etalon, three strong modes spaced by 6 x Av, oscillating inside the gain profile, were obtained. These modes monitored by a FuboPer& interferometer are shown in Fig. 3. Modes occurring between the three strong modes were completely suppressed by mode competitions. The laser beam was tilted about 10 degree with respect to the magnetic field. The magnetic field axis was taken as the quantization axis. With respect to this axis all kinds of polarization (cr+ , CT-, T) are possible. Thus the beat frequency of 1665 MHz (6 x Av) can exactly match the specially selected resonance between the level IF = 2, MF = -2) in the 32Pr,2 excited state and the levels (/F = ~,MF = -2);lF = ~,MF = -I)) in the 3’St/a ground state of sodium at the magnetic field of 54 G. By modulating the weak magnetic field at 1.5 Hz, the black line is scanned along the direction of the magnetic field. The modulated black line signal was detected by a photomultiplier via a monochroma-
*I_.-.--
,
/._-“._._._-.-_‘-
._.^
i
20
Magnetic field
Fig. 4. A typical dark resonance of buffer gas.
spectrum
measured
in absence
tor, whose slit was set parallel to the black line which is orthogonal to the magnetic field direction. The signal was collected and averaged by a digitizing oscilloscope, and printed on a IBM colour plotter. We paid special attention to the behavior of CPT at high buffer gas pressure. The experiment was carried out up to the disappearance of the black line when increasing the buffer gas pressure. The laser intensity used for the experiment is 170 mW with a beam diameter of 1.5 mm. A typical dark resonance signal measured in absence of buffer gas is shown in Fig. 4. We define a contrast C to evaluate the dark resonance strength, c = LX, - Iti” I max + Li” ’
(1)
where Imnx and Z,,, are the maximum and minimum fluorescence intensity measured, respectively, at one side of the black line and inside the black line. The
J.H. Xu. G. Abettu/Physics
Letters A 248 (1998)
1.4 He Ne Ar Kr
n l
80-VA.
g
z g 5 0
’
.
60-
.
.
i
.
A .
.
40-
.
.
A .
0
,
.
1.0.
I 200
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b 0.6.
.
l
.
l
. 400
l
.
. *
0
.1
G 5 0.8-
.
20-
1.2
80-85
. I 600
*
I 800
’
. . I 1000
.
0.4 -
.
I 1200
0.2’1 0
I 20
I 40
I 60
P (Torr) Fig. 5. Dependence of the normalized dark resonance strengths on the pressure of various buffer gases.
contrast C is normalized to 1, when no buffer gas is present. The dark resonance strengths at different buffer gas pressures were thus evaluated and shown in Fig. 5. It was found that the dark resonance strength gets less pronounced with increasing buffer gas pressure but it can eventually survive up to a dramatic high value of buffer gas pressure: 1100 Torr of He. We also investigated the pressure dependence of the dark resonance intensity for other buffer gases: Ne, Ar and Kr at the same experimental conditions. We found that they cause a similar decay tendency but the limit pressure decreases from 1100 Torr of He to 1000 Torr of Ne, to 800 Tot-r of Ar and to 500 Torr of Kr, when increasing the mass of the buffer gas atoms. Moreover, the line width of the dark resonance gets narrower with increasing pressure of the buffer gas. The line width was calibrated [ 111 using Zeeman resonances produced by a weak radio frequency field at about 40 MHz. Results obtained with He as buffer gas are shown in Fig. 6. It is demonstrated that the line width of the dark resonance is reduced by buffer gas from 1.3 MHz to 0.4 MHz, when the pressure increases from 10e4 to 100 Torr.
3. Discussion The present experimental results show an evidence that the strength of dark resonance decreases very slowly when increasing the pressure, for all the buffer gases used. Consequently, the coherent dark state can be preserved at very high pressure of buffer gas. More-
.
. I 80
1
, 100
I 120
I 140
I 160
P (Torr) Fig. 6. The line width of the dark resonance reduced as a function of the pressure of helium gas.
over, buffer gas with heavier mass can more effective destroy the dark resonance. We are going to discuss these results in more detail. The destruction of the dark resonance due to buffer gas is reasonable because collisions dephase the coherence. But the decrease is surprisingly insensitive to the buffer gas pressure. This may be mainly caused by: (a) optical pumping increases the population of the levels involved in forming the coherent population trapping state; (b) velocity changing collisions (VCCs) increases the population of the levels involved in the two photon resonance. We should emphasize that the CPT configuration we selected is different from the one of Ref. [ 91. In our case, the Zeeman level pair (]F=~,MF=-2);lF=l,M~=-1))oftheground state is chosen for the dark resonance preparation. The population of this pair is increased by optical pumping effects which are enhanced by increasing the buffer gas pressure. Consequently, the coherent population trapping is then enhanced by the pressure enhanced optical pumping. On the other hand, the collisions induce a dephasing which decreases the coherent trapping present contemporaneously in the system. Therefore, the consequence is that the dark resonance is destroyed with increasing buffer gas pressure, but very slowly. In contrast, if another level pair, for example (IF = ~,MF = -1);IF = ~,MF = -l)), of the ground state is chosen for the dark resonance preparation, the population in these levels is decreased by optical pumping. As a result, the dark resonance is dramatically destroyed by the increase of optical pumping with increasing buffer gas, in addition to the col-
84
J.H. Xu. G. AIzettcr/Physics
lisional dephasing. This effect has been observed in Ref. [ 91 where the dark resonance is very sensitive to the presence of buffer gas. The dark resonance is completely destroyed at only 10 Torr of helium. Therefore it is so important to choose proper Zeeman levels allowing optical pumping effects to increase the population of the levels involved in CPT. In the case of velocity selective excitation using single mode laser light, only one velocity group of atoms can be in resonance. Therefore, only a small quantity of atoms can take part in the interaction process. Mostly the unexcited atoms can be considered as a reservoir. If the collision rate is smaller than the decay rate of the excitation, fresh atoms can easily transit into the interaction region and be excited. In case of two-photon excitation, these atoms can be trapped on the dark state. When the collision rate is larger than the decay rate, a dual phenomenon occurs: fresh atoms may require a higher number of collisions to enter the interaction region, resulting in a destruction of the coherent trapping process: on the other hand, the VCCs may eventually allow CPT to survive due to the following: In the presence of large density of buffer gas, the VCCs process for sodium is Na(3p,c,)+M~Na(3p,ul)+M,
(2)
where ~1~is the component of velocity along the laser direction initially selected by laser excitation and US is the final velocity component after collision, and M is the collision partner. Because of the VCCs, all velocity groups of atoms in the above case can experience resonances, a reservoir is then not longer present in the system. Therefore, all velocity groups of atoms can be trapped to the dark state even in the presence of high buffer gas pressure. On the other hand, the VCCs depends very much on the mass of the colliding partner M. The heavier M, the more the amount of the atomic momentum changes along the laser beam direction. Higher collision numbers are needed to enter into the resonance for heavier buffer gases. Therefore, the dark resonance is destroyed more efficiently with heavier buffer gases than with light buffer gases, as shown in Fig. 5. This explanation is also supported by a hole burning experiment [ 131, showing that the redistribution of atomic velocities in a heavier buffer gas is less efficient than in a light buffer gas. Collisions with buffer gas atoms may not affect the
Letters A 248 (1998) 80-85
coherence between the Zeeman levels of the ground state from the interaction potential point of view, since the nuclear spin orientation involving the trap state is not significantly affected by the interaction potential between the two colliding partners [ 141. The experimental results showing that CPT still exists at high pressure of buffer gas are well consistent with the above explanations. Our results show that the line width of the dark resonance depends very much on the buffer gas pressure. The line width narrows sharply with the pressure of buffer gas in the range of lop4 to 60 Torr, and then tends slightly to a broadening at higher pressure. In absence of buffer gas the line width is mainly determined by the time-of-flight broadening. With increasing the buffer gas pressure, the time-of-flight can be prolonged by a reduction of the mean free path. The line width gets then narrower with increasing buffer gas pressure. The collisional narrowing of a line width can be traced back to the pioneer work of Dicke [ 151. On the other hand, the line width becomes also broadened due to the collisional broadening. Therefore, a balance between narrowing and broadening takes place at certain pressures. The collisional broadening will overcome the Dicke narrowing if the pressure is increased further. The present experimental result shown in Fig. 6 is in a good agreement with this explanation.
4. Summary An experiment aimed to study high buffer gas pressure perturbation of coherent population trapping in sodium vapors has been performed in a PDMS coated cell at room temperature. Two adjacent modes from a modulated three mode laser beam have been used as a light source for the establishment of CPT, derived by means of an intracavity mode selection technique in a commercial cw multimode dye laser. Specific Zeeman levels (IF = 2, MF = -2); IF = I, MF = - 1)) have been selected for preparing the coherent trapping effect. The purpose is evident that the population in these levels can be increased by optical pumping. We predict that the same results should be obtained if the symmetric pair (IF = 2, MF = 2); IF = 1, MF = I)) is chosen. The existence of the trapping effect even at a pressure over one atmosphere for helium confirms that optical pumping and velocity changing collisions
J.H. Xu. G. Alzettu/Plrysics
play key roles in preserving the CPT in presence of high buffer gas pressure. Heavier buffer gases can more efficiently destroy the dark resonance than light buffer gases. A pressure induced line width narrowing of the dark resonance is caused by collisions which prolongs the time atoms need to cross the laser beam. The present work can be applied to study not only the optical pumping induced but also the collision induced coherence transfer among different A systems. In a high magnetic field, the whole dark resonance spectra of the sodium atom have been obtained [ 161. When the optical pumping alters the population in different Zeeman levels of the ground state, the coherent trapping among the all dark resonances will be changed with changing buffer gas pressure. The dark lines intensity should also change if the collision induced coherence transfers population from one to another very close dark line. Since in case of the dark resonance the atomic medium has very small absorption and since CPT can resist at high pressure of buffer gas, the present study may have applications to open a window permitting light transmission in high pressure circumstances, for example, to some particular cases where absorption is a serious problem at a very long propagation length.
Acknowledgement This work was supported by the Italian Institute of Physics of Condensed matter (INFM). The authors wish to thank R. Bernheim for the critical reading of the manuscript. They also gratefully acknowledge the interest and encouragement of F. Bassani.
Letter.? A 2JR (1998) 80-85
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