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The pressure-induced Hanle effect in fluorescence
Volume 59, number 3
OPTICS COMMUNICATIONS
1 September 1986
THE PRESSURE-INDUCED HANLE EFFECT IN FLUORESCENCE W. L A N G E
lnstitut fftr Quantenoptik der Universiti~tHannover, 3000 Hannover 1, Fed. Rep. Germany Received 17 April 1986
The existence of a pressure-induced Hante effect in fluorescence is shown in the case of the ISo-1Pl-transition (h = 553.5 nm) of Ba. In contrast to the corresponding collision-induced effect in degenerate 4-wave mixing, the effect is linear in the laser intensity. The relation to the conventional Hanle effect and unexpected signal features are discussed.
1. Introduction Within recent years there has been considerable interest in the phenomenon of pressure-induced extra resonances in 4-wave mixing (PIER 4). The exciting feature of the phenomenon lies in the fact that dephasing can help in creating coherence between atomic levels [1]. It has been noted that in the special case of degenerate 4-wave mixing (DFWM) a pressure-induced coherence between Zeeman levels can play a role [2]. By varying a magnetic field through zero a Hanle resonance can be observed. DFWM experiments involving a pressure-induced Hanle resonance in the excited state have been performed in Yb [3] and Ba [4,5] ; more recently a series o f beautiful experiments involving the ground state of sodium have been reported [6,7]. It has been mentioned in ref. [5] that the pressure° induced Zeeman coherence cannot only be detected in 4-wave mixing, but also in fluorescence; in this case the set-up is very similar to a conventional Hanle experiment and therefore the term "pressure-induced Hanle effect" has first been used in ref. [5]. Though some experimental material has been presented [5], the method does not seem to have generally been recognized until very recently a theoretical paper has predicted the existence of pressure-induced resonances in fluorescence spectroscopy [8]. That paper deals with excitation by modulated light, but it obviously includes the Hanle effect in the case of zero modulation frequency. In this paper I am going to
present more details on the experiment mentioned in ref. [5]. I am also going to discuss the relation between the pressure-induced form of the Hanle effect and its conventional counter-part. It will turn out that in the experiment novel physical effects play a role, which have not been considered in the theoretical treatment.
2. Theory The pressure-induced effects discussed here occur in 3-level systems either o f the v-type or the A-type; more complicated schemes can be reduced to these basic configurations. Here we will focus our attention on the v-type case (cf. fig. 1). I will restrict m y considerations to coherence between nearly degenerate Zeeman sublevels m and m ' coupled to a ground state g by a light field of the single frequency 6o detuned by A from the atomic resonance. IA I is assumed to be much larger than the splitting ~ between the sublevels and than the homogeneous linewidth. In the standard semiclassical perturbative treatment the pressure-induced effects can be pin-pointed in the second step o f the perturbation chain. In this step the density matrix of the excited state is given by p(2)
mm'
~ IEI2 (
a2
1+
7gm+Tgm'--"/mm'] m-7 Tff I
a(2) ~ 'EI2(A21 + 27grn--Tmm ~'mrn Tmm "1 '
(la) (lb) 243
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1 September 1986
state, however, is the observation of fluorescence. The corresponding contributions depend linearly on p(2) m m P and thus they depend linearly on the laser intensity via eq. (la). As a consequence there are no special requirements on the laser power. It should be emphasized that the signal varies with l/A2, when the detuning is changed, while there is a variation with l/A6 in a DFWM experiment. Therefore the fluorescence method may have advantages for large detunings and it has in fact been used for studying the breakdown of the impact approximation in ref. [5].
m #
m
:i: ° 60
Fig. 1. Energy level diagram for pressure-induced Hanle effect. 3. and a corresponding equation for p(2m)m,. Here E is the electric field of the light and it is assumed for simplicity that the effect of collisions can be incorporated into relaxation constants 7i1 describing the decay of p~.2). This implies the validity of the "impact approximation", i.e. it implies IA I% ~ 1 ; here r c characterizes the typical duration of a collision and is of the order of 1 ps. A more general discussion will be given elsewhere [9]. In the following we will use the assumptions Tgm = Tgm' = "}'opt= 1/2r + aoptP,
(2a)
Trnm' = Tm'm = Tcoh = 1/r + acohP ,
(2b)
Tram = Tm'm' = 3'pop = 1/7" + apopP.
(2c)
Here r is the radiative lifetime o f the excited state and p is the pressure of a buffer gas; the linear dependence of the relaxation constants is expected for binary collisions between the "active" atoms and atoms of the buffer gas being prevealing. It can be concluded that the second terms in the brackets of eqs. (la) and (lb) vanish for p = 0 and increase linearly with pressure for 2O~opt > aco h and small p; thus these terms are "pressurednduced". The first terms in the brackets are purely radiative. It is important to note that only the pressure induced term of the "Zeeman coherence" (2) ram' displays a Hanle resonance. The pressure-induced terms in O(2) give contributions to the nonlinear susceptibility X(3) and thus show up in DFWM. Therefore the methods of nonlinear optics provide means of observing the pressureinduced Hanle resonance. The classical meads of detecting stationary Zeeman coherence in the excited 244
Experimental
It should be clear by now that the experimental set-up needed for observing the pressure-induced Hanle effect in fluorescence is very similar to a con. ventional Hanle experiment. The only difference is that the light source is detuned with respect to the atomic resonance and that a buffer gas is added. ExperimentaUy these conditions are less favorable than the conventional case, of course. The principle of our experiment is shown in fig. 2. The active medium is Ba vapor contained in a heated stainless steel cell. The light source is a N2-1aser pumped dye laser; it was typically detuned by 1011 to 1012 Hz from the 1S0-1P 1 transition (X = 553.5 nm) in our experiments. The spectral width of the dye laser was in the order o f 109 Hz. Unfortunately there is, however, some "superradiant" broadband background
Pulsed Dye Laser Absorber P L2 PM
I"> holtz coils
Fig. 2. Experimental scheme. P: polarizer, A: analyzer, L 1 and L2: lenses, PM: photomultiplier.
Volume 59, number 3
OPTICS COMMUNICATIONS
in the power spectrum. Though the spectral density is less than 3 permiUe of the spectral density in the laser line, this background would have completely obscured the important features of the experiment, when large detunings were used. In order to get rid of any resonant components of the light field an absorption cell was placed between the dye laser and the fluorescence cell. The absorption cell contained Ba vapor in an argon atmosphere (p = 100 hPa) and weakened the resonant components of the radiation background by more than two orders of magnitude. A pair of Helmholtz coils modified according to Fanselau [10] in order to give increased homogenity produces a magnetic field perpendicular to the direction of the laser beam and of the observation. The polarizer P and the analyzer A between the Ba cell and the photomultiplier pass only light polarized perpendicularly to B. The distance between the cell and the photomultiplier was about 0.6 m in order to avoid an influence of the magnetic field on the sensitivity. In the experiment the reduction of sensitivity was <1 percent, when the full magnetic field was switched on. The pulse length of the dye laser was about 5 ns. It was longer than the decay time of the optical coherence 1/7opt and of the Zeeman coherence 1/Tcoh for a buffer gas pressure of more than about 20 hPa. The time constant of the multiplier was about 50 Vs. Thus the experiment, even though performed with a pulsed laser, was essentially a steady state experiment, with the exception of the low pressure range (r = 8.2 ns). The output pulse of the multiplier is fed to a sample-and-hold circuit (SH) suitably triggered in synchronism with the dye laser. The SH is used with a duty cycle of about 10 -3 and thus reduces the influence of the thermal radiation of the heated Ba cell (T ~ 1000 K). The output is digitized and averaged over many laser pulses by means of a small computer. The computer also controls the magnetic field, which was scanned from - 9 0 mT to +90 mT. The results of several scans of the magnetic field were averaged. The signal expected for the geometry of the experiment might easily be calculated from eqs. (la) and (lb). The description of the decay of the population by a single relaxation constant is oversimplified, however, and we have to distinguish between the decay of the average population of the excited state, described by 7 (0), and the decay of the "longitudinal alignment",
1 September 1986
I (a.u.)
AI
i
-80
r
-40
i
i
0
40
i
80
120
t
B (mT)
Fig. 3. Hanle resonance obtained with laser detuned by 2.5 X 10I1 rad/s to the red. Buffergas is argon (p = 25 hPa). The drawn line is a lorentzlan fit.
described by 3'(2) . The more detailed calculation [9] yields a result of the form I~
1 + A p (1/70 +B/72) -- Cp/("/coh 2 + ~22),
(3)
with definite predictions for A, B and C. The first term results from the purely radiative terms, the second term from the pressure4nduced population and the third term represents the pressure-induced Hanle effect. It should be kept in mind that 7(0), 3`(2) and 7coh increase with pressure; we can expect 3`(2) = 7coh. g~ is two times the Larmor frequency, since we have a Am = 2 coherence. A typical signal curve obtained for a detuned laser and with buffer gas added is displayed in fig. 3. The solid line represents a lorentzian fitted to the experimental result. It can be concluded that the signal curve can be represented by the sum of a contribution not depending on the magnetic field and an inverted lorentzian; the contributions can be characterized by the quantities/max, I0 and ZX/,resp., defined in the figure. The values o f I 0 and Imax obtained for different values of the buffer gas pressure are displayed in fig. 4 and fig. 5 for helium and argon, respectively. It can be concluded that I 0 and/max coincide in zero pressure, i.e. the amplitude ZX/of the lorentzian vanishes for p = 0. This indicates that the Hanle effect observed here is pressure-induced indeed. It was also verified that zM increases linearly with laser power. The width of the Hanle curves increases with in245
Volume 59, number 3
I (a.u,i
OPTICS COMMUNICATIONS
He
Imax
1
x
0.5
2 0
p(hPa)
Fig. 4. Pressure dependence of the detector signal for He. Upper curve: B = 90 mT, lower curve: B = 0. Laser was detuned by 3.1 X 1011 rad/s to the blue. Curves axe drawn for guiding the eye only.
creasing buffer gas pressure. Due to the poor signal-tonoise ratio the effect is not well-suited for studying the pressure dependence of 7coh. The experimental data are compatible, however, with eq. (2b), and we find for O~coh the values 25 + 8, 21 + 7, and 15 -+ 5 MHz/hPa for He, Ar, and Xe respectively. C%pt is ex-
imax
Ar
100
2£)0
D p(hPa)
Fig. 5. Pressure dependence of the detector signal for argon (details see fig. 4). 246
pected to be in the same order of magnitude. It is to be emphasized that the experimental resuits displayed here are obtained at very low particle densities (109 cm -3) and at fairly low laser powers ( < 800 W, beam diameter 5 mm). For increased particle densities the behaviour changes completely as discussed below.
4. Discussion
100
I (a.u.
1 September 1986
The experiment shows very clearly that the pressure-induced Hanle effect can be observed in fluorescence indeed, and that the shape of the Hanle resonance is lorentzian within the accuracy of the experiment. This fact may need some discussion. It is well-known that the normal Hanle effect [11] is obtained under conditions of "broad band excitation", i.e. I if the spectrum of the exciting light does not depend on frequency in the region of the atomic transition. More accurately the convolution of the excitation spectrum and the Doppler profile is the important quantity [ 12]. The lorentzian shapes can heavily be disturbed, if the condition of broad-band excitation is not fulfilled. Corresponding experiments have previously been performed by use of special incoherent illumination schemes [13] or by lasers [14, 15]. In these experiments the Doppler effect has been eliminated by using atomic beams and collisions did not play any role, of course. The experiments were in excellent agreement with theory, and it is well-established now that under collision-free conditions normal Hanle curves can be obtained by near resonant monochromatic laser excitation only due to inhomogeneous broadening. For excitation far outside the inhomogeneously broadened absorption curve, no Hanle effect exists in the configuration of fig. 1 as long as collisions are absent (p = 0); this is also seen in eq. (3). The physical process occurring is Rayleigh scattering in this case; the scattering process can be interpreted to be so fast that the interaction with the magnetic field can be neglected during the atom "virtually" being in the excited state. Obviously the Rayleigh scattering is described by the first term in eq. (3). In ref. [8] the spectrum of the fluorescence has not been discussed. It is quite evident, however, that for p = 0 the usual frequency distribution of the Rayleigh
Volume 59, number 3
OPTICS COMMUNICATIONS
component is found. On the other hand it is wellknown that a close connection exists between collisionally induced coherent signals and collisional redistribution [16,17]. The latter phenomenon can be attributed to atoms excited to the upper state by "optical collisions", i.e. by the combined action of the light field and a collision. The spontaneous emission of these atoms does not seem to depend on the way they are excited as long as the light field is weak. In eq. (3) the second term describes the contribution of atoms excited to level m and m' by optical collisions; it should be related to a resonant component in the fluorescence spectrum as a consequence of "real" population. We have shown in ref. [4], how the pressure induced Hanle resonance can be attributed to optical collisions; a detailed analysis has been performed [9]. I would like to add now the conjecture that the Hanle term in eq. (3) corresponds to the emission o f resonant light, i.e. I assume that the Zeeman coherence induced by optical collisions behaves in the same was as the population. This would imply that there is no fundamental difference between the Hanle effect excited by optical collisions and the Hanle effect induced by other incoherent processes like absorption of broadband radiation, electron impact or whatever, where excitation and fluorescence are independent processes. It would also imply, however, that the pressure-independent and the pressure-dependent contributions to the Zeeman coherence in eq. (1 a) are of different nature: The first term might be called '~¢irtual", the second "real". Obviously this conjecture needs theoretical and experimental treatment. In our experiment, however, there is some indication that the Hanle resonance corresponds to the emission of resonant light. If we increase the number density of the Ba atoms to a few 1011/cm 3, the sample is still completely transparent for a laser beam detuned by more than 1011 Hz from the resonance. It is nearly opaque, however, for resonant radiation. In the scattered light an "elastic" (Rayleigh) component would pass the vapor zone between the scattering region and the exit window in the direction of observation unattenuated. A resonant component would strongly be absorbed for increased number densities. If my conjecture is right, then the Hanle resonance, even though excited by off-resonant light, should vanish for increased
1 September 1986
number densities due to reabsorption and multiple scattering. In fact we see a continuous decrease of the ratio A//Ima x with increased particle density and cannot detect a Hanle resonance for number densities exceeding 1011/cm 3, if the laser power density is low. When the laser power density is increased, then the Hanle resonance recovers. This is well in agreement with my conjecture. In an intense light field the atoms will certainly not emit the undisturbed resonant frequency. Whatever the excitation mechanism, there will be a light shift of the atomic levels. At moderate power densities of I00 kW/cm 2 and detunings of IAI = 1011 Hz the light shift well exceeds the Doppler width in our experiment. Since there is no light shift in the region between the scattering region and the exit window, the effect of reabsorption would be reduced. The physical effects just mentioned certainly complicate a quantitative analysis of the experimental data. On the other hand it is my feeling that they might help to gain more insight into the physical mechanism of the "pressure induced Hanle effect".
Acknowledgements The author has the pleasure of thanking Prof. W. Hanle for illuminating discussions and critical questions. He also thanks Dr. A. Gierulski for experimental help in early stages of the experiment and Dr. R. Scholz for numerous discussions. Most of the measurements have been performed by A. Zuck. The work was supported by the Deutsche Forschungsgemeinschaft.
References [1] L.J. Rothberg and N. Bloembergen,Phys. Rev. A30 (1984) 820; L.J. Rothberg, in: Progressin optics, ed. E. Wolf (North Holland, in press) [2] G. Grynberg, Optics Comm. 38 (1981) 439. [3] R. Scholz, J. Mlynek, A. Gierulski and W. Lange, Appl. Phys. B28 (1982) 191. [4] R. Scholz, J. Mlynek and W. Lange, Phys. Rev. Lett. 51 (1983) 1761. [5] W. Lange, R. Scholz, A. Gierulski and J. Mlynek, in: Laser spectroscopyVI, eds. H.P. Weber and W. Liithy (Springer 1983).
247
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OPTICS COMMUNICATIONS
[6] N. Bloembergen, Y.H. Zou and L.J. Rothberg, Phys. Rev. Lett. 54 (1985) 186. [7] Y.H. Zou and N. Bloembergen, Phys. Rev. A 33 (1986) 1730. [8] G.S. Agrawal, Optics Comm. 57 (1986) 129. [9] R. Scholz and W. Lange, to be published. [10] G. Fanselau, Z. Phys. 54 (1929) 260. [11] W. Hanle, Naturwissenschaften 11 (1923)691. [12] G.W. Series, Proc. Phys. Soc. 89 (1966) 1017.
248
1 September 1986
[13] D. Lecler, R. Ostermann, W. Lange and J. Luther, J. de Phys. 36 (1975) 647. [14] W. Rasmussen, R. Schieder and H. Walther, Optics Comm. 12 (1974) 315. [15] H. Brand, W. Lange, J. Luther and B. Nottbeck, Optics Comm. 13 (1975) 286. [16] M. Dagenais, Phys. Rev. A 26 (1982) 869. [17] Y. Prior and A. Ben-Reuven, Phys. Rev. A 33 (1986) 2363.
OPTICS COMMUNICATIONS
1 September 1986
THE PRESSURE-INDUCED HANLE EFFECT IN FLUORESCENCE W. L A N G E
lnstitut fftr Quantenoptik der Universiti~tHannover, 3000 Hannover 1, Fed. Rep. Germany Received 17 April 1986
The existence of a pressure-induced Hante effect in fluorescence is shown in the case of the ISo-1Pl-transition (h = 553.5 nm) of Ba. In contrast to the corresponding collision-induced effect in degenerate 4-wave mixing, the effect is linear in the laser intensity. The relation to the conventional Hanle effect and unexpected signal features are discussed.
1. Introduction Within recent years there has been considerable interest in the phenomenon of pressure-induced extra resonances in 4-wave mixing (PIER 4). The exciting feature of the phenomenon lies in the fact that dephasing can help in creating coherence between atomic levels [1]. It has been noted that in the special case of degenerate 4-wave mixing (DFWM) a pressure-induced coherence between Zeeman levels can play a role [2]. By varying a magnetic field through zero a Hanle resonance can be observed. DFWM experiments involving a pressure-induced Hanle resonance in the excited state have been performed in Yb [3] and Ba [4,5] ; more recently a series o f beautiful experiments involving the ground state of sodium have been reported [6,7]. It has been mentioned in ref. [5] that the pressure° induced Zeeman coherence cannot only be detected in 4-wave mixing, but also in fluorescence; in this case the set-up is very similar to a conventional Hanle experiment and therefore the term "pressure-induced Hanle effect" has first been used in ref. [5]. Though some experimental material has been presented [5], the method does not seem to have generally been recognized until very recently a theoretical paper has predicted the existence of pressure-induced resonances in fluorescence spectroscopy [8]. That paper deals with excitation by modulated light, but it obviously includes the Hanle effect in the case of zero modulation frequency. In this paper I am going to
present more details on the experiment mentioned in ref. [5]. I am also going to discuss the relation between the pressure-induced form of the Hanle effect and its conventional counter-part. It will turn out that in the experiment novel physical effects play a role, which have not been considered in the theoretical treatment.
2. Theory The pressure-induced effects discussed here occur in 3-level systems either o f the v-type or the A-type; more complicated schemes can be reduced to these basic configurations. Here we will focus our attention on the v-type case (cf. fig. 1). I will restrict m y considerations to coherence between nearly degenerate Zeeman sublevels m and m ' coupled to a ground state g by a light field of the single frequency 6o detuned by A from the atomic resonance. IA I is assumed to be much larger than the splitting ~ between the sublevels and than the homogeneous linewidth. In the standard semiclassical perturbative treatment the pressure-induced effects can be pin-pointed in the second step o f the perturbation chain. In this step the density matrix of the excited state is given by p(2)
mm'
~ IEI2 (
a2
1+
7gm+Tgm'--"/mm'] m-7 Tff I
a(2) ~ 'EI2(A21 + 27grn--Tmm ~'mrn Tmm "1 '
(la) (lb) 243
Volume 59, number 3
OPTICS COMMUNICATIONS
1 September 1986
state, however, is the observation of fluorescence. The corresponding contributions depend linearly on p(2) m m P and thus they depend linearly on the laser intensity via eq. (la). As a consequence there are no special requirements on the laser power. It should be emphasized that the signal varies with l/A2, when the detuning is changed, while there is a variation with l/A6 in a DFWM experiment. Therefore the fluorescence method may have advantages for large detunings and it has in fact been used for studying the breakdown of the impact approximation in ref. [5].
m #
m
:i: ° 60
Fig. 1. Energy level diagram for pressure-induced Hanle effect. 3. and a corresponding equation for p(2m)m,. Here E is the electric field of the light and it is assumed for simplicity that the effect of collisions can be incorporated into relaxation constants 7i1 describing the decay of p~.2). This implies the validity of the "impact approximation", i.e. it implies IA I% ~ 1 ; here r c characterizes the typical duration of a collision and is of the order of 1 ps. A more general discussion will be given elsewhere [9]. In the following we will use the assumptions Tgm = Tgm' = "}'opt= 1/2r + aoptP,
(2a)
Trnm' = Tm'm = Tcoh = 1/r + acohP ,
(2b)
Tram = Tm'm' = 3'pop = 1/7" + apopP.
(2c)
Here r is the radiative lifetime o f the excited state and p is the pressure of a buffer gas; the linear dependence of the relaxation constants is expected for binary collisions between the "active" atoms and atoms of the buffer gas being prevealing. It can be concluded that the second terms in the brackets of eqs. (la) and (lb) vanish for p = 0 and increase linearly with pressure for 2O~opt > aco h and small p; thus these terms are "pressurednduced". The first terms in the brackets are purely radiative. It is important to note that only the pressure induced term of the "Zeeman coherence" (2) ram' displays a Hanle resonance. The pressure-induced terms in O(2) give contributions to the nonlinear susceptibility X(3) and thus show up in DFWM. Therefore the methods of nonlinear optics provide means of observing the pressureinduced Hanle resonance. The classical meads of detecting stationary Zeeman coherence in the excited 244
Experimental
It should be clear by now that the experimental set-up needed for observing the pressure-induced Hanle effect in fluorescence is very similar to a con. ventional Hanle experiment. The only difference is that the light source is detuned with respect to the atomic resonance and that a buffer gas is added. ExperimentaUy these conditions are less favorable than the conventional case, of course. The principle of our experiment is shown in fig. 2. The active medium is Ba vapor contained in a heated stainless steel cell. The light source is a N2-1aser pumped dye laser; it was typically detuned by 1011 to 1012 Hz from the 1S0-1P 1 transition (X = 553.5 nm) in our experiments. The spectral width of the dye laser was in the order o f 109 Hz. Unfortunately there is, however, some "superradiant" broadband background
Pulsed Dye Laser Absorber P L2 PM
I"> holtz coils
Fig. 2. Experimental scheme. P: polarizer, A: analyzer, L 1 and L2: lenses, PM: photomultiplier.
Volume 59, number 3
OPTICS COMMUNICATIONS
in the power spectrum. Though the spectral density is less than 3 permiUe of the spectral density in the laser line, this background would have completely obscured the important features of the experiment, when large detunings were used. In order to get rid of any resonant components of the light field an absorption cell was placed between the dye laser and the fluorescence cell. The absorption cell contained Ba vapor in an argon atmosphere (p = 100 hPa) and weakened the resonant components of the radiation background by more than two orders of magnitude. A pair of Helmholtz coils modified according to Fanselau [10] in order to give increased homogenity produces a magnetic field perpendicular to the direction of the laser beam and of the observation. The polarizer P and the analyzer A between the Ba cell and the photomultiplier pass only light polarized perpendicularly to B. The distance between the cell and the photomultiplier was about 0.6 m in order to avoid an influence of the magnetic field on the sensitivity. In the experiment the reduction of sensitivity was <1 percent, when the full magnetic field was switched on. The pulse length of the dye laser was about 5 ns. It was longer than the decay time of the optical coherence 1/7opt and of the Zeeman coherence 1/Tcoh for a buffer gas pressure of more than about 20 hPa. The time constant of the multiplier was about 50 Vs. Thus the experiment, even though performed with a pulsed laser, was essentially a steady state experiment, with the exception of the low pressure range (r = 8.2 ns). The output pulse of the multiplier is fed to a sample-and-hold circuit (SH) suitably triggered in synchronism with the dye laser. The SH is used with a duty cycle of about 10 -3 and thus reduces the influence of the thermal radiation of the heated Ba cell (T ~ 1000 K). The output is digitized and averaged over many laser pulses by means of a small computer. The computer also controls the magnetic field, which was scanned from - 9 0 mT to +90 mT. The results of several scans of the magnetic field were averaged. The signal expected for the geometry of the experiment might easily be calculated from eqs. (la) and (lb). The description of the decay of the population by a single relaxation constant is oversimplified, however, and we have to distinguish between the decay of the average population of the excited state, described by 7 (0), and the decay of the "longitudinal alignment",
1 September 1986
I (a.u.)
AI
i
-80
r
-40
i
i
0
40
i
80
120
t
B (mT)
Fig. 3. Hanle resonance obtained with laser detuned by 2.5 X 10I1 rad/s to the red. Buffergas is argon (p = 25 hPa). The drawn line is a lorentzlan fit.
described by 3'(2) . The more detailed calculation [9] yields a result of the form I~
1 + A p (1/70 +B/72) -- Cp/("/coh 2 + ~22),
(3)
with definite predictions for A, B and C. The first term results from the purely radiative terms, the second term from the pressure4nduced population and the third term represents the pressure-induced Hanle effect. It should be kept in mind that 7(0), 3`(2) and 7coh increase with pressure; we can expect 3`(2) = 7coh. g~ is two times the Larmor frequency, since we have a Am = 2 coherence. A typical signal curve obtained for a detuned laser and with buffer gas added is displayed in fig. 3. The solid line represents a lorentzian fitted to the experimental result. It can be concluded that the signal curve can be represented by the sum of a contribution not depending on the magnetic field and an inverted lorentzian; the contributions can be characterized by the quantities/max, I0 and ZX/,resp., defined in the figure. The values o f I 0 and Imax obtained for different values of the buffer gas pressure are displayed in fig. 4 and fig. 5 for helium and argon, respectively. It can be concluded that I 0 and/max coincide in zero pressure, i.e. the amplitude ZX/of the lorentzian vanishes for p = 0. This indicates that the Hanle effect observed here is pressure-induced indeed. It was also verified that zM increases linearly with laser power. The width of the Hanle curves increases with in245
Volume 59, number 3
I (a.u,i
OPTICS COMMUNICATIONS
He
Imax
1
x
0.5
2 0
p(hPa)
Fig. 4. Pressure dependence of the detector signal for He. Upper curve: B = 90 mT, lower curve: B = 0. Laser was detuned by 3.1 X 1011 rad/s to the blue. Curves axe drawn for guiding the eye only.
creasing buffer gas pressure. Due to the poor signal-tonoise ratio the effect is not well-suited for studying the pressure dependence of 7coh. The experimental data are compatible, however, with eq. (2b), and we find for O~coh the values 25 + 8, 21 + 7, and 15 -+ 5 MHz/hPa for He, Ar, and Xe respectively. C%pt is ex-
imax
Ar
100
2£)0
D p(hPa)
Fig. 5. Pressure dependence of the detector signal for argon (details see fig. 4). 246
pected to be in the same order of magnitude. It is to be emphasized that the experimental resuits displayed here are obtained at very low particle densities (109 cm -3) and at fairly low laser powers ( < 800 W, beam diameter 5 mm). For increased particle densities the behaviour changes completely as discussed below.
4. Discussion
100
I (a.u.
1 September 1986
The experiment shows very clearly that the pressure-induced Hanle effect can be observed in fluorescence indeed, and that the shape of the Hanle resonance is lorentzian within the accuracy of the experiment. This fact may need some discussion. It is well-known that the normal Hanle effect [11] is obtained under conditions of "broad band excitation", i.e. I if the spectrum of the exciting light does not depend on frequency in the region of the atomic transition. More accurately the convolution of the excitation spectrum and the Doppler profile is the important quantity [ 12]. The lorentzian shapes can heavily be disturbed, if the condition of broad-band excitation is not fulfilled. Corresponding experiments have previously been performed by use of special incoherent illumination schemes [13] or by lasers [14, 15]. In these experiments the Doppler effect has been eliminated by using atomic beams and collisions did not play any role, of course. The experiments were in excellent agreement with theory, and it is well-established now that under collision-free conditions normal Hanle curves can be obtained by near resonant monochromatic laser excitation only due to inhomogeneous broadening. For excitation far outside the inhomogeneously broadened absorption curve, no Hanle effect exists in the configuration of fig. 1 as long as collisions are absent (p = 0); this is also seen in eq. (3). The physical process occurring is Rayleigh scattering in this case; the scattering process can be interpreted to be so fast that the interaction with the magnetic field can be neglected during the atom "virtually" being in the excited state. Obviously the Rayleigh scattering is described by the first term in eq. (3). In ref. [8] the spectrum of the fluorescence has not been discussed. It is quite evident, however, that for p = 0 the usual frequency distribution of the Rayleigh
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component is found. On the other hand it is wellknown that a close connection exists between collisionally induced coherent signals and collisional redistribution [16,17]. The latter phenomenon can be attributed to atoms excited to the upper state by "optical collisions", i.e. by the combined action of the light field and a collision. The spontaneous emission of these atoms does not seem to depend on the way they are excited as long as the light field is weak. In eq. (3) the second term describes the contribution of atoms excited to level m and m' by optical collisions; it should be related to a resonant component in the fluorescence spectrum as a consequence of "real" population. We have shown in ref. [4], how the pressure induced Hanle resonance can be attributed to optical collisions; a detailed analysis has been performed [9]. I would like to add now the conjecture that the Hanle term in eq. (3) corresponds to the emission o f resonant light, i.e. I assume that the Zeeman coherence induced by optical collisions behaves in the same was as the population. This would imply that there is no fundamental difference between the Hanle effect excited by optical collisions and the Hanle effect induced by other incoherent processes like absorption of broadband radiation, electron impact or whatever, where excitation and fluorescence are independent processes. It would also imply, however, that the pressure-independent and the pressure-dependent contributions to the Zeeman coherence in eq. (1 a) are of different nature: The first term might be called '~¢irtual", the second "real". Obviously this conjecture needs theoretical and experimental treatment. In our experiment, however, there is some indication that the Hanle resonance corresponds to the emission of resonant light. If we increase the number density of the Ba atoms to a few 1011/cm 3, the sample is still completely transparent for a laser beam detuned by more than 1011 Hz from the resonance. It is nearly opaque, however, for resonant radiation. In the scattered light an "elastic" (Rayleigh) component would pass the vapor zone between the scattering region and the exit window in the direction of observation unattenuated. A resonant component would strongly be absorbed for increased number densities. If my conjecture is right, then the Hanle resonance, even though excited by off-resonant light, should vanish for increased
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number densities due to reabsorption and multiple scattering. In fact we see a continuous decrease of the ratio A//Ima x with increased particle density and cannot detect a Hanle resonance for number densities exceeding 1011/cm 3, if the laser power density is low. When the laser power density is increased, then the Hanle resonance recovers. This is well in agreement with my conjecture. In an intense light field the atoms will certainly not emit the undisturbed resonant frequency. Whatever the excitation mechanism, there will be a light shift of the atomic levels. At moderate power densities of I00 kW/cm 2 and detunings of IAI = 1011 Hz the light shift well exceeds the Doppler width in our experiment. Since there is no light shift in the region between the scattering region and the exit window, the effect of reabsorption would be reduced. The physical effects just mentioned certainly complicate a quantitative analysis of the experimental data. On the other hand it is my feeling that they might help to gain more insight into the physical mechanism of the "pressure induced Hanle effect".
Acknowledgements The author has the pleasure of thanking Prof. W. Hanle for illuminating discussions and critical questions. He also thanks Dr. A. Gierulski for experimental help in early stages of the experiment and Dr. R. Scholz for numerous discussions. Most of the measurements have been performed by A. Zuck. The work was supported by the Deutsche Forschungsgemeinschaft.
References [1] L.J. Rothberg and N. Bloembergen,Phys. Rev. A30 (1984) 820; L.J. Rothberg, in: Progressin optics, ed. E. Wolf (North Holland, in press) [2] G. Grynberg, Optics Comm. 38 (1981) 439. [3] R. Scholz, J. Mlynek, A. Gierulski and W. Lange, Appl. Phys. B28 (1982) 191. [4] R. Scholz, J. Mlynek and W. Lange, Phys. Rev. Lett. 51 (1983) 1761. [5] W. Lange, R. Scholz, A. Gierulski and J. Mlynek, in: Laser spectroscopyVI, eds. H.P. Weber and W. Liithy (Springer 1983).
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[6] N. Bloembergen, Y.H. Zou and L.J. Rothberg, Phys. Rev. Lett. 54 (1985) 186. [7] Y.H. Zou and N. Bloembergen, Phys. Rev. A 33 (1986) 1730. [8] G.S. Agrawal, Optics Comm. 57 (1986) 129. [9] R. Scholz and W. Lange, to be published. [10] G. Fanselau, Z. Phys. 54 (1929) 260. [11] W. Hanle, Naturwissenschaften 11 (1923)691. [12] G.W. Series, Proc. Phys. Soc. 89 (1966) 1017.
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[13] D. Lecler, R. Ostermann, W. Lange and J. Luther, J. de Phys. 36 (1975) 647. [14] W. Rasmussen, R. Schieder and H. Walther, Optics Comm. 12 (1974) 315. [15] H. Brand, W. Lange, J. Luther and B. Nottbeck, Optics Comm. 13 (1975) 286. [16] M. Dagenais, Phys. Rev. A 26 (1982) 869. [17] Y. Prior and A. Ben-Reuven, Phys. Rev. A 33 (1986) 2363.