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Photon echo relaxation in caesium perturbed by noble gases
PHOTON ECHO RELAXATION A.V. DURR4NT Department
15 March 1984
OPTICS COMMUNICATIONS
Volume 49, number 4
IN CAESIUM PERTURBED
BY NOBLE GASES
and J. MANNERS
of Physics, The Open University, Milton Keynes MK 7 6.44,
UK
Received 14 December 1983
The collisional rela?iation of photon echoes generated on the 6s 1,2 -7Pa,, (455 nm) transition in caesium has been observed and measured as a function of perturber pressure. Values for the collision cross-sections have been obtained using helium, neon, argon and krypton as perturbers. There is good agreement between these results and those obtained from high resolution measurements of pressure-broadened line profiles. The echoes were observed using the polarization rotation technique and all the measurements were made at perturber pressures below 0.5 torr.
1. Introduction echoes can be used to make Doppler free measurements of collisional relaxation parameters of atomic states at low perturber pressures, typically less than 1 torr. The case of sodium perturbed by noble gases has been studied extensively in recent years using a variety of echo phenomena, and cross-sections for optical phase destruction have been measured for the first resonance transition [ I] and for transitions involving highly excited states including some electricdipole forbidden transitions [2]. Velocity changing cross-sections have also been measured in sodium [3] and lithium [4] perturbed by helium. We have measured the relaxation rates of photon echoes on the second resonance transition in caesium (6S1,2-7P3,2, 455 nm) perturbed by helium, neon, argon and krypton at pressures of less than 0.5 torr. Our results agree well with the cross-sections for helium, neon and argon perturbers obtained from high resolution, pressure-broadened line proftie measurements in absorption [5,6] and emission [7]. No high resolution results for krypton exist. Our experimental technique makes use of the echo polarisation rotation which takes place in a magnetic field [8,9]. The sample is placed between crossed polarizers which discriminate against the laser excitation pulses but allow the polarisation-rotated echo pulse to pass. This removes the need for fast electro-optical shutters, Photon
0 030-4018/84/$03.00 0 Elsevier Science publishers B.V. (NorthiHolland Physics Publishing Division)
thus greatly simplifying the experiment. The collision cross sections can be derived from the measured photon echo relaxation rates in the following manner. Suppose the sample is excited by two collinear resonant pulses separated by an interval 7, so that the echo appears at a time 27 after the first pulse. Since the echo is a coherent effect in which the amplitudes of the radiating atoms add, its intensity is proportional to f12 where n is the number of radiating atoms, If collisions remove radiating atoms from the coherent emission process at a rate l% during the period 27, then the echo intensity will be reduced by a factor exp(-4I’T). In the case of collisions with foreign gas atoms of number density N then r = Nor where u is the collision cross-section and U is the average relative speed of colliding atoms. Using the ideal gas law we can relate N to the perturber pressure p and temperature T, and obtain for the echo intensity ,
1 a exp(-rlpT) with r) = 4uF/(kT)
.
(1)
77is generally referred to as the collisional relaxation parameter [2]. Q is obtained directly in our experiments by measuring I as a function of perturber pressure p at fixed pulse delay time 7, and the crosssection 0 is then found by using (1) with 293
U = (8kT/np)1/2
,
where y is the reduced mass of the colliding atoms.
2. Experimental
15 March 1984
OPTICS COMMUNICATIONS
Volume 49, number 4
arrangement
Fig. 1 shows a block diagram of the experiment. The Mole&on nitrogen laser pumped dye laser produces optical pulses of 7 ns duration and peak power of 25 kW at a repetition rate of up to 50 Hz. The spectral bandwidth of the laser is about 1 GHz which easily resolves the two hyperfine components of the 6S,/2 Cs ground state which are separated by 9 GHz. The hyperfine components of the 7P,,2 excited state span about 200 MHz and therefore cannot be resolved. In our experiments the laser was tuned to the transition from the F = 3 hyperfine component of the ground state. The optimum conditions for echo production require that the pulse areas of the first and second laser pulses be 7r/2 and 71respectively. To achieve this the beam from the dye laser was expanded to an area of -5 mm2 and then split in the intensity ratio 1 : 4. The more intense beam was guided through an optical delay and then returned and recombined with the undelayed beam to give two collinear excitation pulses separated in time by 32.5 ns. This delay, which is kept fixed during the experiment, is about a quarter of the excited 7P3j2 state lifetime. The two pulses were then linearly polarised by a calcite prism polariser, P, before passing into the
30 cm long stainless steel oven which contained a few grams of caesium. The oven was connected to an oil diffusion pump vacuum system and also to the source of perturber gas. The Helmholz coils could produce a longitudinal magnetic field of up to 30 G along the central 10 cm length of the oven. This region was warmed to 45°C to establish a working caesium vapour pressure of order 10V5 torr. At this vapour pressure caesium-caesium collisions occur at a negligible rate. For most of the experiments the magnetic field was kept below about 9G. This produces negligible Faraday rotation of the excitation pulses but causes the linear polarisation of the radiating atoms to precess about the field direction during the period between the first pulse and the echo time, and so allows a component of the echo to pass the analyser, A. The modulations or quantum beats which can be observed in the echo intensity as a function of magnetic field have been studied elsewhere [8,9]. With this arrangement three pulses emerged from the analysing prism, the two excitation pulses reduced in intensity by a factor of about lo6 (the extinction ratio of the crossed polariser analyser pair) and the echo pulse of roughly the same intensity as these, about lo7 photons per pulse in the absence of collisional relaxation. The pulses were then guided to a fast linear focused photomultiplier tube (EM1 type 9826B) housed in a light-tight metal box as a precaution against stray scattered laser light. The photomultiplier tube output was passed to a Brookdeal linear gate type 9415. The gate was open-
delay line
H
photomultiplier
photodiode
Fig. 1. Experimental arrangement.
294
4
Volume 49, number 4
OPTICS COMMUNICATIONS
ed at the echo time by a reference pulse, 25 ns wide, obtained from a pulse shaping and delay circuit triggered by a photodiode placed in a reflected laser beam. The gated echo signals were averaged by the linear gate with a time constant set at 3s or 10s. With the laser repetition rate at 30 Hz the output from the linear gate therefore represented an average over several hundred echo pulses. This output was sent to the Y input of an X-Y recorder. The X input was taken from the Baratron MKS capacitance manometer which measured the absolute perturber pressure in the oven to within 2%. The perturber gas was allowed to leak slowly into the oven to a pressure of about 0.4 torr over a period of 5 to 8 minutes, and during this time the recorder pen traced out the averaged echo intensity down to about eh4 of its initial value. As a precaution against the effects of laser intensity and frequency drift the echo intensity was recorded at the end of each run after evacuating the perturbing gas from the oven. The traces were kept for analysis only if the echo intensity returned to within 5% of its initial value. The linearity of the detecting and recording systems was checked using neutral density filters and found to be better than 5% over the working range used. The echo relaxation rates were found to be independent of the fixed value of the magnetic field over the range 5-30C to within the accuracy of our measurements.
3. Results and discussion Fig. 2 shows a typical log plot of the echo intensity against perturber pressure. In all cases the first 10 or 20 seconds of the trace were ignored because of the transient distorting effects of the time constant of the linear gate. Since the zero echo intensity level was difficult to establish accurately, it was treated as an adjustable parameter in order to obtain the best straight line fit to the data. The collisional relaxation parameter, n, was obtained from the measured gradient of the log plot. The values of 77listed in table 1 represent the mean and rms deviations from the mean for a large number (-15) of runs. The cross-sections listed were calculated using eq. (1) with T = 3 18 + 10 K. The largest contribution to the errors comes from the rms deviation quoted for 77.We have also included the 3% uncer-
A.
‘a
15 March 1984
0.1 Argon pressure (torr)
0.2
+
Fig. 2. A typical log plot of echo intensity against argon pressure.
tainty in the oven temperature T and the 2% uncertainty in the pressure reading of the Baratron manometer as quoted by the manufacturer. Shown also in table 1 are the results for He, Ne and Ar obtained by other workers as reported in ref. [lo]. These results were obtained from the measured pressure broadening constants using high resolution line profile measurements at low pressures of perturber. Our results however are the first to be obtained directly at pressures below 0.5 torr. It can be seen that even after allowing for a T II5 temperature variation of the cross-sections, corresponding to a van der Waals potential, our results are in good agreement with those of Ch’en et al. [7], Rostas and Lemaire [5] and Smith [6], but disagree substantially with those of Evdokimov [ 1 I]. The question arises as to whether the pressure induced relaxation of the echo which we have measured is due to exactly the same mechanisms as those which produce line broadening. In the case of caesium the fine structure splitting of the ~Ps/~ rj2 levels is quite large and the collisional transfer of’population between these levels by noble gases is known to be very small [10,12], and so the line broadening is almost entirely due to phase destroying collisions. 295
Volume 49, number 4
OPTICS COMMUNICATIONS
15 March 1984
Table 1 Collisional relaxation parameters n and collisional cross sections o for the caesium 6Sr ,* -7P,,2 Perturoer
~$(10-~ torr second)-r
o/A2
T/K
Ref.
helium
6.81 f 0.35
neon
3.17 f 0.17 5.86 f 0.30
318 380 400 318 400 318 380 363 400 400 318
our work 151 [Ill our work
argon
426 f 26 442* 51 1105 * 49 421 * 28 439 t 27 65 1029t 1046 f 108 1055 zr 132 1142k 22 1200 zr 250 1267 f 82
krypton
5.57 f 0.30
It seems likely that this is also the dominant mechanism in photon echo relaxation. It is known however that velocity changing collisions can play a role in photon echo relaxation when atoms of small mass are observed with long delay times, and the cases of sodium and lithium have been studied [3,4]. The effect however is expected to be very small for a heavy radiator such as caesium in our experiment. Finally it should be mentioned that the depolarising crosssection for the caesium 7P3/2 state is also quite large, of order 300 A2 for Ar [lo]. Although most photon echo experiments use an analysing prism, in a Pockels cell shutter or for other reasons, the role of depolarising collisions is never considered, presumably because it is assumed that collisions which are close enough to cause depolarisation will also destroy the optical phase. The fact that our measured crosssections are if anything slightly smaller than those measured from line broadening suggest that collision mechanisms other than phase destruction play little role in our experiment. The present work has shown the polarisation rotation technique for echo detection to be a useful and reliable method for investigating atomic relaxation processes, and we plan to continue with this work.
296
transition perturbed by nobel gases
161 our work ]51 171 ]61 [ill our work
We gratefully acknowledge the SERC.
financial support from
References [ l] A. Flusberg, T. Mossberg and S.R. Hartmann, Optics Comm. 24 (1978) 207. (21 A. Flusberg, R. Kachru, T. Mossberg and S.R. Hartmann, Phys. Rev. Al9 (1979) 1607. [ 31 T.W. Mossberg, R. Kachru and S.R. Hartmann, Phys. Rev. Lett. 44 (1980) 73. [4] R. Kachru, T.J. Chen and S.R. Hartmann, Phys. Rev. Lett. 47 (1981) 902. [5] F. Rostas and J.L. Lemaire, J. Phys. B: Atom. Molec. Phys. 4 (1971) 555. [6] G. Smith, J. Phys. B: Atom. Molec. Phys. 8 (1975) 2273. [ 71 S.Y. Ch’en, E.L. Lewis and D.N. Stacey, J. Phys. B: Atom. Molec. Phys. 2 (1969) 274. [8] T. Baer and I.D. Abella,Phys. Rev. Al6 (1977) 2093. [9] S. Aoki, Phys. Rev. A20 (1979) 2013. [lo] E.L. Lewis, Physics Reports 58, No. l(l980) 1-71. [ll] Y.V. Evdokimov, Opt. and Spectr. 24 (1968) 448. [12] L. Krause, Appl. Optics 5 (1966) 1375.
15 March 1984
OPTICS COMMUNICATIONS
Volume 49, number 4
IN CAESIUM PERTURBED
BY NOBLE GASES
and J. MANNERS
of Physics, The Open University, Milton Keynes MK 7 6.44,
UK
Received 14 December 1983
The collisional rela?iation of photon echoes generated on the 6s 1,2 -7Pa,, (455 nm) transition in caesium has been observed and measured as a function of perturber pressure. Values for the collision cross-sections have been obtained using helium, neon, argon and krypton as perturbers. There is good agreement between these results and those obtained from high resolution measurements of pressure-broadened line profiles. The echoes were observed using the polarization rotation technique and all the measurements were made at perturber pressures below 0.5 torr.
1. Introduction echoes can be used to make Doppler free measurements of collisional relaxation parameters of atomic states at low perturber pressures, typically less than 1 torr. The case of sodium perturbed by noble gases has been studied extensively in recent years using a variety of echo phenomena, and cross-sections for optical phase destruction have been measured for the first resonance transition [ I] and for transitions involving highly excited states including some electricdipole forbidden transitions [2]. Velocity changing cross-sections have also been measured in sodium [3] and lithium [4] perturbed by helium. We have measured the relaxation rates of photon echoes on the second resonance transition in caesium (6S1,2-7P3,2, 455 nm) perturbed by helium, neon, argon and krypton at pressures of less than 0.5 torr. Our results agree well with the cross-sections for helium, neon and argon perturbers obtained from high resolution, pressure-broadened line proftie measurements in absorption [5,6] and emission [7]. No high resolution results for krypton exist. Our experimental technique makes use of the echo polarisation rotation which takes place in a magnetic field [8,9]. The sample is placed between crossed polarizers which discriminate against the laser excitation pulses but allow the polarisation-rotated echo pulse to pass. This removes the need for fast electro-optical shutters, Photon
0 030-4018/84/$03.00 0 Elsevier Science publishers B.V. (NorthiHolland Physics Publishing Division)
thus greatly simplifying the experiment. The collision cross sections can be derived from the measured photon echo relaxation rates in the following manner. Suppose the sample is excited by two collinear resonant pulses separated by an interval 7, so that the echo appears at a time 27 after the first pulse. Since the echo is a coherent effect in which the amplitudes of the radiating atoms add, its intensity is proportional to f12 where n is the number of radiating atoms, If collisions remove radiating atoms from the coherent emission process at a rate l% during the period 27, then the echo intensity will be reduced by a factor exp(-4I’T). In the case of collisions with foreign gas atoms of number density N then r = Nor where u is the collision cross-section and U is the average relative speed of colliding atoms. Using the ideal gas law we can relate N to the perturber pressure p and temperature T, and obtain for the echo intensity ,
1 a exp(-rlpT) with r) = 4uF/(kT)
.
(1)
77is generally referred to as the collisional relaxation parameter [2]. Q is obtained directly in our experiments by measuring I as a function of perturber pressure p at fixed pulse delay time 7, and the crosssection 0 is then found by using (1) with 293
U = (8kT/np)1/2
,
where y is the reduced mass of the colliding atoms.
2. Experimental
15 March 1984
OPTICS COMMUNICATIONS
Volume 49, number 4
arrangement
Fig. 1 shows a block diagram of the experiment. The Mole&on nitrogen laser pumped dye laser produces optical pulses of 7 ns duration and peak power of 25 kW at a repetition rate of up to 50 Hz. The spectral bandwidth of the laser is about 1 GHz which easily resolves the two hyperfine components of the 6S,/2 Cs ground state which are separated by 9 GHz. The hyperfine components of the 7P,,2 excited state span about 200 MHz and therefore cannot be resolved. In our experiments the laser was tuned to the transition from the F = 3 hyperfine component of the ground state. The optimum conditions for echo production require that the pulse areas of the first and second laser pulses be 7r/2 and 71respectively. To achieve this the beam from the dye laser was expanded to an area of -5 mm2 and then split in the intensity ratio 1 : 4. The more intense beam was guided through an optical delay and then returned and recombined with the undelayed beam to give two collinear excitation pulses separated in time by 32.5 ns. This delay, which is kept fixed during the experiment, is about a quarter of the excited 7P3j2 state lifetime. The two pulses were then linearly polarised by a calcite prism polariser, P, before passing into the
30 cm long stainless steel oven which contained a few grams of caesium. The oven was connected to an oil diffusion pump vacuum system and also to the source of perturber gas. The Helmholz coils could produce a longitudinal magnetic field of up to 30 G along the central 10 cm length of the oven. This region was warmed to 45°C to establish a working caesium vapour pressure of order 10V5 torr. At this vapour pressure caesium-caesium collisions occur at a negligible rate. For most of the experiments the magnetic field was kept below about 9G. This produces negligible Faraday rotation of the excitation pulses but causes the linear polarisation of the radiating atoms to precess about the field direction during the period between the first pulse and the echo time, and so allows a component of the echo to pass the analyser, A. The modulations or quantum beats which can be observed in the echo intensity as a function of magnetic field have been studied elsewhere [8,9]. With this arrangement three pulses emerged from the analysing prism, the two excitation pulses reduced in intensity by a factor of about lo6 (the extinction ratio of the crossed polariser analyser pair) and the echo pulse of roughly the same intensity as these, about lo7 photons per pulse in the absence of collisional relaxation. The pulses were then guided to a fast linear focused photomultiplier tube (EM1 type 9826B) housed in a light-tight metal box as a precaution against stray scattered laser light. The photomultiplier tube output was passed to a Brookdeal linear gate type 9415. The gate was open-
delay line
H
photomultiplier
photodiode
Fig. 1. Experimental arrangement.
294
4
Volume 49, number 4
OPTICS COMMUNICATIONS
ed at the echo time by a reference pulse, 25 ns wide, obtained from a pulse shaping and delay circuit triggered by a photodiode placed in a reflected laser beam. The gated echo signals were averaged by the linear gate with a time constant set at 3s or 10s. With the laser repetition rate at 30 Hz the output from the linear gate therefore represented an average over several hundred echo pulses. This output was sent to the Y input of an X-Y recorder. The X input was taken from the Baratron MKS capacitance manometer which measured the absolute perturber pressure in the oven to within 2%. The perturber gas was allowed to leak slowly into the oven to a pressure of about 0.4 torr over a period of 5 to 8 minutes, and during this time the recorder pen traced out the averaged echo intensity down to about eh4 of its initial value. As a precaution against the effects of laser intensity and frequency drift the echo intensity was recorded at the end of each run after evacuating the perturbing gas from the oven. The traces were kept for analysis only if the echo intensity returned to within 5% of its initial value. The linearity of the detecting and recording systems was checked using neutral density filters and found to be better than 5% over the working range used. The echo relaxation rates were found to be independent of the fixed value of the magnetic field over the range 5-30C to within the accuracy of our measurements.
3. Results and discussion Fig. 2 shows a typical log plot of the echo intensity against perturber pressure. In all cases the first 10 or 20 seconds of the trace were ignored because of the transient distorting effects of the time constant of the linear gate. Since the zero echo intensity level was difficult to establish accurately, it was treated as an adjustable parameter in order to obtain the best straight line fit to the data. The collisional relaxation parameter, n, was obtained from the measured gradient of the log plot. The values of 77listed in table 1 represent the mean and rms deviations from the mean for a large number (-15) of runs. The cross-sections listed were calculated using eq. (1) with T = 3 18 + 10 K. The largest contribution to the errors comes from the rms deviation quoted for 77.We have also included the 3% uncer-
A.
‘a
15 March 1984
0.1 Argon pressure (torr)
0.2
+
Fig. 2. A typical log plot of echo intensity against argon pressure.
tainty in the oven temperature T and the 2% uncertainty in the pressure reading of the Baratron manometer as quoted by the manufacturer. Shown also in table 1 are the results for He, Ne and Ar obtained by other workers as reported in ref. [lo]. These results were obtained from the measured pressure broadening constants using high resolution line profile measurements at low pressures of perturber. Our results however are the first to be obtained directly at pressures below 0.5 torr. It can be seen that even after allowing for a T II5 temperature variation of the cross-sections, corresponding to a van der Waals potential, our results are in good agreement with those of Ch’en et al. [7], Rostas and Lemaire [5] and Smith [6], but disagree substantially with those of Evdokimov [ 1 I]. The question arises as to whether the pressure induced relaxation of the echo which we have measured is due to exactly the same mechanisms as those which produce line broadening. In the case of caesium the fine structure splitting of the ~Ps/~ rj2 levels is quite large and the collisional transfer of’population between these levels by noble gases is known to be very small [10,12], and so the line broadening is almost entirely due to phase destroying collisions. 295
Volume 49, number 4
OPTICS COMMUNICATIONS
15 March 1984
Table 1 Collisional relaxation parameters n and collisional cross sections o for the caesium 6Sr ,* -7P,,2 Perturoer
~$(10-~ torr second)-r
o/A2
T/K
Ref.
helium
6.81 f 0.35
neon
3.17 f 0.17 5.86 f 0.30
318 380 400 318 400 318 380 363 400 400 318
our work 151 [Ill our work
argon
426 f 26 442* 51 1105 * 49 421 * 28 439 t 27 65 1029t 1046 f 108 1055 zr 132 1142k 22 1200 zr 250 1267 f 82
krypton
5.57 f 0.30
It seems likely that this is also the dominant mechanism in photon echo relaxation. It is known however that velocity changing collisions can play a role in photon echo relaxation when atoms of small mass are observed with long delay times, and the cases of sodium and lithium have been studied [3,4]. The effect however is expected to be very small for a heavy radiator such as caesium in our experiment. Finally it should be mentioned that the depolarising crosssection for the caesium 7P3/2 state is also quite large, of order 300 A2 for Ar [lo]. Although most photon echo experiments use an analysing prism, in a Pockels cell shutter or for other reasons, the role of depolarising collisions is never considered, presumably because it is assumed that collisions which are close enough to cause depolarisation will also destroy the optical phase. The fact that our measured crosssections are if anything slightly smaller than those measured from line broadening suggest that collision mechanisms other than phase destruction play little role in our experiment. The present work has shown the polarisation rotation technique for echo detection to be a useful and reliable method for investigating atomic relaxation processes, and we plan to continue with this work.
296
transition perturbed by nobel gases
161 our work ]51 171 ]61 [ill our work
We gratefully acknowledge the SERC.
financial support from
References [ l] A. Flusberg, T. Mossberg and S.R. Hartmann, Optics Comm. 24 (1978) 207. (21 A. Flusberg, R. Kachru, T. Mossberg and S.R. Hartmann, Phys. Rev. Al9 (1979) 1607. [ 31 T.W. Mossberg, R. Kachru and S.R. Hartmann, Phys. Rev. Lett. 44 (1980) 73. [4] R. Kachru, T.J. Chen and S.R. Hartmann, Phys. Rev. Lett. 47 (1981) 902. [5] F. Rostas and J.L. Lemaire, J. Phys. B: Atom. Molec. Phys. 4 (1971) 555. [6] G. Smith, J. Phys. B: Atom. Molec. Phys. 8 (1975) 2273. [ 71 S.Y. Ch’en, E.L. Lewis and D.N. Stacey, J. Phys. B: Atom. Molec. Phys. 2 (1969) 274. [8] T. Baer and I.D. Abella,Phys. Rev. Al6 (1977) 2093. [9] S. Aoki, Phys. Rev. A20 (1979) 2013. [lo] E.L. Lewis, Physics Reports 58, No. l(l980) 1-71. [ll] Y.V. Evdokimov, Opt. and Spectr. 24 (1968) 448. [12] L. Krause, Appl. Optics 5 (1966) 1375.