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Synchronized quantum beat echoes in Cs vapor with diode lasers
Volume 62, number 3
OPTICS COMMUNICATIONS
1 May 1987
SYNCHRONIZED QUANTUM BEAT ECHOES IN Cs VAPOR WITH DIODE LASERS T. MISHINA, M. TANIGAWA, Y. FUKUDA and T. HASHI Departmentof Physics, Faculty of Science, Kyoto University, Kyoto 606, Japan Received 29 December 1986
Sublevel echoes (synchronized quantum beat echoes) produced by purely optical means have been observed for the Zeeman transitions in the ground state of Cs atoms at ~ 5 MHz by using modulated light from diode lasers tuned to the D~ transition. An echo signal as large as a few percent of the free induction decay is obtained with a laser power of ~ 1 mW. Echo envelope decay and the dependence of the echo intensity on the intensity of the second light pulse train are examined. Experimental results are compared with theoretical predictions based on a simple model.
Sublevel echoes like electron spin echoes are usually obtained by exciting sublevel transitions by rf or microwave pulses. In a previous paper [ 1 ], we have shown that sublevel echoes can be produced by purely optical means; i.e., by applying two resonant light pulses without any use of rf or microwave pulses. The refocusing action of the second light pulse is essentially based on the spinor character of the relevant optical transition. We .call sublevel echoes thus obtained "quantum beat echoes (QBE)". By introducing the idea of periodic impact excitation [2-4], experimentally, by replacing two light pulses with two light-pulse trains, this technique is extended to achieve selective excitation of sublevel echoes [5]. The term "synchronized quantum beat echoes (SQBE)" means sublevel echoes obtained by this extended technique. The SQBE for the Zeeman and hyperfine transitions in the ground state of sodium atoms were already observed by using light-pulse trains from a cw mode-locked dye laser pumped by an argon ion laser [5]. In this paper we report on the SQBE using diode lasers. Diode lasers are usually low power lasers (order o f m W ) but in some cases the power is large enough to observe higher-order non-linear effects. We demonstrate that the SQBE can be observed for the Zeeman transitions in the ground state of Cs atoms by using light pulse trains from diode lasers tuned to the D~ transition. This is the first successful application, to our knowledge, of diode lasers for such a 166
higher order non-linear transient effect. The stability and low-noise character of the diode lasers are advantageous. In our experiment the echo phenomena can be detected without photomultipliers and the noise of the laser is much lower than that of the electronic amplifiers. We could also measure the precise optical power dependence of the echo signals. The detailed theory of SQBE will be published elsewhere. Here we will give a simple explanation of the SQBE using a three level system as shown in fig. l(a). Both the ground state sublevels la> and Ib> are optically connected with the excited state 13 > by the excitation pulses and the relevant dipole moments of the transitions are assumed to be cos 0 and sin 0, respectively. The following base change of the ground state by a unitary transformation
[ll>] =F 12>
cos0 L-sin 0
sinoIFla>] cosOdllb>
(1)
leads to superposed states l l> and 12>. In this scheme only the transition from I 1 > to 13 > is allowed as shown in fig. 1 (b) together with the spontaneous emission processes. The density-matrix equations of motion for the simple model system we consider are /913 "~-Pl 3 ( ~ -- it2)
= iX(P11 --P33 ),
P23 q - P 2 3 ( y - - i Q )
=izp21,
0 030-4018/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 62, number 3
OPTICS COMMUNICATIONS
1 May 1987
F=4 13>
13> ~ /
I iI
/
'~l xx.
t I
62plt2
\ \\
~/ /r rll ,
tl
~t
ii
I I1>
CsD18
4
~
v 125
~
62Slr2 3
H (Q)
(b)
(c)
Fig. 1. (a) A three level system. Optical transitions Ia ) *--, 13 ) and Ib) ~ 13 > are allowed. (b) The transformed level diagram. Only
the optical transition between I 1> and [ 3 ) is allowed. F and F ' indicate spontaneous emission processees. (c) Level diagram relevant to the Cs D~ line.
/033--/033(2F + F ' ) = - iZ(Pl 3 -P31), /oil + [(Pll --P22)712 -- (P12 --P21)iO9 sin 20]/2 = F p 3 3 + iX(pl 3 -/931 ), /012 "~-[P12(712 --iO9 cos 20)
+ (Pll --p22)iO9 sin 20]/2= --i~P32 , /022 + [(P22 -Pl,)712 - (P21 -p12)ico sin
20]/2=1-'p33,
(2)
where F is the returning rate to each of the ground states I 1 ) and 12 ), F ' is the escaping rate into other levels, 7 ( = I/T2) is the optical coherence decay rate, #2 is the optical frequency and Z = 2Xo cos(12t) is the optical driving term with the Rabi frequency Zo. co is the sublevel splitting between Ia ) and Ib ), and 712 is the ground state relaxation rate. Since the optical T2 is much shorter than the
inverse of the Rabi frequency in the present experiment, the effect of light pulse can be described in terms of the optical pumping. In the level scheme in fig. 1 (b), a light pulse pumps out the state [ 1 ) and the population difference is created between the states I 1 > and 12 >. In the original base it corresponds to the generation of sublevel coherence Pab. The coherence oscillates at the frequency o9, and correspondingly the population difference (pl ~-P22) oscillates at this frequency. If light pulses are synchronous with this oscillation, the effect of pumping by each pulse is accumulated and the coherence at the frequency co is selectively enhanced. In the following we consider square wave pulse trains. The generation of the sublevel coherence by the first pulse train can be understood as a result of a cw-like pumping from the state I1 >. The macroscopic coherence generated by the first pulse train at t = 0 decays due to the inhomogeneous distribution of sublevel splitting co around the center frequency O9o. The optical pumping due to the second light pulse train at t = z occurs similarly. In addition to the for167
Volume 62, number 3
OPTICS COMMUNICATIONS
mation of the new sublevel coherence, this pulse train introduces anisotropic depletion of the sublevel coherence generated by the first pulse train. The latter effect partially time-reverses the sublevel coherence and gives rise to an echo at t = 2r as is usual with spin echoes [ 1 ]. The echo refocusing efficiency 17(the ratio of the coherence generated by the first pulse and the coherence refocused by the second pulse) can be represented as Pab = t/pba + remainder,
(3)
where Pab and P~'b are the values of the coherence immediately before and immediately after the second pulse train. If the optical T~ and T2 are much shorter than Z6-~ , the terms/~3,/~23 and/933 c a n be neglected. (The approximation /J33=0 does not always hold in our case but it does not change the result appreciably.) Ignoring the time evolution of sublevel coherence during each pulse (m and 7 ~2 are taken to be zero) and solving eq. (2) with the initial c o n d i t i o n 1933= 0, w e get ~/= ~ sin2(20) ×
[r
F~F'
2exp(-atp)+
o~=zglT, fl=2o~
21-'+F' ~-~--~; e x p ( - f l t p )
F+F' ( F + 2 F ' ) +2or '
]
(4)
where tp is the duration of a single pulse of the second pulse train and 2or is the optical pumping rate. If the optical transients or the time delay of the system response is negligible compared to the pulse interval of the pulse train (7, F and F ' are much larger than to), no optical processes take place during the off-periods in the second pulse train. Thus the effects of the pulses are the same as those of one long pulse whose duration is the sum of each pulse duration. In the limiting case t~<
ot2tp ( F ' tp + 4) sin 2(20) 4(2F+F')
(5)
which means that r/is proportional to the square of the light intensity in the low intensity region. The experimental setup is shown in fig. 2. The 168
,
1 May 1987
diode laser (Mitsubishi ML3101 ) is tuned to the Cs D~ transition. The temperature of the diode laser is maintained within 10- 4 degree and the spectral width of the laser is about 30 MHz. Fig. 1 (c) is the level scheme of the Cs D~ lines. Each hyperfine level is well resolved by the laser light. In our experiment the laser wavelength is tuned to the 62S1/2(F=4) 62pt/2 ( F = 3) transition. The output of the diode laser is deflected by the two acousto-optic modulators and used as the probe and pump beams, respectively. These deflections are selected so that the optical frequency of the beams are shifted in opposite directions (by + 80 MHz). To avoid undesirable pumping effects, the probe beam is switched off except in the signal region. The pump beam is chopped at about 5 MHz to form the 1st and 2nd pulse trains of 50% duty ratio and circularly polarized by the 2/4 plate. The beams are crossed and focused at the sample and the beam diameters are about 0.2 mm. The Cs sample cell contains a 50 torr Ar buffer gas which shortens the optical 7"2 to about 300 ps [6]. Its temperature is maintained at 50°C. The magnetic field Ho of about 14 Oe is applied perpendicular to the light beam. Under these conditions, IAml= 1 sublevel coherences or precessing orientations with frequencies about 5 MHz are generated in the ground state 62S~/2(F=4). There are eight IzJml = 1 sublevel pairs but the applied magnetic field is low enough so that the relevant Zeeman splittings are nearly equal 5 MHz. After passing through the sample, the probe beam reaches the polarimeter where the coherence is detected as Faraday rotation. The oscillation at the frequency 5 MHz of the Faraday rotation is phase sensitively detected and the signal is obtained. Fig. 3 shows the free induction decay signal produced by the first pulse train only. The beat pattern is due to the slightly different Zeeman splittings in the 62S1/2(F=4) state. Fig. 4(a) is the typical echo (SQBE) signal. The traces of the 1st and 2nd pulse trains are due to leakage from the pumping light. The durations of the two pump pulse trains are 5 and 3 as, respectively. The probe pulse is 40 as long and covers the echo position. The beam powers are 0.6 mW (pump) and 10/tW (probe). A small artificial inhomogeneity of the magnetic field is introduced to enhance the echo signal. Fig. 4(b) shows the echo amplitude versus the interval between the 1st and 2nd
Volume 62, number 3
OPTICS COMMUNICATIONS
I May 1987
o~e ~
I Loser ] Diode
>
i ".o.
[J~l '"I l-~-[~'rO'vler[ Pul
A.O.
.......
[ Driier I
ier
~"
CSaloml ~ /
Ho
RF [ ertSfPhase RF PohriOsciator[4"9~-~ I hi . ~' , P.S.D. ~-~ Amplifie~-I r m~:er signal Fig. 2. Experimentalsetup. A.O.;acousto-opticmodulator.
~f~
A
i
I
i
i
0
200
zOO
600
time(IJ.S)
Fig. 3. Free inductiondecaysignalat 5 MI-Izassociatedwith Zeeman coherencesin the Cs ground state 6:S~/2(F=4) obtainedby a light pulse train. The beat pattern is due to unequal Zeeman splittings. pulse trains. The decay constant, about 100/ts, is attributed to the transit time which represents the mean time for the atoms to escape from the light beam region. Fig. 5(a) is the theoretical curve of the echo refocusing efficiency t/calculated from eq. (4) versus the pumping rate 2o~ which is proportional to the intensity of the 2nd light pulse. The real system is not a
three level system but a complex multi-level system as mentioned above before, so the parameters F , F ' and 0 cannot be directly related to the real ones. In the calculation, we choose values for tp, F , F ' and 0 of 1.5 gs, ( 9 0 n s ) -~, ( 4 5 n s ) -~ and 7t/4, respectively. In the low pump intensity region, q is proportional to the square of the 2nd light intensity; with the increase of light power, it is saturated and approaches the maximum value sinE(20)F'/4(F +F'). Fig. 5(b) depicts the experimental results of the echo amplitude versus the power of the 2nd light pulse, keeping the power of the 1st pulse constant at 0.6 mW. It also shows intensity squared dependence and saturation behavior. We observed the SQBE using a low power diode laser. The result is qualitatively explained by the simple three level model. Although the perfect recovery of sub-level coherence by the spinor character of two level systems [ 1 ] requires a coherent 2if-pulse, our result shows that even the optical pumping effect by an incoherent pulse train using a low power laser can reverse the sublevel coherence with quite a high efficiency of as much as a few percent.
169
Volume 62, number 3
OPTICS COMMUNICATIONS
1 May 1987
A tn
"E
1st pulse
D
2nd pulse echo
.D g
v 10 !
E o
O
O
5 I
I
60
120 its >
I
0
I
I
I
I
0
1
I
I
|
50
I
100
t •me lst-2nd (a)
pulse interval ( ~ s )
(b)
Fig. 4. (a) Typical echo (SQBE) signal associated with the same sublevel coherences as in fig. 3, obtained by the 1st and 2nd light pulse trains whose traces are indicated by arrows. (b) Observed echo amplitude versus the interval between the 1st and 2nd pulse trains. / I
/
SLOPE2 ,'
0 ~
SLOPE2 ,'
i
t
it
0.8
-1 -
t
uJ
,~f
• •
/i //e
I'--
n-
-2
0.4
/ /
F
s
O
8-3 ..J
I-
CA UJ
0.2 o I
i/
0.1
I
I
I
I
0.1
1
10
100
2 0 l i l t S -13 (a)
i /
I
I
I
1
0.1
0.2
0.4
0.8
2nd
PULSE I N T E N S I T Y
EmW3
(b)
Fig. 5. Echo refocusing efficiency r/as a function of 2nd pulse intensity. (a), (b) Theoretical and experimental results. The broken lines indicate squared intensity dependence.
References [ 1 ] Y. Fukuda, K. Yamada and T. Hashi, Optics Comm azt (1983) 297, [2] Y. Fukuda, Y. Takagi and T. Hashi, Phys. Lett. 48A (1974) 183.
170
[ 3 ] Y. Fukuda, J. Hayashi, K. Kondo and T. Hashi, Optics Comm. 38 (1981) 357. [4] J. Mlynek and W. Lange, H. Harde and H. Burggraf, Phys. Rev. A 24 (1981) 1099. [ 5 ] M. Tanigawa, Y. Fukuda, T. Kohmoto, K. Sakuno and T. Hashi, Optics Lett. 8 (1983) 620. [6] N. Allard and J. Kielkopf, Rev. Mod. Phys. 54 (1983) 1103.
OPTICS COMMUNICATIONS
1 May 1987
SYNCHRONIZED QUANTUM BEAT ECHOES IN Cs VAPOR WITH DIODE LASERS T. MISHINA, M. TANIGAWA, Y. FUKUDA and T. HASHI Departmentof Physics, Faculty of Science, Kyoto University, Kyoto 606, Japan Received 29 December 1986
Sublevel echoes (synchronized quantum beat echoes) produced by purely optical means have been observed for the Zeeman transitions in the ground state of Cs atoms at ~ 5 MHz by using modulated light from diode lasers tuned to the D~ transition. An echo signal as large as a few percent of the free induction decay is obtained with a laser power of ~ 1 mW. Echo envelope decay and the dependence of the echo intensity on the intensity of the second light pulse train are examined. Experimental results are compared with theoretical predictions based on a simple model.
Sublevel echoes like electron spin echoes are usually obtained by exciting sublevel transitions by rf or microwave pulses. In a previous paper [ 1 ], we have shown that sublevel echoes can be produced by purely optical means; i.e., by applying two resonant light pulses without any use of rf or microwave pulses. The refocusing action of the second light pulse is essentially based on the spinor character of the relevant optical transition. We .call sublevel echoes thus obtained "quantum beat echoes (QBE)". By introducing the idea of periodic impact excitation [2-4], experimentally, by replacing two light pulses with two light-pulse trains, this technique is extended to achieve selective excitation of sublevel echoes [5]. The term "synchronized quantum beat echoes (SQBE)" means sublevel echoes obtained by this extended technique. The SQBE for the Zeeman and hyperfine transitions in the ground state of sodium atoms were already observed by using light-pulse trains from a cw mode-locked dye laser pumped by an argon ion laser [5]. In this paper we report on the SQBE using diode lasers. Diode lasers are usually low power lasers (order o f m W ) but in some cases the power is large enough to observe higher-order non-linear effects. We demonstrate that the SQBE can be observed for the Zeeman transitions in the ground state of Cs atoms by using light pulse trains from diode lasers tuned to the D~ transition. This is the first successful application, to our knowledge, of diode lasers for such a 166
higher order non-linear transient effect. The stability and low-noise character of the diode lasers are advantageous. In our experiment the echo phenomena can be detected without photomultipliers and the noise of the laser is much lower than that of the electronic amplifiers. We could also measure the precise optical power dependence of the echo signals. The detailed theory of SQBE will be published elsewhere. Here we will give a simple explanation of the SQBE using a three level system as shown in fig. l(a). Both the ground state sublevels la> and Ib> are optically connected with the excited state 13 > by the excitation pulses and the relevant dipole moments of the transitions are assumed to be cos 0 and sin 0, respectively. The following base change of the ground state by a unitary transformation
[ll>] =F 12>
cos0 L-sin 0
sinoIFla>] cosOdllb>
(1)
leads to superposed states l l> and 12>. In this scheme only the transition from I 1 > to 13 > is allowed as shown in fig. 1 (b) together with the spontaneous emission processes. The density-matrix equations of motion for the simple model system we consider are /913 "~-Pl 3 ( ~ -- it2)
= iX(P11 --P33 ),
P23 q - P 2 3 ( y - - i Q )
=izp21,
0 030-4018/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 62, number 3
OPTICS COMMUNICATIONS
1 May 1987
F=4 13>
13> ~ /
I iI
/
'~l xx.
t I
62plt2
\ \\
~/ /r rll ,
tl
~t
ii
I I1>
CsD18
4
~
v 125
~
62Slr2 3
H (Q)
(b)
(c)
Fig. 1. (a) A three level system. Optical transitions Ia ) *--, 13 ) and Ib) ~ 13 > are allowed. (b) The transformed level diagram. Only
the optical transition between I 1> and [ 3 ) is allowed. F and F ' indicate spontaneous emission processees. (c) Level diagram relevant to the Cs D~ line.
/033--/033(2F + F ' ) = - iZ(Pl 3 -P31), /oil + [(Pll --P22)712 -- (P12 --P21)iO9 sin 20]/2 = F p 3 3 + iX(pl 3 -/931 ), /012 "~-[P12(712 --iO9 cos 20)
+ (Pll --p22)iO9 sin 20]/2= --i~P32 , /022 + [(P22 -Pl,)712 - (P21 -p12)ico sin
20]/2=1-'p33,
(2)
where F is the returning rate to each of the ground states I 1 ) and 12 ), F ' is the escaping rate into other levels, 7 ( = I/T2) is the optical coherence decay rate, #2 is the optical frequency and Z = 2Xo cos(12t) is the optical driving term with the Rabi frequency Zo. co is the sublevel splitting between Ia ) and Ib ), and 712 is the ground state relaxation rate. Since the optical T2 is much shorter than the
inverse of the Rabi frequency in the present experiment, the effect of light pulse can be described in terms of the optical pumping. In the level scheme in fig. 1 (b), a light pulse pumps out the state [ 1 ) and the population difference is created between the states I 1 > and 12 >. In the original base it corresponds to the generation of sublevel coherence Pab. The coherence oscillates at the frequency o9, and correspondingly the population difference (pl ~-P22) oscillates at this frequency. If light pulses are synchronous with this oscillation, the effect of pumping by each pulse is accumulated and the coherence at the frequency co is selectively enhanced. In the following we consider square wave pulse trains. The generation of the sublevel coherence by the first pulse train can be understood as a result of a cw-like pumping from the state I1 >. The macroscopic coherence generated by the first pulse train at t = 0 decays due to the inhomogeneous distribution of sublevel splitting co around the center frequency O9o. The optical pumping due to the second light pulse train at t = z occurs similarly. In addition to the for167
Volume 62, number 3
OPTICS COMMUNICATIONS
mation of the new sublevel coherence, this pulse train introduces anisotropic depletion of the sublevel coherence generated by the first pulse train. The latter effect partially time-reverses the sublevel coherence and gives rise to an echo at t = 2r as is usual with spin echoes [ 1 ]. The echo refocusing efficiency 17(the ratio of the coherence generated by the first pulse and the coherence refocused by the second pulse) can be represented as Pab = t/pba + remainder,
(3)
where Pab and P~'b are the values of the coherence immediately before and immediately after the second pulse train. If the optical T~ and T2 are much shorter than Z6-~ , the terms/~3,/~23 and/933 c a n be neglected. (The approximation /J33=0 does not always hold in our case but it does not change the result appreciably.) Ignoring the time evolution of sublevel coherence during each pulse (m and 7 ~2 are taken to be zero) and solving eq. (2) with the initial c o n d i t i o n 1933= 0, w e get ~/= ~ sin2(20) ×
[r
F~F'
2exp(-atp)+
o~=zglT, fl=2o~
21-'+F' ~-~--~; e x p ( - f l t p )
F+F' ( F + 2 F ' ) +2or '
]
(4)
where tp is the duration of a single pulse of the second pulse train and 2or is the optical pumping rate. If the optical transients or the time delay of the system response is negligible compared to the pulse interval of the pulse train (7, F and F ' are much larger than to), no optical processes take place during the off-periods in the second pulse train. Thus the effects of the pulses are the same as those of one long pulse whose duration is the sum of each pulse duration. In the limiting case t~<
ot2tp ( F ' tp + 4) sin 2(20) 4(2F+F')
(5)
which means that r/is proportional to the square of the light intensity in the low intensity region. The experimental setup is shown in fig. 2. The 168
,
1 May 1987
diode laser (Mitsubishi ML3101 ) is tuned to the Cs D~ transition. The temperature of the diode laser is maintained within 10- 4 degree and the spectral width of the laser is about 30 MHz. Fig. 1 (c) is the level scheme of the Cs D~ lines. Each hyperfine level is well resolved by the laser light. In our experiment the laser wavelength is tuned to the 62S1/2(F=4) 62pt/2 ( F = 3) transition. The output of the diode laser is deflected by the two acousto-optic modulators and used as the probe and pump beams, respectively. These deflections are selected so that the optical frequency of the beams are shifted in opposite directions (by + 80 MHz). To avoid undesirable pumping effects, the probe beam is switched off except in the signal region. The pump beam is chopped at about 5 MHz to form the 1st and 2nd pulse trains of 50% duty ratio and circularly polarized by the 2/4 plate. The beams are crossed and focused at the sample and the beam diameters are about 0.2 mm. The Cs sample cell contains a 50 torr Ar buffer gas which shortens the optical 7"2 to about 300 ps [6]. Its temperature is maintained at 50°C. The magnetic field Ho of about 14 Oe is applied perpendicular to the light beam. Under these conditions, IAml= 1 sublevel coherences or precessing orientations with frequencies about 5 MHz are generated in the ground state 62S~/2(F=4). There are eight IzJml = 1 sublevel pairs but the applied magnetic field is low enough so that the relevant Zeeman splittings are nearly equal 5 MHz. After passing through the sample, the probe beam reaches the polarimeter where the coherence is detected as Faraday rotation. The oscillation at the frequency 5 MHz of the Faraday rotation is phase sensitively detected and the signal is obtained. Fig. 3 shows the free induction decay signal produced by the first pulse train only. The beat pattern is due to the slightly different Zeeman splittings in the 62S1/2(F=4) state. Fig. 4(a) is the typical echo (SQBE) signal. The traces of the 1st and 2nd pulse trains are due to leakage from the pumping light. The durations of the two pump pulse trains are 5 and 3 as, respectively. The probe pulse is 40 as long and covers the echo position. The beam powers are 0.6 mW (pump) and 10/tW (probe). A small artificial inhomogeneity of the magnetic field is introduced to enhance the echo signal. Fig. 4(b) shows the echo amplitude versus the interval between the 1st and 2nd
Volume 62, number 3
OPTICS COMMUNICATIONS
I May 1987
o~e ~
I Loser ] Diode
>
i ".o.
[J~l '"I l-~-[~'rO'vler[ Pul
A.O.
.......
[ Driier I
ier
~"
CSaloml ~ /
Ho
RF [ ertSfPhase RF PohriOsciator[4"9~-~ I hi . ~' , P.S.D. ~-~ Amplifie~-I r m~:er signal Fig. 2. Experimentalsetup. A.O.;acousto-opticmodulator.
~f~
A
i
I
i
i
0
200
zOO
600
time(IJ.S)
Fig. 3. Free inductiondecaysignalat 5 MI-Izassociatedwith Zeeman coherencesin the Cs ground state 6:S~/2(F=4) obtainedby a light pulse train. The beat pattern is due to unequal Zeeman splittings. pulse trains. The decay constant, about 100/ts, is attributed to the transit time which represents the mean time for the atoms to escape from the light beam region. Fig. 5(a) is the theoretical curve of the echo refocusing efficiency t/calculated from eq. (4) versus the pumping rate 2o~ which is proportional to the intensity of the 2nd light pulse. The real system is not a
three level system but a complex multi-level system as mentioned above before, so the parameters F , F ' and 0 cannot be directly related to the real ones. In the calculation, we choose values for tp, F , F ' and 0 of 1.5 gs, ( 9 0 n s ) -~, ( 4 5 n s ) -~ and 7t/4, respectively. In the low pump intensity region, q is proportional to the square of the 2nd light intensity; with the increase of light power, it is saturated and approaches the maximum value sinE(20)F'/4(F +F'). Fig. 5(b) depicts the experimental results of the echo amplitude versus the power of the 2nd light pulse, keeping the power of the 1st pulse constant at 0.6 mW. It also shows intensity squared dependence and saturation behavior. We observed the SQBE using a low power diode laser. The result is qualitatively explained by the simple three level model. Although the perfect recovery of sub-level coherence by the spinor character of two level systems [ 1 ] requires a coherent 2if-pulse, our result shows that even the optical pumping effect by an incoherent pulse train using a low power laser can reverse the sublevel coherence with quite a high efficiency of as much as a few percent.
169
Volume 62, number 3
OPTICS COMMUNICATIONS
1 May 1987
A tn
"E
1st pulse
D
2nd pulse echo
.D g
v 10 !
E o
O
O
5 I
I
60
120 its >
I
0
I
I
I
I
0
1
I
I
|
50
I
100
t •me lst-2nd (a)
pulse interval ( ~ s )
(b)
Fig. 4. (a) Typical echo (SQBE) signal associated with the same sublevel coherences as in fig. 3, obtained by the 1st and 2nd light pulse trains whose traces are indicated by arrows. (b) Observed echo amplitude versus the interval between the 1st and 2nd pulse trains. / I
/
SLOPE2 ,'
0 ~
SLOPE2 ,'
i
t
it
0.8
-1 -
t
uJ
,~f
• •
/i //e
I'--
n-
-2
0.4
/ /
F
s
O
8-3 ..J
I-
CA UJ
0.2 o I
i/
0.1
I
I
I
I
0.1
1
10
100
2 0 l i l t S -13 (a)
i /
I
I
I
1
0.1
0.2
0.4
0.8
2nd
PULSE I N T E N S I T Y
EmW3
(b)
Fig. 5. Echo refocusing efficiency r/as a function of 2nd pulse intensity. (a), (b) Theoretical and experimental results. The broken lines indicate squared intensity dependence.
References [ 1 ] Y. Fukuda, K. Yamada and T. Hashi, Optics Comm azt (1983) 297, [2] Y. Fukuda, Y. Takagi and T. Hashi, Phys. Lett. 48A (1974) 183.
170
[ 3 ] Y. Fukuda, J. Hayashi, K. Kondo and T. Hashi, Optics Comm. 38 (1981) 357. [4] J. Mlynek and W. Lange, H. Harde and H. Burggraf, Phys. Rev. A 24 (1981) 1099. [ 5 ] M. Tanigawa, Y. Fukuda, T. Kohmoto, K. Sakuno and T. Hashi, Optics Lett. 8 (1983) 620. [6] N. Allard and J. Kielkopf, Rev. Mod. Phys. 54 (1983) 1103.