- Email: [email protected]
Photon echo “decay” in LaF3 : Pr3+ as a modulation process
PHOTON ECHO “DECAY”
August 1978
OPTICS COMMUNICATIONS
Volume 26, number 2
IN LaF, : Pr3+ AS A MODULATION
PROCESS *
Y.C. CHEN, K.P. CHIANG and S.R. HARTMANN Columbia Radiation Laboratory,
Department
of Physics, Columbia University, New York, 10027,
USA
The variation of photon echo intensity in LaFs : Pr* measured as a function of pulse separation for short times is shown to be a consequence of echo modulation as caused by isolated non-interacting Pr* ions.
The study of transient optical phenomena in LaF, : Pr3+ holds promise of being particularly interesting since the low C, site symmetry [l] of the La ion precludes non-zero values of(J); consequently on a nanosecond time scale the Pr3+ ion is effectively isolated magnetically from the fluorine, lanthanum and other praseodymium ions which surround it. From the work of Erickson [2], we know that the lowest level of the 3H4 ground state is actually a triplet with level spacings of 8.47 MHz and 16.7 MHz. It follows that any wave function mixing in the excited state will cause a short excitation pulse to produce a coherent superposition of several ground and excited states. Therefore photonecho data plotted vs the excitation pulse separation T should be characterized by a modulated behavior such as is observed in the more complicated Al,O, : Cr3+ ruby, system in which each Cr3+ ion interacts with a host of Al neighbors [3,4]. This modulated behavior has now been observed in zero magnetic field in both the 3H, (0 cm-‘) ++ 3P0 (20926 cm-l) and 3H4 * ‘D, (16872 cm-‘) transitions of Pr3+ in LaF3 and it is shown in fig. 1 and fig. 2 respectively. The observed modulation period of 117 ns corresponds closely, as it should, to the inverse of the lower 8.47 MHz groundstate splitting. The mixing of the nuclear-spin levels of the 3P, state is provided by the interaction of the Pr nucleus with the local electric-field gradient [5,6]. For the ID, state the mixing is provided by the more effective pseudo-quadrupolar interaction brought about by the action of the second-order nuclear hyperfine in*
This work was supported by the National Science Foundation under Grant NSF-DMR77-05995, and the Joint Services Electronics Programm (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract DAAG29-77-C-0019.
I
TRANSITION
‘H4e3Po
0.05 ,
too PULSE
200 SEPARATION
300
(nS)
Fig. 1. Dependence of photon echo intensity on pulse separation in zero magnetic field for the 3H4 * 3Pc transition of Pr* in LaFs at 4777 A. The solid curves are theoretical curves calculated with the excited state interaction parameters having the same sign (solid curve) and opposite sign (dotted curve) relative to-the ground state interaction parameters. In both cases thezaxis is parallel to the two fold axis of Ca (j-axis) while the X-axis is in the xz plane at an angle of 30’ from the z-axis.
teraction [7,8]. To check that the action of the relatively weak electric-quadrupolar interaction in the 3Po state together with the groundstate interaction inferred from Erickson’s measurements suffices to account for the character of fig. 1, we have made explicit calculations of echo behavior. Although we can infer, from other peoples work [2,5,6], the hamiltonians associated with the ground and excited states separately, we know neither the relative sign of the hamiltonians not the relative orientation of their associated principle axes. For the two 269
Volume
26, number
2
OPTICS COMMUNICATIONS
August
1978
pr3+
LaF,:
HlfCOXlS r 203ns
L100
200 PULSE
300
400
SEPARATION
500
600
700
(nS)
Fig. 2. Dependence of photon echo intensity on pulse separation for the 3H4 ++ ‘Da transition of Pr* in LaF3 at 5925 A. The dashed lines are drawn between data points to bring out their modulated character.
choices of relative sign and a particular orientation of axes we obtain the curves shown in fig. 1. The particulars of this calculation are discussed later. Although the first measurement of hoton echo intensity in LaF, : Pr3+ (on the 3H4 ++ %, transition) as a function of pulse separation displayed a featureless exponential decay [9], measurements of echo intensity (at fixed pulse separation) as a function of magnetic field showed strong modulation [8]. This was explained by the magnetic coupling and mixing of atomic states. Whereas our previous measurements at fixed pulse separations of 97 ns and 237 ns were characterized by the maximum echo intensity signal occurring at zero applied magnetic field, we have now found that at a pulse separation of 203 ns the application of an appropriately large magnetic field results in an increased echo intensity over that which it has in zero magnetic field, (see fig. 3). This implies that at 7 = 203 ns coherent dephasing already occurs in zero field. It was this result which motivated the zero field measurements just discussed. The apparatus we used is similar to that described previously [S] . A Htisch-type nitrogen-laser-pumped dye laser whose beam is split into two, with one beam delayed, is used to provide the two several-hundred-watt pulses, 10 GHz wide and 7 ns long, for photon echo excitation. These pulses are linearly polarized and directed normal to the crystal c-axis. In order to ensure that the two excitation pulses overlap at the sample we first focus them at a pinhole ,outside the dewar and 270
P
F 0 L
~~
_.I
1
Fig. 3. Dependence of photon echo intensity on magnetic field for the 3H4 ++ 3 Po transition at a pulse separation of 203 ns. The magnetic field is applied parallel to the crystal Ixis.
then image the pinhole onto the sample. The size of the pinhole (100 m) is made equal to the waist of the focussed beams, so that 80% of the laser intensity passes through. Testing for transmission through the pinhole is accomplished by placing a beam splitter after the sample. Intensity variations in the excitation pulses due to laser drift and/or optics misalignment are recorded during the experiment. The echo pulses, as well as the excitation pulses, are detected by a photomultiplier tube and averaged with a PDP8/E computer. Our optical delay line introduces a 30% loss at 20926 cm-’ for each 34-ns increment. This is corrected by inserting an attenuator into the delayed beam path. The attenuator consists of a Pockels cell between two parallel polarizers. All excitation pulses are monitored and are attenuated to a fixed average intensity so that the data need not be corrected. An external magnetic field can be applied along the crystal c-axis by an electromagnet. The sample temperature is below 2.5 K. For experiments involving the 3H, * 3Po transition a sample with 0.1 atomic% impurity concentration is used. For experiments involving the 3H, ++ ‘D, transition a 1 .O atomic% impurity concentration sample is used in order to compensate for the factor-of-three reduction in the oscillator strength of this transition [LOI. The hamiltonian
for Pr3+ in LaF, is given by
where g and gn are the electronic and nuclear g-factors respectively, fl and 0, are the electronic and nuclear
Volume
26, number
OPTICS COMMUNICATIONS
2
Bohr magnetons respectively, His the external field, .Z and Z are the electonic and nuclear angular momentum vectors, A, is the hyperfine constant, Ha is the nuclear quadrupole interaction, and Hsp is the superhyperfine Interaction coupling the Pr3+ ion to its neighboring fluorine and lanthanum magnetic nuclei. Since (.Z) = 0 the effects of the electrons are greatly reduced, and it is only because of the close spacing for some of the Stark-split levels that an appreciable secondorder effect remains [7]. The effective hamiltonian, neglectingZZsp because of the reduced Pr3+ magnetic interaction, IS then [7,11,12]
with A
P=A;
(
+ AYY
xx2
-Azz
1
, $yy*
-Axx
(394)
(OIJjln)(nlJilO) Ki=2gflAJAiilgnPn> 'ii=~~~ En
-E0
3 (536)
where En and In) are the energy and wave function of the nth level, E. and IO)are the energy and wave function of the ground state, eQ represents the electric quadrupole moment of the Pr nucleus, eq is the major component of the electric field gradient at the Pr site, and n is the asymmetry factor of the electric field gradient. The labels X, Y,Z and X’, Y’,Z’ refer to the principle axes of the A tensor and the electric-field-gradient tensor, respectively [5,11]. These.axes need not be identical. The two-fold axis of C2 must, however, be parallel to one axis of each system. Our local coordinate axes are chosen with z^parallel to the crystal caxis, ,G parallel to the two-fold axis of C,, and x perpendicular to j and z^. For the 3Po state J is identically equal to zero, so that both P and the KJsmust also be zero. The only interaction for this state is then the electric-quadrupole interaction which we estimate by assuming 1) that the field gradient at a Pr site in the LaF, crystal is the same as that at the La site and 2) the electronic antishielding factors for Pr3+ and La3+ are identical [ 131.
August
1978
From Anderson and Proctor [5] we find that 2’ lies in the xz plane at an angle of 53.6” from the P axis, while the Y’ axis coincides with j. The measurements of Anderson and Proctor were made at room temperature. The work of Lee et al. [6] shows that the field gradient changes as the temperature is lowered. No measurements have been made of the change in the orientation of the i’, Y’, 2’ axis as a function of temperature. Since low temperature measurements go down to only 88 K we have had to extrapolate in order to estimate the interaction parameters at -4 K. We obtain k2Qq/hIL.= 17.2MHz and n = 0.78 MHz. Using the known ratio of QLa/QPr = -3.1 we then obtain le2Qq/hlp, = 5.54MHz and V= 0.78 MHz [14]. For the 3H4 ground state we use Erickson’s measurement of the level splittings to obtain P= 4.185MHz and t/3 = 0.105 [2]. It is to be understood that this pseudo-quadrupole interaction contains the effect of the electric-quadrupole interaction. The remaining question to be decided in calculating the 3H4 * 3Po transition echo intensity as a function of pulse separation is the relative orientation of the principle x, Y’,.? and _?, ?‘“, 2’ axes. We have calculated the echo behavior for this transition as a function of pulse separation for several relative orientations of the principle axes. For x’, ?‘“, and 2’ as given in the text and for 2 parallel to 9 with _%in the xz plane at an angle of 30” from the z-axis, we obtain the solid curve of fig. 1 if we assume that P and e2Qq have the same sign, and the dashed curve if we assume their signs are opposite. In both cases strong rephasings are predicted at pulse separations which are integral multiples of 117 ns. This rephasing at r = 240 ns is in fact a general feature which is common to all relative orientations and is a direct consequence of the ground-state splittings of 8.47 MHz and 16.7 MHz. For the excited ’ D, state J # 0 and consequently P and the K,'sare not a priori zero. If we use for the ‘D2 state the hamiltonian inferred by Erickson from his enhanced-absorption-spectroscopy experiment [ 151, we are unable to fit the data of fig. 2 with an accuracy approaching that displayed for the 3H4 ++ 3Po transition data shown in fig. 1. We are presently planning to perform PENDOR [ 161 experiments to examine the ’ D, state in more detail. Recent measurements by Yamagishland Szabo [ 171 ofphoton echo intensity for the 3H4 ft 3Po transition as a function of pulse separation have shown an inde271
Volume
26, number
2
OPTICS COMMUNICATIONS
pendence of concentration over the range of 0.01 to 1 .O atomic %. These results support our view that the Pr3+ ion is effectively isolated. Their data agrees with ours except for one point at r = 240 ns where we measure rephasing to occur; indeed if we exclude our data point at r = 240 ns we obtain a good fit to a straight line with the time constant they ‘measure of 5 15 ns. However, we found have our data to be reproducible on runs taken on different days even if we make major changes in re-allignment In support of our observation of the rephasing of the 3H, ++ 3Po transition photon echo at r x 240 ns we cite, 1) a theoretical calculation using hamiltonians obtained from experiments unrelated to ours, 2) observation of a modulated echo decay (3H, cf ‘D, transition) with similar rephasing modulation characteristics, 3) observation of echo signals in high fields greater than that observed in zero field (fig. 3). Our calculations indicate that the rephasing of the 3H4 * 3P0 transition photon echo at about 240 ns is quite sharp (less than 40 ns) and care must be taken in determining the absolute time of pulse arrival. The complete rephasing observed at - 240 ns shows that on this time scale homogeneous relaxation processes are negligible. Our calculations seem to be quite successful in describing the experimental results of fig. 1 and lead us to surmise that they correctly describe the physics involved in transient coherent experiments of this type.
272
August
1978
We thank Allen Flusberg for helpful discussions.
References [l]
PI [31 [41 [51 [61 [71
S. Matthies and D. Welsh, Phys. Stat. Sol. (b) 68 (1975) 125. L.E. Erickson, OpticsComm. 21 (1977) 147. D. Grischkowsky and S.R. Hartmann, Phys. Rev. B2 (1970) 60. S. Meth and S.R. Hartmann, Optics Comm. 24 (1978) 100. L.O. Anderson and W.G. Proctor, Z. Krist. 127 (1968) 366. K. Lee, A. Sher, L.O. Anderson and W.G. Proctor, Phys. Rev. 150 (1967) 168. B. Bleaney, J. Appl. Phys. 34 (1963) 1024; Physica 69 (1973)
317.
PI Y.C. Chen and S.R. Hartmann,
Phys. Lett. 58A (1976) 201. The pulse separation in fig. 2 should be 237 ns. [91 N. Takeuchi, J. Lumin. 12/13 (1976) 743. [lOI M.J. Weber, J. Chem. Phys. 48 (1968) 4774. [ill M.A. Teplov, Sov. Phys. JETP 26 (1968) 872. iI21 F.L. Aukhadeev and I.S. Konov, Sov. Phys. Solid State 15 (1974) 1929. [I31 R.E. Watson and A.J. Freeman, Phys. Rev. 135 (1964) 1209. iI41 G.H. Fuller and V.W. Cohen, Nuclear Data Sheet, A5 (1969) 433. [I51 L.E. Erickson, Phys. Rev. B16 (1977) 4731. [I61 P.F. Liao, P. Hu, R. Leigh and S.R. Hartmann, Phys. Rev. A9 (1974) 332. 1171 A. Yamagishi and A. Szabo, Optics Letters, 2 (1978) 160.
August 1978
OPTICS COMMUNICATIONS
Volume 26, number 2
IN LaF, : Pr3+ AS A MODULATION
PROCESS *
Y.C. CHEN, K.P. CHIANG and S.R. HARTMANN Columbia Radiation Laboratory,
Department
of Physics, Columbia University, New York, 10027,
USA
The variation of photon echo intensity in LaFs : Pr* measured as a function of pulse separation for short times is shown to be a consequence of echo modulation as caused by isolated non-interacting Pr* ions.
The study of transient optical phenomena in LaF, : Pr3+ holds promise of being particularly interesting since the low C, site symmetry [l] of the La ion precludes non-zero values of(J); consequently on a nanosecond time scale the Pr3+ ion is effectively isolated magnetically from the fluorine, lanthanum and other praseodymium ions which surround it. From the work of Erickson [2], we know that the lowest level of the 3H4 ground state is actually a triplet with level spacings of 8.47 MHz and 16.7 MHz. It follows that any wave function mixing in the excited state will cause a short excitation pulse to produce a coherent superposition of several ground and excited states. Therefore photonecho data plotted vs the excitation pulse separation T should be characterized by a modulated behavior such as is observed in the more complicated Al,O, : Cr3+ ruby, system in which each Cr3+ ion interacts with a host of Al neighbors [3,4]. This modulated behavior has now been observed in zero magnetic field in both the 3H, (0 cm-‘) ++ 3P0 (20926 cm-l) and 3H4 * ‘D, (16872 cm-‘) transitions of Pr3+ in LaF3 and it is shown in fig. 1 and fig. 2 respectively. The observed modulation period of 117 ns corresponds closely, as it should, to the inverse of the lower 8.47 MHz groundstate splitting. The mixing of the nuclear-spin levels of the 3P, state is provided by the interaction of the Pr nucleus with the local electric-field gradient [5,6]. For the ID, state the mixing is provided by the more effective pseudo-quadrupolar interaction brought about by the action of the second-order nuclear hyperfine in*
This work was supported by the National Science Foundation under Grant NSF-DMR77-05995, and the Joint Services Electronics Programm (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract DAAG29-77-C-0019.
I
TRANSITION
‘H4e3Po
0.05 ,
too PULSE
200 SEPARATION
300
(nS)
Fig. 1. Dependence of photon echo intensity on pulse separation in zero magnetic field for the 3H4 * 3Pc transition of Pr* in LaFs at 4777 A. The solid curves are theoretical curves calculated with the excited state interaction parameters having the same sign (solid curve) and opposite sign (dotted curve) relative to-the ground state interaction parameters. In both cases thezaxis is parallel to the two fold axis of Ca (j-axis) while the X-axis is in the xz plane at an angle of 30’ from the z-axis.
teraction [7,8]. To check that the action of the relatively weak electric-quadrupolar interaction in the 3Po state together with the groundstate interaction inferred from Erickson’s measurements suffices to account for the character of fig. 1, we have made explicit calculations of echo behavior. Although we can infer, from other peoples work [2,5,6], the hamiltonians associated with the ground and excited states separately, we know neither the relative sign of the hamiltonians not the relative orientation of their associated principle axes. For the two 269
Volume
26, number
2
OPTICS COMMUNICATIONS
August
1978
pr3+
LaF,:
HlfCOXlS r 203ns
L100
200 PULSE
300
400
SEPARATION
500
600
700
(nS)
Fig. 2. Dependence of photon echo intensity on pulse separation for the 3H4 ++ ‘Da transition of Pr* in LaF3 at 5925 A. The dashed lines are drawn between data points to bring out their modulated character.
choices of relative sign and a particular orientation of axes we obtain the curves shown in fig. 1. The particulars of this calculation are discussed later. Although the first measurement of hoton echo intensity in LaF, : Pr3+ (on the 3H4 ++ %, transition) as a function of pulse separation displayed a featureless exponential decay [9], measurements of echo intensity (at fixed pulse separation) as a function of magnetic field showed strong modulation [8]. This was explained by the magnetic coupling and mixing of atomic states. Whereas our previous measurements at fixed pulse separations of 97 ns and 237 ns were characterized by the maximum echo intensity signal occurring at zero applied magnetic field, we have now found that at a pulse separation of 203 ns the application of an appropriately large magnetic field results in an increased echo intensity over that which it has in zero magnetic field, (see fig. 3). This implies that at 7 = 203 ns coherent dephasing already occurs in zero field. It was this result which motivated the zero field measurements just discussed. The apparatus we used is similar to that described previously [S] . A Htisch-type nitrogen-laser-pumped dye laser whose beam is split into two, with one beam delayed, is used to provide the two several-hundred-watt pulses, 10 GHz wide and 7 ns long, for photon echo excitation. These pulses are linearly polarized and directed normal to the crystal c-axis. In order to ensure that the two excitation pulses overlap at the sample we first focus them at a pinhole ,outside the dewar and 270
P
F 0 L
~~
_.I
1
Fig. 3. Dependence of photon echo intensity on magnetic field for the 3H4 ++ 3 Po transition at a pulse separation of 203 ns. The magnetic field is applied parallel to the crystal Ixis.
then image the pinhole onto the sample. The size of the pinhole (100 m) is made equal to the waist of the focussed beams, so that 80% of the laser intensity passes through. Testing for transmission through the pinhole is accomplished by placing a beam splitter after the sample. Intensity variations in the excitation pulses due to laser drift and/or optics misalignment are recorded during the experiment. The echo pulses, as well as the excitation pulses, are detected by a photomultiplier tube and averaged with a PDP8/E computer. Our optical delay line introduces a 30% loss at 20926 cm-’ for each 34-ns increment. This is corrected by inserting an attenuator into the delayed beam path. The attenuator consists of a Pockels cell between two parallel polarizers. All excitation pulses are monitored and are attenuated to a fixed average intensity so that the data need not be corrected. An external magnetic field can be applied along the crystal c-axis by an electromagnet. The sample temperature is below 2.5 K. For experiments involving the 3H, * 3Po transition a sample with 0.1 atomic% impurity concentration is used. For experiments involving the 3H, ++ ‘D, transition a 1 .O atomic% impurity concentration sample is used in order to compensate for the factor-of-three reduction in the oscillator strength of this transition [LOI. The hamiltonian
for Pr3+ in LaF, is given by
where g and gn are the electronic and nuclear g-factors respectively, fl and 0, are the electronic and nuclear
Volume
26, number
OPTICS COMMUNICATIONS
2
Bohr magnetons respectively, His the external field, .Z and Z are the electonic and nuclear angular momentum vectors, A, is the hyperfine constant, Ha is the nuclear quadrupole interaction, and Hsp is the superhyperfine Interaction coupling the Pr3+ ion to its neighboring fluorine and lanthanum magnetic nuclei. Since (.Z) = 0 the effects of the electrons are greatly reduced, and it is only because of the close spacing for some of the Stark-split levels that an appreciable secondorder effect remains [7]. The effective hamiltonian, neglectingZZsp because of the reduced Pr3+ magnetic interaction, IS then [7,11,12]
with A
P=A;
(
+ AYY
xx2
-Azz
1
, $yy*
-Axx
(394)
(OIJjln)(nlJilO) Ki=2gflAJAiilgnPn> 'ii=~~~ En
-E0
3 (536)
where En and In) are the energy and wave function of the nth level, E. and IO)are the energy and wave function of the ground state, eQ represents the electric quadrupole moment of the Pr nucleus, eq is the major component of the electric field gradient at the Pr site, and n is the asymmetry factor of the electric field gradient. The labels X, Y,Z and X’, Y’,Z’ refer to the principle axes of the A tensor and the electric-field-gradient tensor, respectively [5,11]. These.axes need not be identical. The two-fold axis of C2 must, however, be parallel to one axis of each system. Our local coordinate axes are chosen with z^parallel to the crystal caxis, ,G parallel to the two-fold axis of C,, and x perpendicular to j and z^. For the 3Po state J is identically equal to zero, so that both P and the KJsmust also be zero. The only interaction for this state is then the electric-quadrupole interaction which we estimate by assuming 1) that the field gradient at a Pr site in the LaF, crystal is the same as that at the La site and 2) the electronic antishielding factors for Pr3+ and La3+ are identical [ 131.
August
1978
From Anderson and Proctor [5] we find that 2’ lies in the xz plane at an angle of 53.6” from the P axis, while the Y’ axis coincides with j. The measurements of Anderson and Proctor were made at room temperature. The work of Lee et al. [6] shows that the field gradient changes as the temperature is lowered. No measurements have been made of the change in the orientation of the i’, Y’, 2’ axis as a function of temperature. Since low temperature measurements go down to only 88 K we have had to extrapolate in order to estimate the interaction parameters at -4 K. We obtain k2Qq/hIL.= 17.2MHz and n = 0.78 MHz. Using the known ratio of QLa/QPr = -3.1 we then obtain le2Qq/hlp, = 5.54MHz and V= 0.78 MHz [14]. For the 3H4 ground state we use Erickson’s measurement of the level splittings to obtain P= 4.185MHz and t/3 = 0.105 [2]. It is to be understood that this pseudo-quadrupole interaction contains the effect of the electric-quadrupole interaction. The remaining question to be decided in calculating the 3H4 * 3Po transition echo intensity as a function of pulse separation is the relative orientation of the principle x, Y’,.? and _?, ?‘“, 2’ axes. We have calculated the echo behavior for this transition as a function of pulse separation for several relative orientations of the principle axes. For x’, ?‘“, and 2’ as given in the text and for 2 parallel to 9 with _%in the xz plane at an angle of 30” from the z-axis, we obtain the solid curve of fig. 1 if we assume that P and e2Qq have the same sign, and the dashed curve if we assume their signs are opposite. In both cases strong rephasings are predicted at pulse separations which are integral multiples of 117 ns. This rephasing at r = 240 ns is in fact a general feature which is common to all relative orientations and is a direct consequence of the ground-state splittings of 8.47 MHz and 16.7 MHz. For the excited ’ D, state J # 0 and consequently P and the K,'sare not a priori zero. If we use for the ‘D2 state the hamiltonian inferred by Erickson from his enhanced-absorption-spectroscopy experiment [ 151, we are unable to fit the data of fig. 2 with an accuracy approaching that displayed for the 3H4 ++ 3Po transition data shown in fig. 1. We are presently planning to perform PENDOR [ 161 experiments to examine the ’ D, state in more detail. Recent measurements by Yamagishland Szabo [ 171 ofphoton echo intensity for the 3H4 ft 3Po transition as a function of pulse separation have shown an inde271
Volume
26, number
2
OPTICS COMMUNICATIONS
pendence of concentration over the range of 0.01 to 1 .O atomic %. These results support our view that the Pr3+ ion is effectively isolated. Their data agrees with ours except for one point at r = 240 ns where we measure rephasing to occur; indeed if we exclude our data point at r = 240 ns we obtain a good fit to a straight line with the time constant they ‘measure of 5 15 ns. However, we found have our data to be reproducible on runs taken on different days even if we make major changes in re-allignment In support of our observation of the rephasing of the 3H, ++ 3Po transition photon echo at r x 240 ns we cite, 1) a theoretical calculation using hamiltonians obtained from experiments unrelated to ours, 2) observation of a modulated echo decay (3H, cf ‘D, transition) with similar rephasing modulation characteristics, 3) observation of echo signals in high fields greater than that observed in zero field (fig. 3). Our calculations indicate that the rephasing of the 3H4 * 3P0 transition photon echo at about 240 ns is quite sharp (less than 40 ns) and care must be taken in determining the absolute time of pulse arrival. The complete rephasing observed at - 240 ns shows that on this time scale homogeneous relaxation processes are negligible. Our calculations seem to be quite successful in describing the experimental results of fig. 1 and lead us to surmise that they correctly describe the physics involved in transient coherent experiments of this type.
272
August
1978
We thank Allen Flusberg for helpful discussions.
References [l]
PI [31 [41 [51 [61 [71
S. Matthies and D. Welsh, Phys. Stat. Sol. (b) 68 (1975) 125. L.E. Erickson, OpticsComm. 21 (1977) 147. D. Grischkowsky and S.R. Hartmann, Phys. Rev. B2 (1970) 60. S. Meth and S.R. Hartmann, Optics Comm. 24 (1978) 100. L.O. Anderson and W.G. Proctor, Z. Krist. 127 (1968) 366. K. Lee, A. Sher, L.O. Anderson and W.G. Proctor, Phys. Rev. 150 (1967) 168. B. Bleaney, J. Appl. Phys. 34 (1963) 1024; Physica 69 (1973)
317.
PI Y.C. Chen and S.R. Hartmann,
Phys. Lett. 58A (1976) 201. The pulse separation in fig. 2 should be 237 ns. [91 N. Takeuchi, J. Lumin. 12/13 (1976) 743. [lOI M.J. Weber, J. Chem. Phys. 48 (1968) 4774. [ill M.A. Teplov, Sov. Phys. JETP 26 (1968) 872. iI21 F.L. Aukhadeev and I.S. Konov, Sov. Phys. Solid State 15 (1974) 1929. [I31 R.E. Watson and A.J. Freeman, Phys. Rev. 135 (1964) 1209. iI41 G.H. Fuller and V.W. Cohen, Nuclear Data Sheet, A5 (1969) 433. [I51 L.E. Erickson, Phys. Rev. B16 (1977) 4731. [I61 P.F. Liao, P. Hu, R. Leigh and S.R. Hartmann, Phys. Rev. A9 (1974) 332. 1171 A. Yamagishi and A. Szabo, Optics Letters, 2 (1978) 160.