A theory of photon echoes using double-resonance optical pulses (PEDROP) is presented. Two double-resonance pulses, separated by a time interval T, are used to cause transitions among three states of an atom. Each double-resonance pulse consists of two simultaneously applied laser pulses that drive coupled transitions in the atom. It is shown that for time t > T, six photon echoes are produced (three on each of the coupled transitions) at five distinct times. Moreover, a nonradiating macroscopic coherence is also produced between states of the same parity. With the use of an interrogation pulse to monitor this coherence, three additional photon echoes can be produced on either of the coupled transitions. A Doppler phase diagram is constructed that enables one easily to predict the times and conditions of echo formation. PEDROP combines features of both two-photon and trilevel echoes but offers advantages over these methods for studying relaxation phenomena.
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Term n, given in the first column, denotes the nth term in Eqs. (3.11). The second and third columns give the density-matrix elements in the field-free regions 0 → t and T → t, respectively, leading to echo formation at time tn.
Term n, given in the first column, corresponds to the nth term in Eqs. (3.11) and term n in Table 1. The photon-echo amplitude at time tn is proportional to the product of |
(0+)| and |ajlakm*| regardless of decay factor. Recall that the definitions of Φ and θ are given in Eqs. (2.25) and (2.24), respectively.
Table 3
Isolation of PEDRQP: Condition for Isolating nth Contribution (Term n) to PEDROPa
Recall that echo number n occurs at time tn given in Table 1. Note that without an interrogation pulse, echoes numbers 11–15 will not occur.
The choice of angles Φi and θi (i = 1, 2) for maximizing this echo also leads to its isolation.
Accompanied by echo number 6.
Accompanied by echo number 1.
Term n, given in the first column, denotes the nth term in Eqs. (3.11). The second and third columns give the density-matrix elements in the field-free regions 0 → t and T → t, respectively, leading to echo formation at time tn.
Term n, given in the first column, corresponds to the nth term in Eqs. (3.11) and term n in Table 1. The photon-echo amplitude at time tn is proportional to the product of |
(0+)| and |ajlakm*| regardless of decay factor. Recall that the definitions of Φ and θ are given in Eqs. (2.25) and (2.24), respectively.
Table 3
Isolation of PEDRQP: Condition for Isolating nth Contribution (Term n) to PEDROPa
Recall that echo number n occurs at time tn given in Table 1. Note that without an interrogation pulse, echoes numbers 11–15 will not occur.
The choice of angles Φi and θi (i = 1, 2) for maximizing this echo also leads to its isolation.
Accompanied by echo number 6.
Accompanied by echo number 1.