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Physical Review A

Double-quantum photon echo in an adiabatic-vector-model approximation

Steven Aoki

Published Dec 1, 1976• 9 citations
Publisher

Abstract

The possible generation of photon echoes is discussed for a system where the incident radiation resonantly drives two-photon transitions. Use of the adiabatic-vector-model approximation of Grischkowsky, Loy, and Liao allows echo behavior to be calculated in a multilevel system by methods similar to those previously employed for two-level atoms. We find that observation of the double-quantum photon echo requires the presence of a nonresonant probe field at the time of formation of the echo pulse. The echo then radiates at the sum and difference of the probe and two-photon frequencies. As an example, we consider a possible experimental arrangement for the detection of double-quantum photon echoes in Rb vapor.

DOI
10.1103/physreva.14.2258

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Coherent excitation, incoherent excitation, and adiabatic states

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Coherent excitation of an atomic excited state occurs during the propagation of near-resonant light pulses and is responsible for the induced polarization. Simultaneously, incoherent excitation occurs due to the relaxation processes described by the absorption coefficient. Here, the theory for the coherent and incoherent excitation is initially presented in terms of the traditional vector model. While a complete understanding of the two-level system is provided by the vector model, it is shown to be incomplete when the problem of directly monitoring the coherent and incoherent excitation is considered. This is because this latter problem involves more than two levels. For this more complicated multilevel problem, adiabatic states are introduced to gain further understanding. The adiabatic states are the stationary states of the atom in the presence of the near-resonant laser field; they help to explain the intimate connection between the coherent excitation and the two-photon resonance. Experimental measurements of the coherent and incoherent excitation associated with near-resonant pulse propagation in Rb vapor are presented. The double-resonance technique used a relatively strong pulsed dye laser tuned near the $5{S}_{\frac{1}{2}}\ensuremath{\leftrightarrow}5{P}_{\frac{1}{2}}$ transition (7948 \AA{}A) of Rb to produce the coherent and incoherent excitation, and a weak, tunable cw dye laser tuned in the region of the $5{P}_{\frac{1}{2}}\ensuremath{\leftrightarrow}6{D}_{\frac{3}{2}}$ transition (6206 \AA{}A) to monitor this excitation. In agreement with theory, the experimental results demonstrate that coherent excitation is responsible for two-photon absorption, while the incoherent excitation corresponds to one-photon absorption to the $5{P}_{\frac{1}{2}}$ state.

Physical Review A•Aug 1, 1976•80 citations
The possible generation of photon echoes is discussed for a system where the incident radiation resonantly drives two-photon transitions. Use of the adiabatic-vector-model approximation of Grischkowsky, Loy, and Liao allows echo behavior to be calculated in a multilevel system by methods similar to those previously employed for two-level atoms. We find that observation of the double-quantum photon echo requires the presence of a nonresonant probe field at the time of formation of the echo pulse. The echo then radiates at the sum and difference of the probe and two-photon frequencies. As an example, we consider a possible experimental arrangement for the detection of double-quantum photon echoes in Rb vapor.
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.
An analytical study of the photon echoes associated with the three-level system interacting resonantly with optical pulses possessing two different frequencies is performed. It is predicted that photon echoes arise at anomalous times corresponding to the correlation between the inhomogeneous broadenings for the different spectral lines as well as at the normal time expected in a simple two-level system. This new effect is caused by the coupling of the two resonant transitions through the common energy level. Furthermore, if the particle does not have inversion symmetry, the echoes with the sum or difference frequency of the exciting optical pulses can be observed in such a system. The quantitative analysis is also given for intensities, direction of propagation and polarizations of the anomalous echoes which depend upon the exciting pulses with different frequency.
It is shown theoretically that, when two-level atoms are nonresonantly excited by a double light pulse that is a superposition of two rectangular pulses of identical frequency but different amplitude, it is possible to form multiple nutational echo signals whose amplitude is determined by the relationships between the Rabi frequencies of the double pulse, the inhomogeneous line width, and the detuning from resonance. It is established that these signals result from null beats between polarization vibrations at variable frequencies and at the generalized Rabi frequency. The optimum conditions for observing multiple echo signals in different experimental situations are considered.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Coherent excitation of an atomic excited state occurs during the propagation of near-resonant light pulses and is responsible for the induced polarization. Simultaneously, incoherent excitation occurs due to the relaxation processes described by the absorption coefficient. Here, the theory for the coherent and incoherent excitation is initially presented in terms of the traditional vector model. While a complete understanding of the two-level system is provided by the vector model, it is shown to be incomplete when the problem of directly monitoring the coherent and incoherent excitation is considered. This is because this latter problem involves more than two levels. For this more complicated multilevel problem, adiabatic states are introduced to gain further understanding. The adiabatic states are the stationary states of the atom in the presence of the near-resonant laser field; they help to explain the intimate connection between the coherent excitation and the two-photon resonance. Experimental measurements of the coherent and incoherent excitation associated with near-resonant pulse propagation in Rb vapor are presented. The double-resonance technique used a relatively strong pulsed dye laser tuned near the $5{S}_{\frac{1}{2}}\ensuremath{\leftrightarrow}5{P}_{\frac{1}{2}}$ transition (7948 \AA{}A) of Rb to produce the coherent and incoherent excitation, and a weak, tunable cw dye laser tuned in the region of the $5{P}_{\frac{1}{2}}\ensuremath{\leftrightarrow}6{D}_{\frac{3}{2}}$ transition (6206 \AA{}A) to monitor this excitation. In agreement with theory, the experimental results demonstrate that coherent excitation is responsible for two-photon absorption, while the incoherent excitation corresponds to one-photon absorption to the 5P125{P}_{\frac{1}{2}}5P21​​ state.