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Physical Review A

Free-precession decay of two-photon-induced coherence in Ca vapor

Masahiro Matsuoka, Hiroki Nakatsuka, Jumpei Okada

Published Sep 1, 1975• 35 citations
Publisher

Abstract

Calcium vapor has been excited by two-photon absorption of a mode-locked dye-laser pulse, and emission from a coherent superposition state of the $4{s}^{2}^{1}S_{0}$ and $4s3d^{1}D_{2}$ levels has been observed using a delayed off-resonant interrogation pulse in the picosecond regime. The emission signal intensity was measured as a function of the delay time of the interrogation pulse, and showed a peak well delayed from that of the dye-laser pulse. This reflects the fact that the induced coherence is expressed by a time integral of the excitation. The emission signal was then found to decay as a result of the Doppler effect. The above process is analyzed by Bloch and Maxwell equations. This is the first reported observation of the coherence of an atomic system induced by two-photon absorption, a coherence which persists after the passage of the excitation pulse and decays inhomogeneously as a result of thermal motion. In carrying out the experiment, deformation of the input dye-laser pulse during propagation through the two-photon resonant medium was carefully avoided.

DOI
10.1103/physreva.12.1062

Related papers

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Hiroki Nakatsuka, Jumpei Okada, Masahiro Matsuoka

Free precession beat of two-photon induced coherence was observed by the use of delayed probe pulses in atomic rubidium vapor. The two-photon coherence was created in the superposition state of the 5S 1/2 and 5D 5/2 levels of Rb by two-photon resonant excitation with a mode-locked dye laser pulse. The origin of the beat is attributed to the hyperfine splittings of the 5S 1/2 ground state of both Rb 85 and Rb 87 . The observed results are explained by a theory presented in this paper.

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Obsevation of Coherence in Two-Photon Excited Rb Vapor

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A coherent superposition state of 5S and 5D levels of Rb vapor, when it was excited by two-photon resonant transition between these levels, was observed by applying an interrogation pulse which was non-resonant to the system. The emphasis is laid on this coherence in the atomic excitation, instead of just the population inversion, in explaining the origin of various strong collimated emissions observed by many authors. Saturation of the off diagonal density matrix element between 5S and 5D levels was observed at higher excitation level due to the population change. An analysis of the saturation is given using a simple model for the coherence of the dye laser beam.

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Synchronous mode locking of two dye lasers was employed to obtain pairs of independently tunable picosecond pulses that were precisely synchronized in time. Overlapped pulses in strontium vapor were used to generate tunable picosecond pulses in the vacuum uv. The tunability was employed to study resonant enhancement of a four-wave parametric process by the 4d6p autoionizing resonance. Mutually separated pulses were employed to measure the build-up and decay of coherence for a two-quantum excited state. The decay was found to be faster than theoretical predictions that assume only velocity dephasing.

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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

Laser mode statistics probed by time delayed four-wave mixing in an atomic vapor

Michael Scott Belsley, M. Kaczmarek, P. Ewart

Coherent signals produced by time delayed, fluctuating optical pulses interacting with atoms in the vapor phase have attracted much interest recently, due to their potential as a source of sub-picosecond time resolution. The theoretical description of such experiments brings into play many profound questions connected with stochastic Bloch equations. For example, even though the noise properties of a single laser beam may be Markovian in nature, in these experiments the atoms are subjected to at least two time-delayed fields which may be correlated. Because the atoms retain some memory of the first field at the time when the second field acts, the entire process becomes non-Markovian. In principle, the variation of such parameters as the homogeneous and inhomogeneous widths, allows the experimenter some degree of control over this memory time associated with the atomic medium.\n&more...

European Quantum Electronics Conference (EQEC)•Aug 24, 2005•0 citations

Two-photon self-induced transparency in a resonant medium. II. Transient pulse behaviour

N Tan-no, Kenichi Yokoto, Humio Inaba

For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.

Journal of Physics B Atomic and Molecular Physics•Feb 21, 1975•10 citations
Calcium vapor has been excited by two-photon absorption of a mode-locked dye-laser pulse, and emission from a coherent superposition state of the 4{s}^{2}^{1}S_{0} and 4s3d1D24s3d^{1}D_{2}4s3d1D2​ levels has been observed using a delayed off-resonant interrogation pulse in the picosecond regime. The emission signal intensity was measured as a function of the delay time of the interrogation pulse, and showed a peak well delayed from that of the dye-laser pulse. This reflects the fact that the induced coherence is expressed by a time integral of the excitation. The emission signal was then found to decay as a result of the Doppler effect. The above process is analyzed by Bloch and Maxwell equations. This is the first reported observation of the coherence of an atomic system induced by two-photon absorption, a coherence which persists after the passage of the excitation pulse and decays inhomogeneously as a result of thermal motion. In carrying out the experiment, deformation of the input dye-laser pulse during propagation through the two-photon resonant medium was carefully avoided.
A coherent superposition state of 5S and 5D levels of Rb vapor, when it was excited by two-photon resonant transition between these levels, was observed by applying an interrogation pulse which was non-resonant to the system. The emphasis is laid on this coherence in the atomic excitation, instead of just the population inversion, in explaining the origin of various strong collimated emissions observed by many authors. Saturation of the off diagonal density matrix element between 5S and 5D levels was observed at higher excitation level due to the population change. An analysis of the saturation is given using a simple model for the coherence of the dye laser beam.
Synchronous mode locking of two dye lasers was employed to obtain pairs of independently tunable picosecond pulses that were precisely synchronized in time. Overlapped pulses in strontium vapor were used to generate tunable picosecond pulses in the vacuum uv. The tunability was employed to study resonant enhancement of a four-wave parametric process by the 4d6p autoionizing resonance. Mutually separated pulses were employed to measure the build-up and decay of coherence for a two-quantum excited state. The decay was found to be faster than theoretical predictions that assume only velocity dephasing.
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.
Coherent signals produced by time delayed, fluctuating optical pulses interacting with atoms in the vapor phase have attracted much interest recently, due to their potential as a source of sub-picosecond time resolution. The theoretical description of such experiments brings into play many profound questions connected with stochastic Bloch equations. For example, even though the noise properties of a single laser beam may be Markovian in nature, in these experiments the atoms are subjected to at least two time-delayed fields which may be correlated. Because the atoms retain some memory of the first field at the time when the second field acts, the entire process becomes non-Markovian. In principle, the variation of such parameters as the homogeneous and inhomogeneous widths, allows the experimenter some degree of control over this memory time associated with the atomic medium.\n&more...
For pt.I see ibid., vol.8, no.3, 339 (1975). The transient behaviour of two short optical pulses in two-photon coherent propagation is obtained by calculating numerically the coherent propagation equations which couple the two electromagnetic pulses and the atomic system in self-consistent fashion. The coherent interaction of the two different frequency pulses gives rise to lossless propagation in the absorptive medium. This description is characterized by a two-photon area theorem. Novel coherent propagation effects of peak amplification and multiple pulse breakup are found. These effects are ascribed to two-photon self-induced transparency analogous to that of a one-photon transition in a two-level system. A difference of input intensity between the two different frequency pulses yields curious modulation effects involving sharp peak amplification and marked pulse breakup for the low-intensity input. In contrast, the high-intensity input pulse displays a smooth variation with distance and time. Low-loss pulse transmission above threshold, and pulse advance and delay are found for the present case in contrast to that for one-photon self-induced transparency.