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Optics Communications

Multiphoton time-delay spectroscopy using not transform-limited laser pulses

Stefano Cavalieri, Marzia Materazzi, R. Eramo, Lorenzo Fini, Andrea Giugni

Published Aug 1, 2000• 9 citations
Publisher
DOI
10.1016/s0030-4018(00)00805-1

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We theoretically demonstrate that the (2+1) resonance-enhanced multiphoton-ionization (REMPI) photoelectron spectrum in a cesium (Cs) atom can be effectively manipulated by two time-delayed femtosecond laser pulses, involving its photoelectron spectral structure and photoelectron energy. We show that the photoelectron spectrum exhibits interference fringes and the fringe spacing is determined by the time delay of the two laser pulses, and the photoelectron energy is periodically modulated and the modulation period is determined by the two-photon transition frequency of the excited state. Finally, we utilize the power spectrum of the two time-delayed laser pulses and the two-photon transition probability of the excited state to respectively explain the modulations of the photoelectron spectrum and photoelectron energy.

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A recently proposed collisional time-correlation function method for resonance laser–target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field and molecular target dipole/susceptibility correlation functions. The first and second order laser field correlation functions, also known as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser–target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump–probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.

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Pulse overlap artifacts and double quantum coherence spectroscopy

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The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.

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•Aug 27, 2026•0 citations
We theoretically demonstrate that the (2+1) resonance-enhanced multiphoton-ionization (REMPI) photoelectron spectrum in a cesium (Cs) atom can be effectively manipulated by two time-delayed femtosecond laser pulses, involving its photoelectron spectral structure and photoelectron energy. We show that the photoelectron spectrum exhibits interference fringes and the fringe spacing is determined by the time delay of the two laser pulses, and the photoelectron energy is periodically modulated and the modulation period is determined by the two-photon transition frequency of the excited state. Finally, we utilize the power spectrum of the two time-delayed laser pulses and the two-photon transition probability of the excited state to respectively explain the modulations of the photoelectron spectrum and photoelectron energy.
A recently proposed collisional time-correlation function method for resonance laser–target interactions in molecular targets is modified and extended to include time-delayed multiphoton processes in the dynamics. The explicitly time-dependent laser and target dynamics in this method is separated into laser electric field and molecular target dipole/susceptibility correlation functions. The first and second order laser field correlation functions, also known as Glauber field correlation functions, are evaluated in a continuum mode description of photon number representation for both resonance and time-delayed multiphoton processes. We show that such a description allows for the incorporation of laser pulse shape and phase coherence in the formalism, while the laser–target interaction dynamics is still described similarly to the resonance single- and multiphoton processes. As an example, the transition rates for a two-photon Gaussian pump–probe dynamics are derived in which we show that the phase coherence between the Gaussian pump and probe pulses can be incorporated and controlled through a single delay-time-dependent parameter.
The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.