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Journal of Shaanxi Normal University

Enhancement of the transition probabilities for the two-photon transition with shaped chirped-pulse

Minhua Zhang

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Based on the second-order perturbation theory,the two-photon processes in the atom system excited by a shaped chirped-pulse are analyzed.The evolution of the two-photon transition probability is studied under the two cases of non-resonance and resonance.It′s shown that the transition probabilities disappeared at some corresponding frequencies under the non-resonance case,and thus the laser pulse can get through the medium without loss. Meanwhile,the maximum two-photon transition probability is obtained by choosing the best shaping function under the resonance case.

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Based on the second-order perturbation theory,the two-photon processes in the atom system excited by a shaped chirped-pulse are analyzed.The evolution of the two-photon transition probability is studied under the two cases of non-resonance and resonance.It′s shown that the transition probabilities disappeared at some corresponding frequencies under the non-resonance case,and thus the laser pulse can get through the medium without loss. Meanwhile,the maximum two-photon transition probability is obtained by choosing the best shaping function under the resonance case.
The interaction between the laser pulse with a small-area and a three-level atomic system is investigated.The formation and characterization of the shaped laser pulse are analyzed and the two-photon transition is studied with the shaped laser pulse.The influence of the relaxation of the excited state and the length of the shaping medium on the two-photon absorption is discussed.Based on the dispersion theory the oscillation of the transient twophoton transition is explained.The result indicates that the transition probability of two-photon absorption evolves regularly with the several values of parameters such as the length of medium(l),relaxation time(t2) and bandwidth(Δω).Meanwhile the transition probability appears in the transient oscillation.
Abstract In this study, the nonresonant two-photon absorption process in a two-level atom, induced by a weak chirped pulse, is theoretically investigated in the frequency domain. An analytical expression of the wave function expressed by Fresnel functions is obtained, and the two-photon transition probability (TPTP) versus the integral bandwidth, spectral width, and chirp parameter is analyzed. The results indicate that the oscillation evolution of the TPTP result from quantum diffraction of the wave function, which can be explained by analogy with Fresnel diffraction from a wide slit in the spatial domain. Moreover, the ratio between the real and imaginary parts of the excited state wave function and, hence, the atomic polarization, can be controlled by the initial phase of the excitation pulse. In some special initial phase of the excitation pulse, the wave functions with purely real or imaginary parts can be obtained by measuring the population probability. This work provides a novel perspective for understanding the physical details of the interactions between atoms and chirped light pulses in the multiphoton process.
We study the interaction between the shaped chirped laser pulse and a two-level atomic system. The analytical solution of the population probability on the excited state is obtained by the first order perturbation theory. We show that the temporal evolution of the wave function on the excited state is similar to the grating diffraction. By varying the modulation adepth and the compensation phase we demonstrate that the quantum coherent control for the population probability on the excited state can be achieved. We present a new method for measuring the wave function by the quantum holography principle.
In general cases of strong field excitation, the Stark effect has a significant influence on transient two-photon transitions, and the analytic description of this process is quite challenging. By combining analytical solutions and numerical simulations, the transient two-photon transition processes excited by weak and strong chirped pulses are systematically investigated, showing the important influences of parameters such as light field intensity, chirp factor, and detuning on the time-domain evolution of two-photon transition probabilities. Firstly, an approximate analytical expression is derived for the amplitude of the time-domain two-photon transition probability by using the second-order perturbation theory. This analytical solution indicates that the transient two-photon transition process under weak field excitation is similar to the Fresnel rectangular edge diffraction effect. As the light field intensity increases, the influence of the Stark effect on two-photon transitions also intensifies. Secondly, through a series of approximations, the approximate analytical solutions of the Schrödinger equation under strong field interactions are obtained. The analytical solutions show that the strong field Stark effect induces energy level to split, which disrupts the symmetry of the time-domain two-photon transition probability distribution, and its frequency domain process is similar to the “double-slit interference” effect. The research results indicate that the efficiency of population transfer during strong field excitation is closely related to the light field intensity, while the chirp factor can not only regulate the efficiency and time position of population transfer but also change the oscillation frequency of the population probability in the time domain. This work offers new insights into describing the time-domain evolution of the population probability under strong field excitation and lays a scientific basis for research on two-photon microscopy imaging.
On the basis of a vector model, the propagation of laser pulses under the conditions of a two-photon quasiresonance in the case of Stark-chirped rapid adiabatic passage through the resonance is studied with allowance for a diabatic character of the interaction. It is shown that the shape of a pulse propagating in a medium changes, the sweeping of its carrier frequency occurring concurrently. Special features of the spacetime evolution of the population difference in a two-photon transition and of the two-photon coherence during pulse propagation are analyzed. It is established that a complete population inversion and a maximum coherence may exist over a long length of the medium if the corresponding conditions are satisfied at the boundary. A new possibility for achieving a high coherence (close to a maximum value) is proposed.
The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.