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Journal of Physics A Mathematical and Theoretical

Controlling pathway dynamics of a four-level quantum system with pulse shaping

Dewen Cao, Ling Yang, Yaoxiong Wang, Feng Shuang, Fang Gao

Published Jun 6, 2016• 4 citations
Publisher

Abstract

Abstract The dynamics of two two-photon absorption (TPA) pathways in a four-level quantum system driven by a laser pulse is investigated in this work. An analytical solution for pulse shaping is proposed to be globally optimal for constructive interference between the two pathways, and accurate spectral boundaries for phase modulation are obtained. The TPA rate can be enhanced by a factor of 8.33 with the optimal pulse instead of the transform limited pulse (TL pulse). Simple control strategies modulating both amplitudes and phases are also designed to increase the TPA amplitude along one pathway while decreasing that along the other simultaneously. The strategies are intuitive and the two pathway amplitudes can differ by two orders of magnitude.

DOI
10.1088/1751-8113/49/28/285302

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Abstract The dynamics of two two-photon absorption (TPA) pathways in a four-level quantum system driven by a laser pulse is investigated in this work. An analytical solution for pulse shaping is proposed to be globally optimal for constructive interference between the two pathways, and accurate spectral boundaries for phase modulation are obtained. The TPA rate can be enhanced by a factor of 8.33 with the optimal pulse instead of the transform limited pulse (TL pulse). Simple control strategies modulating both amplitudes and phases are also designed to increase the TPA amplitude along one pathway while decreasing that along the other simultaneously. The strategies are intuitive and the two pathway amplitudes can differ by two orders of magnitude.
Two-photon absorption (TPA) is an important quantum process in the light-matter interaction. When more than one TPA pathway exists in a quantum system, it is necessary to utilize the interference of these pathways to increase the sum TPA amplitude. A simple block scheme (Phys. Rev. A 2013, 88, 053427) is proposed to maximize the constructive interference of two TPA pathways in a four-level diamond-configuration quantum system. It can also be expanded to control multiple TPA pathways (Chin. J. Chem. Phys. 2015, 28, 426). The spectral boundaries in the scheme is related to the energy structure of the system. This work tries to give an analysis of the boundaries for general four-level and five-level quantum systems, which have two and three TPA pathways, respectively. How the boundaries and thus the number of blocks change with the energy structure will be explored.
We investigate coherent control of the two-photon transition pathways of a four-level atomic system in a diamond configuration. When an ultrashort laser pulse interacts with this system in the ground state 5S1/25{S}_{1/2}5S1/2​ of rubidium, the two-photon transition probability amplitude of 5D3/25{D}_{3/2}5D3/2​ is obtained by a summation of all possible resonant and nonresonant two-photon transition probability amplitudes via 5P1/25{P}_{1/2}5P1/2​ and 5P3/25{P}_{3/2}5P3/2​. Second-order perturbation theory predicts that the maximal constructive interference of the transition probability amplitudes occurs when the phases of eight different spectrum blocks satisfy four different phase relations. Experiments carried out with spectrally phase-coded laser pulses show good agreement with the theoretical prediction.
We theoretically investigate the nonresonant two-photon absorption (TPA) process in a two-level atom induced by a weak chirped pulse in the frequency domain. According to the extremum condition of the two-photon transition probability (TPTP) at the transition center frequency, we propose a Fresnel-inspired pulse tailoring scheme for TPA that is significantly different from that of Broers et al. [Phys. Rev. A46, 2749 (1992)]. Using this scheme, the TPTP can be focused or eliminated completely by constructively or destructively modulating various pathways of the quantum interference. Our results are a significant improvement on those obtained by Broers et al. and will have potential applications in selective two-photon microscopy and spectroscopy.
Coherent control of the atomic two-photon absorption with shaped single-cycle pulses is examined theoretically in the weak-field regime. The control over the stabilized carrier-envelope phase (CEP) of the pulses is determined as a key parameter allowing the full utilization of the ultrabroad pulse spectrum. This bandwidth is sufficient to provide besides the sequential two-photon pathways, additional Raman-type pathways coupling between the ground and the excited states. The interference between the different pathways is efficiently controlled via the control over the CEP. Simplified two-level model is analyzed in the frequency domain where the rational pulse shaping is applied. The developed intuition is applied to atomic Cs and verified by the exact numerical solution of time-dependent Schrodinger equation.
The manipulation of two 2nd-order quantum pathways has been successfully demonstrated experimentally in atomic Rubidium. This work would explore the coherent control of pathways in the quantum system with N intermediate states connecting the initial and target states. A 4N-block scheme is proposed to control the N 2nd-order pathways which are driven by a weak broadband pulse. The model with N=3 is given as an example to demonstrate our strategy. In this scheme, boundaries of the spectral blocks are functions of the resonant frequencies, and the resonant and non-resonant contributions interfere mutually to achieve the quantum pathway control effectively. The simple strategy may provide a practical choice for pathway manipulation experiments since there are only 2N phase variables to adjust.
Multiphoton transitions can be reached by many routes through a continuum of virtual levels. We show that the transition probability of two-photon and multiphoton processes can be controlled by tailoring the shape of an ultrashort excitation pulse, so that the many paths leading to the final state interfere to give a desired probability amplitude. We analyze the effect of pulse shapes on N-photon absorption as well as on Raman transitions. We show theoretically that certain tailored dark pulses do not excite the system at all, while other shaped pulses induce transitions as effectively as transform limited pulses, even when their peak amplitudes are greatly reduced. These results are confirmed experimentally for two-photon transitions in atomic cesium.