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Physical Review A

Carrier-envelope-phase effect on laser-driven bound-bound transitions in the high-frequency region

Zhen Zhai, Dian Peng, Xi Zhao, Fu-Ming Guo, Yujun Yang, Panming Fu, Jing Chen, Zong-Chao Yan, Bingbing Wang

Published Oct 26, 2012• 9 citations
Publisher

Abstract

We study the carrier-envelope-phase (CEP) effect of a few-cycle laser pulse on bound-bound transitions in helium in the high-frequency region. Specifically, for the one-photon transition from the $1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S$ to the $2{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}P$ state, the CEP effect increases as the frequency increases; while for the two-photon transition from the $1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S$ to the $3{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}D$ state, the CEP effect shows a peak at a frequency that is almost equal to the energy difference between the ${1}^{1}S$ and $3{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}D$ states. By using a four-level model, we find that the CEP effect on the $1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S$--$2{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}P$ transition is attributed to the quantum interference between the positive-frequency and negative-frequency subpaths of the one-photon transition; whereas the CEP effect on the $1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S$--$3{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}D$ transition is attributed to the interference between the sum-frequency and difference-frequency components of the two-photon transition. These results indicate that the CEP effect can occur not only due to the interference between neighboring multiphoton-transition paths, but also due to the interference between two components inside one multiphoton-transition path. Therefore, this work, together with our previous work for the low-frequency region [Peng et al., Phys. Rev. A 82, 053407 (2010)], may provide a complete picture of the CEP effect on bound-bound transitions in the whole range of laser frequency.

DOI
10.1103/physreva.86.043432

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We study the carrier-envelope-phase (CEP) effect of a few-cycle laser pulse on bound-bound transitions in helium in the high-frequency region. Specifically, for the one-photon transition from the 11S1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S11S to the 21P2{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}P21P state, the CEP effect increases as the frequency increases; while for the two-photon transition from the 11S1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S11S to the 31D3{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}D31D state, the CEP effect shows a peak at a frequency that is almost equal to the energy difference between the 11S{1}^{1}S11S and 31D3{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}D31D states. By using a four-level model, we find that the CEP effect on the 11S1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S11S--21P2{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}P21P transition is attributed to the quantum interference between the positive-frequency and negative-frequency subpaths of the one-photon transition; whereas the CEP effect on the 11S1{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}S11S--31D3{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}D31D transition is attributed to the interference between the sum-frequency and difference-frequency components of the two-photon transition. These results indicate that the CEP effect can occur not only due to the interference between neighboring multiphoton-transition paths, but also due to the interference between two components inside one multiphoton-transition path. Therefore, this work, together with our previous work for the low-frequency region [Peng et al., Phys. Rev. A 82, 053407 (2010)], may provide a complete picture of the CEP effect on bound-bound transitions in the whole range of laser frequency.
We investigate numerically with Hylleraas coordinates the frequency dependence of the carrier-envelope phase (CEP) effect on bound-bound transitions of helium induced by an ultrashort laser pulse of a few cycles. We find that the CEP effect is very sensitive to the carrier frequency of the laser pulse, occurring regularly even at far-off-resonance frequencies. By analyzing a two-level model, we find that the CEP effect can be attributed to the quantum interference between neighboring multiphoton transition pathways, which is made possible by the broadened spectrum of the ultrashort laser pulse. A general picture is developed along this line to understand the sensitivity of the CEP effect to the laser's carrier frequency. Multilevel influence on the CEP effect is also discussed.
Using the characteristic of small energy difference between two high Rydberg states, we theoretically investigate the carrier envelope phase (CEP) effect in a bound-bound transition of an atom in a low-frequency long laser pulse with tens of optical cycles. Particularly, we first prepare a Rydberg state of a hydrogen-like atom by a laser field with the resonant frequency between this state and the ground state. Then by using a low-frequency long laser pulse interacting with this Rydberg atom, we calculate the population of another Rydberg state nearby this Rydberg state at the end of the laser pulse and find that the population changes dramatically with the CEP of the low-frequency pulse. This CEP effect is attributed to the interference between the positive-frequency and negative-frequency components in one-photon transition. These results may provide a method to measure the CEP value of a long laser pulse with low frequency.
We present a general framework for understanding carrier-envelope phase (CEP) effects in a quantum system interacting with an intense, short laser pulse. We establish a simple connection between the CEP and the wave function that can be exploited to obtain the full CEP dependence of an observable given the wave function at a single CEP. Within this framework, all CEP effects are interpreted as interference between different photon amplitudes which, in turn, can be used to put limits on the pulse lengths and intensities required to see significant CEP effects.
By solving the full Maxwell-Bloch equations,the effects of the carrier-envelope phase(CEP)on pulse propagating and spectra characteristics of few-cycle ultra short laser pulses in a dense V type three-level atomic medium are investigated.The results show that the carrier propagation and spectrum evolution of the pulse are sensitive to its CEP and the phase sensitivity is more obvious for larger area pulse.The CEP can affect the amplitude,propagating velocity and pulse splitting case.Moreover,under the same condition,the pulse spectra are affected by the initial carrier-envelope phases due to the different coherence effect,which don't induce obvious changes of higher spectral components.When,the super continuum with wider spectral range and better continuity of high frequency components can be obtained.