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Physical Review A

Carrier-envelope phase-dependent atomic coherence and quantum beats

Ying Wu, Xiaoxue Yang

Published Jul 26, 2007• 115 citations
Publisher

Abstract

It is shown that the carrier-envelope phase (CEP) of few-cycle laser pulses has profound effects on the bound-state atomic coherence even in the weak-field regime where both tunneling and multiphoton ionization hardly take place. The atomic coherence thus produced is shown to be able to be mapped onto the CEP-dependent signal of quantum beats (and other quantum-interference phenomena) and hence might be used to extract information about and ultimately to measure the carrier-envelope phase.

DOI
10.1103/physreva.76.013832

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Optics Express•Mar 25, 2011•6 citations
It is shown that the carrier-envelope phase (CEP) of few-cycle laser pulses has profound effects on the bound-state atomic coherence even in the weak-field regime where both tunneling and multiphoton ionization hardly take place. The atomic coherence thus produced is shown to be able to be mapped onto the CEP-dependent signal of quantum beats (and other quantum-interference phenomena) and hence might be used to extract information about and ultimately to measure the carrier-envelope phase.
The quantum dynamics of a two-level system illuminated by a few-cycle pulse with an adjustable carrier-envelope (C-E) phase is investigated theoretically. We consider the weak-field regime where tunneling processes and multiphoton ionization are negligible. It is shown that the upper state population exhibits a strong dependence on the C-E phase and on the time of arrival of the few-cycle pulse if the system is initially prepared in a coherent superposition state. We demonstrate that this effect can be employed to probe the coherence properties of the superposition state and allows one to determine the phase of the laser that prepares this state.
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.
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.
Weak-field coherent phase control of atomic non-resonant multiphoton excitation induced by shaped femtosecond pulses is studied theoretically in the single-cycle regime. The carrier-envelope phase (CEP) of the pulse, which in the multi-cycle regime does not play any control role, is shown here to be a new effective control parameter that its effect is highly sensitive to the spectral position of the ultrabroad spectrum. Rationally chosen position of the ultrabroadband spectrum coherently induces several groups of multiphoton transitions from the ground state to the excited state of the system: transitions involving only absorbed photons as well as Raman transitions involving both absorbed and emitted photons. The intra-group interference is controlled by the relative spectral phase of the different frequency components of the pulse, while the inter-group interference is controlled jointly by the CEP and the relative spectral phase. Specifically, non-resonant two- and three-photon excitation is studied in a simple model system within the perturbative frequency-domain framework. The developed intuition is then applied to weak-field multiphoton excitation of atomic cesium (Cs), where the simplified model is verified by non-perturbative numerical solution of the time-dependent Schrödinger equation. We expect this work to serve as a basis for a new line of femtosecond coherent control experiments.