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Chinese Physics Letters

Carrier Envelope Phase Effect of a Long Duration Pulse in the Low Frequency Region

Xi Zhao, Yang Yu-Jun, Xue‐Shen Liu, Bingbing Wang

Published Apr 1, 2014• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/31/4/043202

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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 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.
We present an experimental and theoretical study of carrier-envelope-phase (CEP) effects on the population transfer between two bound atomic states interacting with pulses consisting of many cycles. Using intense radio-frequency pulse with Rabi frequency of the order of the atomic transition frequency, we investigate the influence of the CEP on the control of phase-dependent multiphoton transitions between the Zeeman sublevels of the ground state of 87Rb^{87}\mathrm{Rb}87Rb. Our scheme has no limitation on the duration of the pulses. Extending the CEP control to longer pulses creates interesting possibilities to generate pulses with accuracy that is better than the period of optical oscillations.
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.
We present an experimental and theoretical study of the carrier-envelope phase effects on population transfer between two bound atomic states interacting with intense ultrashort pulses. Radio frequency pulses are used to transfer population among the ground state hyperfine levels in rubidium atoms. These pulses are only a few cycles in duration and have Rabi frequencies of the order of the carrier frequency. The phase difference between the carrier and the envelope of the pulses has a significant effect on the excitation of atomic coherence and population transfer. We provide a theoretical description of this phenomenon using density matrix equations. We discuss the implications and possible applications of our results.
The interaction of a two-level dipolar molecule with two laser pulses, where one laser's frequency is tuned to the energy level separation (pump laser) while the second laser's frequency is extremely small (probe laser), is investigated. A dipolar molecule is one with a nonzero difference between the permanent dipole moments of the molecular states. As shown previously [A. Brown, Phys. Rev. A 66, 053404 (2002)], the final population transfer between the two levels exhibits a dependence on the carrier-envelope phase of the probe laser. Based on the rotating-wave approximation (RWA), an effective Hamiltonian is derived to account for the basic characteristics of the carrier-envelope phase dependence effect. By analysis of the effective Hamiltonian, scaling properties of the system are found with regard to field strengths, pulse durations, and frequencies. According to these scaling properties, the final-state population transfer can be controlled by varying the carrier-envelope phase of the probe laser field using lasers with weak field strengths (low intensities) and relatively long pulse durations. In order to examine the possible roles of background states, the investigation is extended to a three-level model. It is demonstrated that the carrier-envelope phase effect still persists in a well-defined manner even when neighboring energy levels are present. These results illustrate the potential of utilizing excitation in dipolar molecules as a means of measuring the carrier-envelope phase of a laser pulse or if one can manipulate the carrier envelope phase, as a method of controlling population transfer in dipolar molecules. The results also suggest that the carrier-envelope phases must be taken into account properly when performing calculations involving pump-probe excitation schemes with laser frequencies which differ widely in magnitude.