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AIP conference proceedings

Extreme Nonlinear Optics: Effect of Carrier Envelope Offset Phase on the Dynamics of Two Level Atomic Systems

Parvendra Kumar, Amarendra K. Sarma, P. Predeep, Mrinal Thakur, M. K. Ravi Varma

Published Jan 1, 2011• 0 citations
Publisher
DOI
10.1063/1.3643646

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Carrier-envelope phase effects for a dipolar molecule interacting with two-color pump-probe laser pulses

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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.

Physical Review A•Dec 17, 2004•19 citations
We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.The analytical solutions for subsequent intervals are then stuck together in an iterative procedure to cover the whole scale time of the laser pulse.Very good quality of the iterative method is shown by recovering with it a number of subtle effects met in earlier numerically calculated photon--emission spectra from model molecular ions, double quantum wells, atoms, and semiconductors.The method is used to describe novel, carrier-envelope offset phase effects in the region of extreme nonlinear optics, i.e., when two--level systems are exposed to pulses of only a few cycles in duration and strength ensuring the Rabi frequency to approach the laser light frequence.
In an approach based on the nonlinear Riccati-type differential equation for the ratio of the level population amplitudes, rather than on the optical Bloch equations, we describe the response of a two-level system to a few--cycle light pulse of intensity from the regime of extreme nonlinear optics, i.e., when the Rabi and transition frequencies are comparable.Emphasis is put on the dependence of the spectra of the scattered light on the carrier--envelope phase, duration and strength of both resonant and off-resonant pulses.
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.