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Journal of Theoretical and Computational Chemistry

Population transfer through multiple channels in two harmonic laser pulses

Rong Wang, Ying‐Yu Niu

Published May 15, 2020• 1 citation
Publisher

Abstract

The processes of population transfer in the ground electronic state of HCl molecule through the three transition schemes are investigated by numerically solving the time-dependent Schrödinger equation. Two harmonic pulses are employed to induce population transfer and the relative phase of the two pulses can control the final population distributions. In the ladder transition scheme, the variation range of the target population with the relative phase is nearly 100% which is larger than that in the multi-photon transition scheme. It is more efficient for the mixed transition scheme to control population transfer between the initial and target states by using the relative phase. Comparing with the multi-photon and ladder schemes, the transition probability of the target population is more sensitive to the two pulse amplitudes in the mixed transition scheme.

DOI
10.1142/s0219633620500236

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The processes of population transfer in the ground electronic state of HCl molecule through the three transition schemes are investigated by numerically solving the time-dependent Schrödinger equation. Two harmonic pulses are employed to induce population transfer and the relative phase of the two pulses can control the final population distributions. In the ladder transition scheme, the variation range of the target population with the relative phase is nearly 100% which is larger than that in the multi-photon transition scheme. It is more efficient for the mixed transition scheme to control population transfer between the initial and target states by using the relative phase. Comparing with the multi-photon and ladder schemes, the transition probability of the target population is more sensitive to the two pulse amplitudes in the mixed transition scheme.
The extended “ladder” transition controlled by two harmonic pulses is investigated by using a time-dependent quantum wave packet method. The molecular population transfers from the state|0, 0> angle to the states|5, 0> angle and|5, 2> angle induced by the fundamental and second-harmonic pulses, and to the states|5, 3> angle and |6, 2> angle induced by the fundamental and third-harmonic pulses. The calculated results show that the two harmonic pulses can induce a nearly 100% of population to transfer to the target state. The relative phase of two pulses can affect the population distribution. The variation of population has a period of π for the fundamental and second-harmonic pulses, and a period of 2π for the fundamental and third-harmonic pulses.
A time-dependent quantum wave-packet method is employed to investigate the rovibrational dynamics of population transfer in the ground electronic state controlled by two-color ($\ensuremath{\omega}+2\ensuremath{\omega}$) pulses analogous to coherently control the processes of ionization and dissociation. The population can be transferred to three target states, $|4,1\ensuremath{\rangle},\phantom{\rule{0.16em}{0ex}}|0,1\ensuremath{\rangle}$, and $|4,0\ensuremath{\rangle}$, at the same time through the ladder $\ensuremath{\Lambda}$ and multiphoton transitions. With the variation of the relative phase between $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ pulses, the population distributions show oscillation behavior with a period of $\ensuremath{\pi}$. The population variation with relative phase depends on the size of the electric field asymmetry. The probabilities transferred to different target states can be controlled by varying the pulse amplitudes.
The multiphoton transition is investigated theoretically by using wave packet method for the ground electronic state of HF molecule. A laser field composed of two overlapping infrared pulses is used in our model, and the ratio of their frequencies is 1:2. States |4,0> and |4,2> are chosen as target states. Calculated results show that the population can be transferred to different target states as the corresponding resonant frequency is chosen. The probability of the population transfer can be controlled by the initial phase difference of the two pulses. When the initial phase difference is of an odd number of π/2, the probability of population transfer reaches the maximal value. When the initial phase difference is of an even number of π/2, the probability of population transfer reaches the minimum value. In comparison with the state |4,2>, the initial phase difference has a stronger in fluence on the population of the state |4,0>.
The population transfer of stimulated Raman adiabatic passage (STIRAP) is investigated using a time-dependent quantum wave packet method. The population is transferred from an initial state to a target state through the interaction of the external laser field with the permanent dipole moment and the transition dipole moment. The laser field is composed of an infrared pulse and a near ultraviolet pulse. The two pulses with small detunings are more efficient to achieve the STIRAP transition. The process of STIRAP is sensitive to the detunings of the two pulses. When the two detunings are the same in a Λ transition or the positive detuning of the pump pulse is equal to the negative detuning of the Stokes pulse in a ladder transition, the final population in the intermediate state can be eliminated and the target population is increased.
A chirped laser pulse transfers population from one level to another level accessible by one photon dipole transition. We have used a pair of phase-locked chirped pulses of same frequency instead of a single chirped pulse to achieve phase control over the population transfer and thus creating coherent population distribution in hydrogen molecule. Simultaneous actions of the phase controlled interference and rapid adiabatic passages due to chirped pulses lead to the control in population transfer from the ground X(v = 0, j = 0) level to the C(v = 2, j = 1) level. We have extended this two-level system to a three-level 1 + 1 ladder system for population transfer from the X level to the J(v = 2, j = 2) level via the C intermediate level using two pairs of phase-locked laser chirped pulses and have achieved laudable control over the coherent population distribution.
Two simple schemes are presented for the selective population transfer in systems where the target state is degenerate with a second level. Both states are coupled with the ground state via a one photon resonance. The schemes use a combination of two laser pulses. The first pulse breaks the degeneracy of the levels by inducing a Stark shift. The second pulse is chirped across the new levels. The idea is illustrated by numerical simulations of the time-dependent Schr\"odinger equation for a four-level system. The efficient population transfer is explained using a dressed state representation. In conclusion, applications for molecules are suggested.