Trichromatic π-Pulse for Ultrafast Total Inversion of a Four-Level Ladder System

Abstract

We present a numerical solution for complete population inversion in a four-level ladder system obtained by using a full π-pulse illumination scheme with resonant ultrashort phase-locked Gaussian laser pulses. We find that a set of pulse areas such as √ 3π, 2π, and √ 3π completely inverts the four-level system considering identical effective dipole coupling coefficients. The solution is consistent provided the involved electric fields are not too strong and it is amply accurate also in the case of diverse transition dipole moments. We study the effect of detuning and chirp of the laser pulses on the complete population inversion using the level structure of atomic sodium interacting with ps and fs pulses as an example. Our result opens the door for multiple applications such as efficient ultrashort pulse lasing in the UV or the engineering of quantum states for quantum computing.

Control of rubidium low-lying Rydberg states with trichromatic femtosecond π pulses for ultrafast quantum information processing

“…This frequency shift of the transition is hence of the order of the linewidth of the 75 fs laser pulse (195.7 cm −1 ) and, as it was also discussed in [38], it prevents optimal π-pulse population inversion (see black-thin lines in Fig. 4).…”

“…In the present paper, we show that this impediment can be circumvented by using trichromatic π-pulse excitation, an approach that was recently reported as a robust method for complete population inversion in a four-level system [38]. We show that the higher values of the dipole coupling coefficients associated to the transitions in a four-level scheme allow for ultrafast excitation of low-lying Rydberg states, without the need of deep UV wavelengths and with field intensities that avoid significant ac-Stark effects.…”

“…Figure 1 illustrates the basic control mechanisms of trichromatic π-pulse excitation in a four-level ladder system, as it was also reported in [38]. From left to right in Fig.…”

“…The ground state is the 5S 1/2 level of Rb (level 1), which is coupled with a 420.2 nm laser pulse to the 6P 3/2 (level 2), with µ 12 = 0.54 × 10 −29 Cm. The laser pulse has an area of √ 3π [38]. The 6P 3/2 level is coupled to the 6D 3/2 (level 3) with a 772.69 nm laser pulse, with µ 23 = 1.01 × 10 −29 Cm.…”

“…For ultrafast control, π-pulse polychromatic control techniques benefit from the fact that no delay between pulses is involved as compared to adiabatic schemes, so that the interaction time remains of the order of the laser pulse temporal width. The control of population transfer between a pair of quantum states involving single or polychromatic transitions by illuminating the atom with resonant π-pulses has extensively been implemented using from long to ultrashort pulses [32,37,38]. For the case of a four-level ladder system, population transfer schemes combining adiabatic and π-pulse techniques have also been proposed [39].…”