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.
Highlights
Control of population transfer in multiphoton transitions in atoms and molecules with laser pulses is a fundamental tool that has been extensively investigated in quantum optics since the advent of ultrashort pulses due to its value in several areas, including nonlinear spectroscopy [1], femtochemistry and biology [2], or in quantum information and in the quantum engineering of light states [3], where quantum systems need to be fully controlled
In this paper we present a numerical solution for complete population inversion in a four-level ladder system by using full π-pulse control
We have solved numerically the Liouville equations for a four-level ladder system coherently interacting with a tricolor pulse without the assumptions of the rotating-wave approximation (RWA)
Summary
Control of population transfer in multiphoton transitions in atoms and molecules with laser pulses is a fundamental tool that has been extensively investigated in quantum optics since the advent of ultrashort pulses due to its value in several areas, including nonlinear spectroscopy [1], femtochemistry and biology [2], or in quantum information and in the quantum engineering of light states [3], where quantum systems need to be fully controlled. Several techniques have been reported for control of population transfer between a pair of quantum states involving multiphoton transitions, such as spectral shaping of the fields illuminating the medium [4,5], adiabatic methods [6,7,8,9] and π-pulse polychromatic control [10,11,12,13]. Full π-pulse polychromatic control techniques are preferred in some cases because the intensities required for optimal excitation are on the order of the intensities for resonantly pumped single-photon transitions, and they result energetically more efficient than adiabatic methods. In this paper we present a numerical solution for complete population inversion in a four-level ladder system by using full π-pulse control
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