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arXiv:1503.00956

Engineering the initial state in broadband population inversion

Bo Y. Chang, Sheokmin Shin, Ignacio R. Solá

Published Mar 3, 2015• 0 citations
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Abstract

Quantum systems with sublevel structures prevent full population inversion from one manifold of sublevels to the other using strong ultrafast resonant pulses. In this work we explain the mechanism by which this population transfer is blocked. We then develop a novel concept of geometric control, assuming full or partial coherent manipulation within the manifolds and show that by preparing specific coherent superpositions in the initial manifold, full population inversion or full population blockade, {\it i.e} laser-induced transparency, can be achieved. In particular, by parallel population transfer we show how population inversion between the manifolds can be obtained with minimal pulse area. As the number of sublevels increases, population inversion can overcome the pulse area theorem at the expense of full control over the initial manifold of sublevels.

DOI
10.48550/arxiv.1503.00956

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Quantum systems with sublevel structures prevent full population inversion from one manifold of sublevels to the other using strong ultrafast resonant pulses. In this work we explain the mechanism by which this population transfer is blocked. We then develop a novel concept of geometric control, assuming full or partial coherent manipulation within the manifolds and show that by preparing specific coherent superpositions in the initial manifold, full population inversion or full population blockade, {\it i.e} laser-induced transparency, can be achieved. In particular, by parallel population transfer we show how population inversion between the manifolds can be obtained with minimal pulse area. As the number of sublevels increases, population inversion can overcome the pulse area theorem at the expense of full control over the initial manifold of sublevels.
Quantum systems with sublevel structures, like molecules, prevent full population inversion from one manifold of sublevels to the other using ultrafast resonant pulses. We explain the mechanism by which this population transfer is blocked. We then develop a novel concept of geometric control, assuming full or partial coherent manipulation within the manifolds, and show that by preparing specific coherent superpositions in the initial manifold, full population inversion or full population blockade, that is, laser transparency, can be achieved. By properly choosing the relative phases of the initial state, one can interfere in the stimulated emission process, changing the pattern of Rabi oscillations so that full population inversion to the excited electronic state can be achieved almost regardless of the pulse intensity after a minimal threshold value. This is the basis of a novel control mechanism, termed parallel transfer.
The manipulation of population transfer and the creation of an arbitrary superposition between two atomic states in the framework of a closed inverse Y-type four-level system driven by a series of pulse pairs and an external control field is reported. It is shown that when the laser fields are tuned to resonance with respective transitions, the non-adiabatic coupling between two degenerate adiabatic states can be reduced tremendously and complete population transfer from the initial state to the target state can be achieved in a piecewise manner. Moreover, an arbitrary superposition between the initial state and target state can be created by suitably tuning the Rabi frequency of the control laser field, inter-pair time delay, pulse number or intra-pair time delay between the pump and Stokes pulses. This scheme combines stimulated Raman adiabatic passage and temporal coherent control, and may be useful for quantum information processing and control of chemical reactions.
We demonstrate a population inversion in a three-level system via three-photon absorption from a single shaped ultrafast laser pulse. The optimal pulse shape for the inversion is discovered using closed-loop learning control and interpreted via pulse shape parameter scans and numerical integration of the Schrödinger equation. The population inversion is measured using a combination of spontaneous and stimulated emissions. Our results illustrate the importance of dynamic Stark shifts in coherent multi-photon excitation.
We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two- and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the well-known technique of “π-pulse transfer” in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the “π-pulse transfer.” This geometrical picture also allows one to analyze the population transfer by adiabatic passage.
We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two- and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the well-known technique of “π-pulse transfer” in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the “π-pulse transfer.” This geometrical picture also allows one to analyze the population transfer by adiabatic passage.
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.