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Journal of Modern Optics

Dynamics and interference of fine-structure wave packets created by strong ultrashort pulses

Céline Nicole, M. A. Bouchène, B. Girard

Published Jan 1, 2002• 5 citations
Publisher

Abstract

This work presents a theoretical study of two coherent schemes which allow the manipulation of wave packets created in atomic systems by strong ultrashort pulses. Our three-state system is composed of a ground state and two excited states simultaneously excited by the laser pulses. The corresponding dynamics are described in the bright state-dark state formalism where spectacular effects appear. (1) The wave packet created initially by a first pulse can be completely frozen through the action of a second strong pulse. (2) For pulses with a generalized pulse area equal to (2 p +1)2π (p integer), the population is preferentially transferred from the ground state to the dark state whatever the pulse duration. This is in complete disagreement with the physical interpretation valid in the weak field regime where the wave packet created by an ultrashort pulse is localized in the bright state at the end of the pulse. This effect can be revealed with wave packet interference induced by a second identical pulse. A simple analytical model using squared pulses is used to highlight the physical insight. This model is ‘reinforced’ by numerical simulations on the (4s–4p 2 P 1/2,1/3) transitions in potassium atoms excited with Gaussian pulses.

DOI
10.1080/09500340110074745

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This work presents a theoretical study of two coherent schemes which allow the manipulation of wave packets created in atomic systems by strong ultrashort pulses. Our three-state system is composed of a ground state and two excited states simultaneously excited by the laser pulses. The corresponding dynamics are described in the bright state-dark state formalism where spectacular effects appear. (1) The wave packet created initially by a first pulse can be completely frozen through the action of a second strong pulse. (2) For pulses with a generalized pulse area equal to (2 p +1)2π (p integer), the population is preferentially transferred from the ground state to the dark state whatever the pulse duration. This is in complete disagreement with the physical interpretation valid in the weak field regime where the wave packet created by an ultrashort pulse is localized in the bright state at the end of the pulse. This effect can be revealed with wave packet interference induced by a second identical pulse. A simple analytical model using squared pulses is used to highlight the physical insight. This model is ‘reinforced’ by numerical simulations on the (4s–4p 2 P 1/2,1/3) transitions in potassium atoms excited with Gaussian pulses.
A sequence of two femtosecond pulses---a strong driving $\ensuremath{\pi}$-polarized pulse and a weak propagating $\ensuremath{\sigma}$-polarized pulse---excites resonantly the ${S}_{1∕2}\ensuremath{\rightarrow}{P}_{1∕2}$ transition of an atomic system. Strong interference effects take place in the system between absorption and emission paths leading to a substantial amplification of the $\ensuremath{\sigma}$ pulse. We study the influence of the fine structure on the medium gain when the contribution of the off-resonant P3∕2{P}_{3∕2}P3∕2​ level is taken into account. A drastic reduction of the medium gain is obtained. This effect is explained within the bright-state--dark-state formalism where the strong driving pulse creates a wave packet that can be trapped in a state---the bright state---leading to a significant reduction of the gain for the $\ensuremath{\sigma}$ pulse. Finally, we also show that periodical gain dependence with the driving pulse energy exhibits a significant change in its period value (compared with expected Rabi oscillations).
A sequence of two identical ultrashort laser pulses creates quantum interferences in an atom. In the weak-field regime, the observed beats between interferences arising from various transitions are not a conclusive signature of wave-packet creation. On the contrary, in the saturation regime, the appearance of slow modulation is. We report on the observation of such modulations in atomic potassium in this field regime. The results are explained within the bright-state--dark-state framework. The wave packet corresponds to the precession of the electronic spin and orbital angular momentum.
Rabi oscillations of quantum population are known to occur in two-level systems driven by spectrally narrow laser fields. In this work we study Rabi oscillations induced by shaped broadband femtosecond laser pulses. Due to the broad spectral width of the driving field, the oscillations are initiated between a ground state and a coherent superposition of excited states, or a ``wave packet,'' rather than a single excited state. Our experiments reveal an intricate dependence of the wave-packet phase on the intensity of the laser field. We confirm numerically that the effect is associated with the strong-field nature of the interaction and provide a qualitative picture by invoking a simple theoretical model.
This thesis investigates quantum dynamics induced in atoms by ultrashort pulses of light. The work is motivated by recent developments in free-electron lasers, which generate ultrashort pulses of intense, coherent light and enable coherent control of quantum dynamics. We develop theoretical models to study the processes of absorption and emission in laser-atom interactions. Additionally, we study photoionisation, which creates an ion and an electron, and the entanglement that can be generated between these particles. Finally, we have investigated how the spontaneous decay of the ion induces entanglement transfer from the ion-electron pair to the electron-photon pair.This thesis compiles seven papers. Paper I investigates the absorption of light from an attosecond pulse by an atom in a prepared coherent superposition of states. We show how the evolution of the phase of the superposition wave packet influences the attosecond transient absorption spectra. Paper II predicts the existence of Mollow-like triplets in the absorption spectra of strongly coupled atoms. We establish the conditions for the pulse envelope under which this triplet pattern can be supported.Paper III studies two-photon Rabi oscillations, establishing which systems can sustain such dynamics. We find that a two-photon Rabi oscillating system can induce giant counter-rotating oscillations in the population dynamics, enabling investigations of physical effects beyond the rotating-wave approximation.Paper IV studies ionisation from an atom strongly coupled by a dichromatic field, where interference between the two frequency components shapes the temporal symmetry of the atomic dynamics, allowing for coherent control of the photoelectron distribution.Paper V considers an experiment performed at a Free-Electron Laser facility where a helium atom is ionised and the resulting ion is subsequently strongly coupled. The photoelectron spectra are theoretically reproduced and the entanglement between the ion and photoelectron is studied. Paper VI investigates how the entanglement in the ion--electron pair, generated via photoionisation followed by strong coupling, can be coherently controlled by harnessing the time symmetry of the pulse. We find that the observable manifestation of the entanglement can be altered in such a way that the electron energy becomes associated with the ionic state, allowing the entanglement to be detected via coincidence measurements. Paper VII investigates how quantum correlations between the ion and the electron can be coherently controlled by sequential strong coupling of the ion. We find that both the build-up of entanglement and its manifestation can be controlled, and we establish a quantitative measure of the amplitude entanglement that explains the dynamics in an intuitive way. Paper VIII studies the process of entanglement transfer induced by the spontaneous decay of the ion. We find that the ion--electron entanglement generated during the ultrashort interaction with the laser field is transferred to the electron--photon system over the much longer timescale of fluorescence.
We theoretically analyze the interaction of a quantum system with a single ground state and three excited states that interacts with a pulsed laser field. The three excited states decay outside of the system to the same state. The dynamics of the system is studied by solving the coupled Maxwell-Schr\"odinger equations. We first present conditions for obtaining dark states of the system. These dark states lead to the phenomenon of coherent population trapping for strong applied fields. In addition, the existence of dark states leads to transparency at two different frequencies of a probe field. Slow light, at two different frequencies, can also occur. We present analytical results and verify those results with numerical solutions of the coupled Maxwell-Schr\"odinger equations.
In this article, we describe an analytic approach to the quantum control of wave-packet dynamics. In particular, we show that the field that will produce a specified wave packet in a Rydberg atom can be found approximately from a simple analytic formula. This analytic solution is shown to hold even in the regime of strong excitation, and is found by limiting the duration of the pulsed control field to less than one Kepler period of the system. Comparison with a direct numerical integration of Schr\"odinger's equation shows that our solution yields the target state and population transfer with very high fidelity. The possibility of ionization to the continuum is also included in the model. The solution provides some insight into the multiplicity of solutions to the control problem and the relative complexity of the control-field shapes in the weak- and strong-response regimes.