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Physical Review A

Influence of wave-packet dynamics on the medium gain of an atomic system

Jean-Christophe Delagnes, M. A. Bouchène

Published Oct 30, 2007• 9 citations
Publisher

Abstract

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 ${P}_{3∕2}$ 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).

DOI
10.1103/physreva.76.045805

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A sequence of two femtosecond pulses---a strong driving \ensuremathπ\ensuremath{\pi}\ensuremathπ-polarized pulse and a weak propagating \ensuremathσ\ensuremath{\sigma}\ensuremathσ-polarized pulse---excites resonantly the S1∕2\ensuremath→P1∕2{S}_{1∕2}\ensuremath{\rightarrow}{P}_{1∕2}S1∕2​\ensuremath→P1∕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 \ensuremathσ\ensuremath{\sigma}\ensuremathσ 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 \ensuremathσ\ensuremath{\sigma}\ensuremathσ 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 femtosecond coherent pulses--a strong pi-polarized pulse and a weak sigma-polarized pulse--excite the S1/2-P1/2 transition of atomic rubidium in an optically dense vapor. The sigma pulse induces transitions between the adiabatic states with a coupling strength that is different for identically and oppositely light-shifted coupled states, and that can be modified by tuning the relative phase between the pulses. An efficient control of the medium gain for the sigma pulse is experimentally demonstrated. It is shown to be the result of interference between the absorption and the stimulated emission paths for sigma photons.
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.
We consider a duplicated two-level system where each two-level subsystem is driven by a strong resonant femtosecond pulse and a weak resonant femtosecond pulse connects cross transitions. Strong interference effects are induced in such a configuration leading to a modulation of the medium gain as a function of the relative phase between the pulses []. We study here the influence of the temporal overlap between the pulses on the dynamics of the system and the medium gain. We show that the dynamics is dominated by two competing phenomena: Light shifts (LS) induced by the driving pulse that prevails for small delays and free induction decay (FID) that prevails for large delays. LS enhance the medium gain for and reduce it for , whereas FID always leads to a decrease of the medium gain.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi.  In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).
An ultrashort weak pulse that propagates resonantly on the $\ensuremath{\mid}a⟩\ensuremath{\rightarrow}\ensuremath{\mid}b⟩$ transition of a three-level system $(\ensuremath{\mid}a⟩,\ensuremath{\mid}b⟩,\ensuremath{\mid}c⟩)$ experiences reshaping effects on a time scale longer than its duration. When a strong field is applied (nonresonantly) on the $\ensuremath{\mid}b⟩\ensuremath{\rightarrow}\ensuremath{\mid}c⟩$ transition, important light shifts are induced. We have theoretically studied the novel behavior of both the medium and weak propagating laser pulses in such conditions. For the transmitted field profile, drastic changes occur: at long times, efficient reduction of the distortion is obtained, while strong oscillations appear for short times, mapping out the dynamical light shift. These shaping effects, which are accompanied by new features in the spectrum for the propagating pulse, are interpreted as the result of the interference between incident field and induced dipole radiated field, whose frequency sweeps in time because of the induced light shift.
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.