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Physical Review A

Effect of a transient light shift on the propagation of an ultrashort pulse in a resonant atomic medium

Jean-Christophe Delagnes, M. A. Bouchène

Published Jun 22, 2004• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.69.063813

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An ultrashort weak pulse that propagates resonantly on the \ensuremath∣a⟩\ensuremath→\ensuremath∣b⟩\ensuremath{\mid}a⟩\ensuremath{\rightarrow}\ensuremath{\mid}b⟩\ensuremath∣a⟩\ensuremath→\ensuremath∣b⟩ transition of a three-level system (\ensuremath∣a⟩,\ensuremath∣b⟩,\ensuremath∣c⟩)(\ensuremath{\mid}a⟩,\ensuremath{\mid}b⟩,\ensuremath{\mid}c⟩)(\ensuremath∣a⟩,\ensuremath∣b⟩,\ensuremath∣c⟩) experiences reshaping effects on a time scale longer than its duration. When a strong field is applied (nonresonantly) on the \ensuremath∣b⟩\ensuremath→\ensuremath∣c⟩\ensuremath{\mid}b⟩\ensuremath{\rightarrow}\ensuremath{\mid}c⟩\ensuremath∣b⟩\ensuremath→\ensuremath∣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.
An ultrashort strong nonresonant pulse induces transient phenomena in an optically thick medium consisting of an ensemble of nondegenerate two-level atoms (nonadiabatic transitions, transient light-shifts,\dots{}). A weak resonant pulse propagates in the system and we study theoretically and numerically the temporal and spectral modifications that are induced. Moreover, we show that the atomic media, modified by a strong pulse can act as a ``pulse-shaper'' device that can modify, in a controlled way, the shape of the weak pulse. It maps out the transient light shift induced by the strong pulse and reduces efficiently the long time dispersion tail of the weak pulse. We study and discuss the physical phenomena that allow such shaping effects and the necessary conditions to satisfy in order to observe them.
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).
A weak resonant femtosecond pulse propagates through an optically thick atomic medium whose properties have been modified by a strong nonresonant ultrashort pulse. We study the energy redistribution between the spectral components of the weak resonant pulse using both experimental and theoretical methods. The transmitted spectrum exhibits an asymmetric feature that reveals an important gain-dispersion coupling. For light shifts that perturb slightly the propagation of the weak resonant pulse, this asymmetry maps out the asymptotic part of the linear susceptibility.
We present a detailed study of the interaction of ultrashort laser pulses with a resonant three level system (fine structure levels of rubidium). As expected, for low intensities a linear model and for higher intensities a semiclassical model (Maxwell-Bloch) is fully sufficient to describe the observed results. In both cases, however, it is essential to have an accurate knowledge of the incident electric field, i.e., the amplitude and the phase, in order to simulate the interaction process. It is shown that on small time scales the phase modulation of the incident pulse influences the reshaping process during pulse propagation whereas on longer time scales the reshaping is solely governed by the dynamics of the atomic system.
The spectrum evolution of a few-cycle optical pulse in a resonant two-level atom medium is studied theoretically by using the full Maxwell-Bloch equations. On the propagating pulse, significantly much faster oscillation components separated with the main pulse appear due to strong self-phase modulation and pulse reshaping. In this case, ideal self-induced transparency cannot occur for a 2π pulse. The spectrum of the 4π pulse shows an evident oscillatory feature because of the continuum interference of the separate pulses. For larger pulse areas, continuum generation from near ultraviolet to infrared occurs.