Laser pulse intense, coherent control

We demonstrate coherent control in strong fields beyond (i) population control and (ii) spectral interference, since (i) control is achieved without altering the population during the second intense laser pulse, i.e., the population during the second laser pulse is frozen, and (ii) the quantum mechanical phase is controlled without changing the spectrum of the pulse sequence. The control mechanism relies on the interplay of the quantum mechanical phase set by the intensity of the first pulse and the phase of the second pulse determined by the time delay. 

VII. Coherent Control with Intense Laser Pulses... 

In order to achieve coherent control in a laboratory experiment, three major requirements are to be met. Well-defined final states cannot be reached without the preparation of a well-defined initial state. Ultrashort, spectrally wide and intense laser pulses at different wavelengths must be produced for excitation and a good characterization of the final product states must be achieved. 

VII. COHERENT CONTROL WITH INTENSE LASER PULSES... 

Abstract Recent advances achieved in the numerical resolution of the Time-Dependent Schrodinger Equation (TDSE), have made possible to address difficult problems in the analysis of highly nonlinear processes taking place when an atom is submitted to an ultra-intense laser pulse. We discuss the main properties of the photoelectron spectra obtained when a high frequency harmonic field is also present in addition to the laser field. This class of processes is believed to serve as a basis to explore new secnarios to achieve a coherent control of atomic photoionization. 

A negative chirped pulse is shown in Figure 6.4c. Experiments and theoretical studies on coherent control of ultrafast electron dynamics by intense chirped laser pulses will be discussed in Sections 6.3.2.3 and 633.2. 

Finally, coherent transfer of population between electronic states was demonstrated using intense ultrashort laser pulses of different durations. Aided by calculations, it was shown that the population in various neutral electronic states of both Na2 and Na3 at the end of the interaction with a laser pulse can be controlled by varying the laser intensity. A second (intense) probe laser was used to ionize the molecules. The Fourier transform obtained from the transient ion signal can be used to experimentally monitor the population distribution created by the first laser pulse. 

Figure 1. Diagram of the intensity / (W/cm2) vs. duration of laser pulse tp(s) with various regimes of interaction of the laser pulse with a condensed medium being indicated very qualitatively. At high-intensity and high-energy fluence 4> = rpI optical damage of the medium occurs. Coherent interaction takes place for subpicosecond pulses with tp < Ti, tivr. For low-eneigy fluence (4> < 0.001 J/cm2) the efficiency of laser excitation of molecules is very low (linear interaction range). As a result the experimental window for coherent control occupies the restricted area of this approximate diagram with flexible border lines.

Selective excitation of wavepackets with ultrashort broadband laser pulses is of fundamental importance for a variety of processes, such as the coherent control of photochemical reactions [36-39] or isotope separation [40--42]. It can also be used to actively control the molecular dynamics in a dissipative environment if the excitation process is much faster than relaxation. For practical applications it is desirable to establish an efficient method that allows one to increase the target product yield by using short laser pulses of moderate intensity before relaxation occurs [38]. 

Finally we note that studies of control in solution [186, 187] indicate that control in the presence of collisional effects is indeed possible. For example, coherent control of the dynamics of I3 in ethanol and acetonitrile has been demonstrated. Specifically, I3 was excited with a 30-fs ultraviolet (UV) laser pulse to the first excited state, The resultant wave function was comprised of a localized wave function on the ground electronic state and a corresponding depletion of wave function density, that is, a hole, on the ground electronic state. In this instance the target of the control was the nature of the spectrum associated with the coherences associated with the symmetric stretch. By manipulating various attributes of the exciting pulse (intensity, frequency, and chirp of the excitation pulse), aspects of the spectrum were controlled, despite the decoherence associated with collision effects. 

The dynamics of populations of the electronic states in a 4,4 -bis(dimethylamino) stilbene molecule (two-photon absorption) was studied against the frequency, intensity, and shape of the laser pulse [52]. Complete breakdown of the standard rotating wave for a two-photon absorption process was observed. An analytical solution for the interaction of a pulse with a three-level system beyond the rotating wave approximation was obtained in close agreement with the strict numerical solution of the amplitude equations. Calculations showed the strong role of the anisotropy of photoexcitation in the coherent control of populations that can affect the anisotropy of photobleaching. The two-photon absorption cross section of an ethanol solution of a trans-stilbene and its derivatives exposed to radiation of the second harmonic of a Nd YAG laser (532 nm) of nanosecond duration has been detected [53]. In experiments, the method based on the measurement of the photochemical decomposition of examined molecules was used. The quantum yield of the photoreaction (y266) of dyes under one-photon excitation (fourth harmonic Nd YAG laser 266 nm) was detected by absorption method. 

The fact that such an experimental window for coherent control in liquids does actually exist was verified in experiments on the selective multiphoton excitation of two distinct electronically and structurally complex dye molecules in solution (Brixner et al. 2001(b)). In these experiments, despite the failure of single-parameter variation (wavelength, intensity or linear chirp control), adaptive femtosecond pulse shaping revealed that complex laser fields could achieve chemically selective molecular excitation. These results prove, first, that the phase coherence of complex molecules persists for more than 100 fs in a solvent environment. Second, this is direct proof that it is the nontrivial coherent manipulation of the excited state and not of the frequency-dependent two-photon cross sections that is responsible for the coherent control of the population of the excited molecular state. 

Fig. 12.8 Diagram of radiation intensity I (W/cm ) versus laser pulse duration Tp (s), with the various laser-pulse-condensed-medium interaction regimes being indicated very qualitatively. At high radiation intensities I and energy fluences

Leaving aside the important problem of interaction between ultrahigh-intensity femtosecond laser pulses and relativistic electrons, we shall consider below only the effects involved in the control of non relativistic electrons, such as coherent diffraction, deflection, focusing, and reflection. The diffraction of an electron beam by a standing light wave (the Kapitza-Dirac effect, Kapitza and Dirac 1933) is essentially the earliest proposal for the control of matter by light. 

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