Laser pulses field control

One of the most widely used theoretical laser optimization routines for molecular laser control is OCT due to its relative ease in implementation and monotonic convergence, see recent reviews [12-14] and the many references therein. Optimization of the laser pulse occurs in the time-domain. Beyond the initial implementation [61], further investigations developed important features such as constraints on the frequency spectrum[62-64] and optimization of the laser pulse duration[65-67], both of which are required to produce laser pulses comparable to those obtained experimentally. Within OCT an objective function, J, is maximized according to constraints on the required excitation, constraints on the laser pulse field and it must also satisfy the TDSE. These constraints are represented by each term in the objective function, respectively. 

Tannor D J 1994 Design of femtosecond optical pulses to control photochemical products Molecules in Laser Fields ed A Bandrauk (New York Dekker) p 403... 

The ability to create and observe coherent dynamics in heterostructures offers the intriguing possibility to control the dynamics of the charge carriers. Recent experiments have shown that control in such systems is indeed possible. For example, phase-locked laser pulses can be used to coherently amplify or suppress THz radiation in a coupled quantum well [5]. The direction of a photocurrent can be controlled by exciting a structure with a laser field and its second harmonic, and then varying the phase difference between the two fields [8,9]. Phase-locked pulses tuned to excitonic resonances allow population control and coherent destruction of heavy hole wave packets [10]. Complex filters can be designed to enhance specific characteristics of the THz emission [11,12]. These experiments are impressive demonstrations of the ability to control the microscopic and macroscopic dynamics of solid-state systems. 

In Section II, the basic equations of OCT are developed using the methods of variational calculus. Methods for solving the resulting equations are discussed in Section III. Section IV is devoted to a discussion of the Electric Nuclear Bom-Oppenhermer (ENBO) approximation [41, 42]. This approximation provides a practical way of including polarization effects in coherent control calculations of molecular dynamics. In general, such effects are important as high electric fields often occur in the laser pulses used experimentally or predicted theoretically for such processes. The limits of validity of the ENBO approximation are also discussed in this section. 

All of the methods for designing laser pulses to achieve a desired control of a molecular dynamical process require the solution of the time-dependent Schrodinger equation for the system interacting with the radiation field. Normally, this equation must be solved many times within an iterative loop. Different possible approaches to the solution of these equations are discussed in Section V. 

Optimal control theory, as discussed in Sections II-IV, involves the algorithmic design of laser pulses to achieve a specified control objective. However, through the application of certain approximations, analytic methods can be formulated and then utilized within the optimal control theory framework to predict and interpret the laser fields required. These analytic approaches will be discussed in Section VI. 

Plasma filaments generated in the atmosphere by ultrashort laser pulses therefore appear to be able to trigger electric events in thunderclouds under high positive electric field. This result constitutes a first step towards laser-controlled lightning. 

Although ordinary STIRAP becomes less effective if the interval between the Stokes and pump lasers is small, higher efficiency is obtained by using shorter T2p - T 25 in the STIRAP + CDF control process. The width of the counter-diabatic pulse field becomes large for small 72... 

The modification of the electronic potentials due to the interaction with the electric field of the laser pulse has another important aspect pertaining to molecules as the nuclear motion can be significantly altered in light-induced potentials. Experimental examples for modifying the course of reactions of neutral molecules after an initial excitation via altering the potential surfaces can be found in Refs 56, 57, where the amount of initial excitation on the molecular potential can be set via Rabi-type oscillations [58]. Nonresonant interaction with an excited vibrational wavepacket can in addition change the population of the vibrational states [59]. Note that this nonresonant Stark control acts on the timescale of the intensity envelope of an ultrashort laser pulse [60]. 

Figure 6.2 Steering of photochemical reactions by coherent control of ultrafast electron dynamics in molecules by shaped femtosecond laser pulses. Ultrafast excitation of electronic target states in molecules launches distinct nuclear dynamics, which eventually lead to specific outcomes of the photochemical reaction. The ability to switch efficiently between different electronic target channels, optimally achieved by turning only a single control knob on the control field, provides an enhanced flexibility in the triggering of photochemical events, such as fragmentation, excited state vibration, and isomerization.

As mentioned in the introduction, the ability to shape femtosecond laser pulses with unprecedented precision is the key to efficient control of photophysical and photochemical processes at the quantum level. In this section, we present the fundamentals of femtosecond pulse shaping and introduce specific pulse shapes that are used in the experiments and simulations presented in the following sections. We start with the electric field of a bandwidth-limited (BWL) femtosecond laser pulse written in terms of its positive frequency analytic signal... 

In the following, we will discuss two basic - and in a sense complementary [44] - physical mechanisms to exert efficient control on the strong-field-induced coherent electron dynamics. In the first scenario, SPODS is implemented by a sequence of ultrashort laser pulses (discrete temporal phase jumps), whereas the second scenario utilizes a single chirped pulse (continuous phase variations) to exert control on the dressed state populations. Both mechanisms have distinct properties with respect to multistate excitations such as those discussed in Section 6.3.3. 

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

In Section 6.3.2, we presented experimental data from strong-field excitation and ionization of K atoms with shaped femtosecond laser pulses. Here we give a description of the apparatus and strategy used in the experiments presented in this contribution. Figure 6.12 gives an overview over the complete experimental two-color setup. For the experiments on strong-field control of K atoms (cf Sections 6.3.2.2, 6.3.2.3, and 6.5) only the one-color beamline was used. An... 

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