Laser pulses, coherence property

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

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. 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

Coherent control Control of the motion of a microscopic object by using the coherent properties of an electromagnetic held. Coherent phase control uses a pair of lasers with long pulse durations and a well-defined relative phase to excite the target by two independent paths. Wave packet control uses tailored ultrashort pulses to prepare a wave packet at a desired position at a given time. 

The first optical laser, the ruby laser, was built in 1960 by Theodore Maiman. Since that time lasers have had a profound impact on many areas of science and indeed on our everyday lives. The monochromaticity, coherence, high-intensity, and widely variable pulse-duration properties of lasers have led to dramatic improvements in optical measurements of all kinds and have proven especially valuable in spectroscopic studies in chemistry and physics. Because of their robustness and high power outputs, solid-state lasers are the workhorse devices in most of these applications, either as primary sources or, via nonlinear crystals or dye media, as frequency-shifted sources. In this experiment the 1064-mn near-infrared output from a solid-state Nd YAG laser will be frequency doubled to 532 nm to serve as a fast optical pump of a raby crystal. Ruby consists of a dilute solution of chromium 3 ions in a sapphire (AI2O3) lattice and is representative of many metal ion-doped solids that are useful as solid-state lasers, phosphors, and other luminescing materials. The radiative and nonradiative relaxation processes in such systems are important in determining their emission efficiencies, and these decay paths for the electronically excited Cr ion will be examined in this experiment. 

This property has been used to measure the coherence properties of laser pulses [28]. Because it is readily obtainable by Fourier transform from the... 

The conceptual framework underlying the control of the selectivity of product formation in a chemical reaction using ultrashort pulses rests on the proper choice of the time duration and the delay between the pump and the probe (or dump) step or/and their phase, which is based on the exploitation of the coherence properties of the laser radiation due to quantum mechanical interference effects [56, 57, 59, 60, 271]. During the genesis of this field. 

Figure 45. Schematic representation of the preparation and detection of rotational coherence in a molecule. The case depicted corresponds to the linearly polarized excitation (polarization vector ,) of a symmetric top molecule in ground-state ro-vibronic level S0v0 J0K0M0) to those rotational levels of the excited vibronic state 15,1 ,) allowed by the rotational selection rules germane to a parallel-type transition moment. The excitation process creates a superposition state of three rotational levels, the coherence properties of which can be probed by time resolving the polarized fluorescence (polarization it) to the manifold of ground-state ro-vibronic levels S0vf JfKfMfy, or by probing with a second, variably time-delayed laser pulse (polarization...

The subject of quantum optics is concerned with the quantum properties of the radiation field, i.e. the properties of photons. Since the word multiphoton has been used, it might seem that strong laser fields are in some way relevant to quantum optics. However, the word multiphoton is something of a misnomer in the strong field regime. In fact, if very many photons are involved, quantisation of the radiation field is more or less irrelevant the intense, coherent laser pulse tends to a quasiclassical beam of light. Indeed, it has been pointed out by several authors [483] that the use of the word photon in the context of laser physics is of questionable validity. 

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. 

The spectral width Aty can be further increased by focusing the laser pulses into a special optical fiber, which consists of a photonic crystal (Fig. 9.88) where by self-phase modulation the spectrum is considerably broadened and extends over one decade (e.g., from 1064 nm to 532 nm) (Fig. 9.89). This corresponds to a frequency span of 300 THz [1327] It was found by interference experiments, that the coherence properties were preserved in this broadened spectmm, i.e. the nonlinear processes in the optical fiber did not destroy the coherence of the original frequency comb. 

When a chirped laser pulse is used for the PA process, a coherent wavepacket is formed in the excited state, and has components in all the vibrational levels within the resonance window. After the pulse, this wavepacket propagates toward short distances. Because population transfer back to the initial state with a second (dump) pulse is a coherent process, it is convenient to use this property to optimize the formation of ultracold stable molecules. For instance, in the chosen example of Cs2 0 (65 -f 6P3/2), the time-dependent Franck-Condon overlap with the bound levels in the lower electronic state can be optimized by achieving a focused wavepacket. 

Over-the past decade, not only have pulse durations decreased from 10 to 10" s but there has been a dramatic increase in the tunability of lasers, such that tunable coherent radiation can now span the VUV to the very long wavelength laser radar. Femtosecond spectroscopy, like most advances, has begun in the visible region and considerable research and development is necessary to expand this present spectral range around 600 nm (4). However, it is also the case that for many problems in photo dynamics, for which the state selectivity or the nature of the optically prepared initial state is of paramount importance, the spectral line-width (Av) of the pulse must remain narrow. Thus the transform-limited bandwidth relationships (AvA K) govern the temporal properties of the laser pulse and, for example, a 5 ns pulse of 0.01 cm" linewidth prepares a different ensemble than a 300 fs pulse of 26 cm linewidth at the same wavelength. 

Explaining the cross sections of collisions and the photoabsorption spectra of molecules is fundamental to understand the properties of materials, but it is even more important to be able to manipulate and control these properties. In traditional chemistry, this is achieved by adjusting external parameters such as temperature, pressure, concentration, solvent, or by adding catalysts. A higher selectivity and precision could be obtained by a systematic use of lasers. In addition, the latter can offer the possibility to control quantum effects such as quantum coherence. In traditional chemistry, the quantum states involved in the chemical process are, in general, populated in a incoherent way described as a mixed state in quanmm statistical mechanics. The systematic use of laser pulses to induce chemical process opens the possibility to create coherent superpositions of the same quantum states, what is called a pure state in quantum statistical mechanics. Such coherent superpositions might drastically increase the efficiency and the control of... 

Many experiments employing LIF to extract the population and or the anisotropy of the nascent angular momentum distribution are carried out with pulsed lasers exhibiting rather limited coherence properties. Under these conditions coherence between the lower and excited state may be neglected and the more simple rate equational approach to model the laser-molecule interaction is appropriate. 

Two main approaches to the control of molecules using wave interference in quantum systems have been proposed and developed in different languages . The first approach (Tannor and Rice 1985 Tannor et al. 1986) uses pairs of ultrashort coherent pulses to manipulate quantum mechanical wave packets in excited electronic states of molecules. These laser pulses are shorter than the coherence lifetime and the inverse rate of the vibrational-energy redistribution in molecules. An ultrashort pulse excites vibrational wave packets, which evolve freely until the desired spacing of the excited molecular bond is reached at some specified instant of time on a subpicosecond timescale. The second approach is based on the wave properties of molecules as quantum systems and uses quantum interference between various photoexcitation pathways (Brumer and Shapiro 1986). Shaped laser pulses can be used to control this interference with a view to achieving the necessary final quantum state of the molecule. The probability of production of the necessary excited quantum state and the required final product depends, for example, on the phase difference between two CW lasers. Both these methods are based on the existence of multiple interfering pathways from the initial... 

In the adiabatic limit, t is considered to be a parameter, and is called an adiabatic state. One of the interesting properties of this limit is that a population can be inverted by evolving the system adiabatically. This process is called adiabatic passage. Population transfer induced by a laser is generally called coherent population transfer. For a two-level system, the complete population inversion is produced by a n -pulse or by adiabatic rapid passage. 

A strict derivation of the comb properties is not feasible as it depends on the special dispersion characteristics of the laser cavity and these data are not accessible with the desired degree of accuracy. Instead we only assume that the laser emits a stable coherent pulse train without any detailed consideration of how this is possible. Further we assume that the electric field E(t), measured for example at the output coupler, can be written as the product of a periodic envelope function A ) and a carrier wave C(t) ... 

Apart from the obvious property of defining pulses within short time intervals, the pulsed laser radiation used in reaction kinetics studies can have additional particular properties (i) high intensity, (ii) high monochromaticity, and (iii) coherence. Depending on the t) e of laser, these properties may be more or less pronounced. For instance, the pulsed CO2 lasers used in IR laser chemistry easily reach intensities between... 

---