Coherent states quantum interference

The results in this chapter make clear that a chiral outcome, the enhancement off j particular enantiomer, can arise by coherently encoding quantum interference infqjS mation in the laser excitation of a racemic mixture. The fact that the initial stall displays a broken symmetry and that the excited state has states that are eith jj symmetric or antisymmetric with respect to ah allows for the creation of a si position state that does not have these symmetry properties. Radiatively couplingfhf states in the superposition then allows for the transition probabilities from L and fi t differ, allowing for depletion of the desired enantiomer. 

The essential principle of coherent control in the continuum is to create a linear superposition of degenerate continuum eigenstates out of which the desired process (e.g., dissociation) occurs. If one can alter the coefficients a of the superposition at will, then the probabilities of processes, which derive from squares of amplitudes, will display an interference term whose magnitude depends upon the a,. Thus, varying the coefficients a, allows control over the product properties via quantum interference. This strategy forms the basis for coherent control scenarios in which multiple optical excitation routes are used to dissociate a molecule. It is important to emphasize that interference effects relevant for control over product distributions arise only from energetically degenerate states [7], a feature that is central to the discussion below. 

The nature of the radiative decay in the resonance and in the statistical limits was considered by Berry and Jortner,7 who examined the interference effects in the radiative decay of coherently excited states. Quantum beat signals can be observed and used to analyze close-lying molecular... 

We end this section with a comparison of the basic concepts of laser control and traditional temperature control. This discussion includes an elementary explanation and definition of concepts such as incoherent superpositions of stationary states versus coherent superpositions of stationary states and quantum interference. 

Control of the type discussed above, in which quantum interference effects are used to constructively or destructively alter product properties, is called coherent control (CC). Photodissociation of a superposition state, the scenario described above, will be seen to be just one particular implementation of a general principle of coherent control Coherently driving a state with phase coherence through multiple, coherent,... 

Another area of interest in quantum interference effects, which has been studied extensively, is the response of a V-type three-level atom to a coherent laser field directly coupled to the decaying transitions. This was studied by Cardimona et al. [36], who found that the system can be driven into a trapping state in which quantum interference prevents any fluorescence from the excited levels, regardless of the intensity of the driving laser. Similar predictions have been reported by Zhou and Swain [5], who have shown that ultrasharp spectral lines can be predicted in the fluorescence spectrum when the dipole moments of the atomic transitions are nearly parallel and the fluorescence can be completely quenched when the dipole moments are exactly parallel. 

So far we have concentrated attention on the vibrational manifold, without considering the rotational structure within this manifold. It should be noted at the outset that the rotational selection rules, AJ = 0, +1, valid for one-photon processes, completely break down for multiphoton processes, although the selection rules AM = 0, AK = 0 for a parallel transition remain valid. Thus, a wide range of J states associated with a particular vibrational state may become populated. Felker et al.22 have recently reported the observation of rotational coherence in large molecules. They observe a coherent superposition of precisely three J states, arising from AJ = 0, +1 in a one-photon process. The multiphoton process prepares a similar coherent population of J states, capable of exhibiting quantum interference phenomena, but many more J levels may be involved. 

Gu Q. Quantum interference between coherent states, In Beloussov LV, Popp FA, eds. Biophotonics. Moscow Bioinform Services Co. 1995 115-35. 

The first example is a three-level A-type system coupled by bichromatic coupling and probe fields, which opens two Raman transition channels [60]. The phase dependent interference between the resonant two-photon Raman transitions depends on the relative phases of the laser fields either constructive interference or destructive interference between the two Raman channels can be obtained by controlling the laser phases. The second example is a four-level system coupled by two coupling fields and two probe fields, in which a double-ElT configuration is created by the phase-dependent interference between the three-photon and one-photon excitation processes, or equivalently two independent Raman transition channels [58,62]. We will provide theoretical analyses of the phase dependent quantum interference in the two multi-level atomic systems and present experimental results obtained with cold Rb atoms. The two systems provide basic platforms to study coherent atom-photon interactions and quantum state manipulations, and to explore useful applications of the phase-dependent interference in the multi-level atomic systems. 

Phase-dependent coherence and interference can be induced in a multi-level atomic system coupled by multiple laser fields. Two simple examples are presented here, a three-level A-type system coupled by four laser fields and a four-level double A-type system coupled also by four laser fields. The four laser fields induce the coherent nonlinear optical processes and open multiple transitions channels. The quantum interference among the multiple channels depends on the relative phase difference of the laser fields. Simple experiments show that constructive or destructive interference associated with multiple two-photon Raman channels in the two coherently coupled systems can be controlled by the relative phase of the laser fields. Rich spectral features exhibiting multiple transparency windows and absorption peaks are observed. The multicolor EIT-type system may be useful for a variety of application in coherent nonlinear optics and quantum optics such as manipulation of group velocities of multicolor, multiple light pulses, for optical switching at ultra-low light intensities, for precision spectroscopic measurements, and for phase control of the quantum state manipulation and quantum memory. 

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... 

The general principle of coherent control based on quantum interference between various photoexcitation pathways, including CW-laser weak excitation, is illustrated in Fig. 12.4. This quantum interference can be constructive or destructive, which allows control of the final state, that is, the control of a given reaction product. As an explicit example, Brumer and Shapiro (1986) have considered the process of photodissociation of methyl iodide, where the following two product channels are possible at an excitation energy of E ... 

---