Quantum interference optical coherence

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 phenomenon of optical interference is commonly describable in completely classical terms, in which optical fields are represented by classical waves. Classical and quantum theories of optical interference readily explain the presence of an interference pattern, but there are interference effects that distinguish the quantum (photon) nature of light from the wave nature. In this section, we present elementary concepts and definitions of both the classical and quantum theories of optical interference and illustrate the role of optical coherence. 

Second, unlike classical electromagnetism, quantum problems for electrons did challenge physicists. Compare, e.g. quantum interference of electrons in the problem of weak localization and its optical counterpart, i.e. coherent back scattering of EM-waves. 

To this end, one may use an analogy. For example, in the interference experiments in optics, the concept of trajectory (of a particle traversing a slit in the diffraction grating) becomes meaningless — existence of trajectories wipes out the interference (diffraction) pattern on the screen. Interference is analogous to the coherent (quantum-mechanical) superpositions of the different positions in f-space. 

The atomic coherence and interference phenomenon in the simple three-level system sueh as EIT can be extended to more eomplicated multi-level atomic systems. A variety of other phenomena and applications involving three or four-level EIT systems have been studied in reeent years. In particular, phase-dependent atomic coherence and interference has been explored [52-66]. These studies show that in multi-level atomic systems coupled by multiple laser fields, there are often various types of nonlinear optical transitions involving multiple laser fields and the quantum interference among these transition paths may exhibit complicated spectral and dynamic features that can be manipulated with the system parameters such as the laser field amplitudes and phases. Here we present two examples of such coherently coupled multi-level atomic systems in which the quantum interference is induced between two nonlinear transition paths and can be eontrolled by the relative phase of the laser fields. 

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. 

In this article we reviewed some of oiu recent research work related to atomic localization via the effects of atomic coherence and quantum interferences. It was found that the localization property was significantly improved due to the interaction of double-dark resonances. The probability of finding the atom at a particular position could be doubled, as well as the loealization preeision could be dramatically enhanced. A scheme of sub-half-wavelength localization was proposed via two standing-wave fields in a ladder-type system. We also presented an application of atom localization in 2D atom nano-lithograph, through two cavities orthogonal to each other. The feasibility of control the atom localization behaviors by the external optical fields is shown. Those work may be helpful in the experimental research of atom localization. 

We have already discussed quantum-beat spectroscopy (QBS) in connection with beam-foil excitation (Fig.6.6). There the case of abrupt excitation upon passage through a foil was discussed. Here we will consider the much more well-defined case of a pulsed optical excitation. If two close-lying levels are populated simultaneously by a short laser pulse, the time-resolved fluorescence intensity will decay exponentially with a superimposed modulation, as illustrated in Fig. 6.6. The modulation, or the quantum beat phenomenon, is due to interference between the transition amplitudes from these coherently excited states. Consider the simultaneous excitation, by a laser pulse, of two eigenstates, 1 and 2, from a common initial state i. In order to achieve coherent excitation of both states by a pulse of duration At, the Fourier-limited spectral bandwidth Au 1/At must be larger than the frequency separation ( - 2)/ = the pulsed excitation occurs at... 

To summarize, the EOM-PMA considerably facilitates the computation of various optical signals and 2D spectra. With shght alterations, the EOM-PMA can also be applied to compute nonlinear responses in the infrared (IR). The three-pulse EOM-PMA can be extended to calculate the A-pulse-induced nonhnear polarization [51], which opens the way for the interpretation of fifth-order spectroscopies, such as heterodyned 3D IR [52], transient 2D IR [53, 54], polarizability response spectroscopy [55], resonant-pump third-order Raman-probe spectroscopy [56], femtosecond stimulated Raman scattering [57], four-six-wave-mixing interference spectroscopy [58], or (higher than fifth order) multiple quantum coherence spectroscopy [59]. 

Next we proceed to develop the theory o resonance fluorescence experiments using the ensemble density matrix to describe the system of atoms. The important concepts of optical and radio-frequency coherence and of the interference of atomic states are discussed in detail. As an illustration of this theory general expressions describing the Hanle effect experiments are obtained. These are evaluated in detail for the frequently employed example of atoms whose angular momentum quantum numbers in the ground and excited levels are J =0 and Jg=l respectively. Finally resonance fluorescence experiments using pulsed or modulated excitation are described. 

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