Atomic systems quantum interference

The optimization procedure yields a set of coefficients a,-. Of considerable interiasff is the question of whether these coefficients merely define a new vector that is simply a vector in a rotated coordinate system. If so, this would indicate that the optimqifl solution corresponds to a simple classical reorientation of the di atomic-moleciilee angular momentum vector. Examination of the optimal results [238] indicate " this is not the case. That is, control is the result of quantum interference effects ... 

As we explore the interaction of cold-atom systems with microwave and terahertz radiation, we find that they have some unique properties as detectors. A comparison with superconductor-based detectors such as SQUlDs is instractive. Because of the third law of thermodynamics, i.e., a system in a single quantum state has zero entropy, the response of a SQUID is almost free of thermal noise. But an additional properly of SQUIDs is that they exhibit the phenomenon of coherence, i.e., wave interference, which leads to entirely new effects, e.g. the AC and DC Josephson effects. Cold atom clouds share this behavior, as we will discuss below. 

The interest in quantum interference stems from the early 1970s when Agarwal [4] showed that the ordinary spontaneous decay of an excited degenerate V-type three-level atom can be modified due to interference between the two atomic transitions. The analysis of quantum interference has since been extended to other configurations of three- and multilevel atoms and many interesting effects have been predicted, which can be used to control optical properties of quantum systems, such as high-contrast resonances [5,6], electro-magnetically induced transparency [7], amplification without population inversion [8], and enhancement of the index of refraction without absorption [9]. 

The effect of quantum interference on spontaneous emission in atomic and molecular systems is the generation of superposition states that can be manipulated, to reduce the interaction with the environment, by adjusting the polarizations of the transition dipole moments, or the amplitudes and phases of the external driving fields. With a suitable choice of parameters, the superposition states can decay with controlled and significantly reduced rates. This modification can lead to subnatural linewidths in the fluorescence and absorption spectra [5,10]. Furthermore, as will be shown in this review, the superposition states can even be decoupled from the environment and the population can be trapped in these states without decaying to the lower levels. These states, known as dark or trapped states, were predicted in many configurations of multilevel systems [11], as well as in multiatom systems [12],... 

Phase dependent effects in spontaneous emission have been predicted in atomic systems with nonorthogonal as well as with orthogonal dipole moments. In the first case the phase-dependent effects, which arise from quantum interference between two nonorthogonal dipole moments, can be observed with two driving fields [25-28]. In the latter case the observation of phase-dependent effects requires at least three driving fields [29,30], It is of particular interest to observe the phase-dependent effects, as they represent interference effects that can be induced by driving fields even in the absence of the vacumm-induced quantum interference. 

The discussion, presented in Section IV, has been concentrated on analysis of the effect of quantum interference on spontaneous emission in a V-type three-level atom. With the specific examples we have demonstrated that spontaneous emission can be controlled and even suppressed by quantum interference. In this section, we extend the analysis to the case of coherently driven systems. We will present simple models for quantum interference in which atomic systems are composed of two coupled dipole subsystems. In particular, we consider interference effects in coherently driven V and A-type three-level atoms. Each of the three systems is represented by two dipole moments, p, and p2, interacting through the vacuum field. 

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. 

Consider the Menon-Agarwal approach to the Autler-Townes spectrum of a V-type three-level atom. The atom is composed of two excited states, 1) and 3), and the ground state 2) coupled by transition dipole moments with matrix elements p12 and p32, but with no dipole coupling between the excited states. The excited states are separated in frequency by A. The spontaneous emission rates from 1) and 3) to the ground state 2) are Tj and T2, respectively. The atom is driven by a strong laser field of the Rabi frequency il, coupled solely to the 1) —> 2) transition. This is a crucial assumption, which would be difficult to realize in practice since quantum interference requires almost parallel dipole moments. However, the difficulty can be overcome in atomic systems with specific selection rules for the transition dipole moments, or by applying fields with specific polarization properties [26]. 

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