Spontaneous emission quantum interference

Thus far we have dealt with the idealized case of isolated molecules that are neither -subject to external collisions nor display spontaneous emission. Further, we have V assumed that the molecule is initially in a pure state (i.e., described by a wave function) and that the externally imposed electric field is coherent, that is, that the " j field is described by a well-defined function of time [e.g., Eq. (1.35)]. Under these. circumstances the molecule is in a pure state before and after laser excitation and S remains so throughout its evolution. However, if the molecule is initially in a mixed4> state (e.g., due to prior collisional relaxation), or if the incident radiation field is notlf fully coherent (e.g., due to random fluctuations of the laser phase or of the laser amplitude), or if collisions cause the loss of quantum phase after excitation, then J phase information is degraded, interference phenomena are muted, and laser controi. is jeopardized. < f... 

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],... 

In this review we discuss the major effects resulting from the modification of spontaneous emission by quantum interference. We begin in Section II by presenting elementary concepts and definitions of the first- and second-order correlation functions, which are frequently used in the analysis of the inter-... 

The presence of the additional damping terms F12 may suggest that quantum interference enhances spontaneous emission from two coupled systems. However, as we shall illustrate in the following sections, the presence of these terms in the master equation can, in fact, lead to a reduction or even suppression of spontaneous emission. According to Eq. (62), the reduction and suppression of spontaneous emission can be controlled by changing the mutual orientation of the dipole moments of the bare systems. 

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. 

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]. 

S.-Y. Zhu, M. Scully, Spectral line elimination and spontaneous emission cancellation via quantum interference, Phys. Rev. Lett. 76 (1996) 388. 

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