An investigation of giant Kerr nonlinearity

Abstract

This thesis investigates the properties of an atomic system exhibiting a giant Kerr nonlinearity. The atomic energy level scheme involves four energy levels. A three level A subsystem in the atom exhibits the effect of electromagnetically induced transparency (EIT), reducing the spontaneous emission noise. The fourth level leads to an ac-Stark shift of the ground state, which in turn leads to a giant, noiseless Kerr nonlinearity. Two different environments are explored. First, a system comprising of large number of atoms in an optical cavity is analysed. Detailed aspects of noise reduction in this system are investigated. In particular, strong squeezing in the quadrature in phase with the field driving the cavity mode is found, if the effective coupling of light to the atoms is strong. However, the linewidth of the predicted squeezing is found to be very narrow. This is attributed to a very steep linear susceptibility of the atomic medium. Since the widening of the squeezing window is possible only for weaker effective coupling, in turn reducing the squeezing level, a different environment is proposed. This involves a single four level atom, strongly coupled to the cavity mode. In such a strongly coupled system, the most appropriate approach is found to be that formulated in terms of polaritons – composite excitations of the 'atom-cavity molecule'. Adopting the polariton approach, nonclassical correlations in the field leaving the cavity are investigated. Strong photon antibunching is found and the effect of photon blockade predicted and described. The photon blockade effect can also be found in a system comprised of a two level atom coupled to the cavity mode, if the external driving is tuned to one of the vacuum Rabi resonances. A comparison between the two schemes is performed, and it is found that the four level scheme exhibits much better photon blockade. The reason for this is quantum interference between secondary transitions in the dressed states picture. Destructive interference cancels the transitions that would otherwise introduce a second photon into the system, hence producing a more robust photon blockade. All of these results are valid in the regime where external driving is weak. If the external driving strength is increased, the photon statistics (as measured by the zero-delay second order correlation function) changes from strong antibunching to strong bunching, over a relatively narrow range of driving strengths. The occurrence of this change can again be attributed to quantum interference. It is shown that the interference effect prevents the excitation of the composite system by a second photon, but not excitation by a two-photon transition (following the first excitation). Therefore, the third excitation manifold is excited, which then decays back to the first manifold in a two photon cascade. This two photon cascade is the source of correlated photon pairs causing an increase in the second order correlation function. The dynamics of forward scattering of light is presented, and nonclassical behaviour of the delay dependence of correlation function ('overshoots' and 'undershoots') is discussed. For the analytical treatment of this system, a method based on the polariton approach is devised, which includes the treatment of driving and damping. It is shown that this method is ideally suited to the analysis of strongly coupled systems, where only a few photons contribute to the dynamics.