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arXiv:0912.4819 · Journal of Mathematical Physics

Correlation of Dirac potentials and atomic inversion in cavity quantum electrodynamics

Agung Trisetyarso

Published Jul 1, 2010• 10 citations

Abstract

Controlling the time evolution of the population of two states in cavity quantum electrodynamics is necessary by tuning the modified Rabi frequency in which the extra classical effect of electromagnetic field is taken into account. The theoretical explanation underlying the perturbation of potential on spatial regime of bloch sphere is by the use of Bagrov–Baldiotti–Gitman–Shamshutdinova–Darboux transformations [Bagrov et al., “Darboux transformation for two-level system,” Ann. Phys. 14, 390 (2005)] on the electromagnetic field potential in one-dimensional stationary Dirac model in which the Pauli matrices are the central parameters for controlling the collapse and revival of the Rabi oscillations. It is shown that by choosing σ1 in the transformation generates the parabolic potential causing the total collapse of oscillations, while {σ2,σ3} yield the harmonic oscillator potentials ensuring the coherence of qubits.

DOI: 10.1063/1.3458598

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Quantum Rabi oscillation in cavity quantum electrodynamics is at the very heart of the interaction of an atomic system with a single electromagnetic field in a resonator. It has proved a powerful tool to entangle the atom with the field in the case of an empty cavity (vacuum Rabi oscillation). On the other side, as soon as the field is macroscopic, its state seems unaffected and one observes the well-known phenomenon of classical Rabi oscillation which only affects the atomic populations. We propose to experimentally investigate the frontier between those two behaviours, when one has to take into account the fluctations of the photon number. In order to do so, we let interact circular Rydberg atoms with a microwave resonator in which a mesocopic field is injected (a few tens of photons). We observe a strong correlation between specific atomic states and the phase of the injected field, which is measured by a homodyne technique. Those correlations explain in an easy way all the standard features of quantum Rabi oscillations (especially the collapses and revivals). Moreover they allow for the preparation of atom-field entangled state as well as non classical Schroedinger cat like states for the field.

The Jaynes-Cummings model provides a useful means of studying several quantum electrodynamic effects in matter-radiation interaction. One such effect is the phenomenon of collapses and revivals of Rabi oscillations. Various aspects of this phenomenon are studied in terms of the dynamical evolution of the atom as well as the statistical properties of the field. In particular, the sensitivity of collapses and revivals on the initial photon statistics, the cavity field damping mechanism is highlighted. For this purpose the basic model of Jaynes and Cummings has been extended and modified. Some multiatom effects are also discussed.