The Jaynes-Cummings model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probabilities for fields with sharply defined energy (or photon number). For fields having a statistical distributions of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive, only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further non-classical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it ha...

The Jaynes-Cummings Model

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

We study the time evolution of Nq two-level atoms (or qubits) interacting with a single mode of a quantized radiation field. In the case of two qubits, we show that for a set of initial conditions the reduced density matrix of the atomic system approaches that of a pure state at , halfway between that start of the collapse and the first mini-revival peak, where tr is the time of the main revival. The pure state approached is the same for a set of initial conditions and is thus termed an 'attractor state'. The set itself is termed the 'basin of attraction' and we concentrate on its features. Extending to more qubits, we find that attractors are a generic feature of the multiqubit Jaynes–Cummings model (JCM) and we therefore generalize the discovery by Gea–Banacloche for the one-qubit case. We give the 'basin of attraction' for Nq qubits and discuss the implications of the 'attractor' state in terms of the dynamics of Nq-body entanglement. We observe both the collapse and revival and the sudden birth/death of entanglement depending on the initial conditions.

https://iopscience.iop.org/article/10.1088/1367-2630/11/10/103047/pdf

Dynamics of entanglement and ‘attractor’ states in the Tavis–Cummings model

The sensitivity of the collapse-revival phenomenon of Rabi oscillations of two identical atoms to dipole-dipole interaction is brought out by deriving the analytical expression of the excitation probability of two interacting atoms in a coherent field. We study this effect in a two-photon model in which the time evolution is exactly periodic.

Effects of Dipole Interaction on the Collapse-revival Phenomenon of Rabi Oscillations

An exact solution for the problem of two two-level atoms interacting with a single-mode detuned quantized radiation field is presented. On resonance, an asymptotic result is derived for large coherent initial fields. It is shown that when the atoms are initially prepared in one of the semiclassical eigenstates, the atom-plus-field wavefunction remains almost factored into an atomic and a field part throughout the interaction. Under certain conditions, the atomic part evolves into a unique pure state at half-revival time. The effects of the cavity detuning on the dynamics of the atomic level occupation probabilities and emission spectra are studied. It is found, for non-symmetrical excitation, that far off-resonance the field acts like a virtual level by means of which the energy is transferred between the atoms. Due to non-zero detuning, nine-peaked spectra are observed and are given a clear explanation from the dressed-state viewpoint. It is established that in the case of symmetrical excitation...

Two Atom-single Mode Radiation Field Interaction: State Evolution, Level Occupation Probabilities and Emission Spectra

Interactions of two two-level atoms with a single-mode quantized radiation field are studied, and exact expressions for the atom-field probability amplitudes in the rotating-wave approximation are presented. These solutions are employed in the study of the quantum collapse and revivals of the atomic coherence.

Interaction of two two-level atoms with a single-mode quantized radiation field

Osteoradionecrosis of the mandible represents a cohort of patients that are notoriously difficult to treat. Complications are commonplace following free tissue transfer reconstructive surgery, including non-osseous union at the osteotomy site. We retrospectively reviewed a cohort of patients that were treated with fibula free tissue transfer reconstruction utilising virtual surgical planning. It was possible to deform previously delivered radiation dosimetry data onto the virtual mandible and superimpose the osteotomy site. This enabled the delivered radiation dose at the osteotomy site to be determined, plus the volume of mandible remaining that had received above 50Gy of irradiation. Two out of the four patients with appropriate follow up demonstrated evidence of bony consolidation at the osteotomy site between the native mandible and the composite fibula reconstruction. On retrospective review of the dosimetry mapping, one patient's resection margins were performed in areas of the mandible with a received irradiation dose of less than 50Gy. The second patient had a received dose of just over 50Gy at the resection margin, with only 0.1 cm [3] of affected mandible remaining at the osteotomy site. Two patients demonstrated a non-osseous union at a resection margin through an area of the mandible that received an irradiation dose way in excess of 50Gy, with one patient demonstrating a high volume of retained mandible receiving a radiation dose in excess of 50Gy. In this known cohort of difficult to manage patients, any technique that aids in the reduction of complications is a welcome addition. 

M. S. Iqbal

Papers

Interaction of two two-level atoms with a single-mode quantized radiation field

Retrospective review of Osteoradionecrosis cases treated with virtual surgical planning following review of received irradiation dose to the mandible