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Journal of Physics A Mathematical and General

Damping of multiphoton Rabi oscillations and multiphoton Purcell effect

Andrzej Janutka

Published Dec 21, 2005• 5 citations
Publisher

Abstract

Damping of multiphoton Rabi oscillations due to a finite lifetime of photons is investigated using an algebraic method of the solution of the master equation. The time dependence of the probability of electron transitions between atomic levels is evaluated. In a regime of weak atom–photon coupling (a coupling constant smaller than the photon decay rate), the spontaneous emission of many photons from a single electron transition due to the interaction with a resonant light is found. Thus, a multiphoton counterpart of the Purcell effect is predicted.

DOI
10.1088/0305-4470/39/3/010

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Damping of multiphoton Rabi oscillations due to a finite lifetime of photons is investigated using an algebraic method of the solution of the master equation. The time dependence of the probability of electron transitions between atomic levels is evaluated. In a regime of weak atom–photon coupling (a coupling constant smaller than the photon decay rate), the spontaneous emission of many photons from a single electron transition due to the interaction with a resonant light is found. Thus, a multiphoton counterpart of the Purcell effect is predicted.
Multiphoton resonant excitation of a three-state quantum system (a qutrit) with a single-mode photonic field is considered in the ultrastrong coupling regime, when the qutrit–photonic field coupling rate is comparable to appreciable fractions of the photon frequency. For ultrastrong couplings, the obtained solutions of the Schrödinger equation that reveal multiphoton Rabi oscillations in qutrits with the interference effects leading to the collapse and revival of atomic excitation probabilities at the direct multiphoton resonant transitions.
The time-dependent spectral properties and nonlinear dynamics of a spontaneous photon emitted by two level atom, trapped in damped nanocavity and coupled to a single resonance mode, have been investigated. The results have been obtained with the help of new nonperturbative approach by solving exactly the Schrödinger equation. The theory accounts exactly and simultaneously processes of emission, reabsorptions and leakage of photon. The solution was found with the Green functions formalism, supplemented with the novel algorithm in operating causal singular functions and fundamentals of the theory of quasi-stationary systems. The obtained distributions and emission dynamics are presented with plots as functions of photon frequency detuning and time for various value Γ/4g. For Γ/4g <1 the spectrum is a triplet inside the cavity and doublet outside it. In this case the total emission probability is described by decaying oscillations. For Γ/4g ≥ 1 and Γ/4g >> 1 the spectrum consists of a single central line decaying exponentially with profile depending on value Γ/4g.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.