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Journal of the Optical Society of America B

Vacuum-field Rabi oscillations of atoms in a cavity

G. S. Agarwal

Published Mar 1, 1985• 198 citations
Publisher

Abstract

The quantum electrodynamics of an atom in a cavity is reexamined from the view point of the vacuum-field Rabi oscillations. Many features of such oscillations in a single atom as well as in a cooperative system are discussed. Various physical quantities that carry the signature of these vacuum-field oscillations are calculated. Even oscillator systems are shown to exhibit such vacuum-field Rabi oscillations, which is in contrast to the external-field-induced Rabi oscillations. Such oscillations are found to occur in situations involving both single-photon and multiphoton transitions.

DOI
10.1364/josab.2.000480

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The quantum electrodynamics of an atom in a cavity is reexamined from the view point of the vacuum-field Rabi oscillations. Many features of such oscillations in a single atom as well as in a cooperative system are discussed. Various physical quantities that carry the signature of these vacuum-field oscillations are calculated. Even oscillator systems are shown to exhibit such vacuum-field Rabi oscillations, which is in contrast to the external-field-induced Rabi oscillations. Such oscillations are found to occur in situations involving both single-photon and multiphoton transitions.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.
We predict a large cooperative effect involving two-atom two-photon vacuum Rabi oscillations in a high-quality cavity. The two-photon emission occurs as a result of simultaneous deexcitation of both atoms with two-photon resonance condition ${\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}\ensuremath{\approx}{\ensuremath{\omega}}_{a}+{\ensuremath{\omega}}_{b}$, where ${\ensuremath{\omega}}_{1}$,${\ensuremath{\omega}}_{2}$ are the atomic transition frequencies and ${\ensuremath{\omega}}_{a}$,${\ensuremath{\omega}}_{b}$ are the frequencies of the emitted photons. The actual resonance condition depends on the vacuum Rabi couplings. The effect can be realized either with identical atoms in a bimodal cavity or with nonidentical atoms in a single-mode cavity.
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.
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.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.