The temporal response of coupled resonators is investigated using a linear systems analysis and coupled mode theory. Damped Rabi oscillations, slow and fast light, and coherent photon transfer techniques are demonstrated in these systems.
Quantum coherence effects in atomic media such as electromagnetically-induced transparency and absorption, lasing without inversion, super-radiance and gain-assisted superluminality have become well-known in atomic physics. But these effects are not unique to atoms, nor are they uniquely quantum in nature, but rather are fundamental to systems of coherently coupled oscillators. In this talk I will review a variety of analogous photonic coherence phenomena that can occur in passive and active coupled optical resonators. Specifically, I will examine the evolution of the response that can occur upon the addition of a second resonator, to a single resonator that is side-coupled to a waveguide, as the coupling is increased, and discuss the conditions for slow and fast light propagation, coupled-resonator-induced transparency and absorption, lasing without gain, and gain-assisted superluminal pulse propagation. Finally, I will discuss the application of these systems to laser stabilization and gyroscopy.
We predict the propagation of slow and fast light in two co-resonant coupled optical resonators. In coupled resonators, slow light can propagate without attenuation by a cancellation of absorption as a result of mode splitting and destructive interference, whereas transparent fast light propagation can be achieved by the assistance of gain and splitting of the intracavity resonances, which consequently change the dispersion from normal to anomalous. The effective steady-state response of coupled-resonators is derived using the temporal coupled-mode formalism, and the absorptive and dispersive responses are described. Specifically, the occurrence of slow light via coupled-resonator-induced transparency and gain-assisted fast light are discussed.
We predict a variety of photonic coherence phenomena in passive and active coupled ring resonators. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived, and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. We also demonstrate that the coupled-mode equations are formally identical to the two-level atom Schrödinger equation in the rotating-wave approximation, and use this result for the analysis of coupled-resonator photon dynamics. Notably, because these effects are predicted directly from coupled-mode theory, they are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators.
An optical analogue of two-photon Rabi oscillations, occurring in a three-level atomic or molecular system coherently driven by two detuned laser fields, is theoretically proposed and experimentally demonstrated using three evanescently coupled optical waveguides realized on an active glass substrate. The optical analogue stems from the formal analogy between spatial propagation of light waves in the three-waveguide structure and the coherent temporal evolution of populations in a three-level atomic medium driven by two laser fields under two-photon resonance. In our optical experiment, two-photon Rabi oscillations are thus visualized as a slow spatial oscillatory exchange of light power between the two outer waveguides of the structure with a small excitation of the central waveguide.
We theoretically analyze the temporal dynamics of strongly coupled quantum-dot--cavity system driven by a resonant laser pulse and observe the signature of Rabi oscillation in the time-resolved response of the system (i.e., in the numerically calculated cavity output). We derive simplified linear and nonlinear semiclassical models that approximate well the system's behavior in the limits of high- and low-power driving pulses and describe the role of quantum coherence in the exact dynamics of the system. Finally, we also present time-resolved transmission measurements showing the dynamics of a quantum-dot--cavity system in the presence of a short laser pulse.
Vacuum Rabi oscillation is a damped oscillation in which energy can transfer between an atomic excitation and a photon when an atom is strongly coupled to a photonic cavity. This process is challenging to be coherently controlled due to the fact that interaction between the atom and the electromagnetic resonator needs to be modulated in a quick manner compared to vacuum Rabi frequency. This control has been achieved at microwave frequencies, but has remained challenging to be implemented in the optical domain. Here we demonstrated coherent control of energy transfer in a semiconductor quantum dot strongly coupled to a photonic crystal molecule by manipulating the vacuum Rabi oscillation of the system. Instead of using a single photonic crystal cavity, we utilized a photonic crystal molecule consisting two coupled photonic crystal defect cavities to obtain both strong quantum dot-cavity coupling and cavityenhanced AC stark shift. In our system the AC stark shift modulates the coupling interaction between the quantum dot and the cavity by shifting the quantum dot resonance, on timescales (picosecond) shorter than the vacuum Rabi period. We demonstrated the ability to transfer excitation between a quantum dot and cavity, and performed coherent control of light-matter states. Our results provides an ultra-fast approach for probing and controlling light-matter interactions in an integrated nanophotonic device, and could pave the way for gigahertz rate synthesis of arbitrary quantum states of light at optical frequencies.