Systems of coupled cavities have the potential to provide bright quantum optical states of light in a highly versatile manner. Micro-ring resonators for instance are highly scalable candidates for photon sources thanks to CMOS fabrication techniques and their small footprint, however, surface roughness of the wave-guides, and defects in the coupler geometry routinely induce splitting of the cavity modes due to back-scattering and back-coupling. The parasitic back-propagating mode in the micro-ring leads to hybridisation of the modes, altering the linear and nonlinear properties of this coupled cavity system, and ultimately constraining the fidelity of quantum light sources that can be produced. In this paper, we derive a comprehensive general model for Gaussian non-linear processes in coupled cavity systems, based on an effective field Hamiltonian and a dispersive input-output model. The resulting dynamics of the equations of motion are evaluated in a Gaussian process formalism via the symplectic transformations on the optical modes. We numerically model and explore the problem of back-scattering in micro-ring resonators in physically relevant parameter regimes, involving the splitting of various resonances, we calculate the consequent impurity and heralding efficiency of various heralded photon schemes, we explore a perturbative explanation of the observations and assess the correspondence between spontaneous and stimulated processes in these systems.Systems of coupled cavities have the potential to provide bright quantum optical states of light in a highly versatile manner. Micro-ring resonators for instance are highly scalable candidates for photon sources thanks to CMOS fabrication techniques and their small footprint, however, surface roughness of the wave-guides, and defects in the coupler geometry routinely induce splitting of the cavity modes due to back-scattering and back-coupling. The parasitic back-propagating mode in the micro-ring leads to hybridisation of the modes, altering the linear and nonlinear properties of this coupled cavity system, and ultimately constraining the fidelity of quantum light sources that can be produced. In this paper, we derive a comprehensive general model for Gaussian non-linear processes in coupled cavity systems, based on an effective field Hamiltonian and a dispersive input-output model. The resulting dynamics of the equations of motion are evaluated in a Gaussian process formalism via the symplectic transformations on the optical modes. We numerically model and explore the problem of back-scattering in micro-ring resonators in physically relevant parameter regimes, involving the splitting of various resonances, we calculate the consequent impurity and heralding efficiency of various heralded photon schemes, we explore a perturbative explanation of the observations and assess the correspondence between spontaneous and stimulated processes in these systems.

Oct 18, 20201 citation

Collective Atomic Recoil Lasing and Superradiant Rayleigh Scattering in a high-Q ring cavity

Sebastian Slama, Gordon Krenz, Simone Bux +6 more

Cold atoms in optical high‐Q cavities are an ideal model system for long‐range interacting particles. The position of two arbitrary atoms is, independent on their distance, coupled by the back‐scattering of photons within the cavity. This mutual coupling can lead to collective instability and self‐organization of a cloud of cold atoms interacting with the cavity fields. This phenomenon (CARL, i.e. Collective Atomic Recoil Lasing) has been discussed theoretically for years, but was observed only recently in our lab. The CARL‐effect is closely linked to superradiant Rayleigh scattering, which has been intensely studied with Bose‐Einstein condensates in free space. By adding a resonator the coherence time of the system, in which the instability occurs, can be strongly enhanced. This enables us to observe cavity‐enhanced superradiance with both Bose‐Einstein condensates and thermal clouds and allows us to close the discussion about the role of quantum statistics in superradiant scattering.Cold atoms in optical high‐Q cavities are an ideal model system for long‐range interacting particles. The position of two arbitrary atoms is, independent on their distance, coupled by the back‐scattering of photons within the cavity. This mutual coupling can lead to collective instability and self‐organization of a cloud of cold atoms interacting with the cavity fields. This phenomenon (CARL, i.e. Collective Atomic Recoil Lasing) has been discussed theoretically for years, but was observed only recently in our lab. The CARL‐effect is closely linked to superradiant Rayleigh scattering, which has been intensely studied with Bose‐Einstein condensates in free space. By adding a resonator the coherence time of the system, in which the instability occurs, can be strongly enhanced. This enables us to observe cavity‐enhanced superradiance with both Bose‐Einstein condensates and thermal clouds and allows us to close the discussion about the role of quantum statistics in superradiant scattering.

arXiv:0711.3101AIP conference proceedingsJan 1, 20086 citations

Instabilities for a coherently driven absorber in a ring cavity

R. Bonifacio, Luigi A. Lugiato

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoApr 1, 1978155 citations

Observation of Self-Induced Rabi Oscillations in Two-Level Atoms Excited Inside a Resonant Cavity: The Ringing Regime of Superradiance

Y. Kaluzny, P. Goy, M. Groß +2 more

A collection of $N$ Rydberg atoms and a resonant millimeter-wave cavity are shown to exchange energy back and forth at a rate $2(\frac{d}{\ensuremath{\hbar}}){\mathcal{E}}_{0}\sqrt{N}$, where $d$ is the electric dipole matrix element of the atomic transition and ${\mathcal{E}}_{0}$ the "field per photon" in the cavity. This experiment is a demonstration of self-induced Rabi oscillations in a two-level atom system coupled to a single electromagnetic field mode and can also be considered as a very simple illustration of "ringings" in superradiant emission.A collection of $N$ Rydberg atoms and a resonant millimeter-wave cavity are shown to exchange energy back and forth at a rate $2(\frac{d}{\ensuremath{\hbar}}){\mathcal{E}}_{0}\sqrt{N}$, where $d$ is the electric dipole matrix element of the atomic transition and ${\mathcal{E}}_{0}$ the "field per photon" in the cavity. This experiment is a demonstration of self-induced Rabi oscillations in a two-level atom system coupled to a single electromagnetic field mode and can also be considered as a very simple illustration of "ringings" in superradiant emission.

Physical Review LettersSep 26, 1983454 citations

A collection of

N

Rydberg atoms and a resonant millimeter-wave cavity are shown to exchange energy back and forth at a rate $2(\frac{d}{\ensuremath{\hbar}}){\mathcal{E}}_{0}\sqrt{N}$, where

d

is the electric dipole matrix element of the atomic transition and

{\mathcal{E}}_{0}

the "field per photon" in the cavity. This experiment is a demonstration of self-induced Rabi oscillations in a two-level atom system coupled to a single electromagnetic field mode and can also be considered as a very simple illustration of "ringings" in superradiant emission.