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Journal of Modern Optics

Coherence phenomena in coupled optical resonators

David D. Smith, Hongrok Chang

Published Nov 10, 2004• 23 citations
Publisher

Abstract

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.

DOI
10.1080/09500340412331285073

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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 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.
Optical response of an active medium can substantially be modified when coherent superpositions of states are excited, that is, when systems display quantum coherence and interference. This has led to fascinating applications in atomic and molecular systems. Examples include coherent population trapping, lasing without inversion, electromagnetically induced transparency, cooperative spontaneous emission, and quantum entanglement. \n \nWe study quantum coherence effects in several quantum optical systems and find interesting applications. We show that quantum coherence can lead to transient Raman lasing and lasing without inversion in short wavelength spectral regions--extreme ultraviolet and x-ray--without the requirement of incoherent pumping. For example, we demonstrate transient Raman lasing at 58.4 nm in Helium atom and transient lasing without inversion at 6.1 nm in Helium-like Boron (triply-ionized Boron). We also investigate dynamical properties of a collective superradiant state prepared by absorption of a single photon when the size of the sample is larger than the radiation wavelength. We show that for large number of atoms such a state, to a good approximation, decays exponentially with a rate proportional to the number of atoms. We also find that the collective frequency shift resulting from repeated emission and reabsorption of short-lived virtual photons is proportional to the number of species in the sample. Furthermore, we examine how a position-dependent excitation phase affects the evolution of entanglement between two dipole-coupled qubits. It turns out that the coherence induced by position-dependent excitation phase slows down the otherwise fast decay of the two-qubit entanglement. We also show that it is possible to entangle two spatially separated and uncoupled qubits via interaction with correlated photons in a cavity quantum electrodynamics setup. Finally, we analyze how quantum coherence can be used to generate continuous-variable entanglement in quantum-beat lasers in steady state and propose possible implementation in quantum lithography.
Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.
Coherent atomic states prepared by laser field can have quantum interference\nbetween the different transition amplitudes. Therefore, the medium susceptibility\nand optical response can be engineered, leading to many interesting phenomena, such\nas coherent population trapping (CPT), electromagnetically induced transparency\n(EIT), and lasing without inversion (LWI).\nWe studied the coherence effects in various prototype atomic systems, and found\nmany interesting applications. We solved the slow light bandwidth problem by decomposing\nthe pulse and matching each frequency to its EIT window using a magnetic\nfield gradient. We also considered the probe field deflection induced by the driving\nfield distribution in EIT, and showed that even a broadband pulse can be deflected\nwithout serious spreading. In the fast light area, we examined the effects of noise and\nparameter deviations in a bichromatic Raman type white light cavity. Taking advantage\nof the adjustable absorption of EIT, we showed that EIT in a laser cavity can\nhave either first-order or second-order phase transitions. Last but not least, we show\nthat the adiabatic population transfer can be used to reverse the weak measurement\nof an arbitrary field with finite photon number.
We predict transparent superluminal pulse propagation in coresonant coupled optical resonators when a gain element is placed in the resonator closest to the excitation waveguide, provided that the structure is overcoupled, but the resonator farthest from the excitation waveguide is undercoupled sufficiently to avoid lasing at the split modes. The effective steady-state absorptive and dispersive response of coupled resonators are derived, and the coupled-mode approximation is used to determine the conditions for transparent superluminal pulse propagation in these systems. In addition, we find that the effect of pulse compression is minimized when the structure is critically coupled.