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Coupled cavity QED for coherent control of photon transmission (II): Slowing light in coupled resonator waveguide doped with $\Lambda $ Atoms

Lan Zhou, Jing Lü, C. P. Sun

Published Nov 15, 2006• 0 citations
OpenAlex

Abstract

In the first paper of our series of articles on photon transmission in the coupled resonator optical waveguide (CROW), we used the two time Green function approach to study the physical mechanism for the coherent control by doping two-level atoms. In present paper, we propose and study a hybrid mechanism for photon transmission in the CROW by incorporating the electromagnetically induced transparency (EIT) effect in the doping artificial atoms and the band structure of the CROW. Here, the configuration setup of system, similar to that in the first paper, consists of a CROW with homogeneous couplings and the artificial atoms with $\\Lambda$-type three levels doped in each cavity. Unlike the stimulated Raman process used in the first paper to reduce the three level systems into the two level ones, the roles of three levels are completely considered based on a kind of mean field approach where the collection of three-level atoms collectively behave as two-mode spin waves. Then the total system is reduced into an exactly solvable coupling boson model. We show that the light pulses can be stopped and stored coherently by controlling the classical field.

Related papers

Coherent control of photon transmission: Slowing light in a coupled resonator waveguide doped with Λ atoms

Lan Zhou, Jing Lu, C. P. Sun

In this paper, we propose and study a hybrid mechanism for coherent transmission of photons in the coupled resonator optical waveguide (CROW) by incorporating the electromagnetically induced transparency (EIT) effect into the controllable band gap structure of the CROW. Here, the configuration setup of system consists of a CROW with homogeneous couplings and the artificial atoms with $\ensuremath{\Lambda}$-type three levels doped in each cavity. The roles of three levels are completely considered based on a mean field approach where the collection of three-level atoms collectively behave as two-mode spin waves. We show that the dynamics of low excitations of atomic ensemble can be effectively described by a coupling boson model. The exact solutions show that the light pulses can be stopped and stored coherently by adiabatically controlling the classical field.

arXiv:quant-ph/0611159•Physical Review A•Jul 16, 2007•41 citations

Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping

F. M. Hu, Lan Zhou, Tao Shi +1 more

This paper theoretically studies the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms in hybrid structures. We provide several approaches correspondingly based on the mean field method and spin wave theory. In the present paper, we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weak-coupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.

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Coupled resonator optical waveguide structures with highly dispersive media

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Analysis of photonic crystal coupled resonator optical waveguide (CROW) structures with a highly dispersive background medium is presented. A finite-difference time-domain algorithm was employed which contains an exact representation of the permittivity of a three-level atomic system which exhibits electromagnetically induced transparency (EIT). We find that the coupling strength between nearestneighbor cavities in the CROW decreases with increasing steepness of the background dispersion, which is continuously tunable as it is directly related to the control field Rabi frequency. The weaker coupling decreases the speed of pulse propagation through the waveguide. In addition, due to the dispersive nature of the EIT background, the CROW band shape is tuned around a fixed k-point. Thus, the EIT background enables dynamic tunability of the CROW band shape and the group velocity in the structure at a fixed operating point in momentum space.

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Single-photon Transport in a Waveguide-cavity-emitter System

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Abstract We investigate the single-photon transport properties in a hybrid waveguide quantum electrodynamics system, in which a one-dimensional waveguide is simultaneously coupled to a cavity and a driven Λ-type three-level atom. The cavity and the atom are also coupled to each other. We show that when the waveguide is coupled to the cavity and the atom at the same point, double electromagnetically induced transparency (EIT) can be observed from the system. The physical mechanism of the double EIT effect has been given by setting up the eigenstate structure for the whole system. When the waveguide is coupled to the cavity and the atom at different points, we demonstrate that the single-photon transmission spectra can be effectively controlled by adjusting the relative separation between the cavity and the atom. Moreover, this non-zero relative separation can lead to the occurrence of the controllable nonreciprocal scattering effect. These results have potential applications in realization of photonic coherent control.

International Journal of Theoretical Physics•Aug 8, 2022•2 citations

Slow and stopped light by light-matter coherence control

Jonas Tidström

In this thesis we study light-matter coherence phenomena related to the interaction of a coherent laser field and the so-called Λ-system, a three-level quantum system (e.g., an atom). We observe electromagnetically induced transparency (EIT), slow and stored light in hot rubidium vapor. For example, a 6 μs Gaussian pulse propagate at a velocity of ~1 km/s (to be compared with the normal velocity of 300 000 km/s). Dynamic changes of the control parameter allows us to slow down a pulse to a complete stop, store it for ~100 μs, and then release it. During the storage time, and also during the release process, some properties of the light pulse can be changed, e.g., frequency chirping of the pulse is obtained by means of Zeeman shifting the energy levels of the Λ-system. If, bichromatic continuous light fields are applied we observe overtone generation in the beating signal, and a narrow `dip' in overtone generation efficiency on two-photon resonance, narrower than the `coherent population trapping' transparency. The observed light-matter coherence phenomena are explained theoretically from first principles, using the Lindblad master equation, in conjunction with the Maxwell's equations. Furthermore, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness today is scant. The combination of EIT and a photonic crystal cavity is inquired into, and we show that the quality value of a small resonator (area of 2.5λ×2.5λ with a missing central rod) can be enhanced by a factor of 500 due to the increased modal density close to two-photon resonance. Open system effects (decoherence effects) are thoroughly investigated using a coherence vector formalism, furthermore, a vector form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain.

•Jan 1, 2009•0 citations

Group delay controls of the photons transmitting through two cavities coupled by an artificial atomic ensemble: controllable electromagnetically induced transparency-like effects

Suirong He, Yufen Li, L. F. Wei

As one of the typical quantum coherence phenomena, electromagnetically induced transparency (EIT) has been extensively applied to implement various quantum coherent manipulations, typically, e.g., optical quantum memories, photonic switches, and optical quantum computations, etc. By applying the input-output theory to the photonic transports through two cavities dispersively coupled by an artificial two-level atomic ensemble, we show here that the EIT-like effects could be observed. Particularly, the transparency windows and phase shift spectra of the transmitting photons could be engineered by manipulating the atomic levels in the ensemble to adjust the effective coupling strength between the cavities. As a consequence, the group delays of the transmitting photons can be manipulated by using the EIT-like effects. The proposal is demonstrated specifically with the experimental superconducting coplanar waveguide resonators coupled by the voltage-biased electrons on liquid Helium.

Optics Express•Dec 15, 2021•7 citations
In the first paper of our series of articles on photon transmission in the coupled resonator optical waveguide (CROW), we used the two time Green function approach to study the physical mechanism for the coherent control by doping two-level atoms. In present paper, we propose and study a hybrid mechanism for photon transmission in the CROW by incorporating the electromagnetically induced transparency (EIT) effect in the doping artificial atoms and the band structure of the CROW. Here, the configuration setup of system, similar to that in the first paper, consists of a CROW with homogeneous couplings and the artificial atoms with Lambda\\LambdaLambda-type three levels doped in each cavity. Unlike the stimulated Raman process used in the first paper to reduce the three level systems into the two level ones, the roles of three levels are completely considered based on a kind of mean field approach where the collection of three-level atoms collectively behave as two-mode spin waves. Then the total system is reduced into an exactly solvable coupling boson model. We show that the light pulses can be stopped and stored coherently by controlling the classical field.
In this paper, we propose and study a hybrid mechanism for coherent transmission of photons in the coupled resonator optical waveguide (CROW) by incorporating the electromagnetically induced transparency (EIT) effect into the controllable band gap structure of the CROW. Here, the configuration setup of system consists of a CROW with homogeneous couplings and the artificial atoms with $\ensuremath{\Lambda}$-type three levels doped in each cavity. The roles of three levels are completely considered based on a mean field approach where the collection of three-level atoms collectively behave as two-mode spin waves. We show that the dynamics of low excitations of atomic ensemble can be effectively described by a coupling boson model. The exact solutions show that the light pulses can be stopped and stored coherently by adiabatically controlling the classical field.
This paper theoretically studies the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms in hybrid structures. We provide several approaches correspondingly based on the mean field method and spin wave theory. In the present paper, we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weak-coupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.
Analysis of photonic crystal coupled resonator optical waveguide (CROW) structures with a highly dispersive background medium is presented. A finite-difference time-domain algorithm was employed which contains an exact representation of the permittivity of a three-level atomic system which exhibits electromagnetically induced transparency (EIT). We find that the coupling strength between nearestneighbor cavities in the CROW decreases with increasing steepness of the background dispersion, which is continuously tunable as it is directly related to the control field Rabi frequency. The weaker coupling decreases the speed of pulse propagation through the waveguide. In addition, due to the dispersive nature of the EIT background, the CROW band shape is tuned around a fixed k-point. Thus, the EIT background enables dynamic tunability of the CROW band shape and the group velocity in the structure at a fixed operating point in momentum space.
Abstract We investigate the single-photon transport properties in a hybrid waveguide quantum electrodynamics system, in which a one-dimensional waveguide is simultaneously coupled to a cavity and a driven Λ-type three-level atom. The cavity and the atom are also coupled to each other. We show that when the waveguide is coupled to the cavity and the atom at the same point, double electromagnetically induced transparency (EIT) can be observed from the system. The physical mechanism of the double EIT effect has been given by setting up the eigenstate structure for the whole system. When the waveguide is coupled to the cavity and the atom at different points, we demonstrate that the single-photon transmission spectra can be effectively controlled by adjusting the relative separation between the cavity and the atom. Moreover, this non-zero relative separation can lead to the occurrence of the controllable nonreciprocal scattering effect. These results have potential applications in realization of photonic coherent control.
In this thesis we study light-matter coherence phenomena related to the interaction of a coherent laser field and the so-called Λ-system, a three-level quantum system (e.g., an atom). We observe electromagnetically induced transparency (EIT), slow and stored light in hot rubidium vapor. For example, a 6 μs Gaussian pulse propagate at a velocity of ~1 km/s (to be compared with the normal velocity of 300 000 km/s). Dynamic changes of the control parameter allows us to slow down a pulse to a complete stop, store it for ~100 μs, and then release it. During the storage time, and also during the release process, some properties of the light pulse can be changed, e.g., frequency chirping of the pulse is obtained by means of Zeeman shifting the energy levels of the Λ-system. If, bichromatic continuous light fields are applied we observe overtone generation in the beating signal, and a narrow `dip' in overtone generation efficiency on two-photon resonance, narrower than the `coherent population trapping' transparency. The observed light-matter coherence phenomena are explained theoretically from first principles, using the Lindblad master equation, in conjunction with the Maxwell's equations. Furthermore, we analyze an optical delay-line based on EIT and show that there is in principle (besides decoherence) no fundamental limitation, but the usefulness today is scant. The combination of EIT and a photonic crystal cavity is inquired into, and we show that the quality value of a small resonator (area of 2.5λ×2.5λ with a missing central rod) can be enhanced by a factor of 500 due to the increased modal density close to two-photon resonance. Open system effects (decoherence effects) are thoroughly investigated using a coherence vector formalism, furthermore, a vector form of the Lindblad equation is derived. Specifically we find an open system channel that lead to slow light and gain.
As one of the typical quantum coherence phenomena, electromagnetically induced transparency (EIT) has been extensively applied to implement various quantum coherent manipulations, typically, e.g., optical quantum memories, photonic switches, and optical quantum computations, etc. By applying the input-output theory to the photonic transports through two cavities dispersively coupled by an artificial two-level atomic ensemble, we show here that the EIT-like effects could be observed. Particularly, the transparency windows and phase shift spectra of the transmitting photons could be engineered by manipulating the atomic levels in the ensemble to adjust the effective coupling strength between the cavities. As a consequence, the group delays of the transmitting photons can be manipulated by using the EIT-like effects. The proposal is demonstrated specifically with the experimental superconducting coplanar waveguide resonators coupled by the voltage-biased electrons on liquid Helium.