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arXiv:quant-ph/0205072 · Physical Review Letters

Manipulating Light Pulses via Dynamically Controlled Photonic Band gap

Axel André, Mikhail D. Lukin

Published Sep 16, 2002• 216 citations
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Abstract

When a resonance associated with electromagnetically induced transparency in an atomic ensemble is modulated by an off-resonant standing light wave, a band of frequencies can appear for which light propagation is forbidden. We show that dynamic control of such a band gap can be used to coherently convert a propagating light pulse into a stationary excitation with nonvanishing photonic component. This can be accomplished with high efficiency and negligible noise even at the level of few-photon quantum fields thereby facilitating possible applications in quantum nonlinear optics and quantum information.

DOI
10.1103/physrevlett.89.143602

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When a resonance associated with electromagnetically induced transparency in an atomic ensemble is modulated by an off-resonant standing light wave, a band of frequencies can appear for which light propagation is forbidden. We show that dynamic control of such a band gap can be used to coherently convert a propagating light pulse into a stationary excitation with nonvanishing photonic component. This can be accomplished with high efficiency and negligible noise even at the level of few-photon quantum fields thereby facilitating possible applications in quantum nonlinear optics and quantum information.
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Resonantly absorbing media supporting electromagnetically induced transparency may give rise to specific periodic patterns where a light probe is found to experience a fully developed photonic band gap yet with negligible absorption everywhere. In ultracold atomic samples the gap is found to arise from spatial regions where Autler-Townes splitting and electromagnetically induced transparency alternate with one another and detailed calculations show that accurate and efficient coherent optical control of the gap can be accomplished. The remarkable experimental simplicity of the control scheme would ease quantum nonlinear optics applications.
We illustrate a mechanism based on coherent optical nonlinearities to realize optically tunable photonic crystals built from media supporting electromagnetically induced transparency. These exhibit specific periodic patterns where a light probe can experience a fully developed photonic band-gap with negligible absorption. An analytical method based on a two-mode approximation is developed to study the optical response of such a periodically modulated medium driven into a regime of standing-wave electromagnetically induced transparency. A comparison with a transfer matrix approach and with techniques based on the coupled Maxwell–Liouville equations shows that our method is very accurate to describe the optical properties of such photonic metamaterials in the frequency region of interest. Nearly perfect reflectivities may be attained for ultracold 87Rb atoms samples which are seen to reflect with little loss and deformation light pulses whose frequency components are contained within the gap. When the same mechanism is implemented for inhomogeneously broadened optical transitions of nitrogen-vacancy centers in diamond, which is more amenable to device applications, fully developed photonic band-gap structures with negligible absorption, reflectivities very close to unity and sufficiently large bandwidths may also be attained. We further examine more flexible schemes based on four level systems under double driving conditions showing more accurate and efficient coherent optical control of the photonic band-gap. The remarkable experimental simplicity of the schemes that we presented is set to ease quantum nonlinear optics applications.
We study the giant Kerr nonlinear interaction between two ultraweak optical fields in which the cross-phase-modulation is not accompanied by spectral broadening of the interacting pulses. This regime is realizable in atomic vapors, when a weak probe pulse, upon propagating through the electromagnetically induced transparency (EIT) medium, interacts with a signal pulse that is dynamically trapped in a photonic band gap created by spatially periodic modulation of its EIT resonance. We find that large conditional phase shifts and entanglement between the signal and probe fields can be obtained with this scheme. The attainable $\ensuremath{\pi}$ phase shift, accompanied by negligible absorption and quantum noise, is shown to allow a high-fidelity realization of the controlled-phase universal logic gate between two single-photon pulses.