Recent results:
Quantum and Nonlinear Optics in Photonic Band Structures and Microcavities
G. Kurizki, A. G. Kofman and D. Petrosyan, Encyclopedia of Modern Optics (Elsevier, 2005) pp. 113-119.
I. Friedler, G. Kurizki and D. Petrosyan, Europhys. Lett. Europhys. Lett. 68, 625-631 (2004); quant-ph/0410019.
Giantly enhanced cross-phase modulation with suppressed spectral broadening is predicted between optically-induced dark-state polaritons whose propagation is strongly affected by photonic bandgaps of spatially periodic media with multilevel dopants. This mechanism is shown to be capable of fully entangling two single-photon pulses with high fidelity.M. V. Jouravlev and G. Kurizki, Phys. Rev. A 70 (2004).
We investigate the scattering threshold and cavity-enhanced gain in nonlinear spheres with second- or third-order permeability. Pairs of pump-driven idler and signal modes are considered, satisfying morphology-dependent resonance conditions. The thresholds and gain coefficients of amplified and stimulated Raman scattering, parametric downconversion, and analogous parametric processes in microspheres are derived and evaluated under typical conditions. Applications may include the measurement of chemical impurity concentrations or the creation of low-threshold optical parametric amplifiers using microspheres.G. Kurizki, I. Friedler and D. Petrosyan, Proc. of SPIE 5161, 26-31 (2004).
We introduce and discuss two shemes for generation and transfer of photon-photon and atom-atom entanglement. First we propose a method to achieve a large conditional phase shift of a probe field in the presence of a single-photon control field whose carrier frequency is within the photonic band gap created by spatially-periodic modulation of the electromagnetically induced transparency resonance. Then we introduce the concept of a reversible transfer of the quantum state of two internally-translationally entangled fragments, formed by molecular dissociation , to a photon pair. Our scheme allows, in principle, high-fidelity state transfer from the entangled dissociated fragments to light, thereby producing a highly correlated photon pair. This process can be followed by its reversal at a distant node of a quantum network resulting in the recreation of the original two-fragment entangled state. The proposed schemes may have advantageous applications in quantum teleportation, cryptography, and quantum computation.D. Petrosyan, and G. Kurizki, Fort. der Physik 51, 402 (2003).
We propose two alternative scheme for highly efficient nonlinear interaction between weak optical fields. The first scheme is based on the attainment of electromagnetically induced transparency simultaneously for two fields via transitions between magnetically split F = 1 atomic sublevels, in the presence of two driving fields. The second scheme relies on simultaneous electromagnetically - and self-induced transparencies of the two fields. Thereby, equal slow group velocities and giant cross-phase modulation of the weak fields over long distances are achieved.G. Kurizki, D. Petrosyan, T. Opatrny, M. Blaauboer, and B. Malomed, J. Opt. Soc. Am. B 19, 2066 (2002), quant-ph/0204076.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear model of optical propagation: (a) Self-induced transparency (SIT) solitons and multi-dimensional localized "bullets" propagating at photonic band gap frequencies. These modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. (b) Cross-coupling between pulses exhibiting electromagnetically induced transparency (EIT) and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.G. Kurizki, T. Opatrny, D. Petrosyan, and M. Blaauboer, Proceedings of SPIE 4655, 200 (2002).
We survey basic quantum optical processes that undergo modifications in photonic crystals doped with resonant atoms: (a) Solitons and multi-dimensional localized "bullets" propagating at photonic band gap frequencies. These novel entities differ substantially from solitons in Kerr-nonlinear photonic crystals. (b) Giant photon-photon cross-coupling that can give rise to fully entangled two-photon states. We conclude that doped photonic crystals have the capacity to form efficient networks for high-fidelity classical and quantum optical communications.G. Kurizki, A.G. Kofman and A. Kozhekin, The Encyclopedia of Optical Engineering (Dekker, 2003).
We survey basic quantum optical processes that undergo modifications in photonic crystals: (a) spontaneous decay and the formation of atomic coherence; (b) two-photon binding and entanglement; (c) self-induced transparency and gap solitons. Interactions of atoms with quantized, multimode electromagnetic fields whose spectra possess photonic band gaps (PBGs) are shown to give rise to a diversity of novel features in the atom and field dynamics.G. Kurizki, A.E. Kozhekin, T. Opatrny, B. Malomed, Progress in Optics 42, ed. E. Wolf, 93 (2001); nlin.PS/0007007.
The properties of optical solitons in periodic nonlinear media are reviewed. The emphasis is on solitons in periodically refractive media (Bragg gratings) incorporating a periodic set of thin layers of two-level systems resonantly interacting with the field. Such media support a variety of bright and dark `gap solitons' propagating in the band gaps of the Bragg gratings, as well as their multi - dimensional analogs (light bullets). These novel gap solitons differ substantially from their counterparts in periodic media with either cubic or quadratic off-resonant nonlinearities.S. Pellegrin, A. Kozhekin, A. Sarfati, V. M. Akulin, and G. Kurizki, Phys. Rev. A 63, 033814 (2001).
We consider the influence of refractive index fluctuations (due to randomly distributed inclusions inside a dielectric spherical droplet) on the line shapes of scattering Mie resonances. The significant difference in the spatial distributions of the mode functions participating in the process does not allow one to employ the standard statistical ensembles used in random matrix theory. We propose to model the system by a simplified random ensemble which gives a very good agreement with the available experimental data, and we predict a type of line shape for narrow scattering resonances.M. Blaauboer, G. Kurizki, and B. A. Malomed, Phys. Rev. E 62, R57 (2000).
We predict the existence of multidimensional solitons that are localized in both space and time ("light bullets") in two- and three-dimensional self-induced-transparency media embedded in a Bragg grating. These fully stable light bullets suggest new possibilities of signal transmission control and self-trapping of light.M. Blaauboer, B. A. Malomed, and G. Kurizki, Phys. Rev. Lett. 84, 1906 (2000).
"Light bullets" are multidimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multidimensional generalization of the one-dimensional sine-Gordon soliton.