Photon localization and photonic band gap materials

Since the invention of the laser, the field of photonics has progressed through the development of engineered materials which mold the flow of light. Photonic band gap (PBG) materials are a new class of dielectrics which are the photonic analogues of semiconductors. They represent a new frontier in quantum optics and offer many new technological application. Unlike semiconductors which facilitate the coherent propagation of electrons, PBG materials facilitate the coherent localization of photons. Our research suggests that PBG materials exhibit fundamentally new physics such as photon-atom bound states, lasing without a cavity mode, quantum optical spin-glass states of impurity atomic dipoles, and optical gap solitons. Applications include zero-threshold micro-lasers with high modulation speed and low threshold optical switches and all-optical transistors for optical telecommunications and high speed optical computers.

Our current research is aimed at developing a theoretical understanding of these novel materials. Specific calculations include N-atom collective spontaneous emission and laser activity. Light emission properties of photonic band gap materials differ dramatically from conventional lasers. The most fundamental novelty of these materials comes from the fact that when an atom or molecule, placed within the material, has an electronic transition which lies within the photonic band gap, spontaneous emission of light from the atom is inhibited. Instead, the photon forms a bound state to the atom! This has profound implications for laser activity. Spontaneous emission is the dominant loss mechanism in a conventional laser. In a PBG, lasing can occur with zero pumping threshold. Lasing can also occur without mirrors and without a cavity mode since each atom creates its own localized photon mode. This suggests that large arrays of nearly lossless microlasers for all-optical circuits can be fabricated with PBG materials.

Near a photonic band edge, the photon density of states exhibits singularities which cause  collective light emission to take place at a much faster rate than in ordinary vacuum. . We have shown that this rate is proportional to the square of the number N of atoms rather than simply N itself as it would be in conventional systems. This demonstrates that microlasers operating near a photonic band edge will exhibit ultrafast modulation and switching speeds for application in high speed data transfer and computing.

Applications such as telecommunications, data transfer, and computing will be greatly enhanced through all-optical processing in which bits of information, encoded in the form of a photon number distribution, can be transmitted and processed without conversion to and from electrical signals. In this manner, the information contained in an entire encyclopedia can be transmitted over a fibre optic phone line in a matter of seconds. This relies on the development of ultra-low noise coherent light sources. We are evaluating the quantum statistics of photons produced by laser emission in a PBG material to evaluate the extent of signal noise reduction referred to as photon-antibunching and squeezing. These are crucial to lowering the bit error rate in optical telecommunication networks. In a PBG material the drastic reduction of spontaneous emission as well as the reduction of propagative pathways for photons, facilitates the realization of very low quantum noise.

A PBG material doped with impurity atoms also exhibits novel nonlinear optical properties due to the resonance dipole-dipole interaction (RDDI) between atoms. Our current calculations show that under pumping by a weak external laser field, this system acts as a nearly lossless, nonlinear material which exhibits  optical bistability. We are currently investigating the possibility of using this system as a very low threshold, ultra-high speed optical switch. This low threshold nonlinearity is a consequence of a new equilibrium state of photons and atoms in a PBG which we refer to as a quantum optical spin-glass state. In this state, the atomic dipoles exhibit a spontaneous, frozen-in, random polarization. The light associated with this state is intermediate between coherent light from a conventional laser and chaotic light from an ordinary light bulb. We refer to this state as a  Bose-glass state of photons .

The photonic band gap is a frequency interval over which the linear electromagnetic propagation effects have literally been turned off. However, the PBG exhibits a rich variety of nonlinear optical propagation phenomena. These include classical gap solitons and quantum gap solitons . These solitons may be important in the transmission of information through the otherwise impenetrable PBG.

The PBG material provides dopant atoms with a high degree of protection from damping effects of spontaneous emission and dipole dephasing. In this case the two-level atom may act as a two-level quantum mechanical register or single photon logic gate for all optical quantum computing . We are currently studying two models for quantum computation within PBG materials. The first involves an atom which is laser-cooled in the void regions of a PBG material. In this case a polarized photon (flying qubit) with frequency just outside of the gap excites a protected atomic level inside the gap (stationary qubit) by resonant coupling to a third atomic level just outside the gap. The second and third atomic levels are coupled by an external laser field which drives a two-photon transition. This single atom acts as a phase sensitive quantum memory device. The resulting qubit is robust to decoherence effects provided that the Rabi frequency of the coherent laser field exceeds the rate of dephasing interactions. In effect, coherence is externally imposed on the system. In the second model for quantum computing, the single photon occupation of a localized field mode within an engineered network of defects in a PBG material acts as the qubit. Qubit operations are then mediated by optically-excited atoms interacting with these localized states of light as the atom traverses an open channel within the extensive void network of the PBG material. Here, quantum information is stored in localized states of light. Quantum computers can perform calculations in relatively short "polynomial time". These calculations require prohibitively long "exponential time" with any classical computer. PBG materials may provide the essential hardware for the realization of a quantum computer. For a quantum computer to function, quantum bits of information must be stored as well as transferred from point to point without decoherence effects taking place. The PBG is an ideal environment for protecting photons and atoms from decoherence over extended periods of time.