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arXiv:quant-ph/0010106 · Physical Review A

Photon-photon correlations and entanglement in doped photonic crystals

David Petrosyan, Gershon Kurizki

Published Jul 11, 2001• 74 citations
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Abstract

We consider a photonic crystal (PC) doped with four-level atoms whose intermediate transition is coupled near resonantly with a photonic band-gap edge. We show that two photons, each coupled to a different atomic transition in such atoms, can manifest strong phase or amplitude correlations: One photon can induce a large phase shift on the other photon or trigger its absorption and thus operate as an ultrasensitive nonlinear photon switch. These features allow the creation of entangled two-photon states and have unique advantages over previously considered media: (i) no control lasers are needed; (ii) the system parameters can be chosen to cause full two-photon entanglement via absorption; (iii) a number of PCs can be combined in a network.

DOI
10.1103/physreva.64.023810

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We consider a photonic crystal (PC) doped with four-level atoms whose intermediate transition is coupled near resonantly with a photonic band-gap edge. We show that two photons, each coupled to a different atomic transition in such atoms, can manifest strong phase or amplitude correlations: One photon can induce a large phase shift on the other photon or trigger its absorption and thus operate as an ultrasensitive nonlinear photon switch. These features allow the creation of entangled two-photon states and have unique advantages over previously considered media: (i) no control lasers are needed; (ii) the system parameters can be chosen to cause full two-photon entanglement via absorption; (iii) a number of PCs can be combined in a network.
We show how highly non-linear interactions between single photon pulses can be realized in a photonic crystal doped with four level atoms. We describe how two photons, each coupled to a different atomic transition in such atoms, can manifest strong amplitude correlations. In some cases one single photon can trigger the absorption of the other and the device could thus operate as an ultrasensitive nonlinear photon-switch. These effects also allow for the creation of three-partite entangled states of the GHZ form. The realization of a possible GHZ type of non-locality test is investigated. We note the simplicity of the above case over the usual EIT type of schemes requiring the existence of external coupling lasers.
We have studied the quantum information processing phenomenon in photonic crystals doped with four-level nanoparticles. This phenomenon occurs due to the switching mechanism in the system. We consider that one of the transition energies of nanoparticles is coupled near resonantly with a photonic band gap edge. The dipole-dipole interaction between the nanoparticles has also been included. It is found that the system switches between the transparent and nontransparent states due to the dipole-dipole interaction and the band edge coupling. This is an interesting finding and can be used to produce logical photon switches in the quantum information processing.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such 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. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency 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.
We coherently probe a quantum dot that is strongly coupled to a photonic crystal nano-cavity by scattering of a resonant laser beam. The coupled system's response is highly nonlinear as the quantum dot saturates with nearly one photon per cavity lifetime. This system enables large amplitude and phase shifts of a signal beam via a control beam, both at single photon levels. We demonstrate photon-photon interactions with short pulses in a system that is promising for ultra-low power switches and two-qubit quantum gates.
We have studied the phenomenon of two-photon absorption in photonic nanowires doped with an ensemble of four-level nanoparticles. The photonic nanowire is made from two photonic crystals, A and B, where A is embedded in B. Photons are confined in the nanowire due to the band structure engineering of photonic crystals. It is considered that one of the resonance levels of nanoparticles lies near a photon-bound state of the nanowire. The two-photon absorption coefficient has been calculated using the time-dependent Schrödinger equation. It is found that there is an inhibition of two-photon absorption in the system. This is due to the strong coupling between nanoparticles and the nanowire.
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.