Generation of Entangled Photons in Graphene in a Strong Magnetic Field

Entangled photon states attract tremendous interest as the most vivid manifestation of nonlocality of quantum mechanics and also for emerging applications in quantum information. Here we propose a mechanism of generation of polarization-entangled photons, which is based on the nonlinear optical interaction (four-wave mixing) in graphene placed in a magnetic field. Unique properties of quantized electron states in a magnetized graphene and optical selection rules near the Dirac point give rise to a giant optical nonlinearity and a high rate of photon production in the mid- or far-infrared range. A similar mechanism of photon entanglement may exist in topological insulators where the surface states have a Dirac-cone dispersion and demonstrate similar properties of magneto-optical absorption.

Figure 1

Geometry of the proposed experiment. Two pump fields at frequencies ${\omega }_{HF}$ and ${\omega }_{LF}$ normally incident on a sheet of graphene placed in a magnetic field $B$ generate entangled photons with opposite senses of the circular polarization.

Figure 2

Energy levels and optical transitions involved in resonant parametric generation of entangled photons in graphene. Left: Landau levels near the Dirac point superimposed on the linear electron dispersion without the magnetic field. Right: A scheme of the entangled photon generation process in the four-level system of LLs with energy quantum numbers $n=-2$, $-1$, 0, 1 that were renamed as states 1, 2, 3, and 4 for convenience of notation.

Figure 3

Parametric gain $\tau$ per monolayer of graphene as a function of normalized detuning of the signal fields $\Delta /⟨\gamma ⟩$ for the pump field intensity $|{\Omega }_p{|}^2=0.1⟨\gamma {⟩}^2$.