Generation of Entangled Photons in Graphene in a Strong Magnetic Field

Abstract

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.

Valley entanglement of excitons in monolayers of transition-metal dichalcogenides

“…In a more general and realistic case, the incident field is not exactly monochromatic but occupies a narrow frequency band ∆ω ω. In this case the creation and annihilation operators are defined for slowly varying amplitudes of the Heisenberg operators (see also [9,10]). Note that the operatorsĉ R andĉ V R , and other similar combinations (same forĉ L ,ĉ V L ) correspond to the field modes with different wave numbers: k = |k| and k = −|k|.…”

“…(26) and (27) correspond to a unit quantization volume V = 1, i.e. the dyadicŝ c † Rĉ R andĉ † Lĉ L are the operators of the photon density (see [9,10,20]), and the quantities like ĉ †…”

“…This coupling can be mediated by classical electromagnetic fields, such as the coupling between two photons in a nonlinear optical medium [8][9][10]. However, as shown in Appendix A, a classical field cannot entangle non-interacting quantum systems.…”

Fluctuation-dissipation relation in a resonantly driven quantum medium

“…For a wide range of regimes of interaction between quantum radiation and dense atomic medium the linear approximation is applicable, whereas the nonlinear response, as well as Langevin effects can be taken into account as small additional terms to the linear relation [18,20]:…”

“…The atoms-quantum field system is described by the set of coupled Heisenberg-Langevin equations. Using continuous medium approximation we describe the ensemble of atoms with collective coordinate-dependent density operators [13,15,20] defined aŝ…”