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/far-infrared range.Comment: 5 pages, 4 figure

Continuous wave lasing between Landau levels in graphene

We predict the general feasibility and demonstrate the specific design of the THz laser operating between Landau levels in graphene placed on a polar substrate in a magnetic field of order 1 T. Steady state operation under a continuous wave optical pumping is possible due to an interplay between Auger and surface-phonon mediated relaxation of carriers. The scheme is scalable to other materials with massless Dirac fermions, for example surface states in 3D topological insulators such as Bi$_2$Se$_3$ or Bi$_2$Te$_3$.Comment: 12 pages, 5 figure

Efficient nonlinear generation of THz plasmons in graphene and topological insulators

Surface plasmons in graphene may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the nonlinear difference frequency generation of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a broad range of frequencies.Comment: 5 pages, 4 figure

Second-order nonlinear optical response of graphene

Although massless Dirac fermions in graphene constitute a centrosymmetric medium for in-plane excitations, their second-order nonlinear optical response is nonzero if the effects of spatial dispersion are taken into account. Here we present a rigorous quantum-mechanical theory of the second-order nonlinear response of graphene beyond the electric dipole approximation, which includes both intraband and interband transitions. The resulting nonlinear susceptibility tensor satisfies all symmetry and permutation properties, and can be applied to all three-wave mixing processes. We obtain useful analytic expressions in the limit of a degenerate electron distribution, which reveal quite strong second-order nonlinearity at long wavelengths, Fermi-edge resonances, and unusual polarization properties.Comment: The new version makes the bold font vector notation uniform throughout the paper and corrects a misprint in Eq. (34): replaces v_F^2 with v_F^3 in the common facto

Strong magneto-optical effects due to surface states in three-dimensional topological insulators

We show that a thin film of a three-dimensional topological insulator such as Bi$_2$Se$_3$ or Bi$_2$Te$_3$ can exhibit strong linear and nonlinear magneto-optical effects in a transverse magnetic field. In particular, one can achieve an almost complete circular polarization of an incident terahertz or mid-infrared radiation and an efficient four-wave mixing.Comment: 11 pages, 6 figure

Maximally efficient biphoton generation by single photon decay in nonlinear quantum photonic circuits

We develop a general nonperturbative formalism and propose a specific scheme for maximally efficient generation of biphoton states by parametric decay of single photons. We show that the well-known critical coupling concept of integrated optics can be generalized to the nonlinear coupling of quantized photon modes to describe the nonperturbative optimal regime of a single-photon nonlinearity and establish a fundamental upper limit on the nonlinear generation efficiency of quantum-correlated photons, which approaches unity for low enough absorption losses.Comment: 6 pages, 3 figure