Analogue Casimir Radiation using an Optical Para- metric Oscillator

We establish an explicit analogy between the dynamical Casimir effect and the photon emission of a thin non-linear crystal pumped inside a cavity. This allows us to propose a system based on a type-I optical parametric oscillator (OPO) to simulate a cavity oscillating in vacuum at optical frequencies. The resulting photon flux is expected to be more easily detectable than with a mechanical excitation of the mirrors. We conclude by comparing different theoretical predictions and suggest that our experimental proposal could help discriminate between them.Comment: 7 pages, 2 figures, epl2 stylefile necessary to compil

Dynamical Casimir Effect in Optically Modulated Cavities

Cavities with periodically oscillating mirrors have been predicted to excite photon pairs out of the quantum vacuum in a process known as the Dynamical Casimir effect. Here we propose and analyse an experimental layout that can provide an efficient modulation of the effective optical length of a cavity mode in the near-infrared spectral region. An analytical model of the dynamical Casimir emission is developed and compared to the predictions of a direct numerical solution of Maxwell's equations in real time. A sizeable intensity of dynamical Casimir emission is anticipated for realistic operating parameters. In the presence of an external coherent seed beam, we predict amplification of the seed beam and the appearance of an additional phase-conjugate beam as a consequence of stimulated dynamical Casimir processes.Comment: 6 pages, 5 figure

The Pauli equation in scale relativity

In standard quantum mechanics, it is not possible to directly extend the Schrodinger equation to spinors, so the Pauli equation must be derived from the Dirac equation by taking its non-relativistic limit. Hence, it predicts the existence of an intrinsic magnetic moment for the electron and gives its correct value. In the scale relativity framework, the Schrodinger, Klein-Gordon and Dirac equations have been derived from first principles as geodesics equations of a non-differentiable and continuous spacetime. Since such a generalized geometry implies the occurence of new discrete symmetry breakings, this has led us to write Dirac bi-spinors in the form of bi-quaternions (complex quaternions). In the present work, we show that, in scale relativity also, the correct Pauli equation can only be obtained from a non-relativistic limit of the relativistic geodesics equation (which, after integration, becomes the Dirac equation) and not from the non-relativistic formalism (that involves symmetry breakings in a fractal 3-space). The same degeneracy procedure, when it is applied to the bi-quaternionic 4-velocity used to derive the Dirac equation, naturally yields a Pauli-type quaternionic 3-velocity. It therefore corroborates the relevance of the scale relativity approach for the building from first principles of the quantum postulates and of the quantum tools. This also reinforces the relativistic and fundamentally quantum nature of spin, which we attribute in scale relativity to the non-differentiability of the quantum spacetime geometry (and not only of the quantum space). We conclude by performing numerical simulations of spinor geodesics, that allow one to gain a physical geometric picture of the nature of spin.Comment: 22 pages, 2 figures, accepted for publication in J. Phys. A: Math. & Ge