Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

Abstract

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. Gravitational fields can be incorporated as background spacetime if the back-action of matter on it can be neglected, yielding modified Dirac or Klein-Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many scenarios including expanding universe, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in some background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in curved 2D spacetime. The extent to which such a single-particle description can be said to mimic particle creation is discussed.

11 pages, 8 figures. Corrected typos

References in corpus (4)

• Pair production in laser fields oscillating in space and time
• Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
• Optical simulation of neutrino oscillations in binary waveguide arrays
• Photonic lattice simulation of dissipation-induced correlations in bosonic systems

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• Different models of gravitating Dirac fermions in optical lattices
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