Photon reflection by a quantum mirror: a wave function approach

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Abstract

We derive from first principles the momentum exchange between a photon and a quantum mirror upon reflection, by considering the boundary conditions imposed by the mirror surface on the photon wave equation. We show that the system generally ends up in an entangled state, unless the mirror position uncertainty is much smaller than the photon wavelength, when the mirror behaves classically. Our treatment leads us directly to the conclusion that the photon momentum has the known value hk/2{\pi}. This implies that when the mirror is immersed in a dielectric medium the photon radiation pressure is proportional to the medium refractive index n. Our work thus contributes to the longstanding Abraham-Minkowski debate about the momentum of light in a medium. We interpret the result by associating the Minkowski momentum (which is proportional to n) with the canonical momentum of light, which appears naturally in quantum formulations.

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State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime

, , … (2013)

Recently, macroscopic mechanical oscillators have been coaxed into a regime of quantum behavior, by direct refrigeration [1] or a combination of refrigeration and laser-like cooling [2, 3]. This exciting result has encouraged notions that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits [1, 4-7], either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems [8, 9]. As yet, the transfer of an itinerant state or propagating mode of a microwave field to and from a mechanical oscillator has not been demonstrated owing to the inability to agilely turn on and off the interaction between microwave electricity and mechanical motion. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in, and retrieved from a mechanical oscillator with amplitudes at the single quanta level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store and transduce quantum information.