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Physical Review Letters

Experimental Observation of a Photon Bouncing Ball

Giuseppe Della Valle, Matteo Savoini, Marco Ornigotti, P. Laporta, Vittorio Foglietti, Marco Finazzi, Lamberto Duò, Stefano Longhi

Published May 7, 2009• 57 citations
Publisher

Abstract

An optical analogue of a quantum particle bouncing on a hard surface under the influence of gravity (a quantum bouncer) is experimentally demonstrated using a circularly curved optical waveguide. Spatially resolved tunneling optical microscopy measurements of multiple beam reflections at the waveguide edge clearly show the appearance of wave packet collapses and revivals (either integer and fractional), corresponding to the full quantum regime of the quantum bouncer.

DOI
10.1103/physrevlett.102.180402

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An optical analogue of a quantum particle bouncing on a hard surface under the influence of gravity (a quantum bouncer) is experimentally demonstrated using a circularly curved optical waveguide. Spatially resolved tunneling optical microscopy measurements of multiple beam reflections at the waveguide edge clearly show the appearance of wave packet collapses and revivals (either integer and fractional), corresponding to the full quantum regime of the quantum bouncer.
An optical realization of a quantum bouncing ball on a truncated lattice is theoretically proposed for light waves propagating near the edge of a circularly curved waveguide array. As compared to the analogous problem of matter waves bouncing on a perfectly reflecting surface under the influence of gravity, where the wave packets basically behave as classical particles, it is shown that the genuine quantum regimes of wave packet collapse and revival are accessible for the discrete optical system.
The usual 'quantum bouncer' is a quantum particle bouncing elastically under the influence of gravity. Here we consider a particle bouncing off an impenetrable wall, and bound to it by the harmonic potential instead of by the gravitational potential mgx . An analytic solution is possible, easily accessible to classes in intermediate quantum mechanics. The solution is related to Schrödinger's oscillating wavepacket (the original coherent state ). Although periodic, it changes its form during the oscillation, in contrast to Schrödinger's packet. The uncertainties in the position (Δ x ) and the momentum (Δ p ) oscillate also, as does the product Δ x Δ p .
We discuss the time development of Gaussian wave packet solutions of the “quantum bouncer” (a quantum mechanical particle subject to a uniform downward force, above an impermeable flat surface). We focus on the evaluation and visualization of the expectation values and uncertainties of position and momentum variables during a single quasi-classical period as well as during the long-term collapsed phase and several revivals. This approach complements existing analytic and numerical analyses of this system, as well as being useful for comparison with similar results for the harmonic oscillator and infinite well cases.
An experimental demonstration of a classical analogue of the quantum Zeno effect for light waves propagating in engineered arrays of tunneling-coupled optical waveguides is reported. Quantitative mapping of the flow of light, based on scanning tunneling optical microscopy, clearly demonstrates that the escape dynamics of light in an optical waveguide side-coupled to a tight-binding continuum is slowed down when projective measurements, mimicked by sequential interruptions of the decay, are performed on the system.