# Experimental realization of a relativistic harmonic oscillator

 Title Experimental realization of a relativistic harmonic oscillator Publication Type Journal Article Year of Publication 2018 Authors Fujiwara KM, Geiger ZA, Singh K, Senaratne R, Rajagopal SV, Lipatov M, Shimasaki T, Weld DM Journal New Journal of Physics Volume 20 Pagination 063027 Abstract We report the experimental study of a harmonic oscillator in the relativistic regime. The oscillator is composed of Bose-condensed lithium atoms in the third band of an optical lattice, which have an energy‚Ä{\`ımomentum relation nearly identical to that of a massive relativistic particle, with an effective mass reduced below the bare value and a greatly reduced effective speed of light. Imaging the shape of oscillator trajectories at velocities up to 98% of the effective speed of light reveals a crossover from sinusoidal to nearly photon-like propagation. The existence of a maximum velocity causes the measured period of oscillations to increase with energy; our measurements reveal beyond-leading-order contributions to this relativistic anharmonicity. We observe an intrinsic relativistic dephasing of oscillator ensembles, and a monopole oscillation with exactly the opposite phase of that predicted for non-relativistic harmonic motion. All observed dynamics are in quantitative agreement with longstanding but hitherto-untested relativistic predictions.