Observation of quantum interference between separated mechanical oscillator wavepackets

TL;DR

This paper demonstrates the creation and observation of quantum superpositions of separated mechanical oscillator wavepackets using trapped ions, revealing quantum interference and introducing new measurement and reconstruction techniques.

Contribution

It reports the first in-situ observation of quantum interference in spatially separated mechanical superpositions and develops methods for phase-space reconstruction using squeezed Fock bases.

Findings

Quantum interference observed in separated wavepackets with phase space separation of 15.6.

Successful reconstruction of Wigner functions showing negative interference fringes.

Achieved 8 dB squeezing to enhance measurement of large superposition states.

Abstract

The ability of matter to be superposed at two different locations while being intrinsically connected by a quantum phase is among the most counterintuitive predictions of quantum physics. While such superpositions have been created for a variety of systems, the in-situ observation of the phase coherence has remained out of reach. Using a heralding measurement on a spin-oscillator entangled state, we project a mechanical trapped-ion oscillator into a superposition of two spatially separated states, a situation analogous to Schr\"odinger's cat. Quantum interference is clearly observed by extracting the occupations of the energy levels. For larger states, we encounter problems in measuring the energy distribution, which we overcome by performing the analogous measurement in a squeezed Fock basis with each basis element stretched along the separation axis. Using 8 dB of squeezing we observe quantum interference for cat states with phase space separations of $\Delta \alpha = 15.6$, corresponding to wavepackets with a root-mean-square extent of 7.8 nm separated by over 240 nm. We also introduce a method for reconstructing the Wigner phase-space quasi-probability distribution using both squeezed and non-squeezed Fock bases. We apply this to a range of negative parity cats, observing the expected interference fringes and negative values at the center of phase space. Alongside the fundamental nature of these large state superpositions, our reconstruction methods facilitate access to the large Hilbert spaces required to work with mesoscopic quantum superpositions, and may be realized in a wide range of experimental platforms.