# Resolving Phonon Fock States in a Multimode Cavity with a Double-Slit Qubit

## TL;DR

This paper demonstrates the resolution of phonon Fock states in a superconducting qubit coupled to a multimode acoustic cavity, utilizing engineered interference effects to achieve spectral resolution of single phonons.

## Contribution

The work introduces a novel double-slit inspired coupling scheme that creates sharp frequency dependence, enabling phonon number state resolution in a multimode acoustic system.

## Key findings

- Resolved single phonons spectrally in a multimode cavity.
- Observed high-contrast frequency interference in qubit-phonon interactions.
- Achieved strong dispersive regime for two phononic modes.

## Abstract

We resolve phonon number states in the spectrum of a superconducting qubit coupled to a multimode acoustic cavity. Crucial to this resolution is the sharp frequency dependence in the qubit-phonon interaction engineered by coupling the qubit to surface acoustic waves in two locations separated by $\sim40$ acoustic wavelengths. In analogy to double-slit diffraction, the resulting self-interference generates high-contrast frequency structure in the qubit-phonon interaction. We observe this frequency structure both in the coupling rate to multiple cavity modes and in the qubit spontaneous emission rate into unconfined modes. We use this sharp frequency structure to resolve single phonons by tuning the qubit to a frequency of destructive interference where all acoustic interactions are dispersive. By exciting several detuned yet strongly-coupled phononic modes and measuring the resulting qubit spectrum, we observe that, for two modes, the device enters the strong dispersive regime where single phonons are spectrally resolved.