Leading quantum platforms are largely limited to one or two dimensions, whereas three-dimensional Coulomb crystals of trapped ions self-assemble into dense qubit arrays with no rearrangement overhead. Coherent optical control of such crystals has nonetheless been out of reach, because the optical transition couples to nearly all
3N collective modes, i.e., a thermally occupied quasi-continuum bath. Here we cool about 3,600 modes of a crystal of over 1,200 ions below single-phonon occupation, using a continuous cooling band that spans more than five octaves in vibrational spectrum, from about 50 kHz to 2.1 MHz. The crystal then serves as a register of optical qubits, allowing global initialization, coherent manipulation and collective detection. We demonstrate ensemble optical coherence of 21.6 milliseconds and reduce the optical-transition frequency uncertainty from 389 Hz for a single ion to 12 Hz for over a thousand ions, approaching the expected projection-noise scaling. Our approach could be extended to even larger crystals with phonon-mediated many-body couplings, opening a route towards entanglement-enhanced precision metrology and three-dimensional quantum simulation, particularly with spatial-shaped illumination for region-resolved collective control.
We develop a deterministic method to generate and verify arbitrarily high NOON states of quantized vibrations (phonons), through the coupling to the internal state. We experimentally create the entangled states up to N=9 phonons in two vibrational modes of a single trapped ^{171}Yb^{+} ion. We observe an increasing phase sensitivity of the generated NOON state as the number of phonons N increases and obtain the fidelity from the contrast of the phase interference and the population of the phonon states through the two-mode projective measurement, which are significantly above the classical bound. We also measure the quantum Fisher information of the generated state and observe Heisenberg scaling in the lower bounds of phase sensitivity as N increases. Our scheme is generic and applicable to other photonic or phononic systems such as circuit QED systems or nanomechanical oscillators, which have Jaynes-Cummings-type of interactions.