Quantum Correlations Between Mechanical Oscillators via SU(1,1) Interferometry
Context
This work sits on the outskirts of the map of quantum correlations: the only nearby paper concerns quantum entanglement as geometry, and the other neighbors are far away. Researchers can already create entanglement between nanomechanical oscillators, but correlations stronger than entanglement, that is, steering, have never been observed in continuous variables until now. This work fills that gap using a circuit quantum acoustodynamics platform with two resonators and a qubit.
Methods
Two bulk acoustic wave resonators (HBARs) made of aluminum nitride on sapphire are coupled to a transmon qubit. Two microwave tones with frequencies satisfying the condition ω1+ω2=ωa+ωb parametrically drive the qubit, which through nonlinearity creates effective two-mode squeezing between the phonon modes. To detect the correlations, the team implemented an SU(1,1) interferometer: the first squeezing stage prepares the state, and the second, with a phase shift, reads it out by measuring the phonon population. The squeezing rate was calibrated from the growth of the mean phonon number, and the interferometer phase was tuned to minimize the EPR criterion.
Results
The EPR steering criterion E(φ) was measured and dropped below 1 at tTMS2≈11 μs. Its minimum reached 0.90 with 99% confidence for the B→A direction and 98% for A→B, which means two-way steering. Each oscillator has an effective mass of about 16 μg, corresponding to roughly $10^{17}$ atoms. The interference fringes showed phase sensitivity, and comparison with a vacuum reference confirmed the quantum nature of the correlations.
Implications
Unlike neighboring studies that examined entanglement or geometry, this work demonstrates for the first time correlations stronger than entanglement in continuous variables for macroscopic mechanical systems. It expands the toolkit of circuit quantum acoustodynamics and shows that quantum effects survive at the scale of $10^{17}$ atoms. The result matters for probing the boundary between the quantum and classical worlds.
Future development
Quantum teleportation of continuous motional states between mechanical oscillators may become possible, along with quantum networks built from mechanical nodes. Advances in controlling phonon modes in HBARs will enable bosonic quantum computing and simulations of quantum chemistry. Steering could potentially be used for one-way quantum cryptography with mechanical keys.
Impact
Quantum communication, quantum computing, precision measurements.
Next steps
Increase the degree of squeezing and reduce losses to violate the criterion more strongly. Implement teleportation of a quantum state between two oscillators.
Key open problems
For quantum acoustics, the question of the maximum scale of macroscopic quantumness and the role of decoherence in such systems remains open. This work directly links quantum correlations to loss of coherence, which is important for understanding the transition to classical behavior.
Each oscillator weighs 16 micrograms, comparable to a grain of salt, yet the correlations between them are stronger than any classical model allows.
The idea of quantum entanglement between macroscopic objects is explored in Ted Chiang's "Story of Your Life," where nonlinear perception of time is tied to quantum nonlocality.
Key numbers
- oscillator mass: 16 μg
- number of atoms in the oscillator: ~1017
- steering confidence B→A: 99%
- steering confidence A→B: 98%
- squeezing rate gTMS: up to 20 kHz