[Paper Review] Schrödinger cat states of a 16-microgram mechanical oscillator

Marius Bild, Matteo Fadel+5 more|arXiv (Cornell University)|Nov 1, 2022

Mechanical and Optical Resonators12 citations

TL;DR

This paper demonstrates the creation of Schrödinger cat states in a 16.2-microgram mechanical resonator using circuit quantum acoustodynamics, where a superconducting transmon qubit entangles with phononic modes to prepare superpositions of opposite-phase lattice oscillations. The key result is the observation of macroscopic quantum superpositions with coherence times up to 40 µs, confirming scalable quantum control in massive mechanical systems and advancing continuous-variable quantum technologies.

ABSTRACT

The superposition principle is one of the most fundamental principles of quantum mechanics. According to the Schrödinger equation, a physical system can be in any linear combination of its possible states. While the validity of this principle is routinely validated for microscopic systems, it is still unclear why we do not observe macroscopic objects to be in superpositions of states that can be distinguished by some classical property. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schrödinger cat states of motion, where the constituent atoms are in a superposition of oscillating with two opposite phases. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states. Apart from shedding light at the boundary between the quantum and the classical world, our results are of interest for quantum technologies, as they pave the way towards continuous-variable quantum information processing and quantum metrology with mechanical resonators.

Motivation & Objective

• To test the limits of quantum superposition in macroscopic mechanical systems by preparing large-scale Schrödinger cat states in a 16.2-μg resonator.
• To investigate decoherence dynamics of macroscopic superpositions in massive oscillators, particularly how size and phase affect decay rates.
• To demonstrate control over the amplitude and phase of cat states in a mechanical resonator, enabling potential applications in quantum metrology and information processing.
• To probe the boundary between quantum and classical behavior by observing non-classical features such as Wigner negativity in a system with macroscopic mass.

Proposed method

• The experiment uses a high-overtone bulk acoustic wave resonator (HBAR) coupled to a superconducting transmon qubit via piezoelectric interaction, enabling quantum control of phononic modes.
• Cat states are prepared by initializing the qubit in a superposition state and using the Jaynes-Cummings interaction to entangle it with a coherent phonon state, creating a superposition of opposite-phase lattice oscillations.
• Full Wigner function tomography is performed to reconstruct the quantum state, with 1D crosscuts used to extract Wigner negativity and track decoherence over time.
• Decoherence is quantified by measuring the decay of Wigner negativity over variable delay times, with simulations using a master equation to model free evolution and compare with experimental data.
• The system is tuned to address multiple longitudinal phononic modes, and the mode volume is minimized to enhance quantum coupling and reduce decoherence.
• Numerical simulations of the full master equation are used to predict cat state decay times, accounting for realistic noise and qubit detuning, with results compared to experimental measurements.

Experimental results

Research questions

• RQ1 Can macroscopic mechanical oscillators with masses on the order of 16 μg be prepared in non-classical superposition states with observable quantum features?
• RQ2 How does the size and phase of the cat state affect its decoherence rate in a massive mechanical system?
• RQ3 To what extent do standard quantum mechanical predictions, such as the decay of Wigner negativity, hold for large-amplitude cat states in a realistic experimental setup?
• RQ4 What is the role of environmental coupling and intrinsic decoherence mechanisms in limiting the lifetime of macroscopic superpositions in mechanical resonators?

Key findings

• The experiment successfully prepared Schrödinger cat states in a 16.2-μg mechanical resonator, with cat state sizes up to D = 1.61, demonstrating macroscopic quantum superpositions.
• Wigner negativity decay was observed with time constants of 24.68, 12.34, and 10.52 µs for cat states of size D = 1.09, 1.43, and 1.61, respectively, confirming size-dependent decoherence.
• The measured decay rates for larger cat states showed good agreement with numerical simulations, while discrepancies for small α values were attributed to inaccuracies in analytical approximations and background noise in the Wigner function.
• The coherence time of the largest cat state was measured to be approximately 10 µs for the interference fringe contrast, while the coherent state components decayed on the slower timescale of 2T1^ph.
• The system demonstrated control over both the amplitude and phase of the superposition, as evidenced by interference fringes in the Wigner function that varied with qubit preparation basis.
• Simulations of the full master equation process confirmed that the observed decay dynamics are consistent with standard quantum mechanical predictions, validating the model for larger-scale systems.