Schrödinger cat states of a 16-microgram mechanical oscillator

Abstract: The superposition principle is one of the most fundamental principles of quantum mechanics. According to the Schr\"odinger 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 Schr\"odinger 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.

Insightful Overview of Schrödinger Cat States of a 16-Microgram Mechanical Oscillator

The study conducted by Marius Bild, Matteo Fadel, Yu Yang, et al., and presented in their paper, focuses on the realization of Schrödinger's cat states within a mechanical resonator possessing a significant mass, emphasizing the implications for quantum mechanics and quantum technologies. The concept of Schrödinger's cat states fundamentally arises from quantum superposition, which typifies the simultaneous existence of a system in multiple distinct states. While historically this principle is well-documented in microscopic systems, its manifestation in macroscopic systems remains elusive, a conundrum this study addresses.

Experimental Implementation and Outcomes

The authors demonstrate the preparation of a Schrödinger cat state in a mechanical resonator with an effective mass of 16.2 micrograms. This resonator is a high-overtone bulk acoustic-wave resonator (HBAR) interfaced with a superconducting transmon qubit. The coupling facilitates the generation and manipulation of cat states in the mechanical resonator, showcasing the principles of circuit quantum acoustodynamics (cQAD).

Significantly, the experiment achieves control over the superposition size and phase using the Jaynes-Cummings (JC) interaction model. The JC model's Hamiltonian governs the resonant interactions between the transmon qubit and phonons, leading to observable quantum collapse and revival phenomena—key signatures of quantum coherence in the setup. This aspect underscores the quantum mechanical interactions bridging light and mechanical systems.

The experimental dynamics reveal the collapse and subsequent revival of Rabi oscillations as a function of interaction time, with critical timings being the collapse time ($t_{\text{collapse}}$) and revival time ($t_R$). The qubit's population oscillations and phonon mode entanglement elaborately illustrate the transition into cat states. The collapse occurs due to the dephasing of oscillation frequency components, while the revival stems from the discrete spectrum's re-phasing, at times producing a notable resemblance to coherent states.

Implications and Future Outlook

Analyzing Schrödinger cat states in massive mechanical systems probes the classical-quantum boundary, with profound implications for theories extending standard quantum mechanics, such as those proposing intrinsic stochastic noise or gravitational decoherence. Moreover, this research extends practical avenues in quantum metrology and information processing. The ability to generate mechanical superpositions with controlled parameters showcases potential for advancements in Heisenberg-limited parameter estimation and quantum error correction methodologies, pivotal for fault-tolerant quantum computation.

The results signal potential for scaling mechanical quantum states toward larger mass objects, a necessary venture for testing hypotheses related to gravitational influences on state superposition. As the decoherence characteristics of these superpositions are further examined, they could provide empirical feedback on proposed quantum gravity models.

Numerical and Analysis Highlights

• The prepared superposition corresponds to an RMS effective oscillating mass of approximately 16.2 micrograms, with an atomic displacement delocalization measure of around $2.1 \times 10^{-18}$ meters.
• The study presents a maximum coherence time ($\tau_\text{cat}$) at approximately 10.52 microseconds for the largest cat state size, indicating rapid decoherence exacerbated by state size.
• Master equation simulations and empirical negativity volume measurements reinforce the discussed decoherence characteristics.

Conclusion

This paper effectively bridges theoretical propositions with experimental advances in macroscopic quantum superpositions, progressing the boundaries of quantum mechanical applications and understanding. The detailed examination of collapse and revival phenomena within the JC framework provides valuable insights into quantum coherence and entanglement dynamics. Future exploration is likely to enhance the interface of superconducting qubits and mechanical resonators, refining both theoretical and practical frameworks of quantum information technologies.