Measurement-based quantum control of mechanical motion (1805.05087v2)

Abstract: Controlling a quantum system based on the observation of its dynamics is inevitably complicated by the backaction of the measurement process. Efficient measurements, however, maximize the amount of information gained per disturbance incurred. Real-time feedback then enables both canceling the measurement's backaction and controlling the evolution of the quantum state. While such measurement-based quantum control has been demonstrated in the clean settings of cavity and circuit quantum electrodynamics, its application to motional degrees of freedom has remained elusive. Here we show measurement-based quantum control of the motion of a millimetre-sized membrane resonator. An optomechanical transducer resolves the zero-point motion of the soft-clamped resonator in a fraction of its millisecond coherence time, with an overall measurement efficiency close to unity. We use this position record to feedback-cool a resonator mode to its quantum ground state (residual thermal occupation n = 0.29 +- 0.03), 9 dB below the quantum backaction limit of sideband cooling, and six orders of magnitude below the equilibrium occupation of its thermal environment. This realizes a long-standing goal in the field, and adds position and momentum to the degrees of freedom amenable to measurement-based quantum control, with potential applications in quantum information processing and gravitational wave detectors.

• The paper demonstrates measurement-based quantum control by feedback-cooling a membrane resonator to a near-ground state with a residual thermal occupation of 0.29 ± 0.03.
• It employs an optomechanical setup with a silicon nitride membrane and soft clamping to achieve high measurement efficiency (η = 56%) and near-Heisenberg-limited precision.
• The results surpass traditional sideband cooling by about 9 dB, paving the way for enhanced quantum information processing and ultra-sensitive measurement applications.

Measurement-Based Quantum Control of Mechanical Motion

This paper presents a significant advancement in the field of quantum mechanics by demonstrating measurement-based quantum control of a mechanical system, particularly the motion of a millimeter-sized membrane resonator. This achievement fills a crucial gap in quantum control application to motional degrees of freedom, which had been previously challenging.

Core Concepts

The central theme of this research is the implementation of measurement-based quantum control, which involves measuring the quantum state of a system and applying feedback to control that state. This is contrasted with coherent quantum control, which avoids direct measurement to prevent disturbance to the system. Measurement-based control, on the other hand, requires an efficient measurement process that minimizes the backaction—the disturbance caused by measurement—while maximizing the information gained.

The paper indicates that efficient measurement is key to successful quantum control, requiring measurement efficiency ($\eta$) close to unity, a benchmark previously achieved in cavity and circuit quantum electrodynamics.

Experimental Achievement

The authors achieve this control by employing an optomechanical system where the zero-point motion of a soft-clamped resonator is well-resolved within its coherence time. The significant achievement is feedback-cooling a resonator mode to its quantum ground state, with a residual thermal occupation of $0.29 \pm 0.03$. This result is approximately 9 dB below the quantum backaction limit of sideband cooling and significantly below the equilibrium thermal occupation. Such an outcome represents a longstanding goal in the field, demonstrating that the combination of measurement efficiency and feedback allows surpassing the limits of traditional sideband cooling.

Measurement and Results

The research outlines a sophisticated setup involving a silicon nitride membrane with a defect mode of interest, which is confined by a phononic crystal and exhibits high quality factors due to soft clamping. Measurement efficiency achieved is $\eta = 56\%$, comparable to high-standard circuit QED systems. This high efficiency is a critical enabler for the quantum control exhibited.

The paper further discusses the realization of a near-Heisenberg-limited measurement precision. The balance between imprecision noise and measurement-induced quantum backaction noise approaches the limits set by quantum mechanics, a noteworthy demonstration of precision.

Implications and Future Directions

The implications of this research are profound for the future of quantum information processing and gravitational wave detection, where precise control over mechanical systems plays a crucial role. This achievement now allows for integration of mechanical systems into various quantum technologies, promising improved performance in applications requiring ultra-sensitive measurements.

Moreover, the successful demonstration suggests upcoming advancements in quantum state preparation, including non-Gaussian states through nonlinear measurement schemes. The potential for implementing quantum control of motion at room temperature is highlighted as a realistic near-future goal, given the achieved efficiency at cryogenic temperatures.

In summary, this paper underscores a significant leap in measurement-based quantum control, expanding the horizons of what can be controlled in mechanical systems. This paves the way for broadening the toolkit in quantum mechanics with applications in next-generation quantum technologies. Future enhancements could explore improved feedback filters, extended coherence times, and broader applicability across quantum systems.