Real-time optimal quantum control of mechanical motion at room temperature (2012.15188v2)

Abstract: The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering. Today, the increasing demand for applied quantum technologies requires to adapt this level of control to individual quantum systems. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback. Successful implementations thus far include experiments on the level of optical and atomic systems. Here we demonstrate real-time optimal control of the quantum trajectory of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of $n=0.56\pm0.02$ quanta, realizing quantum ground state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.

• The paper achieves real-time optimal quantum control by integrating near-Heisenberg sensing with a Kalman filter and LQR feedback to cool a nanoparticle towards its quantum ground state.
• The methodology employs confocal optical sensing and linear quadratic Gaussian control, achieving a mean thermal occupation number of n = 0.56 ± 0.02.
• The study overcomes environmental decoherence at room temperature, surpassing the standard quantum limit by achieving displacement sensitivity at only 1.76 times above SQL.

Real-time Optimal Quantum Control of Mechanical Motion at Room Temperature

The paper presents a significant advancement in the field of quantum control by demonstrating real-time optimal control of an optically trapped nanoparticle in a high-temperature environment. This is achieved through the integration of near-Heisenberg-limit sensing, optimal state estimation, and feedback protocols, using the principles of quantum Kalman filtering and the linear quadratic Gaussian (LQG) control.

Key Methodologies

The central methodology involves a combination of confocal optical sensing with state-of-the-art Kalman filtering techniques. In this setup, a silica nanoparticle is trapped using an optical tweezer and its motion is continuously monitored via high-efficiency backscattered light detection. The real-time position of the nanoparticle is estimated using a Kalman filter, which is an optimal linear estimator known for its utility in systems where measurements are corrupted by Gaussian noise. The filter utilizes the measurement data to provide an accurate estimate of the nanoparticle's state in phase space.

The feedback control is implemented using a linear quadratic regulator (LQR), which calculates the control input required to minimize the energy of the nanoparticle, effectively cooling it towards its quantum ground state. The entire process is made possible by the high quantum efficiency of the measurement setup, which is crucial for reducing the measurement noise to quantum-limited levels.

Numerical Results and Analysis

One of the prominent outcomes is the demonstrated ground-state cooling of the nanoparticle. By optimizing the feedback loop parameters, the research team achieved a mean thermal occupation number of $n = 0.56 \pm 0.02$. This result signifies successful ground-state cooling from room temperature, directly comparing with the limits set by quantum mechanics for systems of this scale.

Furthermore, this paper established that even in the presence of environmental decoherence, the combination of quantum-limited measurement precision and optimal feedback can stabilize the mechanical system at quantum-level energies. The researchers achieved an overall information efficiency ($\eta$) of about 0.34, which considers the setup's detection and environmental noise losses. Impressively, this system surpassed the standard quantum limit (SQL) in displacement measurement, achieving sensitivity at a factor of only 1.76 times above SQL under certain conditions.

Theoretical and Practical Implications

Theoretically, this work opens pathways for deeper investigations into quantum supervision and control of macroscopic systems, merging classical and quantum regimes. The successful real-time application of Kalman filtering in quantum mechanics reflects a harmonization of control theory and quantum dynamics, potentially applicable to a wide array of quantum systems beyond optical trapping.

Practically, the implications are vast. The ability to operate quantum control in ambient conditions rather than requiring cryogenic environments significantly broadens the potential applications. In sensing, for instance, real-time monitoring could usher advances in gravitational wave detection, where the sensitivity to quantum-level displacements is crucial. Additionally, this technique has the potential to revolutionize fields that require precise motional control, including opto-mechanical systems used in quantum information processing and potentially influencing the design of sensors for fundamental physics experiments.

Future Research Directions

The integration of this methodology with more complex quantum systems could further push the boundaries of what can be achieved in room-temperature quantum control. Future work could explore scaling the approach to multi-dimensional systems or increasing the mass of the objects under control. Furthermore, advancements in computational technologies may alleviate constraints related to implementation on FPGA platforms, thereby enhancing the range and precision of the feedback systems.

In conclusion, this paper contributes a crucial step forward in quantum mechanics, particularly in real-time control and precision measurements, establishing a foundation for future innovations in quantum technology deployments in practical, everyday environments.