Quantum feedback: theory, experiments, and applications (1407.8536v3)

Abstract: The control of individual quantum systems is now a reality in a variety of physical settings. Feedback control is an important class of control methods because of its ability to reduce the effects of noise. In this review we give an introductory overview of the various ways in which feedback may be implemented in quantum systems, the theoretical methods that are currently used to treat it, the experiments in which it has been demonstrated to-date, and its applications. In the last few years there has been rapid experimental progress in the ability to realize quantum measurement and control of mesoscopic systems. We expect that the next few years will see further rapid advances in the precision and sophistication of feedback control protocols realized in the laboratory.

• The paper provides a comprehensive review of quantum feedback control, covering its theoretical frameworks, experimental implementations, and applications for managing quantum systems.
• It details two primary approaches: measurement-based feedback, which uses real-time monitoring, and coherent feedback, which utilizes ancillary systems for control without measurement.
• Experimental realizations across quantum optics, atomic physics, superconducting circuits, and mechanical systems demonstrate its effectiveness in state stabilization and noise reduction, highlighting its importance for future quantum technologies.

Quantum Feedback: Theory, Experiments, and Applications

The paper "Quantum feedback: theory, experiments, and applications" explores the concept of quantum feedback control, a vital strategy in reducing environmental noise, which is crucial for maintaining the coherence of quantum systems. Quantum feedback can be implemented through measurement-based strategies or by employing coherent feedback without measurements. This paper provides a meticulous review of both methodologies, theoretical frameworks, and practical applications across various physical systems.

Overview of Quantum Feedback Control

Quantum feedback involves dynamically manipulating quantum systems to achieve specific outcomes, such as noise reduction, state stabilization, or quantum error correction. The paper outlines two primary feedback types:

1. Measurement-based Feedback: This involves continuous monitoring of a system to adjust its dynamics in real-time based on the measurement results. The feedback adjusts the system Hamiltonian to counteract decoherence effects. Key examples include photon-counting for error correction and homodyne detection schemes in cavity QED systems.
2. Coherent Feedback: Unlike measurement-based feedback, coherent feedback uses ancillary quantum systems to control the primary system without extracting classical information from measurements. It is typically realized using field-mediated connections where quantum states interact directly through coherent couplings.

Theoretical Frameworks

Theoretical foundations in quantum control cover Markovian dynamics, coherent feedback networks, and stochastic master equations. The paper elaborates on the formulation of quantum filtering, highlighting how measurement results are used to update the observer's state of knowledge continuously. In the context of coherent feedback, it discusses input-output theory formalized by Collett and Gardiner which provides a mathematical framework for designing quantum feedback networks.

Experimental Realizations

Several experiments across different platforms demonstrate the practical applications of quantum feedback. Highlights include:

• In Quantum Optics: Adaptive phase measurement using homodyne detection has been successfully demonstrated, providing enhanced precision over traditional methods like heterodyne detection.
• In Atomic Systems: Continuous feedback techniques have been applied to stabilize atomic states and perform quantum state reduction, notably in cavity QED systems where states such as Fock and Bell have been prepared and maintained using feedback loops.
• In Superconducting Circuits: Recently, feedback has been utilized to stabilize qubit states amidst decoherence, marking significant progress in the practical deployment of quantum feedback in solid-state systems.
• In Mechanical Systems: Both measurement-based and coherent feedback methods are used for ground-state cooling of mechanical resonators, an essential step toward achieving macroscopic quantum states.

Implications and Future Directions

Quantum feedback control not only enhances the robustness of quantum systems but also enables complex operations like error correction and entanglement distribution. As experimental capabilities continue to advance, particularly in the precision of quantum measurements and coherent interactions, feedback control will likely play an integral role in the development of reliable quantum technologies.

The paper suggests that future research might focus on further optimizing feedback strategies under realistic constraints, investigating non-Markovian dynamics, and expanding coherent feedback architectures. Exploring these areas could reveal new insights into the fundamental limits of quantum control and expand the horizon of quantum system applications.

In conclusion, this comprehensive review underlines the significant strides in quantum feedback control, bridging theoretical advances with experimental achievements. It serves as a crucial resource for understanding the current landscape and potential future of quantum feedback mechanisms.