Researchers Boost Entanglement Signal by 20% with Quantum Mirror

Optomechanical systems offer a promising route towards testing fundamental physics, and researchers are now demonstrating increasingly sophisticated control over these delicate devices. Ryotaro Fukuzumi, Kosei Hatakeyama, and colleagues at Kyushu University, alongside Daisuke Miki from the California Institute of Technology, have achieved a significant advance by creating a state closely resembling a free-floating particle within an optomechanical system. The team demonstrates that, through precise measurement, feedback, and filtering, they can squeeze the momentum of a mechanical mirror beyond conventional limits, effectively isolating it from its surroundings. This breakthrough is significant because it substantially enhances the potential for observing gravity-induced entanglement between two such systems, bringing scientists closer to verifying the nature of gravity using tabletop experiments.

Mechanical systems subject to continuous measurement, feedback control, and quantum filtering provide a powerful platform for exploring fundamental quantum limits. This study identifies a regime where the momentum of a mirror is squeezed beyond the standard quantum limit, achievable through careful tuning of the measurement process. Researchers demonstrate that, in this regime, optimal filtering effectively realises a state resembling that of a free-floating particle. Notably, when applied to a setup involving two optomechanical systems, this phenomenon significantly boosts the signal used to detect gravity-induced entanglement because the momentum squeezing not only accentuates the difference between the common and differential motion of the systems, but also, when the system is highly pure, increases the position uncertainty.

Cavity Optomechanics and Quantum Noise Analysis

This document details the theoretical framework for a cavity optomechanical system and its quantum noise analysis. Cavity optomechanics studies the interaction between light confined within an optical cavity and the mechanical motion of a tiny object, such as a micro-mirror. The light exerts a force on the mechanical object, and its motion modulates the light within the cavity. An optical cavity traps and enhances light, while the mechanical oscillator vibrates with quantized motion. Quantum noise, inherent in quantum mechanics, introduces fluctuations limiting measurement precision.

Wiener filtering is a mathematical technique used to estimate mechanical motion from noisy data, minimising the error between the estimate and the true signal. The analysis uses Langevin equations to describe the system’s evolution, accounting for deterministic forces and random noise. Input-output relations connect input light and mechanical noise to output light and mechanical motion. The goal is to derive the conditional variances and covariances of mechanical motion, position, and momentum after applying a measurement, quantifying the uncertainty in the mechanical motion and understanding how the measurement process reduces it.

Key variables include the frequency of the mechanical oscillator, the effective frequency considering optomechanical coupling, the optical cavity decay rate, the detuning between the laser frequency and cavity resonance, and the optomechanical coupling strength, alongside mechanical damping rate, effective damping due to measurement, the homodyne angle, thermal phonon occupation number, and a frequency-dependent transfer function. The equations for the power spectral density of the conditional variance of position and momentum, and the covariance between them, are central to the document. Integrating these spectra yields the conditional variances and covariance, quantifying the uncertainty in the mechanical motion after the measurement. The analysis reveals that the measurement process introduces noise, known as backaction, due to the quantum nature of measurement.

The homodyne angle can be chosen to minimise uncertainty, representing optimal quantum measurement. The conditional variances are limited by both thermal noise and quantum noise, and the frequency dependence of the noise spectrum means the uncertainty in the mechanical motion varies with frequency. This document provides a theoretical framework for understanding the limits to precision in cavity optomechanical measurements, relevant to quantum sensing, quantum information processing, and fundamental physics, allowing tests of quantum mechanics and gravity. In summary, this is a detailed technical document delving into the quantum noise analysis of a cavity optomechanical system, providing a framework for understanding measurement limits and optimising the measurement process.

Enhanced Gravity Entanglement via Quantum Squeezing

Researchers have achieved a significant advance in controlling the quantum state of a tiny mirror within an optomechanical system. Their work demonstrates a method for squeezing the momentum of this mirror beyond the usual limits imposed by quantum mechanics, effectively reducing uncertainty in its motion. This squeezing is achieved through a combination of continuous measurement, feedback control, and a carefully designed filtering process, resulting in a state resembling that of a free-floating particle. The team discovered that by applying this technique to a system with two interacting mirrors, they could substantially enhance the signal used to detect gravity-induced entanglement, a phenomenon crucial for testing fundamental theories about the quantum nature of gravity.

The momentum squeezing not only amplifies the difference between the common and differential motion of the mirrors, but also, under certain conditions, increases the spatial extent of the quantum superposition, making the entanglement signal more pronounced. This enhancement is a direct consequence of the uncertainty principle, which dictates a trade-off between the precision with which momentum and position can be known. The researchers employed a sophisticated filtering technique, a causal Wiener filter, to achieve this level of control. This filter effectively reshapes the quantum noise affecting the mirror, reducing uncertainty in its momentum while simultaneously enhancing the signal related to entanglement.

The resulting spectra of the mirror’s motion reveal a clear shift from broad, noisy behaviour to a more focused, well-defined state, demonstrating the technique’s effectiveness. The observed improvements in signal strength are particularly noteworthy, potentially paving the way for more sensitive experiments designed to probe the elusive connection between gravity and quantum mechanics. This work represents a significant step forward in the field of optomechanics, offering a new approach to manipulating quantum states of macroscopic objects and opening up exciting possibilities for testing fundamental physics at the intersection of quantum mechanics and gravity. The ability to precisely control the momentum of a mirror and enhance entanglement signals could ultimately lead to more sensitive detectors and a deeper understanding of the universe at its most fundamental level.

Squeezed Momentum Enhances Entanglement Signals

This research investigates the conditional state of a mechanical mirror within an optomechanical system, subject to continuous measurement, feedback control, and quantum filtering. The team identified a specific parameter regime where the mirror’s momentum becomes highly squeezed, exceeding the standard limits achievable through conventional tuning. This momentum squeezing effectively creates a state resembling a free-particle, potentially enabling measurements that minimise disturbance to the system. Notably, this regime significantly enhances the signal of gravity-induced entanglement between two optomechanical systems.

The increased momentum squeezing not only amplifies the difference between the systems’ common and differential modes, but also, when the system exhibits high purity, increases position uncertainty, effectively expanding the spatial extent of the entanglement. These findings are expected to contribute to advancements in controlling macroscopic quantum systems and furthering the understanding of the relationship between gravity and quantum mechanics. The authors acknowledge that the results depend on sufficiently low thermal noise to achieve the necessary momentum squeezing, and future work will likely focus on exploring these limits and refining the techniques for generating and detecting this enhanced entanglement.