Quantum limits in optical interferometry (1405.7703v3)

Abstract: Non-classical states of light find applications in enhancing the performance of optical interferometric experiments, with notable example of gravitational wave-detectors. Still, the presence of decoherence hinders significantly the performance of quantum-enhanced protocols. In this review, we summarize the developments of quantum metrology with particular focus on optical interferometry and derive fundamental bounds on achievable quantum-enhanced precision in optical interferometry taking into account the most relevant decoherence processes including: phase diffusion, losses and imperfect interferometric visibility. We introduce all the necessary tools of quantum optics as well as quantum estimation theory required to derive the bounds. We also discuss the practical attainability of the bounds derived and stress in particular that the techniques of quantum-enhanced interferometry which are being implemented in modern gravitational wave detectors are close to the optimal ones.

• The paper demonstrates that quantum-enhanced interferometry can surpass classical shot noise limits using non-classical states, while decoherence imposes fundamental precision constraints.
• It shows how phase diffusion, photon losses, and imperfect visibility quantitatively limit measurement precision via a rigorous quantum Fisher information framework.
• Adaptive Bayesian estimation strategies are proposed to optimize phase sensitivity in realistic interferometric setups, with implications for gravitational wave detection.

Analysis of Quantum Limits in Optical Interferometry

The paper "Quantum limits in optical interferometry" by Demkowicz-Dobrzański et al. provides an extensive theoretical evaluation of the limits to precision achievable in quantum-enhanced optical interferometry. It addresses a critical aspect of quantum metrology, focusing on how non-classical states of light can be leveraged to improve measurement precision. This work is particularly relevant for applications such as gravitational wave detection.

Quantum Metrology and Interferometry

Optical interferometry involves precise measurement of phase differences, typically encountered in setups like the Mach-Zehnder interferometer. Classical interferometry techniques are limited by shot noise, often scaling as $1/\sqrt{N}$, where $N$ is the number of photons. Quantum-enhanced methods using non-classical states, such as squeezed states, offer the potential to surpass this standard quantum limit.

Decoherence Effects

The authors discuss that the presence of decoherence, resulting from environmental interactions, poses a significant barrier to achieving quantum-enhanced precision. The paper describes fundamental bounds that decoherence imposes on precision, focusing on three primary decoherence effects: phase diffusion, photon losses, and imperfect visibility.

Phase Diffusion

This refers to random fluctuations in the phase due to environmental factors, modeled as a Gaussian noise process. It is shown that phase diffusion fundamentally limits the estimation precision to a constant value dependent on the diffusion strength, which cannot be reduced by increasing the number of photons.

Photon Losses

In realistic interferometry setups, photon loss is inevitable. The paper conveys that the precision bounds are reduced due to photon loss, with scaling adjusted to $1/\sqrt{\eta N}$, where $\eta$ is the transmission factor. Despite this, the paper details that practical interferometric techniques, such as squeezing combined with coherent states, can approach these fundamental limits.

Imperfect Visibility

Imperfect visibility, often caused by mode mismatch, is modeled as local dephasing. The authors derive bounds showing that imperfect visibility similarly dictates a precision reduction that can approach optimal bounds under ideal preparation.

Quantum Fisher Information (QFI) and Bayesian Analysis

Using Quantum Fisher Information, the authors rigorously quantify sensitivity limits and identify optimal strategies for phase estimation under various decoherence models. When decoherence is significant, they propose the use of adaptive techniques and robust states to achieve nearly optimal results. The QFI approach is complemented by Bayesian analysis, allowing a comprehensive examination of both local and global estimation scenarios.

Practical Implications and Future Directions

The paper underscores that even with decoherence, significant quantum improvements in measurement precision are feasible, albeit limited compared to ideal theoretical scenarios. Current experimental strategies, notably those implemented in gravitational wave observatories, already operate close to these bounds, exemplifying the practical applicability.

Furthermore, this work invites future research into refining theoretical models for specific decoherence types and extending multi-parameter estimation frameworks—critical steps toward fully exploiting quantum sensing capabilities across various scientific disciplines.

Conclusion

Demkowicz-Dobrzański et al. contribute significantly to understanding the realistic capabilities and limitations of quantum-enhanced optical interferometry. They provide a foundational framework for interpreting experimental results within the context of quantum metrology and set the stage for ongoing improvements in precision measurement technology through quantum resources.