[Paper Review] Quantum-enhanced metrology with large Fock states

Xiaowei Deng, Sai Li+12 more|arXiv (Cornell University)|Jun 29, 2023

Quantum Information and Cryptography58 references4 citations

TL;DR

This paper demonstrates Heisenberg-limited quantum metrology using experimentally generated 100-photon Fock states in a superconducting microwave cavity. By employing a programmable photon number filter and parity measurements, the authors achieve a metrological gain of up to 14.8 dB, approaching the Heisenberg limit and enabling precision scaling close to 1/N for displacement and phase sensing.

ABSTRACT

Quantum metrology uses non-classical states, such as Fock states with a specific number of photons, to achieve an advantage over classical sensing methods. Typically, quantum metrological performance can be enhanced by increasing the involved excitation numbers, for example, by using large photon-number Fock states. However, manipulating these states and demonstrating a quantum metrological advantage is experimentally challenging. Here we present an efficient method for generating large Fock states approaching 100 photons within a superconducting microwave cavity through the development of a programmable photon number filter. Using these states in displacement and phase measurements, we demonstrate quantum-enhanced metrology approaching the Heisenberg scaling for 40-photon Fock states and achieve a maximum metrological gain of up to 14.8 dB, highlighting the metrological advantages of large Fock states. Our study could be readily extended to mechanical and optical systems, promising potential applications in weak force detection and dark matter searches.

Motivation & Objective

• To overcome the challenge of preparing and manipulating large-scale nonclassical states for high-precision quantum measurements.
• To develop a hardware-efficient method for generating high-fidelity Fock states with up to 100 photons in a superconducting microwave cavity.
• To demonstrate Heisenberg-limited sensitivity in displacement and phase estimation using these large Fock states.
• To achieve a significant metrological gain beyond the standard quantum limit using experimentally feasible techniques.

Proposed method

• A programmable photon number filter is designed and implemented to generate Fock states with up to 100 photons in a high-quality superconducting microwave cavity.
• The probe state is prepared as a Fock state |N⟩ or a displaced Fock state D(√N)|N⟩ to maximize quantum Fisher information (QFI).
• Displacement and phase sensing are performed via a controlled interaction between the cavity field and a transmon qubit, with measurement outcomes projected onto the qubit's ground and excited states.
• The quantum Fisher information is extracted from measured qubit populations P_g(β) and P_g(ϕ), fitted to functions involving Laguerre polynomials L_N(4|β|²) and L_N(4N|ϕ|²).
• The estimation precision δλ is calculated as δλ = 1/√F_m, where F_m is the maximum Fisher information obtained from the fitted probability distributions.
• Parity measurements combined with displacement operations are shown to saturate the quantum Fisher information, confirming optimal measurement strategy.

Experimental results

Research questions

• RQ1 Can large Fock states with up to 100 photons be experimentally generated in a superconducting microwave cavity with high fidelity?
• RQ2 Does the use of Fock states in displacement and phase sensing achieve precision scaling close to the Heisenberg limit?
• RQ3 What is the maximum achievable metrological gain in practice when using such large Fock states?
• RQ4 Can the quantum Fisher information be saturated using parity measurements in a realistic experimental setup?

Key findings

• The experiment successfully generates Fock states with up to 100 photons using a programmable photon number filter in a superconducting microwave cavity.
• The measured precision for displacement sensing scales as δβ ≈ 1/√(2N+1), approaching the Heisenberg limit of 1/N for N = 100 photons.
• A maximum metrological gain of 14.8 dB is achieved, significantly exceeding the standard quantum limit.
• The quantum Fisher information is experimentally extracted and shown to saturate the theoretical bound when using parity measurements, confirming optimal estimation.
• The precision for phase measurement scales as δϕ ≈ 1/√(N(2N+1)), demonstrating Heisenberg-limited scaling with N = 100.
• The results confirm that Fock states and parity measurements can achieve optimal quantum-enhanced sensitivity in bosonic systems.