[Paper Review] Phase estimation with weak measurement using a white light source

Xiao‐Ye Xu, Yaron Kedem+4 more|arXiv (Cornell University)|Jun 20, 2013

Photonic and Optical Devices3 citations

TL;DR

This paper demonstrates high-precision phase estimation using weak measurements with a commercial white-light LED source, exploiting the imaginary part of the weak value of a polarization operator induced by longitudinal momentum coupling. The method achieves attosecond-level resolution and remains robust against chromatic dispersion, outperforming conventional interferometry and quantum metrology techniques using N00N or squeezed states.

ABSTRACT

We report results of a high precision phase estimation based on a weak measurements scheme using commercial light-emitting diode. The method is based on a measurement of the imaginary part of the weak value of a polarization operator. The imaginary part of the weak value appeared due to the measurement interaction itself. The sensitivity of our method is equivalent to resolving light pulses of order of attosecond and it is robust against chromatic dispersion.

Motivation & Objective

• To develop a robust, high-precision phase estimation method that does not require coherent light sources.
• To demonstrate that white light, typically considered unsuitable for quantum metrology, can enable sub-attosecond phase resolution via weak measurements.
• To exploit the imaginary part of the weak value—generated by non-negligible polarization evolution during measurement—rather than relying on transverse spatial shifts.
• To validate the method’s resilience to chromatic dispersion, a major limitation in conventional phase measurement setups.
• To achieve phase sensitivity comparable or superior to state-of-the-art quantum metrology techniques using N00N or squeezed states.

Proposed method

• The experiment uses a white-light LED source with a central wavelength of 805 nm and spectral width Δλ = 41.6 nm.
• A birefringent plate induces a time delay between orthogonal polarization components, creating a phase shift α proportional to the plate’s effective width.
• Pre- and post-selection of polarization states via polarization beam splitters prepares the system in a superposition, enabling weak measurement of the polarization operator A with eigenvalues ±1.
• The key innovation lies in measuring the longitudinal momentum shift (via spectral shift δλ), which is proportional to the imaginary part of the weak value of A, rather than the real part.
• The interaction Hamiltonian is H = g(t)PA, where P is the longitudinal momentum and g(t) is time-dependent coupling, with ∫g(t)dt = k.
• Theoretical modeling accounts for spectral uncertainty and polarization filtering, with the shift δλ given by δλ = (λ₀ / Δλ²) × (α / 2) × sin(β) × (1 + cos(α)) for small α, derived from the weak value formalism.

Experimental results

Research questions

• RQ1 Can white light from a commercial LED be used to achieve high-precision phase estimation via weak measurements?
• RQ2 Does the imaginary part of the weak value, generated by non-negligible polarization evolution, enable phase resolution at the attosecond scale?
• RQ3 Is the method robust against chromatic dispersion, a common challenge in ultrafast optics?
• RQ4 Can the precision of phase estimation with white light surpass that of coherent light-based weak measurements or N00N state schemes?
• RQ5 What is the optimal post-selection parameter β for maximizing phase sensitivity in the presence of spectral and polarization uncertainty?

Key findings

• The method achieves phase resolution on the order of 10⁻⁴ of the measured phase α, with α ≈ 10⁻³ detectable with uncertainty Δα ≈ 10⁻⁴.
• For β = 0, the phase shift α ≃ 10⁻³ can be estimated with precision of the order of 10⁻⁴, indicating sub-attosecond sensitivity.
• Theoretical and experimental results show excellent agreement, particularly for orthogonal post-selection (β = 0), where the system is most stable and controllable.
• Chromatic dispersion introduced by a 1 mm ZnSe crystal (broadening pulses by hundreds of femtoseconds) causes only a small shift in the measured spectrum, demonstrating robustness.
• Reducing the spectral width from Δλ = 41.6 nm to 18.9 nm via filtering leads to a measurable reduction in spectral shift, confirming the theoretical dependence on Δλ².
• The method outperforms current quantum metrology techniques using N00N and squeezed states, which still face experimental challenges, and competes favorably with coherent-light weak measurement schemes.