[Paper Review] Flux qubit as a sensor for a magnetometer with quantum limited sensitivity

E. Il’ichev, Ya. S. Greenberg|arXiv (Cornell University)|Aug 18, 2006

Physics of Superconductivity and Magnetism4 citations

TL;DR

This paper proposes using a superconducting flux qubit as a magnetometer with quantum-limited sensitivity by exploiting its high voltage-to-flux and phase-to-flux transfer functions—exceeding 10 mV/Φ₀, an order of magnitude better than conventional SQUIDs. The system achieves energy resolution near the Planck constant, with flux noise as low as 1.6×10⁻⁷ Φ₀/Hz¹ᐟ² in phase detection mode, demonstrating quantum-limited performance.

ABSTRACT

We propose to use the quantum properties of a superconducting flux qubit in the construction of a magnetometer with quantum limited sensitivity. The main advantage of a flux qubit is that its noise is rather low, and its transfer functions relative to the measured flux can be made to be about 10mV/$Φ_0$, which is an order of magnitude more than the best value for a conventional SQUID magnetometer. We analyze here the voltage-to-flux, the phase-to-flux transfer functions and the main noise sources. We show that the experimental characteristics of a flux qubit, obtained in recent experiments, allow the use of a flux qubit as magnetometer with energy resolution close to the Planck constant.

Motivation & Objective

• To develop a superconducting flux qubit as a high-sensitivity magnetic flux sensor with quantum-limited performance.
• To overcome the sensitivity limitations of conventional SQUID magnetometers by leveraging the qubit’s superior transfer functions.
• To analyze and minimize noise sources, particularly amplifier current and voltage noise, to achieve near-quantum-limited flux resolution.
• To demonstrate that the energy resolution of the magnetometer can approach the Planck constant, enabling single-quantum-level detection.

Proposed method

• The flux qubit is inductively coupled to an LC tank circuit via mutual inductance M, enabling flux-dependent resonance shifts detectable via voltage or phase output.
• The system operates in a flux-locked loop mode, with the working point set at the maximum slope of the voltage-to-flux or phase-to-flux transfer function for optimal sensitivity.
• Key equations (1)–(4) describe the tank circuit’s voltage and phase response as functions of external flux, with flux-dependent detuning ξ(fₓ) derived from qubit parameters.
• The transfer functions VΦ = ∂v/∂Φₓ and χΦ = v∂χ/∂Φₓ are calculated to quantify sensitivity, with values exceeding 10 mV/Φ₀ for optimal bias conditions.
• Noise analysis uses spectral densities of amplifier voltage (Sᵥ) and current (Sᵢ), with flux noise referred to input via SΦ = M²Q²Sᵢ + Sᵥ/VΦ² + R_D²Sᵢ/VΦ² (Eq. 5).
• Phase detection is favored due to lower overall noise and reduced sensitivity to bias current I₀, with optimization of k, Q, ωₜ, and L to minimize SΦ,1 = k²Q(4k_BTₙL/ωₜ) (Eq. 6).

Experimental results

Research questions

• RQ1 Can a superconducting flux qubit achieve magnetic flux sensitivity approaching the quantum limit?
• RQ2 How do the voltage-to-flux and phase-to-flux transfer functions of a flux qubit compare to those of conventional SQUIDs?
• RQ3 What are the dominant noise sources in a qubit-based magnetometer, and how can they be minimized?
• RQ4 Can the energy resolution of the magnetometer reach values close to the Planck constant?

Key findings

• The flux qubit achieves a voltage-to-flux transfer function exceeding 10 mV/Φ₀, surpassing the best conventional SQUID performance of ~1 mV/Φ₀.
• Phase detection yields lower flux noise than voltage detection, with a minimum sensitivity of 1.6×10⁻⁷ Φ₀/Hz¹ᐟ² at 200 MHz resonance.
• The dominant noise source is amplifier current noise via magnetic coupling, contributing SΦ,1 = k²Q(4k_BTₙL/ωₜ), which is minimized by optimizing k, Q, ωₜ, and L.
• For ωₜ = 200 MHz and I₀ = 200 pA, the energy resolution reaches ε = 2h, corresponding to 1.3×10⁻³³ J/Hz, approaching the Planck constant.
• The qubit’s intrinsic critical current noise (SΦ,IC¹ᐟ² ≈ 2×10⁻⁸ Φ₀/Hz¹ᐟ²) is negligible compared to amplifier noise, allowing it to be neglected in sensitivity analysis.
• The total flux noise is minimized in phase detection mode and is weakly dependent on bias current I₀, making it more robust for practical implementation.