Time domain non-linear quantum interferometry

AI summary

Overview

• Research area: Quantum sensing and nonlinear microwave interferometry.
• Technical level: Intermediate.
• Scope: The paper demonstrates a microwave interferometer that uses a nonlinear superconducting circuit to detect very weak coherent signals, and investigates its sensitivity, bandwidth, and operation in a magnetic field.

What This Paper Is About

Conventional interferometers face shot noise: fluctuations in the reference light or microwave field that limit how small a signal they can measure. The researchers build an interferometer using a cavity and a granular-aluminum superconducting circuit, aiming to make weak microwave signals easier to detect by using the circuit’s nonlinearity and measuring the signal’s phase.

Key Contributions

1. Demonstrated a nonlinear microwave interferometer. A granular-aluminum circuit is dispersively coupled to a microwave cavity, so changes in the cavity field affect the circuit’s Ramsey interference pattern.
2. Compared two measurement approaches. Protocol A measures the cavity field’s in-phase and quadrature components; Protocol B reads the phase shift in the circuit’s Ramsey signal.
3. Measured weak coherent signals. The experiment detected signals with an estimated cavity population as low as (10^{-5}) photons over (400) ms, and below one photon with a measurement time of (200) μs.
4. Tested operation beyond the main readout configuration. The researchers demonstrated detection using an auxiliary cavity mode and showed that Protocol B operates at a magnetic field of (100) mT.

Main Findings

• Weak-signal sensitivity: The paper reports detection down to about (10^{-5}) photons over (400) ms. It gives a corresponding figure of merit of (1.2 \times 10^{-22}) W/(\sqrt{\text{Hz}}).
• Fast detection: The abstract reports detection of a cavity signal with a photon number as small as (10^{-2}) in (400) μs. The main text also reports detection below one photon with a measurement time of (200) μs.
• Two protocols give consistent noise estimates: Protocols A and B show comparable variance, which the researchers report decreases as (1/t), where (t) is the measurement time.
• Nonlinear response: The Ramsey phase responds to the interference between the cavity drive and the weak signal. The signal size scales with the square root of the weak-signal photon number, rather than simply requiring a power measurement.
• Shot-noise comparison: With an auxiliary cavity mode, the measured interferometer contrast varies nonlinearly with pump power and peaks at about (0) dBm. The authors interpret this behavior, alongside keeping the interferometer readout photon number constant, as evading the usual shot-noise limitation in several respects. They do not report reaching the Heisenberg limit.
• Magnetic-field resilience: Protocol B was demonstrated at (100) mT, with a reported sensitivity limit of (5 \times 10^{-4}) photon over (400) ms.
• Limits of the demonstration: The weak signal was a controlled coherent test signal, not a detected axion, dark photon, gravitational wave, or astronomical maser. The nonlinear circuit’s measured preamplification in Protocol A was modest—about (10%).

Methodology in Plain English

The team placed a granular-aluminum superconducting circuit inside a microwave cavity and drove the system with a strong cavity field and a much weaker test signal. Because the circuit’s frequency depends on the cavity field, interference between the strong and weak fields changes the circuit’s accumulated phase.

They measured that phase using a Ramsey sequence: brief microwave pulses prepare and then read out a superposition in the circuit, while the phase accumulated between the pulses carries information about the weak signal. They also measured the cavity field directly in a second approach. By changing the test signal’s phase and strength, and varying measurement time, they compared the signal response with the measurement noise. For a further test, they used an auxiliary cavity mode and applied a magnetic field.

Why This Matters

The work offers a phase-sensitive alternative to measuring microwave power. The authors’ motivation is that sensing amplitude and phase may help detect weak, narrow-linewidth signals, including signals relevant to searches for dark matter.

Potential applications discussed in the paper include:

• Axion dark-matter searches using microwave cavities in haloscopes.
• Dark-photon searches, since dark photons may also affect electromagnetic fields.
• High-frequency gravitational-wave detection through their effects on microwave fields.
• Astronomical maser measurements, including signals such as the OH maser discussed by the authors.

Research and industry relevance: The experiment shows a route to microwave sensing with a conventional HEMT amplifier, rather than relying on a traveling-wave parametric amplifier in this setup. Its magnetic-field resilience may also be useful for sensing configurations that require strong magnetic fields. The paper suggests that dispersive detection could work over a frequency range beyond the HEMT bandwidth, potentially exceeding (10) GHz, but that capability is a prospect rather than a demonstrated scan range.

Future Directions

• Test the method with signals from an actual haloscope or another physical source, rather than a simulated coherent test signal.
• Improve the nonlinear circuit’s contribution to amplification while preserving the Ramsey contrast and sensitivity.
• Investigate operation at magnetic fields above the demonstrated (100) mT, as the paper identifies magnetic-field-resilient granular-aluminum circuits as a possible route.
• Establish experimentally how broadly dispersive detection can cover frequencies beyond the readout amplifier’s bandwidth, and assess its use in searches over unknown signal frequencies.

Target Audience

This paper is most relevant to researchers in quantum sensing, superconducting circuits, microwave cavity experiments, and dark-matter detection. It may also interest experimentalists working on gravitational-wave sensing, astronomical microwave signals, and quantum interferometry. The main idea is accessible to readers familiar with basic quantum measurement, while the circuit and measurement details are aimed at readers with a background in quantum optics or superconducting devices.

Authors’ abstract

Interferometry is a powerful method for studying many fundamental phenomena ranging from gravitational waves to anyon excitations. Besides loss of coherence in the interferometer paths, quantum mechanics sets an incompressible bound for linear interferometry arising from the quantum noise of the light beam, called the shot noise limit. Here, we implement a non-linear quantum interferometer that uses a microwave cavity and a magnetic field resilient anharmonic superconducting quantum circuit made of granular aluminum. The circuit enables interferometry beyond the shot noise limit. A direct application of our findings is the detection of dark matter (axions or dark photons), high-frequency gravitational waves or astronomical masers.