On-chip squeezed light in the audio frequency band

AI summary

Overview

• Research area: Integrated photonics / continuous-variable (CV) quantum optics — specifically, generation and detection of squeezed and entangled light on a chip in the audio-frequency band.
• Technical level: Intermediate (assumes some familiarity with squeezing, homodyne detection, and covariance matrices, but the core ideas are explained physically).
• Scope: The paper demonstrates on-chip two-mode squeezed states in a silica microtoroid microcavity that remain measurable down to 60 Hz, using a pump-derived electro-optic reference comb ("coherent-comb control") to stabilize the measurement phase without disturbing the fragile quantum modes, and verifies entanglement with the PPT criterion.

What This Paper Is About

Many precision measurements — gravitational-wave detection, weak-force readout, magnetic and ultrasonic sensing — carry their signal in the audio-frequency band (roughly hertz to kilohertz), where shot noise limits sensitivity. Squeezed light can beat that limit, and bulk-optics experiments have shown audio-band squeezing, but chip-scale demonstrations have stayed at radio-frequency sidebands. The problem is that at low frequencies, technical noise, cavity detuning drift, and slow phase wander rotate the measurement quadrature and wash out the nonclassical correlations, and directly locking the quantum modes with a bright tone would inject noise into exactly the channel being measured. The goal is to produce phase-stable, on-chip two-mode squeezing down to 60 Hz and to certify entanglement from the reconstructed covariance matrix.

Key Contributions

1. A coherent-comb control (CCC) method for phase-stable quadrature measurement. A weak electro-optic (EO) comb derived from the pump co-propagates with the quantum modes in an orthogonal polarization, frequency-shifted by an offset (ω_b), and is deliberately kept off resonance with the microcavity. After the cavity the reference is separated by a polarizing beam splitter and detected independently, so phase sensing and feedback act only on the reference path — no bright locking tone enters the quantum signal frequencies.

2. On-chip audio-band two-mode squeezing in a silica microtoroid. Using a 732 μm diameter silica microresonator (FSR ≈ 72.8 GHz, intrinsic Q ≈ 4×10⁷), the authors measure ∼1.03 dB of two-mode squeezing below the shot-noise level from 60 Hz to 5 kHz, corresponding to an inferred on-chip squeezing of 1.73 dB after correcting for efficiency.

3. Entanglement certification via covariance-matrix reconstruction. Rather than a single joint measurement, the two-mode covariance matrix is assembled from a set of single-mode and inter-mode quadrature combinations (q₁−q₂, p₁−p₂, q₁−p₂, p₁−q₂, plus q₁, p₁, q₂, p₂) obtained by switching the locking angle and local-oscillator configuration, then tested with the PPT criterion.

4. A quantified non-invasiveness check on the reference field. The authors characterize how much noise the reference adds as a function of its power and coupling condition, and show that at P_ref = 0.5 mW the measurement noise floor is indistinguishable from the reference-free case.

Main Findings

• Squeezing down to 60 Hz: Within the quantitative analysis band of 60 Hz to 5 kHz, the spectra show ∼1.03 dB of two-mode squeezing below the shot-noise level, with an inferred on-chip value of 1.73 dB. The upper frequency of 5 kHz is set by the 10 kSa/s sampling rate.

• A deliberate low-frequency cutoff: Although spectra are plotted from 50 Hz, the calibrated shot-noise level begins to rise appreciably below approximately 60 Hz, meaning the readout is no longer demonstrably shot-noise-limited there. The authors therefore exclude everything below 60 Hz from the covariance reconstruction and do not use the apparent separation between the squeezed trace and the elevated shot-noise trace in that region as evidence of quantum noise reduction.

• Entanglement confirmed: The reconstructed covariance matrix yields a minimum symplectic eigenvalue ν̃₋ = 0.395, below the 0.5 threshold of the PPT criterion, confirming inseparability.

• Robust statistics: A moving-block bootstrap on the 100 s trace (∼10⁶ samples, 400 replicates) gives ν̃₋ = 0.395 ± 0.001 (one standard deviation), with percentile intervals [0.394, 0.396] at 68% and [0.393, 0.397] at 95% — all well below the PPT threshold.

• Reference light is not perturbing the measurement: Without the reference, no noise-floor elevation is resolved for uncoupled, off-resonance, or on-resonance conditions. With the reference at 2 mW, the spectrum stays unchanged for uncoupled and off-resonance cases, but a clear elevation appears when tuned on resonance; this elevation shrinks with power and becomes indistinguishable from the off-resonance case at ∼0.5 mW — the operating point chosen for the squeezing runs.

• Stable locking over long acquisition: Time-domain traces of anti-squeezed, shot-noise, and squeezed quadratures recorded over 100 s with ∼10⁶ samples show stable locked operation and deterministic switching between quadratures.

• Device characteristics: Escape efficiency of 64.3% under overcoupling; a non-Lorentzian (Fano-like) transmission lineshape under overcoupling, consistent with interference from a background or parasitic channel; tapered-fiber transmittance 94%; detection-chain transmission 66.0%; homodyne detection efficiency 97.4%.

Methodology in Plain English

The team fabricated a silica microtoroid — a small racetrack-shaped optical cavity on a chip — and pumped it below threshold at 1549.768 nm with 54.2 mW, so that four-wave mixing in the Kerr nonlinearity spontaneously produces pairs of correlated frequency modes, the two-mode squeezed vacuum. The pump wavelength is chosen so that the signal and idler sit at ±1 free spectral range, where two independent local oscillators at 1549.184 nm and 1550.352 nm (3.5 mW each) beat against them in a balanced homodyne detector.

The tricky part is knowing which quadrature you are measuring. The authors split off a small part of the pump, shift it by 181.4 MHz with an acousto-optic modulator, amplify it, and phase-modulate it deeply at 36.4 GHz to create an electro-optic frequency comb. This weak comb (0.5 mW) travels through the same fiber and the same cavity as the pump but in the orthogonal polarization and at a frequency offset, so the cavity is not resonant with it and it never mixes into the quantum channel. After the cavity, a polarizing beam splitter sends the reference one way and the squeezed light the other. The reference is detected separately and used to sense and correct the homodyne phase — so the locking loop only ever touches the reference beam, never the quantum modes.

For entanglement, they switch the locking angle and the local-oscillator configuration to record inter-mode combinations and single-mode quadratures, filter out technical noise below 60 Hz and spurious lines from acquisition oversampling, and build the covariance matrix using standard variance relations with a moving-block bootstrap for error bars. Welch's method with a rectangular window converts the time traces to spectra, with no additional filtering applied.

Why This Matters

Impact on research: This closes a gap between bulk-optics audio-band squeezing and chip-scale implementations, which had largely been confined to radio-frequency sidebands. It also introduces a control architecture — an orthogonally polarized, off-resonant, independently detected reference — that could serve as a general phase-referencing scheme for distributed, multi-node CV quantum photonics, where each quantum mode needs its own non-invasive phase reference.

Real-world applications:

• Gravitational-wave detection and radiation-pressure-limited optomechanical readout, where audio-band squeezing directly lowers the quantum noise floor.
• Quantum-enhanced magnetometry, ultrasound sensing, and nanoscale particle detection using microcavity platforms.
• Quantum metrology and quantum sensing protocols that operate at low Fourier frequencies, where signals of interest actually live.
• Secure communication and CV quantum information processing (computation, cluster states) that require stable quadrature control.

Industry relevance: The device is fabricated with foundry-compatible processes, and the control scheme is compatible with packaging workflows. A chip-scale, phase-stable source of audio-band squeezing is a practical prerequisite for field-deployable quantum sensors, and arrayed/distributed sensing architectures would need exactly the scalable phase referencing demonstrated here.

Future Directions

• Raise the squeezing level. The authors state that the ∼1.03 dB result can be improved by increasing escape efficiency and reducing parasitic loss, mode mismatch, and unwanted background-channel coupling (the Fano-like lineshape points to such a parasitic channel).

• Push below 60 Hz. Reaching lower frequencies requires suppressing residual technical noise on three fronts: channel isolation (stronger polarization isolation, lower EO-comb technical noise, better microcavity modal selectivity, suppression of parasitic background channels), phase control (optimizing optical routing and servo electronics to counter operating-point drift and parasitic interference), and detection (better electromagnetic shielding, thermal stability, and acoustic isolation).

• Scale to multi-node architectures. The CCC scheme is presented as a non-invasive phase reference per mode, which suggests extending it to many-node, arrayed, distributed quantum sensing — an open question is how well the approach performs when modes are physically separated across a photonic circuit.

Target Audience

Researchers and graduate students in quantum optics, integrated photonics, and optomechanics who work on squeezed-light sources, CV quantum information, or precision metrology; quantum-sensing engineers interested in chip-scale deployment; and anyone tracking the transition of squeezing technology from bulk optics to foundry-compatible integrated platforms. Readers without a background in homodyne detection and covariance-matrix entanglement criteria will need to consult the cited background literature and supplementary material.

Authors’ abstract

Squeezed light in the audio-frequency band is a key resource for quantum metrology and quantum sensing. However, realizing stable audio-frequency squeezed light on integrated photonic platforms remains challenging due to technical noise and the difficulty of scalable phase referencing. Here, we demonstrate on-chip generation of audio-band two-mode squeezed states down to 60 Hz in a silica microcavity. To enable phase-stable operation without directly locking fragile quantum modes, we develop a coherent-comb control method in which a weak electro-optic reference comb co-propagates with the vacuum at the quantum frequency modes in an orthogonal polarization. This scheme provides quadrature measurement and long-timescale phase stability, thereby enabling covariance-matrix reconstruction. We verify the entanglement with the positive partial transposition criterion, which confirms inseparability via a minimum symplectic eigenvalue of 0.395 ($<0.5$). Our results establish an experimentally accessible route toward on-chip phase-stable audio-band squeezing and support the scalable framework for continuous-variable quantum information processing with integrated photonics.