Broadband Quadrature Squeezing in Quantum Photonics

• Broadband quadrature squeezing is the reduction of quantum noise below the shot noise limit over a wide optical range, achieved via nonlinear optical interactions (χ(2) or χ(3)).
• It leverages integrated platforms like Si₃N₄ microrings and thin-film lithium niobate to enable high-speed quantum communication, computation, and multimode entanglement.
• Advanced detection methods such as balanced homodyne and optical parametric amplification mitigate technical noise and losses, paving the way for scalable quantum photonics.

Broadband quadrature squeezing refers to the reduction of quantum noise below the standard quantum limit (shot noise) in one field quadrature, realized across a wide optical bandwidth. This phenomenon is a cornerstone for continuous-variable (CV) quantum optics, enabling high-speed quantum communication, computation, and sensing. Generating and detecting meaningful broadband squeezing—especially in integrated or nanophotonic platforms—entails stringent control of nonlinear interactions, losses, and technical noise across a gigahertz to terahertz window. Progress in silicon nitride (Si₃N₄) microrings, thin-film lithium niobate (TFLN), photonic crystal fibers, and monolithic OPOs has driven both the magnitude and spectral reach of quadrature squeezing.

1. Fundamental Theory and Hamiltonian Modelling

Broadband quadrature squeezing is usually generated via second-order ($\chi^{(2)}$) or third-order ($\chi^{(3)}$) nonlinearities within a resonant or waveguide medium. For a generic parametric process (spontaneous four-wave mixing or degenerate parametric down-conversion), the effective Hamiltonian takes the form: $$\hat{H}_{\text{int}} = i\hbar \left[g \hat{a}^\dagger \hat{b}^\dagger - g^* \hat{a} \hat{b}\right]$$ for two-mode squeezing ($\hat{a}$, $\hat{b}$), or, in the single-mode degenerate case,

$$\hat{H}_{\text{int}} = i \hbar \kappa\Big(\hat{a}^{\dagger 2} - \hat{a}^2\Big)$$

The squeezing operator $$S(r) = \exp\left[\frac{r}{2}(\hat{a}^2 - \hat{a}^{\dagger 2})\right]$$ transforms vacuum into a squeezed state, with $r$ set by the nonlinear interaction strength, pump amplitude, and effective interaction time.

Cavity-based systems (e.g., silicon nitride microrings) require a full input-output treatment. For a driven $\chi^{(3)}$ ring, the normalized quadrature noise spectra for symmetric ($+$) and antisymmetric ($-$) bichromatic modes are given by (Vaidya et al., 2019): $$V_\pm(\Omega) = 1 + 4\eta g \bigl(2g \pm \sqrt{1 + 4g^2}\bigr)$$ where $g = \Lambda |\beta_P|^2/\bar{\Gamma}$, $\Lambda$ is the FWM strength, $\beta_P$ the pump amplitude, $\bar{\Gamma}$ the cavity linewidth, and $\eta$ the total collection efficiency.

The observable bandwidth is set either by the cavity linewidth ($\bar{\Gamma}$) or the phase-matching bandwidth in traveling-wave architectures.

2. Device Architectures and Material Platforms

Significant advances in broadband squeezing have emerged from both integrated photonics and fiber-based platforms.

Microring devices: Si₃N₄ microrings exploit a high-Q resonator geometry with engineered normal (or anomalous) dispersion and strong over-coupling ($\eta_\text{esc}\to1$) to enhance the nonlinear interaction per intracavity photon while providing spectral selectivity via the free spectral range (FSR) (Vaidya et al., 2019, Shen et al., 6 May 2025). Detailed device parameters include:

• Typical cross sections: $800$–$1000$ nm (height/width)
• Radii: $30$–$120$ µm (FSR $\sim 190$–$450$ GHz)
• Loaded $Q$ factors: $2\times10^5$ or higher, yielding linewidths $\bar{\Gamma}/2\pi$ of several hundred MHz to $\sim$1 GHz

Thin-film lithium niobate (TFLN): Ridge and strip-loaded waveguides support single-pass, phase-matched $\chi^{(2)}$ PDC (periodic poling period $\Lambda \sim 3\,\mu$m), achieving tight confinement, high effective nonlinearity ($d_{33} \approx -25$ pm/V), low propagation loss ($<0.5$ dB/cm), and broadband phase matching (Chen et al., 2021, Peace et al., 2022).

Non-cavity platforms: Fiber-based OPAs (e.g., photonic crystal fibers) and opto-magnomechanical platforms offer THz-class phase-matching, with FWM gain engineered for flat response across tens of THz (Shaked et al., 2017, Di et al., 7 Feb 2024).

A summary of leading architectures and representative bandwidths:

Platform	Squeezing (on-chip/detected)	Bandwidth	Reference
Si₃N₄ microring, $\chi^{(3)}$	$\sim$4 dB/$1.0(1)$ dB	$\sim1$ GHz	(Vaidya et al., 2019)
TFLN ridge, $\chi^{(2)}$	$\sim$3 dB/0.56 dB	$\sim7$ THz	(Chen et al., 2021)
PCF fiber OPA	1.7 dB	55 THz	(Shaked et al., 2017)
Quantum dot laser	0.9 dB	3–12 GHz	(Zhao et al., 2023)
Opto-magnomechanical	$-4.95$ dB	$\sim$16 MHz	(Di et al., 7 Feb 2024)

3. Detection Methodologies and Characterization

Balanced homodyne detection is the gold standard for measuring quadrature noise. In broadband settings, challenges arise when the squeezing spans frequencies inaccessible to conventional electronics. Approaches include:

• Bichromatic local oscillators (two phase-locked CW lasers at signal and idler frequencies) enable detection of squeezing when correlated bands are separated by several GHz (Vaidya et al., 2019, Embrey et al., 2016).
• All-optical parametric homodyne: An OPA acting as a measurement-stage amplifier can resolve quadrature noise over the intrinsic nonlinear bandwidth (tens of THz), bypassing electronic limitations (Shaked et al., 2017, Inoue et al., 2022). In this regime, the OPA amplifies one quadrature to macroscopic levels, rendering detection robust to post-OPA loss.

Detection efficiency is a product of escape from the device, fiber-chip transmission, and photodiode quantum efficiency, typically $\eta\sim0.3$–0.9, with higher values attainable through further integration and improved coupling.

4. Loss, Technical Noise, and Scalability Constraints

Losses—internal propagation, facet, coupling, and detector inefficiency—directly degrade measurable squeezing via admixture with vacuum fluctuations: $S^{\text{meas}} = 1 + \eta(S^{\text{gen}}-1)$ Technical noise sources, such as thermorefractive noise in Si₃N₄ (Cernansky et al., 2019) (scaling as $1/\Omega^2$), back-reflection noise, or electrical dark noise, can mask true squeezing over broad bands. For example, thermorefractive noise can dominate below $\sim500$ MHz, but is mitigated by cryogenic operation or improved design.

Routes to boost on-chip squeezing and bandwidth include:

• Lower propagation loss ($<0.1$ dB/cm)
• Higher $Q$ and escape efficiency ($\eta_{\rm esc} \gtrsim 95\%$)
• Improved edge and fiber coupling ($\lesssim0.5$ dB)
• Near-unit detector quantum efficiency

These approaches predict $>10$ dB on-chip squeezing with tens of milliwatts pump and GHz–THz bandwidths (Cernansky et al., 2019).

5. Multimode and Frequency-Comb Squeezing

Broadband squeezing platforms naturally support multimode entanglement:

• Microrings: The FSR enables selection of distinct, pairwise squeezed resonances. A QFC comprising 16 qumodes (8 symmetric pairs) spanning $\sim$11 THz and tunable over one FSR has been realized with seed-assisted detection (Shen et al., 6 May 2025).
• Frequency-bin decomposition: Experiments in warm Rb vapor show discrete frequency bins as independent two-mode squeezed qumodes, with up to $10^6$ parallel EPR pairs per millisecond window (Araujo et al., 2023).
• Cluster states and MBQC: Broadband squeezed combs directly provide resource states for Gaussian boson sampling, continuous-variable cluster-state computing, and quantum communication multiplexing.

6. Limits of Measurement and Emerging Paradigms

Standard homodyne electronics pose spectral limitations, yet broadband squeezing enables measurement via OPA-assisted detection (“magic-wand” effect), which renders post-amplifier loss negligible for large gain, allowing true loss-tolerant quantum noise characterization from DC to the detector bandwidth (Inoue et al., 2022).

Quantum-dot lasers harness sub-Poissonian electrical injection and ultrafast carrier dynamics for room-temperature squeezing spanning 3–12 GHz (Zhao et al., 2023), suggesting an emerging class of electrically pumped, chip-scale sources.

Opto-magnomechanical devices extend the paradigm to hybrid magnon–phonon–photon systems, yielding robust $\sim$5 dB squeezing over tunable tens-of-MHz windows—an alternative to OPO- or fiber-based squeezing, well suited for quantum networking and metrology across a range of temperatures (Di et al., 7 Feb 2024).

7. Outlook and Applications

Broadband quadrature squeezing across GHz–THz bands is indispensable for scaling up CV quantum processors, quantum-enhanced sensing, and photonic quantum networks. Integration advances in Si₃N₄, TFLN, and compound semiconductors, coupled with loss-tolerant detection, are converging toward on-chip, wideband, multi-qumode squeezed-light sources that can catalyze high-throughput CV quantum computations. Further improvements in fabrication, noise suppression, and monolithic integration are expected to yield $>10$ dB useful squeezing over multi-GHz–THz bandwidths with tens of milliwatts of pump power, supporting both time- and frequency-multiplexed quantum architectures.