Squeezing-Enhanced Quantum Sensing

• Squeezing-enhanced quantum sensing is a technique that employs quantum correlations to redistribute uncertainty between conjugate observables, lowering measurement noise below the standard quantum limit.
• It leverages methods such as optical parametric amplification, spin squeezing, and Kerr nonlinearity to achieve precise noise suppression across platforms like optomechanics and atomic systems.
• Advances in squeezing generation and robust estimator protocols enable applications in atomic interferometry, force sensing, and gravitational-wave detection while addressing challenges like loss and decoherence.

Squeezing-enhanced quantum sensing is a central paradigm within quantum metrology, leveraging quantum correlations—particularly quantum squeezing of optical, atomic, or spin degrees of freedom—to reduce measurement noise below the standard quantum limit (SQL) and thereby enable precision measurements with sensitivities unattainable by classical means. It encompasses a broad suite of methods and platforms, including intense development in optomechanics, atomic systems, nonlinear optics, spin ensembles, and robust estimator design. The efficacy and impact of quantum squeezing in real-world sensing contexts are determined by the interplay between achievable quantum noise suppression, susceptibility to loss and decoherence, estimator protocols, and the physical mechanisms available for squeezing generation and detection.

1. Fundamentals of Squeezing and Quantum Noise Suppression

Quantum squeezing refers to the redistribution of quantum uncertainty between conjugate observables, such that the noise variance in one quadrature (e.g., phase, amplitude, spin component) is reduced below the SQL, at the expense of increased variance in the conjugate quadrature. The canonical photon-number-phase, or spin-projection, uncertainty relations set the SQL, which is a fundamental bound for unentangled (coherent) states.

In quantum metrology, squeezing directly lowers noise in the measurement observable relevant to parameter estimation, yielding a phase uncertainty scaling as $\Delta\phi\propto\xi/\sqrt{N}$ with $\xi<1$ for the squeezing parameter and $N$ the number of resources (e.g., atoms, photons) (Kritsotakis et al., 2020, Wei et al., 10 Sep 2025). For optomechanical, atomic, or magnetometry platforms, the SQL forms a barrier for classical-like states, and squeezing thus enables surpassing this barrier to approach the Heisenberg limit in sensitivity.

Representative mechanisms and observables:

• Intensity-difference squeezing (optical): Parametrically amplified four-wave mixing leads to quantum correlations between probe and conjugate beams; internal energy-level modulation can push squeezing from an initial $-8.5\,\textrm{dB}$ to $-13.9\,\textrm{dB}$ below the SQL (Zhang et al., 2016).
• Spin squeezing (atomic, spin-ensemble): Nonlinear interactions, such as one-axis twisting (OAT), QND measurement, or circuit-mediated couplings, produce entanglement in atomic or nuclear spins, reducing projection noise in the measured component (Kritsotakis et al., 2020, Mao et al., 2022, Boyers et al., 19 Feb 2025).
• Quadrature squeezing (optomechanics): Intracavity or injected squeezed light suppresses imprecision/backaction noise in force or displacement measurements, with squeezing rates and directions governed by parametric amplifier phase and gain (Zhao et al., 2019, Zhang et al., 2022).

2. Squeezing Generation, Amplification, and Control

Most squeezing-enhanced protocols require robust and scalable squeezing sources, with diverse generation methods tailored to the sensor platform:

• Optical Parametric Amplification (OPA): Nonlinear crystals in Fabry–Pérot cavities or waveguides yield single-mode or multi-mode squeezed states. Techniques such as Ti:PPLN waveguide squeezing (Domeneguetti et al., 2023) or internal OPA in optomechanical cavities (Korobko et al., 2023) enable integration and improved loss tolerance.
• Atomic QND Measurement: Weak measurement of atomic spin projection using off-resonant probe light entangles the spin ensemble, with the balance between information gain and decoherence set by measurement strength, probe detuning, and atomic loss (Kritsotakis et al., 2020).
• Kerr Nonlinearity: Weak Kerr oscillators, driven with displacement-enhanced protocols and Trotterization, amplify squeezing rates without strong decoherence, achieving squeezing levels up to $14.6\,\textrm{dB}$ in superconducting cavities (Cai et al., 11 Mar 2025).
• Magnomechanics: Intrinsic Kerr effects in ferromagnetic YIG spheres under strong microwave drive yield magnon squeezing, with quadrature noise minimized through optimized homodyne angle (Zhang et al., 31 Mar 2024).
• Mechanical Frequency Modulation (levitated/oscillators): Temporal control of trapping potential frequency in levitated nanoparticles implements Bogoliubov transformations, generating squeezing below the ground state of motion even under continuous measurement and environmental noise (Wu et al., 27 Mar 2024).

Mechanisms for "squeezing amplification" and adaptation include displacement-enhanced squeezing with Trotterization (Cai et al., 11 Mar 2025) and phase-sensitive output amplification for loss-tolerance (Frascella et al., 2020, Korobko et al., 2023). Noiseless amplification prior to detection can render squeezed-state sensing robust to detection loss and technical noise, allowing sub-SQL operation with detection efficiencies as low as $13\%$ and background noise exceeding quantum noise by more than $50\times$ (Frascella et al., 2020).

3. Quantum Estimation Protocols, Robustness, and Performance Scaling

Effective exploitation of squeezed resources demands estimator protocols capable of operating under realistic noise, decoherence, and technical fluctuations:

a. Bayesian Quantum Estimation:

Adaptive Bayesian protocols maintain the interferometer working point near the optimal phase (where squeezing manifests maximal quantum enhancement). At each step, an auxiliary phase shift $\Phi_\ell$ is applied (set adaptively from the most recent estimate), ensuring the phase offset $\tilde{\phi}_\ell = \phi - \Phi_\ell$ remains near zero (Wei et al., 10 Sep 2025). A Gaussian likelihood (incorporating both quantum projection and technical noise) is used to update the posterior, yielding an estimate with uncertainty $$\sigma_\phi^{(\ell)} \approx \xi/(N^{1/2}\ell^{1/2})$$ after $\ell$ iterations. Phase noise, depolarization, and other technical noises are naturally incorporated by modifying the likelihood variance.

b. Differential Interferometry and Robust Fitting:

In high-fluctuation regimes (common-mode phase noise spanning $2\pi$), model-free ellipse fitting procedures (either algebraic or geometric) extract differential phase between two interferometers from their population imbalance outputs $(z_A, z_B)$, which follow an ellipse in the presence of sinusoidal signal and common noise (Corgier et al., 30 Jan 2025). Squeezed probe states, when optimized for noise balance in the ellipse's major/minor axes, achieve bias-free estimation with phase uncertainty scaling as $N^{-2/3}$, reflecting improved SQL scaling.

c. Multi-parameter Sensing:

Squeezing-enabled protocols extend to simultaneous estimation of multiple parameters, with the operationally defined "multiparameter squeezing matrix" $\xi^2[\rho, H, X]$ providing saturable (via moments) sensitivity bounds (Gessner et al., 2019). Nonlocal (entangling) squeezing strategies and optimal selection of observables (commuting quadrature or spin projections) are shown to reduce the uncertainty of linear combinations of parameters below the classical shot-noise bounds.

d. Quantum and Classical Hybrid Approaches:

Hybrid estimation (e.g., auxiliary sensor fringe tracking) is contrasted with squeezing-enhanced, model-free estimators; while hybrid methods can perform well near optimal points, they are sensitive to the auxiliary sensor's noise and may require external calibration, unlike the ellipse fitting approach (Corgier et al., 30 Jan 2025). Bayesian approaches generally outperform fringe fitting for spin-squeezed states, especially under noise (Wei et al., 10 Sep 2025).

4. Loss and Decoherence: Mitigation Strategies

While squeezing is resilient compared to more fragile quantum states, it remains sensitive to optical loss, technical noise, and decoherence. The quantum advantage is diminished by vacuum mixing and added noise, mandating mitigation schemes:

• Internal squeezing operations inside the sensing cavity, as opposed to injected squeezing, overcome decoherence due to detection loss by performing signal amplification (or deamplification) before the loss channel. Theoretical and experimental results demonstrate up to $4\,\textrm{dB}$ enhancement independent of detection loss over a wide range, with the ultimate limit set by intra-cavity losses (Korobko et al., 2023).
• Noiseless amplification prior to detection ensures that the quadrature carrying the phase signal is boosted above technical backgrounds, preserving squeezing advantage even at low detection efficiency (down to $13\%$ efficient) and high detector noise (Frascella et al., 2020).
• Operating in intermediate squeezing regimes preserves anti-correlated spectral-temporal structure, as in ultrafast squeezed-photon spectroscopy. Strong squeezing regimes may degrade time–energy resolution due to excess noise in the anti-squeezed quadrature (Fan et al., 15 Aug 2025).

5. Platforms, Physical Implementations, and Applications

Quantum squeezing-enhanced sensing has been widely implemented and proposed in a diversity of systems:

• Atomic Interferometry: Spin-squeezed atomic ensembles in gravimeters, gyroscopes, atomic clocks, and equivalence principle tests (Corgier et al., 30 Jan 2025, Wei et al., 10 Sep 2025).
• Optomechanical Force Sensing: Squeezed light optimizes force detection in micro-cavities, reaching up to two orders of magnitude below the SQL; further improvements realized through quadratic coupling, optomechanical nonreciprocity (one-way squeezing), and parametric drives (Zhao et al., 2019, Zhang et al., 2022, Wang et al., 15 Mar 2024).
• Quantum Magnomechanics: Squeezing of magnon-phonon hybrids dramatically improves force sensitivity in YIG sphere-based platforms, with up to $100\times$ reduction of quantum-added noise under optimal Kerr nonlinearity and homodyne angle (Zhang et al., 31 Mar 2024).
• Large Spin Ensembles: Macroscopic nuclear spin ensembles coupled to resonant circuits can be squeezed via parametrically modulated LC interactions, boosting both the absolute SNR and the bandwidth for scanning weak oscillating signals (such as axion or dark-matter induced spin precession) (Boyers et al., 19 Feb 2025).
• Non-equilibrium Spectroscopy: Squeezed-photon transient absorption allows combined high time- and energy-resolution (beyond the Fourier limit), enabling real-time monitoring of ultrafast processes in TMDs and similar systems (Fan et al., 15 Aug 2025).

Representative Applications

Application Area	Squeezed System	Specific Impact
Gravitational-wave det.	Optical squeezing	Reduced SQL, loss-robust detection
Atom interferometry	Spin squeezing	$N^{-2/3}$ scaling, robust to large phase noise
Magnetometry	Spin/nuclear ensembles	Enhanced SNR, broadband detection
Optomechanical sensing	Quadrature squeezing	Sub-SQL force/acceleration/mass detection
Quantum imaging	Multiparameter squeezing	Sub-shot-noise, multi-parameter field estimation
Quantum spectroscopy	Squeezed photons	Ultrafast, high-resolution, correlation control

6. Challenges, Limitations, and Future Prospects

Despite considerable progress, squeezing-enhanced sensing remains constrained by several practical issues:

• Decoherence and Loss: The degree of squeezing is ultimately limited by technical and fundamental losses (optical absorption, atomic decay, finite cavity Q), and the demands of balancing strong nonlinear interactions with low decoherence rates (Boyers et al., 19 Feb 2025, Korobko et al., 2023).
• Estimator Optimization: For spin-squeezed states, the quantum advantage is typically "windowed"—effective only near optimal phase regions. Adaptive estimation (e.g., Bayesian feedback) extends this advantage but increases control complexity (Wei et al., 10 Sep 2025). Model-free fitting techniques may present bias or complexity trade-offs (Corgier et al., 30 Jan 2025).
• State Preparation: Achieving high-fidelity squeezed, entangled, or non-Gaussian states in macroscopic or solid-state systems remains experimentally demanding. Systematic improvement in control (e.g., resistive circuit optimization, dynamical nuclear polarization) is needed for scalable deployment (Boyers et al., 19 Feb 2025, Nikolov et al., 2022).
• Nonreciprocal and Critical Sensing: Exploiting non-Hermitian degeneracies (exceptional points), critical phenomena (Jaynes–Cummings with squeezing drive), and nonreciprocal geometries (spinning optomechanics) for quartic or higher sensitivity scalings is promising but requires precise parameter tuning and exceptional noise control (Lü et al., 2022, Wang et al., 15 Mar 2024, Wang et al., 23 Jul 2025).
• Extending Multi-parameter Protocols: Implementation of optimal measurement observables, saturation of Cramér–Rao bounds, and measurement of multiparameter Fisher information in large-scale sensor networks remain ongoing areas of development (Gessner et al., 2019).

7. Summary and Outlook

Squeezing-enhanced quantum sensing remains at the forefront of quantum metrology, with robust theoretical underpinnings, diverse experimental realizations, and relevance across a spectrum of applications from gravimetry to photon-driven spectroscopy. Key advances include internal and loss-tolerant squeezing, robust adaptive estimators, and mechanisms for quantum noise cancellation. Ongoing work focuses on integrating squeezing into large-scale and networked sensors, developing multi-parameter estimation strategies, and harnessing nontrivial system dynamics (nonreciprocity, criticality, high-order squeezing). As squeezing sources continue to improve in efficiency, stability, and scalability, and as estimation protocols become increasingly sophisticated, squeezing-enhanced sensors are positioned to push the limits of precision measurement and enable sensitive tests of fundamental physics (Zhang et al., 2016, Corgier et al., 30 Jan 2025, Wei et al., 10 Sep 2025, Korobko et al., 2023, Cai et al., 11 Mar 2025, Zhang et al., 31 Mar 2024, Wang et al., 23 Jul 2025, Fan et al., 15 Aug 2025).