RF-QPC Readout for Quantum Charge Sensing

• RF-QPC readout is a quantum-limited charge sensing scheme that employs an RF-resonant circuit with quantum point contacts for rapid and precise detection of minute charge signals.
• Integration with phononic-crystal transducers in germanium enhances athermal phonon capture, enabling nanosecond timing discrimination and background-free rare-event detection.
• The approach utilizes optimized LC tank circuits and spatial-temporal coincidence methods to achieve sensitivities down to 10⁻³ eV and single-phonon SNR greater than 5 within microsecond windows.

A radio-frequency quantum point-contact (RF-QPC) readout is a quantum-limited charge sensing scheme in which a quantum point contact—typically formed in a low-dimensional electron system—is embedded in a high-frequency (RF) resonant circuit to enable rapid, high-sensitivity, and effectively non-dissipative detection of minute charge signals. When integrated with phonon-mediated transducers in cryogenic germanium (Ge) detectors, RF-QPCs enable the conversion of athermal phonon excitations from rare energy-depositing events (such as low-mass dark matter or neutrino interactions) into measurable charge signals, with threshold sensitivities in the $10^{-3}$–$10^{-2}$ eV range and nanosecond-scale timing discrimination. The integration of slow-phonon phononic-crystal structures with RF-QPC charge transducers at the quantum limit underpins the next generation of germanium-based quantum sensors for rare-event searches (Mei et al., 2 Jul 2025, Mei et al., 11 Nov 2025).

1. Physical Principles of RF-QPC Readout

Quantum point contacts are narrow constrictions in a two-dimensional electron gas (2DEG) or analogous quantum dot structure, whose conductance $G$ is quantized in units of $2e^2/h$ and responds sharply to small changes in local electrostatic potential. When operated at RF, a QPC is coupled to an external impedance-matching tank circuit, typically an $LC$ resonator, at frequencies in the 200–500 MHz range. Charge displacements $\delta Q$ near the QPC (such as those induced by phonon–electron interactions) lead to a conductance shift $\Delta G$, which modulates the complex reflection coefficient $r(\omega_{\rm RF})$ of the carrier field.

The reflected signal is amplified by a low-noise cryogenic amplifier and demodulated for real-time detection, yielding charge sensitivities of $\delta q\sim 10^{-3}\,e/\sqrt{\mathrm{Hz}}$ (or down to $10^{-4}\,e/\sqrt{\mathrm{Hz}}$ in optimized geometries). High tank Q ($\sim 50–100$) yields MHz-scale bandwidth and $\sim$nanosecond charge acquisition windows. This architecture enables single-shot detection of sub-elementary charge displacements as induced by localized charge redistribution.

When coupled to phonon-mediated charge transduction, the QPC is proximate to a quantum dot or dipole-bound impurity, where acoustic phonons—specifically in the 10–30 GHz "slow-phonon" band—drive electron displacement or occupation changes. The Ramo–Shockley theorem relates the displacement $\delta x$ to an induced charge $Q_\mathrm{ind}$ on the QPC: $Q_{\rm ind} = Q\,\frac{\delta x}{d_{\rm qpc}}$ where $Q$ is the carrier charge and $d_{\rm qpc}$ is the relevant separation ($\sim$1 μm). For resonant phonon-induced $\delta x$ up to 1 nm, $Q_\mathrm{ind} \sim 10^{-3}–10^{-2}\,e$ per phonon is achievable at the band of interest (Mei et al., 2 Jul 2025, Mei et al., 11 Nov 2025).

2. Integration with Phononic-Crystal Transducers in Ge

The effective deployment of RF-QPC readout in rare-event detection leverages engineered phononic-crystal (PnC) structures at the Ge surface. These PnCs, realized as 1 μm-thick patterned Ge layers with sub-30-nm lattice constants, create a Bragg stop band in the 100–120 GHz range to suppress thermal background and trap ballistic acoustic phonons in designed cavity resonances (10–30 GHz), with Q-factors $\sim10^3$ (Mei et al., 2 Jul 2025, Mei et al., 11 Nov 2025).

Energy depositions in the Ge bulk—either via dark matter (DM) electron/nucleon scattering, or coherent neutrino-nucleus scatter—produce primary acoustic phonons. Through specular geometric guiding (surface roughness $\eta<1$ nm, specularity parameter $p \gtrsim 0.95$ for relevant wavelengths) and PnC band-structure engineering (effective refractive index $n_{\rm eff} \sim 5$–8), a substantial fraction of these ballistic phonons are funneled into a quantum dot region that is in capacitive proximity to the QPC.

The cross-section for deformation-potential phonon–electron coupling is enhanced by the slow-phonon confinement ($V_{\rm mode}\sim10^{-5}\,\mu\text{m}^3$, $g/2\pi\sim10$–100 MHz at 10–30 GHz) and by the increased local phonon density of states. The athermal phonon collection efficiency from geometric collection, bulk propagation survival ($\eta_{\rm prop}\simeq0.95$ for $n_d\sim10^{10}\,\mathrm{cm}^{-3}$ defect density over 10 cm), and localized athermal capture ($\eta_{\rm ath}\sim0.1$–0.3) leads to overall signal transduction efficiencies $\sim$0.7–0.8 (Mei et al., 11 Nov 2025).

3. Signal Collection, Energy Threshold, and Calibration

The overall signal collection and energy threshold are quantitatively determined by folding geometric guiding/return, phonon propagation survivability, and the local capture probability for each athermal (non-thermalized) phonon. This is encapsulated as: $$\eta_{\rm coll}(\omega,\Omega) = \eta_{\rm geom}(\Omega) \times \eta_{\rm prop}(\omega) \times \eta_{\rm ath}(\omega)$$ Simulations and calibration with on-chip heaters and narrowband phonon injection yield selection-corrected turn-on curves with error-function form: $$\varepsilon(E) = \frac{1}{2}\,\mathrm{erfc}\left(\frac{E_{\rm thr} - E}{\sqrt{2}\sigma_E}\right)$$ Experimental data set energy thresholds at $E_{\rm th} \approx 10^{-3}$–$10^{-2}\,\mathrm{eV}$ (for the collection-corrected event-level turn-on), and per-phonon SNR $\gtrsim5$ in a 1 μs window. The induced charge ($Q_{\rm ind}\sim 10^{-3}$–$10^{-2}\,e$ per phonon) is typically above RF-QPC baseline noise, with nanosecond-scale timing accuracy set by circuit bandwidth (Mei et al., 11 Nov 2025).

4. Background Rejection and Signal Discrimination

Background discrimination is achieved via two principal methodologies:

1. Nanosecond Timing Gates: The rapid anharmonic decay of a primary high-frequency phonon yields a correlated cluster of $M\sim$16–64 phonons in the 10–30 GHz band within a $\sim$1 ns time window. Requiring detection of $N\geq10$ phonons within this nanosecond-scale gate suppresses random thermal phonon background ($n(f,T)\gtrsim2$ at 30 GHz), with false-alarm probabilities individually tuned to much less than one per operational year.
2. GHz-Band Power Spectral Density Windows: By constructing a weighted power spectral density statistic matched to the phonon frequency window of interest ($W(f)$ sharply peaked in 10–30 GHz), and applying 2-of-4 pixel (spatial) and sub-2 ns temporal coincidence criteria, background rejection factors exceeding $10^3$ are achievable while retaining $\gtrsim80\%$ signal efficiency (Mei et al., 11 Nov 2025).

This combined timing and spectral cut framework enables operation in the background-free regime for exposures up to several kg·yr, limited ultimately by irreducible solar CE$\nu$NS backgrounds as exposure increases.

5. Sensitivity Projections and Systematic Uncertainties

A calibrated signal model incorporating detection efficiency, noise, and background rejection projects sensitivities to dark-matter–electron and –nucleon scattering below $\bar{\sigma}_e=10^{-43}$ cm$^2$ for $m_\chi \in [0.01,100]$ MeV/c$^2$ in a 100 g Ge module with $E_{\rm th} \approx 10^{-3}$–$10^{-2}$ eV (Mei et al., 11 Nov 2025). Systematics include:

• Threshold and noise performance ($E_{\rm th}$, $\sigma_E$): determined through heater pulses, blank triggers, and phonon injection (fractional uncertainty $\sim5$–10%).
• PnC band-edge and Q: characterized by S-parameter sweeps and transient ringdown, with $\pm 1$ GHz and $\pm 20$–30% uncertainties, respectively.
• Bulk defect density ($n_d$) and absorption cross-section: measured by time-of-flight echo attenuation and independent material assays, with $\sim$10% prior on propagation efficiency.
• QPC responsivity and system noise temperature ($T_{\rm sys}$): calibrated by single-electron steps and hot/cold load methods; uncertainty $\sim$5–10%.
• ER/NR selection, operational stability, and live time: driven by data from neutron/LED-tagged events and device monitoring.

The systematic effects are incorporated as nuisance parameters in a profile-likelihood statistical framework to anchor discovery/exclusion claims.

6. Device Architecture, Fabrication, and Scalability

GeQuLEP-type integration (Germanium-based Quantum Sensors for Low-Energy Physics) realizes a platform with:

• High-purity crystalline Ge (∼100 g per module), with near-surface 1 μm-thick PnC region (lattice constant $a\sim25$ nm, bandgap 100–120 GHz), fabricated via electron-beam or DUV lithography, reactive ion etching (RIE), and subsequent planarization (CMP/passivation) to sub-nm surface roughness (Mei et al., 2 Jul 2025, Mei et al., 11 Nov 2025).
• Quantum dot (QD) regions formed by impurity freeze-out (dipole separation $d\sim250$ nm, well width $\sigma'\sim7$ nm) at $T=4$ K, acting as localized phonon-coupled charge centers.
• Proximate QPCs patterned and contacted on the Ge surface, with L–C tanks tuned to 200–500 MHz for reflectometry.
• Readout multiplexing via frequency-division or time-division architectures, allowing $10^4$ transducers/cm$^2$ and $\lesssim10^{-9}$ W thermal dissipation per channel, fitting dilution refrigerator cooling budgets for large-scale arrays.

Device yields, cross-talk (mitigated by phononic bandgaps), and uniformity are addressed by staged engineering validation, scalable up to kg·yr exposures with controlled variations in $E_{\rm th}$ and efficiency.

7. Staged Program and Future Outlook

Planned deployments proceed through three stages (Mei et al., 11 Nov 2025):

• Stage I (device coupon validation, cm scale): PnC unit cells ($a=25$ nm, $Q\geq5\times10^3$), single-device RF-QPC sensitivity $<10^{-3}e/\sqrt{\mathrm{Hz}}$, and $>10^3$ background rejection; $E_{\rm th}\lesssim 10^{-2}$ eV.
• Stage II (10–100 g modules): full PnC+QD+QPC integration with spatial multiplexing; demonstration of $E_{\rm th}\sim10^{-3}$–$10^{-2}$ eV, selection-corrected, and background-free operation to 0.05 kg·yr.
• Stage III (∼1 kg arrays): multiplexed RF-QPC readout (frequency or cold combine), controlled threshold variability $<15\%$, $>80\%$ live time, and approach to solar CE$\nu$NS background-limited sensitivity with exposures $\gtrsim1$ kg·yr.

The phased program is designed to systematically constrain dominant systematics, validate signal models, and anchor rare-event searches precisely at the quantum sensitivity frontier.

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Key Experimental and Device Parameters

Parameter	Value/Range	Context
Operating temperature	$T\approx 4$ K	Quantum regime; impurity freeze-out
PnC thickness, constant	$t=1\,\mu$m, $a=25$–$30$ nm	$f_{\rm gap} = 100$–$120$ GHz
Slow-phonon $n_{\rm eff}$	5–8	Enhanced phonon DOS, mode volume
QPC tank frequency	200–500 MHz	Reflectometry readout
Charge sensitivity	$10^{-3}e/\sqrt{\mathrm{Hz}}$	Typical; $10^{-4}e/\sqrt{\mathrm{Hz}}$ in optimum
Energy threshold	$E_{\rm th} = 10^{-3}$–$10^{-2}$ eV	Collection-corrected, selection efficiency folded
Ballistic phonon SNR	$>5$ (1 μs window)	Single-phonon regime
Readout bandwidth	$5$–$10$ MHz	Tank $Q\sim50$–100
Module mass	$0.1$–$1$ kg	Scaling to kg·yr exposures

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RF-QPC readout embedded in engineered Ge/phononic-crystal quantum architectures enables charge-limited, contact-free detection of sub-eV acoustic phonons from rare, low-energy events in the bulk. This technology achieves $\mathcal{O}(1)$ single-phonon SNR and $\gtrsim 10^{-3}$ eV threshold, with nanosecond timing and GHz-band PSD cuts for background suppression, and it sets the standard for quantum-limited rare-event Ge detectors in the sub-MeV to sub-GeV sector (Mei et al., 2 Jul 2025, Mei et al., 11 Nov 2025).