Quantum Computing RF

DC SQUID

Q: What is the difference between a DC SQUID and an RF SQUID?

A DC SQUID uses two Josephson junctions in a superconducting loop and is biased with a steady DC current above the combined critical current, so the loop voltage oscillates with period Phi_0 (2.07e-15 Wb) as flux changes. An RF SQUID uses a single junction and is coupled to a resonant tank circuit driven at radio frequency; the flux is read indirectly from the RF impedance of the tank. The DC SQUID offers roughly an order of magnitude better flux noise (1 to 5 micro-Phi_0 per root-Hz versus about 30 for an RF SQUID) and lower 1/f noise, which is why almost all modern quantum-readout and magnetometry instruments use the DC variant. The RF SQUID was historically preferred because it needs only one junction, simplifying early fabrication, but submicron junction processes have made two-junction DC devices routine.

Q: Why does a DC SQUID need a flux-locked loop?

The voltage-versus-flux curve of a DC SQUID is periodic and nonlinear, repeating every flux quantum Phi_0, so the raw output is ambiguous and only linear over a small portion of one period. A flux-locked loop solves this by applying negative feedback: a feedback coil injects a counter-flux that holds the SQUID at a fixed operating point on the steepest part of the V-Phi curve, typically near Phi_0/4. The feedback current then becomes the linearized output, proportional to the input flux, with dynamic range of many flux quanta and excellent linearity. The loop usually adds an AC flux modulation at 100 kHz to 2 MHz with lock-in detection to suppress the amplifier 1/f noise and offset drift.

Q: How is a DC SQUID used to read out a superconducting qubit?

In flux-qubit and early phase-qubit experiments, the qubit state corresponds to circulating currents that produce slightly different magnetic flux in a nearby pickup loop. A DC SQUID inductively coupled to that loop senses the flux difference between the two states and converts it to a voltage or switching-current change that classical electronics can measure. Modern transmon processors more commonly use dispersive readout with a Josephson parametric amplifier rather than a switching DC SQUID, but the DC SQUID remains central as a tunable inductor: a SQUID embedded in a resonator forms a flux-tunable cavity or a near-quantum-limited parametric amplifier, and it provides the tunable coupling element in many qubit architectures.

/dee-see skwid/ · Direct-Current Superconducting Quantum Interference Device

Built from a superconducting loop interrupted by two parallel Josephson junctions, this device is biased with a steady current just above its critical current so that the voltage across the loop becomes a periodic function of the magnetic flux threading it, repeating every flux quantum Φ₀ = 2.07 × 10⁻¹⁵ Wb. Because the period is so small, a well-designed SQUID resolves flux changes of 1 to 5 μΦ₀/√Hz, equivalent to magnetic fields in the femtotesla range. Operated near 10 to 100 mK inside a dilution refrigerator, DC SQUIDs serve as the flux-to-voltage front end for superconducting qubit readout, as tunable inductors in flux-tunable resonators, and as the heart of near-quantum-limited parametric amplifiers.

Category: Quantum Computing RF

Flux noise: 1 to 5 μΦ₀/√Hz

Operating temp: 10 to 100 mK

How Two Junctions Turn Flux Into Voltage

The DC SQUID exploits two quantum effects at once: the Josephson relation, which sets the supercurrent through each junction, and fluxoid quantization, which forces the total flux enclosed by a superconducting loop to be an integer number of flux quanta plus the screening contribution. When two junctions share a loop and the device is biased above its critical current, the two supercurrent paths interfere like the two slits of an optical interferometer. As external flux is swept, the critical current of the pair oscillates between a maximum (constructive interference at integer Φ₀) and a minimum (destructive interference at half-integer Φ₀), and the resulting voltage at fixed bias current traces the same period.

That periodic voltage-versus-flux (V-Φ) characteristic is the SQUID's transfer function. The slope on its steepest flank, the flux-to-voltage transfer coefficient V_Φ = ∂V/∂Φ, typically reaches 100 μV to 1 mV per Φ₀ for a low-inductance washer design. Sensitivity improves as loop inductance L shrinks, but a smaller loop captures less external flux, so practical magnetometers add a large superconducting pickup coil coupled through an input transformer. The dimensionless screening parameter β_L = 2LI₀/Φ₀ (with I₀ the single-junction critical current) is held near 1 to maximize modulation depth without washing out the oscillation.

Noise sets the ultimate floor. Each shunt resistor that damps the junctions contributes Johnson noise, and at millikelvin temperatures the energy resolution approaches the quantum limit set by the reduced Planck constant. Engineers quote flux noise in μΦ₀/√Hz and coupled energy resolution in units of ℏ; the best low-temperature devices reach a few ℏ, within a small factor of the ≈ ℏ quantum bound.

Governing Equations

Flux quantum:
Φ₀ = h / (2e) ≈ 2.07 × 10⁻¹⁵ Wb

Critical-current modulation (symmetric junctions):
I_c(Φ) = 2I₀ × |cos(π Φ / Φ₀)|

Flux-to-voltage transfer coefficient:
V_Φ = ∂V / ∂Φ (peak ≈ R / L near β_L ≈ 1)

Screening parameter:
β_L = 2 × L × I₀ / Φ₀

Where h = Planck constant, e = electron charge, I₀ = single-junction critical current (the pair critical current is 2I₀), R = shunt resistance, L = loop inductance. Example: L = 100 pH, I₀ = 10 μA → β_L ≈ 1.0; R = 5 Ω → V_Φ ≈ R/L ≈ 100 μV/Φ₀.

DC SQUID Versus Other Flux Sensors

Device	Junctions	Flux noise (μΦ₀/√Hz)	Bandwidth	Operating temp	Primary use
DC SQUID	2 (DC biased)	1 to 5	DC to ~1 GHz	10 mK to 4 K	Qubit readout, magnetometry
RF SQUID	1 (tank coupled)	20 to 50	DC to ~100 MHz	1 to 4 K	Legacy magnetometers
SQUID array amplifier	10s to 100s	0.5 to 2	DC to ~6 GHz	10 to 100 mK	Cryogenic preamps, TES readout
Josephson parametric amp	SQUID-tuned	Near quantum limit	4 to 12 GHz	10 to 50 mK	Dispersive qubit readout
Fluxgate magnetometer	None (ferromagnetic)	~1000 (room temp)	DC to ~1 kHz	300 K	Geophysics, navigation

Common Questions

Frequently Asked Questions

What is the difference between a DC SQUID and an RF SQUID?

A DC SQUID uses two Josephson junctions and a steady DC bias above critical current, giving a loop voltage that oscillates with period Φ₀ = 2.07 × 10⁻¹⁵ Wb. An RF SQUID has a single junction read out through a resonant tank at radio frequency. The DC device delivers roughly 10× lower flux noise (1 to 5 vs. ~30 μΦ₀/√Hz) and less 1/f noise, so it dominates modern quantum readout; the RF SQUID survived early on only because one junction was easier to fabricate.

Why does a DC SQUID need a flux-locked loop?

The V-Φ curve is periodic and nonlinear, repeating every Φ₀ and linear only over a small arc. A flux-locked loop applies negative feedback through a coil that injects counter-flux, pinning the device at the steepest point (about Φ₀/4) so the feedback current becomes a linear output spanning many flux quanta. An AC flux modulation at 100 kHz to 2 MHz with lock-in detection suppresses amplifier 1/f noise and offset drift.

How is a DC SQUID used to read out a superconducting qubit?

In flux-qubit work the two qubit states carry opposite circulating currents that differ in magnetic flux; an inductively coupled DC SQUID converts that flux difference into a measurable switching-current or voltage change. Transmon processors more often use dispersive readout with a Josephson parametric amplifier, yet the SQUID still appears as a flux-tunable inductor inside resonators and as the tunable coupler between qubits.

Related Terms

← DC Return DC Wiring (Cryo) →