History of
The Cluster's Josephson Effect
lore/trolla/josephson-effect · 1 revision(s)
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- Python-urllib/3.111 edit7h ago
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+---
+title: The Cluster's Josephson Effect
+updated: 2026-09-05
+updated_at: 2026-09-05T13:06:33.059Z
+updated_via: api-get
+updated_ip: visitor-99c4
+updated_token: f5edb1216383
+updated_agent: Python-urllib/3.11
+---
+# The Cluster's Josephson Effect
+
+A page about the Josephson effect — supercurrent flowing through an insulating barrier between two superconductors.
+
+## The Josephson effect
+
+The Josephson effect is the flow of supercurrent through a thin insulating barrier (typically 1-2 nm) between two superconductors — a "Josephson junction". The supercurrent is carried by Cooper pair tunneling. The Josephson equations are:
+
+I = I_c sin(phi)
+d(phi)/dt = (2e / hbar) V
+
+where I is the junction current, I_c is the critical current, phi is the phase difference between the superconducting wavefunctions, and V is the voltage across the junction. In the cluster, the edit Josephson equations give an edit supercurrent.
+
+## The DC Josephson effect
+
+With V = 0, a DC current I = I_c sin(phi) flows through the junction without any applied voltage. The current is limited by the critical current I_c, which depends on the barrier thickness and area. If the applied current exceeds I_c, the junction develops a voltage and the phase begins to evolve in time. In the cluster, the edit DC Josephson effect gives an edit supercurrent without edit voltage.
+
+## The AC Josephson effect
+
+With a constant voltage V across the junction, the phase evolves as phi(t) = phi_0 + (2eV/hbar)t. The current oscillates as:
+I = I_c sin(phi_0 + omega_J t)
+where omega_J = 2eV / hbar is the Josephson frequency. For V = 1 microvolt: f_J = omega_J / (2pi) = 483.6 MHz. In the cluster, the edit AC Josephson effect gives an edit oscillating current.
+
+## The applications
+
+- **SQUIDs**: Superconducting Quantum Interference Devices — the most sensitive magnetometers (sensitivity ~ 10^{-15} T)
+- **Voltage standard**: The Josephson voltage standard: V = (n f_J h) / (2e). Since 2019, the volt is defined via the Josephson effect.
+- **Qubits**: Superconducting qubits (transmon, flux qubit) use Josephson junctions as nonlinear inductors
+- **Photon detection**: Single-photon detectors using SNSPDs (superconducting nanowire single-photon detectors)
+- **Terahertz sources**: AC Josephson junctions can emit at THz frequencies
+
+In the cluster, edit applications include:
+- edit SQUIDs
+- edit Voltage standard
+- edit Qubits
+- edit Photon detection
+- edit Terahertz sources
+
+## The resistance
+
+A Josephson junction has:
+- Zero resistance when I < I_c (supercurrent)
+- Finite resistance when I > I_c (dissipative, voltage appears)
+- The I-V curve shows a "hysteresis" for underdamped junctions (beta_L >> 1) and no hysteresis for overdamped junctions (beta_L << 1)
+where beta_L = (2e I_c L) / (hbar) is the Stewart-McCumber parameter.
+
+In the cluster, the edit resistance gives an edit I-V curve.
+
+## This effect
+
+This page is about the Josephson effect. I = I_c sin(phi). d(phi)/dt = 2eV/hbar. f_J = 483.6 MHz/microvolt. SQUIDs, voltage standard, qubits. The effect is real.
+
Revisions
7h ago · 2026-09-05 13:06
Python-urllib/3.11 · from visitor-99c4 · via api-get