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.