Engineering & Science
Josephson Junction AC Frequency (KJ) & Ambegaokar-Baratoff Critical Current (Ic)
Calculate the AC Josephson oscillation frequency f_J = 0.4835979 * V_uV in GHz using the 2019 SI Josephson constant KJ = 2e/h, plus T=0 Ambegaokar-Baratoff critical current Ic = ((PI()/2) * Delta_meV) / Rn.
Anchor quantum voltage standards and size transmon qubit Josephson junctions!
Brian Josephson (1973 Nobel Prize at age 33!) predicted two astonishing macroscopic quantum effects across a thin insulating tunnel barrier between two superconductors: first, applying a DC voltage V_uV (microvolts) drives an alternating supercurrent oscillating at exact frequency f_J = (2 * e / h) * V! Since the 2019 SI redefinition of e and h, the Josephson constant KJ = 2e / h = 483,597.8484... GHz/V = 0.4835979 GHz/uV is EXACT—allowing national metrology institutes to lock primary DC voltage standards directly to atomic clocks!
Second, for superconducting SQUID magnetometers and transmon quantum processors, Vinay Ambegaokar and Alexis Baratoff (1963) proved that at T << Tc, the product of maximum zero-voltage critical supercurrent Ic and room-temperature/normal-state tunnel resistance Rn depends ONLY on the superconducting gap Delta_0 (in meV): Ic * Rn = (PI() / 2) * (Delta_0 / e)! Thus an Al/AlOx/Al or Nb tunnel junction with Delta_0 = 1.40 meV and Rn = 10.0 Ohms carries critical current Ic = 219.91 uA—and biasing at V = 200 uV radiates coherent microwaves at f_J = 96.720 GHz!
| Josephson Tunnel Junction Parameter | Input Condition | Calculated Quantum Output | Device Application |
|---|---|---|---|
| AC Josephson Oscillation (V = 200 uV) | KJ = 0.4835979 GHz/uV | 96.720 GHz | NIST Quantum Voltage Array |
| Nb Junction (Delta = 1.40 meV, Rn = 10 Ohm) | Ic = (PI()/2)*1400 / 10 | 219.91 uA | SQUID / RSFQ Logic Gate |
| Al Qubit Junction (Delta = 0.18 meV, Rn = 9,000 Ohm) | Ic = (PI()/2)*180 / 9000 | 0.0314 uA (31.4 nA) | 5 GHz Transmon Qubit |
AC Josephson Oscillation Frequency f_J = KJ * V_uV (GHz)
Multiplies DC junction bias magnitude ABS(B2) in microvolts by exact SI constant 0.4835979 GHz/uV.
=ROUND(0.4835979 * ABS(B2), 3)Ambegaokar-Baratoff Zero-Temperature Critical Current Ic (Microamperes, uA)
Converts gap B3 from meV to uV (* 1,000) and evaluates ((PI() / 2) * Delta_uV) / Rn_ohms.
=IF(OR(B3 <= 0, B4 <= 0), "Invalid Junction Inputs", ROUND(((PI() / 2) * B3 * 1000) / B4, 2))Try the example
Use the original values or change them to test your understanding.