Superconducting qubits (Phase qubit) Quantum informatics (FKA 172)

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Equation of motion for the current biasedJosephson junctionChalmers University of TechnologyThe bias current splits into three currents. Fromthe currents through the resistor, capacitor, andJosephson element we get:I b R C I c or L JBy replacing the voltage across the parallel RCL Jcircuit using the second Josephson equation (see2 slides before) we get the equation of motion forthe fictitious phase particle with massproportional to the capacitance:From this equation we candirectly determine thepotential of the system U.
Chalmers University of TechnologyDynamics of the current biased Josephson junctionjunction capacitanceJosephson inductanceThe shunting admittance=(impedance) -1 is frequencydependent and accountsfor all processescausing dissipation.ω PΔUbarrierheightplasmafrequencyquality factor,only the real part of theadmittance causesdissipation
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Superconducting qubits (Phase qubit) Quantum informatics (FKA 172)

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