Calculating eigen-frequencies

Qcircuit.eigenfrequencies(**kwargs)

Returns the normal mode frequencies of the circuit.

Frequencies are provided in units of Hertz, not in angular frequency.

Parameters

kwargs – Values for un-specified circuit components, ex: L=1e-9.

Returns

Normal mode frequencies of the circuit, ordered from lowest to highest frequency, given in Hertz.

Return type

numpy.array

Notes

These eigen-frequencies \(f_m\) correspond to the real parts of the complex frequencies which make the conductance matrix singular, or equivalently the real parts of the poles of the impedance calculated between the nodes of an inductor or josephson junction.

The Hamiltonian of the circuit is

\(\hat{H} = \sum_m hf_m\hat{a}_m^\dagger\hat{a}_m + \hat{U}\),

where \(h\) is Plancks constant, \(\hat{a}_m\) is the annihilation operator of the m-th normal mode of the circuit and \(f_m\) is the frequency of the m-th normal mode. The frequencies \(f_m\) would be the resonance frequencies of the circuit if all junctions were replaced with linear inductors. In that case the non-linear part of the Hamiltonian \(\hat{U}\), originating in the junction non-linearity, would be 0.

For more information on the underlying theory, see https://arxiv.org/pdf/1908.10342.pdf.