Calculating eigenfrequencies¶

Qcircuit.
eigenfrequencies
(**kwargs)[source]¶ Returns the normal mode frequencies of the circuit.
Frequencies are provided in units of Hertz, not in angular frequency.
 Parameters
kwargs – Values for unspecified circuit components, ex:
L=1e9
. Returns
Normal mode frequencies of the circuit, ordered from lowest to highest frequency, given in Hertz.
 Return type
numpy.array
Notes
These eigenfrequencies \(f_m\) 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 mth normal mode of the circuit and \(f_m\) is the frequency of the mth 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 nonlinear part of the Hamiltonian \(\hat{U}\), originating in the junction nonlinearity, would be 0.
For more information on the underlying theory, see https://arxiv.org/pdf/1908.10342.pdf.