Josephson junction array (JJA)

Models an array of Josephson junctions as a metamaterial, computing plasma frequencies, resonance modes, dispersion relations, and Kerr nonlinearities.

class HybridSuperQubits.jja.JosephsonJunctionArray(Lj, Cj, Cg, N)[source]

Bases: object

Parameters:

Lj (float)
Cj (float)
Cg (float)
N (int)

__init__(Lj, Cj, Cg, N)[source]

Initialize the Josephson Junction Array with the given parameters.

Parameters: Lj (float): Inductance of the junctions in Henries. Cj (float): Capacitance of the junctions in Farads. Cg (float): Capacitance to ground in Farads. N (int): Number of junctions in the array.

Parameters:

Lj (float)
Cj (float)
Cg (float)
N (int)

property plasma_frequency: float

Calculate the plasma frequency of the Josephson Junction Array.

Returns: float: Plasma frequency in GHz.

property C_ratio: float

Calculate the capacitance ratio Cg/Cj.

Returns: float: Capacitance ratio.

resonance_frequencies()[source]

Calculate the resonance frequencies in Hz of the Josephson Junction Array.

Returns:

np.ndarray: Resonance frequencies in Hz.

Return type:: ndarray

group_velocity()[source]

Calculate the group velocity of the Josephson Junction Array.

Returns: np.ndarray: Group velocity in GHz for each mode.

Return type:: float

kerr_matrix()[source]

Compute the Kerr matrix K_{kk’} for the Josephson Junction Array using the analytical formula. Units in GHz.

This implementation is based on Eq. (14) from: Krupko et al., “Kerr nonlinearity in a superconducting Josephson metamaterial”.

Returns:: A (N, N) matrix of Kerr coefficients.
Return type:: np.ndarray

static analytical_mode_frequencies(f_p, c_ratio, N, k=None)[source]

Static helper method to calculate resonance frequencies from parameters.

Parameters:

f_pfloat: Plasma frequency in Hz.
c_ratiofloat: Capacitance ratio (Cg/Cj).
Nint: Number of junctions in the array.
knp.ndarray, optional: Indices of the modes to calculate. If None, all modes from 1 to N are calculated.

Returns:

np.ndarray: Resonance frequencies in Hz.

Parameters:

f_p (float)
c_ratio (float)
N (int)
k (ndarray | None)

Return type:

ndarray

static fit_from_measurements(measured_frequencies, N, mode_indices=None, initial_params=None, param_bounds=None, fixed_params=None)[source]

Fit JJA parameters to measured resonance frequencies.

Parameters:

measured_frequenciesnp.ndarray: Experimentally measured resonance frequencies in GHz.
Nint: Number of junctions in the array.
mode_indicesList[int], optional: Indices of the modes corresponding to the measured frequencies. If None, assumes consecutive modes starting from 1.
initial_paramsDict[str, float], optional: Initial guess for parameters. Can include ‘f_p’ (plasma frequency in GHz) and ‘C_ratio’ (Cg/Cj ratio). If None, reasonable defaults will be used.
param_boundsDict[str, Tuple[float, float]], optional: Bounds for parameters as (min, max) tuples. Can include ‘f_p’ and ‘C_ratio’.
fixed_paramsDict[str, float], optional: Fixed parameters during fitting. Can include ‘Cj’ to fix the junction capacitance, which allows converting fitted parameters back to Lj and Cg.

Returns:

Dict[str, Any]: Dict with detailed results.

Parameters:

measured_frequencies (ndarray)
N (int)
mode_indices (list[int] | None)
initial_params (dict[str, float] | None)
param_bounds (dict[str, tuple[float, float]] | None)
fixed_params (dict[str, float] | None)

Return type:

dict[str, Any]