scqubits.TunableTransmon.t1

TunableTransmon.t1(i, j, noise_op, spectral_density, T=0.015, total=True, esys=None, get_rate=False)

Calculate the transition time (or rate) using Fermi’s Golden Rule due to a noise channel with a spectral density spectral_density and system noise operator noise_op. Mathematically, it reads:

\[\frac{1}{T_1} = \frac{1}{\hbar^2} |\langle i| A_{\rm noise} | j \rangle|^2 S(\omega)\]

We assume that the qubit energies (or the passed in eigenspectrum) has units of frequency (and not angular frequency).

The spectral_density argument should be a callable object (typically a function) of one argument, which is assumed to be an angular frequency (in the units currently set as system units.

Parameters:

  • i (int >=0) – state index that along with j defines a transition (i->j)

  • j (int >=0) – state index that along with i defines a transition (i->j)

  • noise_op (Union[ndarray, csc_matrix]) – noise operator

  • T (float) – Temperature defined in Kelvin

  • spectral_density (Callable) – defines a spectral density, must take two arguments: omega and T (assumed to be in units of 2 pi * <system units>)

  • total (bool) – if False return a time/rate associated with a transition from state i to state j. if True return a time/rate associated with both i to j and j to i transitions

  • esys (Tuple[ndarray, ndarray]) – evals, evecs tuple

  • get_rate (bool) – get rate or time

Returns:

time or rate – decoherence time in units of \(2\pi ({\rm system\,\,units})\), or rate in inverse units.

Return type:

float