ejec2duffing.m

Converts the Josephson and charging energies of a transmon into the Duffing oscillator frequency and anharmonicity expected by the bosonic mode specification interface of create.m, using the asymptotic transmon expressions of Koch et al. (https://doi.org/10.1103/PhysRevA.76.042319):

    frq=sqrt(8*ej*ec)-ec,     anharm=-ec

Superconducting circuit papers quote transmon parameters as E_J and E_C, while Spinach expects a transition frequency and an anharmonicity; this function is the bridge between the two conventions. The anharmonicity comes out negative, as it should for a physical transmon.

Syntax

    [frq,anharm]=ejec2duffing(ej,ec)

Parameters

    ej      - Josephson energies in Hz (energy over the
              Planck constant), an array of positive
              real numbers

    ec      - charging energies in Hz (energy over the
              Planck constant), an array of positive
              real numbers of the same size as ej

Outputs

    frq     - transition frequencies in Hz, to be placed
              into inter.modes.frqs

    anharm  - Duffing anharmonicities in Hz, to be placed
              into inter.modes.anharms

Examples

A transmon with E_J/h = 20 GHz and E_C/h = 300 MHz, declared with three energy levels:

    % Transmon parameters from the device paper
    [frq,anharm]=ejec2duffing(20e9,300e6);

    % Transmon with three energy levels
    sys.isotopes={'T3'};
    inter.modes.frqs={frq};
    inter.modes.anharms={anharm};

Notes

1. The asymptotic expressions are only accurate deep in the transmon regime ej/ec>>1; a warning is issued when the ratio is smaller than 20.
2. Spinach warns when a positive anharmonicity is declared for a transmon, because physical transmons have negative anharmonicity.

See also

create.m, cart2mode.m, kelvin2hz.m, mev2hz.m, Spin system specification, Kernel utilities

Version 2.12, authors: Ilya Kuprov