https://spindynamics.org/wiki/index.php?action=history&feed=atom&title=Ejec2duffing.mEjec2duffing.m - Revision history2026-10-04T05:20:01ZRevision history for this page on the wikiMediaWiki 1.31.15https://spindynamics.org/wiki/index.php?title=Ejec2duffing.m&diff=9874&oldid=prevKuprov: Document new Spinach 2.12 spin-boson functionality (PR 195)2026-08-06T04:38:09Z<p>Document new Spinach 2.12 spin-boson functionality (PR 195)</p>
<p><b>New page</b></p><div>{{DISPLAYTITLE:ejec2duffing.m}} __NOTOC__<br />
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):<br />
<br />
frq=sqrt(8*ej*ec)-ec, anharm=-ec<br />
<br />
Superconducting circuit papers quote transmon parameters as E<sub>J</sub> and E<sub>C</sub>, 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.<br />
<br />
==Syntax==<br />
<br />
[frq,anharm]=ejec2duffing(ej,ec)<br />
<br />
==Parameters==<br />
<br />
ej - Josephson energies in Hz (energy over the<br />
Planck constant), an array of positive<br />
real numbers<br />
<br />
ec - charging energies in Hz (energy over the<br />
Planck constant), an array of positive<br />
real numbers of the same size as ej<br />
<br />
==Outputs==<br />
<br />
frq - transition frequencies in Hz, to be placed<br />
into inter.modes.frqs<br />
<br />
anharm - Duffing anharmonicities in Hz, to be placed<br />
into inter.modes.anharms<br />
<br />
==Examples==<br />
<br />
A transmon with E<sub>J</sub>/h = 20 GHz and E<sub>C</sub>/h = 300 MHz, declared with three energy levels:<br />
<br />
% Transmon parameters from the device paper<br />
[frq,anharm]=ejec2duffing(20e9,300e6);<br />
<br />
% Transmon with three energy levels<br />
sys.isotopes={'T3'};<br />
inter.modes.frqs={frq};<br />
inter.modes.anharms={anharm};<br />
<br />
==Notes==<br />
<br />
# 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.<br />
# ''Spinach'' warns when a positive anharmonicity is declared for a transmon, because physical transmons have negative anharmonicity.<br />
<br />
==See also==<br />
[[create.m]], [[cart2mode.m]], [[kelvin2hz.m]], [[mev2hz.m]], [[Spin system specification]], [[Kernel utilities]]<br />
<br />
''Version 2.12, authors: [[Ilya Kuprov]]''</div>Kuprov