rlx_modes.m

Bosonic mode dissipation superoperator. Builds thermalised GKSL dissipators for the amplitude damping and the pure dephasing of the bosonic modes declared in inter.modes, using the amplitude damping rates and the pure dephasing rates ingested by create.m and the Bose-Einstein thermal occupation numbers computed from the physical mode frequencies and the system temperature. The physical frequency of a mode is the sum of the declared carrier and the declared frequency where inter.modes.carriers is present, and the magnitude of the declared frequency otherwise.

This function is called automatically by relaxation.m whenever damping or dephasing is declared for any mode, so it does not usually need to be called by the user.

Syntax

    R=rlx_modes(spin_system)

Parameters

    spin_system  - Spinach spin system description object
                   with bosonic mode information present

Outputs

    R            - bosonic mode dissipation superoperator

Notes

1. The dissipators are kappa*(1+nbar)*D[a], kappa*nbar*D[c], and 2*gamma_phi*D[n], where D[x] is the GKSL dissipator of the operator x, built from ladder operators truncated to the level count of each mode.
2. The Spinach convention of zero temperature meaning the high-temperature limit is not applicable to bosonic modes: zero temperature here produces zero thermal occupation numbers.
3. Because the superoperator is a dissipator, a Liouville space formalism is required. In Hilbert space relaxation.m issues a warning and returns without the mode dissipation terms.
4. The amplitude damping rate is set by inter.modes.lifetimes, inter.modes.linewidths, or inter.modes.qfactors, and the pure dephasing rate is extracted from inter.modes.t2_times at the declared temperature.

See also

relaxation.m, create.m, device.m, coherent.m, rlx_t1_t2.m, lindbladian.m, equilibrium.m, Relaxation theory parameters, Kernel utilities

Version 2.12, authors: Ilya Kuprov