hamiltonian.m

Hamiltonian operator or superoperator and its rotational decomposition.

Bosonic mode terms declared in inter.modes are assembled here as well: mode energies, anharmonicities, exchange, cross-Kerr, longitudinal, dispersive, and spin Hamiltonian modulation terms. Each mode is referenced to a frame frequency determined from the particle connectivity graph built from all six mode coupling channels: modes connected to spins run in a frame at the magnitude of the spin carrier frequency, and modes that are connected to no spin are left at their laboratory frequency, which is reported to the console unless a carrier is declared. Which mode terms survive depends on the assumption set.

Syntax

    [I,Q]=hamiltonian(spin_system,operator_type)

Parameters

In Liouville space, operator_type can be set to

         'left' - produces left side product superoperator

        'right' - produces right side product superoperator

         'comm' - produces commutation superoperator (default)

        'acomm' - produces anticommutation superoperator

In Hilbert space this parameter is ignored.

Outputs

    H   - rotationally invariant part of the Hamiltonian

    Q   - irreducible components of the anisotropic part,
          use orientation.m to get the full Hamiltonian
          at each specific orientation

Notes

1. All spin interactions that go into the Hamiltonian are specified during the spin system setup - see the spin system specification section of the online manual.
2. Descriptor and operator generation are parallelised.
3. Bosonic mode terms declared in inter.modes are added to the invariant part I at their input orientation; the Q part and the orientation machinery refer to the spin subsystem only, for which rotations are well-defined.
4. The retained branch of a spin-mode exchange (Jaynes-Cummings) coupling follows the sign of the spin carrier frequency; the counter-rotating branch is retained in the laboratory frame and dropped under the rotating wave approximation of the 'cavity' assumption set.

See also

relaxation.m, kinetics.m, operator.m, state.m, equilibrium.m, orientation.m, bos2ist.m, boson_mono.m, boson_ortho.m, centrans.m, ct2ist.m, enlev2bm.m, enlev2ist.m, lindbladian.m, oper2bm.m, oper2ist.m, propagator.m, sin_tran.m, weyl.m, device.m, coherent.m, rlx_modes.m, Kernel_functions

Version 2.2, authors: Ilya Kuprov, Luke Edwards, Hannah Hogben, Dmitry Savostyanov