qit.hamiltonian.jaynes_cummings

qit.hamiltonian.jaynes_cummings(om_atom, Omega, m=10, use_RWA=False)

Jaynes-Cummings model, one or more two-level atoms coupled to a single-mode cavity.

Parameters

• om_atom (array[float]) – Atom level splittings

• Omega (array[float]) – Atom-cavity coupling

• m (int) – Cavity Hilbert space truncation dimension

• use_RWA (bool) – Should we discard counter-rotating interaction terms?

Returns

Hamiltonian, dimension vector

Return type

tuple

The Jaynes-Cummings model describes n two-level atoms coupled to a harmonic oscillator (e.g. a single EM field mode in an optical cavity), where n == len(om_atom) == len(Omega).

$$H/\hslash =-\sum _k\frac{{{\omega }_a}_k}{2}{Z}_k+{\omega }_c{a}^{†}a+\sum _k\frac{{\mathrm{\Omega }}_k}{2}(a+a^{†})\otimes X_k$$

The returned Hamiltonian H has been additionally normalized with ${\omega }_c$, and is thus dimensionless. om_atom[k] = ${{\omega }_a}_k/{\omega }_c$, Omega[k] = ${\mathrm{\Omega }}_k/{\omega }_c$.

The order of the subsystems is [cavity, atom_1, …, atom_n]. The dimension of the Hilbert space of the bosonic cavity mode (infinite in principle) is truncated to m. If use_RWA is true, the Rotating Wave Approximation is applied to the Hamiltonian, and the counter-rotating interaction terms are discarded.