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).\[H/\hbar = -\sum_k \frac{{\omega_a}_k}{2} Z_k +\omega_c a^\dagger a +\sum_k \frac{\Omega_k}{2} (a+a^\dagger) \otimes X_k\]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] = \(\Omega_k / \omega_c\).
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.