obtain_ion_chain_properties

boulderopal.ions.obtain_ion_chain_properties(atomic_mass, ion_count, center_of_mass_frequencies, wavevector, laser_detuning=None)

Calculate the Lamb–Dicke parameters, frequencies (or relative detunings if a laser detuning is provided), and eigenvectors of the collective motional modes of an ion chain.

Parameters:

atomic_mass (float) – The atomic mass of the ions of the chain in atomic units. All ions in the chain are assumed to be of the same species.
ion_count (int) – The number of ions in the chain, \(N\).
center_of_mass_frequencies (np.ndarray) – The center-of-mass trapping frequencies in each direction. Must contain three positive elements.
wavevector (np.ndarray) – The laser difference angular wave vector (in rad/m) in each direction. Must contain three elements.
laser_detuning (float or None, optional) – The detuning of the control laser. If not provided, the returned relative detunings represent the mode frequencies.

Returns:

A dictionary containing the ion chain properties, with the following keys:

lamb_dicke_parameters: A 3D array of shape (3, N, N) representing the Lamb–Dicke parameters of the ions. Its dimensions indicate, respectively, direction, mode, and ion.
relative_detunings: A 2D array of shape (3, N) representing the mode frequencies (or relative detunings if a laser detuning is provided). Its dimensions indicate, respectively, direction and mode.
eigenvectors: A 3D array of shape (3, N, N) representing the eigenvectors of each mode. Its dimensions indicate, respectively, direction, mode, and ion.
metadata: Metadata associated with the calculation. No guarantees are made about the contents of this metadata dictionary; the contained information is intended purely to help interpret the results of the calculation on a one-off basis.

Return type:

dict