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, NN.
  • 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

SEE ALSO

boulderopal.ions.ms_optimize : Find optimal pulses to perform Mølmer–Sørensen-type operations on trapped ions systems.

boulderopal.ions.ms_simulate : Simulate a Mølmer–Sørensen-type operation on a trapped ions system.

Notes

The directions of input parameters and returned arrays are ordered as radial x-direction, radial y-direction, and axial z-direction, corresponding, respectively, to the unit vectors (1,0,0)(1, 0, 0), (0,1,0)(0, 1, 0), and (0,0,1)(0, 0, 1).

Examples

Refer to the How to optimize error-robust Mølmer–Sørensen gates for trapped ions user guide to find how to use this function.

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