qom.systems.base module

Module to interface QOM systems.

References

[1]

13. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity Optomechanics, Review of Modern Physics 86, 1931 (2014).

class qom.systems.base.BaseSystem(params: dict = {}, name: str = 'Sys_00', desc: str = 'Base System', num_modes: int = 2, cb_update=None)

Bases: object

Class to interface QOM systems.

Requires system_defaults attribute before initializing parent.

Initializes name, desc, num_modes, dim_corrs, num_corrs, params, A, D and updater.

Parameters:

• params (dict, optional) – Parameters for the system.

• name (str, default='Sys_00') – Name of the interfaced system.

• desc (str, default="Base System") – Description of the interfaced system.

• num_modes (int, default=2) – Number of modes of the interfaced system.

• cb_update (callable, optional) – Callback function to update status and progress, formatted as cb_update(status, progress, reset), where status is a string, progress is a float and reset is a boolean.

Notes

The following system methods follow a strict formatting:

method	returns
func_ode_modes_corrs	the rates of change of the modes and correlations, formatted as func_ode_modes_corrs(t, v, c), where t is the time at which the integration is performed, v is an array of the modes and correlations and c is an array of the derived constants and controls of the system. The output should match the dimension of v. This function is already defined inside this class. If func_ode_corrs parameter is given, this function is treated as the function for the modes only.
func_ode_modes_deviations	the rate equations of the modes and deviations. It follows the same formatting as func_ode_modes_corrs. However, the parameter v contains only the deviations.
func_ode_corrs	the rate equations of the correlations. It follows the same formatting as func_ode_modes_corrs. However, the parameter v contains only the correlations.
get_ivc	the initial values of the modes, correlations and derived constants and controls, formatted as get_ivc().
get_A	the drift matrix, formatted as get_A(modes, c, t), where modes are the mode amplitudes at time t and c are the derived constants and controls of the system.
get_mode_rates	the rate of change of the modes. It follows the same formatting as get_A.
get_coeffs_A	the coefficients of the characteristic equations of the drift matrix. It follows the same formatting as get_A.
get_coeffs_dispersion	the coefficients of \(( i \omega )^{j}\) in the dispersions. It follows the same formatting as get_A.
get_nonlinearities	the nonlinearities. It follows the same formatting as get_A.
get_beta_rates	the rates of change of the mechanical modes. It follows the same formatting as get_A.
get_betas	the mechanical modes. It follows the same formatting as get_A.
get_D	the noise matrix, formatted as get_D(modes, corrs, c, t), where modes and corrs are modes and correlations at time t and c are the derived constants and controls of the system.
get_coeffs_N_o	the coefficients of the polynomial in mean optical occupancy, formatted as get_coeffs_N_o(c), where c are the derived constants and controls of the system.
get_modes_steady_state	the steady state modes with shape (dim, num_modes). It follows the same formatting as get_coeffs_N_o.

func_ode_modes_corrs(t, v, c)

Wrapper function for the rates of change of the real-valued modes and correlations.

Requires system method get_mode_rates. Additionally, get_A should be defined for the correlations. Optionally, get_D may be defined for correlations. Refer to Notes for their implementations.

The variables are casted to real-valued.

Parameters:

• t (float) – Time at which the values are calculated.

• v (numpy.ndarray) – Real-valued modes and flattened correlations. First num_modes elements contain the real parts of the modes, the next num_modes elements contain the imaginary parts of the modes and optionally, the last num_corrs elements contain the correlations.

• c (numpy.ndarray) – Defived constants and controls.

Returns:

rates – Rates of change of the real-valued modes and flattened correlations.

Return type:

numpy.ndarray

func_ode_modes_deviations(t, v, c)

Wrapper function for the rates of change of the real-valued modes and flattened deviations.

Requires system method get_mode_rates. Additionally, get_A should be defined for the deviations. Refer to Notes for their implementations.

The variables are casted to real-valued.

Parameters:

• t (float) – Time at which the values are calculated.

• v (numpy.ndarray) – Real-valued modes and flattened deviations. First num_modes elements contain the real parts of the modes, the next num_modes elements contain the imaginary parts of the modes and optionally, the last num_corrs elements contain the deviations.

• c (numpy.ndarray) – Defived constants and controls.

Returns:

rates – Rates of change of the real-valued modes and flattened deviations.

Return type:

numpy.ndarray

get_mean_optical_occupancies()

Method to obtain the mean optical occupancies.

Requires system methods get_ivc and get_coeffs_N_o. Refer to Notes for their implementations.

For example, the mean optical occupancy of a simple end-mirror optomechanical system can be written as [1],

\[N_{o} = |\alpha_{s}|^{2} = \frac{\left| A_{l} \right|^{2}}{\frac{\kappa^{2}}{4} + \Delta^{2}}\]

where \(\Delta = \Delta_{l} + C N_{o}\). This results in a cubic equation with \(4\) coefficients. The get_coeffs_N_o method should return these coefficients.

Returns:

N_os – Mean optical occupancies.

Return type:

numpy.ndarray

get_mode_rates_real(modes_real, c, t)

Method to obtain the real-valued mode rates from real-valued modes.

Requires the system method get_mode_rates. Refer to Notes for its implementation.

Parameters:

• modes_real (numpy.ndarray) – Real-valued modes.

• c (numpy.ndarray) – Derived constants and controls.

• t (float) – Time at which the drift matrix is calculated.

Returns:

mode_rates_real – Real-valued rates for each mode.

Return type:

numpy.ndarray

init_A_D()

Method to initialize the drift matrix and the noise matrix of the system.

set_params(params: dict)

Method to validate and set the system parameters.

Parameters:

params (dict) – Parameters of the system.

system_defaults = {}

Default parameters of the system.

Type:

dict