rydiqule.experiments.get_snr

rydiqule.experiments.get_snr(sensor: Sensor, param_label: str, phase_quadrature: bool = False, diff_nearest: bool = False, **kwargs) → Tuple[ndarray, List[ndarray]][source]

Calculate a Sensor’s signal-to-noise ratio in standard deviation, in a 1Hz bandwidth, to a specified signal parameter, assuming a homodyne measurement of optical field.

SNR is calculated with respect to the signal parameter, relative to the initial value of the signal parameter. The returned mesh is similarly transformed from the typical sensor mesh, by replacing the total value of the signal parameter with the deviation in the signal parameter.

The conventions used follow that of [1].

Note

The default is to return the SNR of an amplitude quadrature measurement. To convert to a power measurement (i.e. \(\Omega_p^2\)), the amplitude quadrature SNR must be divided by 2. To get the SNR in variance, square the result.

Parameters:

  • sensor (Sensor) – sensor for which SNR should be calculated. The definition of sensor.couplings should contain at least one coupling with a list-like parameter. For the list-like parameter, the first array element is the “base” against which SNR for each other value is calculated.

  • param_label (str) – Label of the axis with respect to which SNR is calculated. See Sensor.axis_labels() for more details on axis labeling. The value corresponding to this label should be the list-like parameter with respect to which SNR should be calculated. This parameter list must have at least two elements, and SNR is calculated relative to the first element in the list for all other elements in the list.

  • phase_quadrature (bool, optional) – Whether the sensor is measured in the phase quadrature of the probe laser. False denotes measurement in the amplitude quadrature. Default is False.

  • diff_nearest (bool, optional) – Controls method by which the SNR is calculated. The default (False) calculates the SNR with respect to the 0 index value. Setting True calculates the SNR with respect to nearest neighbor differences.

  • kwargs (dict, optional) – Additional keyword arguments to pass to rq.solve_steady_state().

Returns:

  • snrs (numpy.ndarray) – Array of SNRs for the sensor with respect to the change in the signal parameter. Calculated in units of amplitude relative to noise standard deviation. SNR referenced to 1 second BW.

  • mesh (tuple(numpy.ndarray)) – Numpy meshgrid of the coupling parameters that yield each snr. The signal parameter axis now shows the signal change.

Raises:

RydiquleError – If the specified param_label is not in Sensor.axis_labels()

Examples

>>> atom = "Rb85"
>>> [g,e] = rq.D2_states("Rb85")
>>> c = rq.Cell('Rb85', [g,e], cell_length=0.0001)
>>> c.add_coupling(states=(g,e), rabi_frequency=np.linspace(1e-6, 1, 5), detuning=1, label="probe")
>>> snr, mesh = rq.get_snr(c, 'probe_rabi_frequency')
>>> print(snr)
[       0.       13654034.1 27301261.5 40934886.9
 54548137.6]
>>> print(mesh)
[array([0.      , 0.25    , 0.499999, 0.749999, 0.999999])]

References