Solver
======

Tools for solving the NV center hamiltonian.


Zeeman Hamiltonian
------------------

.. math::
    \frac{H}{\hbar} = D_{gs}\left(S_z^2 - \frac{1}{3}S(S+1)\right) + E(S_x^2 - S_y^2) + \gamma_{\text{NV}}\vec{B} \cdot \vec{S}


.. code-block:: python

   from nvtools import unit
   from nvtools.solver import Solver

   solver = Solver()

   # calculate absolute field value and angle to NV axis from two resonances
   b_abs, theta = self.solver.field_from_resonances(2865 * unit.MHz, 2875 * unit.MHz)

   # calculate B-Field vector from eight resonance frequencies
   b_field = self.solver.field_vector_from_resonances([<list of eight resonance frequencies>])


.. automodule:: nvtools.solver.zeeman
    :members:
    :undoc-members:


Hyperfine Hamiltonian
---------------------

.. math::
    \frac{H}{\hbar} = D_{gs}S_z^2 + E(S_x^2 - S_y^2) + \gamma_{\text{NV}}\vec{B} \cdot \vec{S} + \vec{S}\cdot\hat{A}\cdot\vec{I} + P I_z^2


.. code-block:: python

   from nvtools import unit
   from nvtools.solver import Solver

   # create a solver for a given nitrogen isotope
   solver = Solver("14N")  # or Solver("15N")

   # get absolute field value and angle to NV axis from two resonances
   b_abs, theta = self.solver.field_from_resonances(2865 * unit.MHz, 2875 * unit.MHz)


.. automodule:: nvtools.solver.hyperfine
    :members:
    :undoc-members: