gharib85/nvham

Mathematica Library to help construct Nitrogen Vacancy Hamiltonians

Dependencies

This package is known to run on Mathematica 11, though earlier versions to about 9 should also work (untested). This package requires Quantum-Utils.

Installation

To install this library, just open up Install.m in Mathematica and goto

Evaluation > Evaluate Notebook

Explanation of installation for those interested: This installer simply moves the contents of the src folder into the search path of Mathematica, which in this case, is the Applications subfolder of

$UserBaseDirectory

On Mac and Linux, simlinks are used for the convenience of developing code in src. On Windows, we do an actual copy.

To uninstall, go to $UserBaseDirectory/Applications in your file explorer and delete the relevant files.

Documentation

Though it is relatively feature-rich and runs smoothly, the documentation is severely limited. See the examples, read the source code, and feel free to help out.

Many functions will have (terse) doc strings attached, which can be viewed by prepending a question mark to the function name and running the cell:

? Nitrogen

Usage: Constructing Hamiltonians

Import a package:

Needs["NVHamiltonian`"]

Create a trivial Hamiltonian:

Create a Hamiltonian with a static magnetic field in cartesian coordinates of the principle axis:

Create a Hamiltonian including a 15-Nitrogen atom:

Create a numerical Hamiltonian including the 14-Nitrogen tensor as measured by Felton '09:

Compute the hyperfine tensor of a 13-Carbon located at the coordinate [5,0,10] (in units of atomic bond lengths) coupled by dipole-dipole interaction (assuming NV is a point):

Compute the average (stroboscopic) Hamiltonian at order-1 of an NV. Here we see the Bloch-Siegert shift. You can throw anything you want into this up to order-2; this example is simple for brevity.

Use PulseSim from QuantumUtils to simulate an NV connected to two 13-Carbons and a 14-Nitrogen under the second order average Hamiltonian, with a microwave field a 5MHz. One carbon has a hyperfine tensor as measured by Taminiau '12.