Reflectometry is a measurement technique which enables spin readout of an electron without collapsing its wavefunction, and can be used in a variety of systems. One such system in which reflectometry can be used measurement of the spin of a quantum dot or a series of quantum dots. Previous analysis of this system has been completed for a two level system coupled with a superconducting resonator, whereby the rotating wave approximation (RWA) is used.

This package is a tool which allows you to simulate the Dispersion Readout for Multilevel Systems, without the use of the RWA. Here the susceptibility of a double quantum dot (DQD) is calculated using a cicuit QED formalism and sweeps are carried out over a range of different magnetic fields and magnetitudes of detuning and a plot of the spectrum is simulated.

For further information on the simulation and derivation, please read the included Pdf 'Dispersive Readout of Multilevel Systems'

The code is no where near complete yet! I still have a couple of tweaks to do and will upload on a regular basis.

• Dispersive readout for 2 level and 3 level systems
• Ability to change parameters such as spin orbit interaction, Temperature for Dispersive Readouts
• Temperature, Frequency and Coherence Sweeps for different applied Magnetic Fields
• Probability Plots as a function of Temperature
• Ability to plot Eigenvectors of given Hamiltonian

If you have any recommendations or graphs you think might benefit you, please don't hesitate to contact me!

• Dispersive Readout for N level System
• Automatic Evaluation of Z matrix given initial Hamiltonian

Multilevel Systems and their Dispersive Readouts are simulated using an approach developed by Kohler et al. where the reflected coefficient of a system is dependant on the susceptibility of the system. Scans of the reflected coefficient as a function of detuning and magnetic fields are simulated for a system containing a double quantum dot coupled with a photon.

To simulate the dispersive readout scan, first import the package

from ECHO import ECHO_3x3 as e3
from ECHO import ECHO_2x2 as e2

Create your class

P =  e3.ECHO_3x3()

Initial Parameters for the system are set as follows

The Hamiltonian and Z matrix are initially set for two singlet and the triplet minus state with spin orbit interaction.

To change the Hamiltonian, Z matrix or any other parameter, one can change these before running the simulation as follows:

P.gamma = 1;
P.so = 0.02;

To run the simulation, one must use the .run() attribute

P.run()

To change the range of values of detuning and magnetic field, one must input in the parameters into the .run() attribute

P.run(Bmin = -2, Bmax = 4, emin = -3, emax = 5)

To change the resolution of your images, simply increase N, the number of points evaluated between each maximum and minumum of the detuning and magnetic field

P.run(N = 250)

After running the simulation, an output of the reflection coefficient for a variety of different magnetic fields and detuning parameters.

To set-up the simulation for a two level system, we first initialize our class:

Q = e2.ECHO_2x2()

To run the simulation:

Q.run()

To plot the eigenenergies of the singlets and triplets of your system for a given Magnetic Field, over a range of detuning values, one can run:

P.plot_eigen(B = 1)

where here the magnetic field was initially set to one.

One can change the range of detuning values accordingly

P.plot_eigen(B = 1, emin = -5, emax = 5)

To print out the relevant parameters for the system, one can use:

P.print_parameters()

If one would like to save the figure simulated for the reflection Coefficient, one must include:

P.run(save = True)

For the three level system, one can simulate the following parameter sweeps:

• Temperature (assuming thermal probabilities)
• Coherence
• Cavity Frequency

To run a temperature sweep for a three level system, we can run the following with the initial parameters shown:

P.temp_sweep(B= 1, emin = -3, emax = 3, Tmin = 0.01, Tmax = 1, N = 150)

To run a coherence sweep for a three level system, we can run the following with the initial parameters shown:

P.coher_sweep(B= 1, emin = -3, emax = 3, gmin = 0.01, gmax = 1, N = 150)

To run a cavity frequency sweep, we run the following:

P.freq_sweep(B= 1, emin = -3, emax = 3, wmin = 0.01, wmax = 1, N = 150)