Classical simulation of quantum dots

In this file we show some of the capabilities of the ClassicalDotSystem, which can simulate simple quantum dot systems.

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

from qtt.simulation.classicaldotsystem import ClassicalDotSystem, TripleDot

We define a linear triple-dot system using the TripleDot class, which inherits from the ClassicalDotSystem.

test_dot = TripleDot()

The function calculate_ground_state calculates the number of electrons in the ground state for given values of the voltages on the gates forming the dots.

temp_state = test_dot.calculate_ground_state(np.array([0,0,0]));
print(temp_state)
temp_state = test_dot.calculate_ground_state(np.array([120,0,100]));
print(temp_state)

[0 0 0]
[1 0 1]

# make a test gate plane
nx = 150
ny = 150
test2Dparams = np.zeros((3,nx,ny))
sweepx = np.linspace(0, 300, nx)
sweepy = np.linspace(0, 300, ny)
xv, yv = np.meshgrid(sweepx, sweepy)
test2Dparams[0] = xv+.1*yv
xv, yv = np.meshgrid(sweepy, sweepx)
test2Dparams[1] = .1*xv+yv

# run the honeycomb simulation
test_dot.simulate_honeycomb(test2Dparams, multiprocess=False, verbose=1)

simulatehoneycomb: 0/150
simulatehoneycomb: 0.48 [s]

plt.pcolor(sweepx,sweepy,test_dot.honeycomb, shading='auto')
plt.colorbar()
plt.show()

test2Dparams[2] = 103

# run the honeycomb simulation again
test_dot.simulate_honeycomb(test2Dparams, multiprocess=False, verbose=1)
plt.pcolor(sweepx,sweepy,test_dot.honeycomb, shading='auto')
plt.colorbar()
plt.show()

simulatehoneycomb: 0/150
simulatehoneycomb: 0.47 [s]

Defining your own system

class TestDot(ClassicalDotSystem):
    def __init__(self, name='testdot', **kwargs):
        super().__init__(name=name, ndots=3, ngates=3, maxelectrons=2, **kwargs)

        vardict = {}

        vardict["mu0_values"] = np.array([-27.0, -20.0, -25.0])  # chemical potential at zero gate voltage
        vardict["Eadd_values"] = np.array([54.0, 52.8, 54.0])  # addition energy
        vardict["W_values"] = np.array([12.0, 5.0, 10.0])  # inter-site Coulomb repulsion (!order is important: (1,2), (1,3), (2,3)) (lexicographic ordering)
        vardict["alpha_values"] = np.array([[1.0, 0.25, 0.1],
                                 [0.25, 1.0, 0.25],
                                 [0.1, 0.25, 1.0]])

        for name in self.varnames:
            setattr(self, name, vardict[name+'_values'])

test_dot_2 = TestDot()

# make a test gate plane
nx = 10
ny = 10
test2Dparams = np.zeros((test_dot_2.ngates,nx,ny))

sweepx = np.linspace(-100, 460, nx)
sweepy = np.linspace(-100, 500, ny)
xv, yv = np.meshgrid(sweepx, sweepy)
test2Dparams[0] = xv+.1*yv
xv, yv = np.meshgrid(sweepy, sweepx)
test2Dparams[2] = .1*xv+yv

# run the honeycomb simulation
test_dot_2.simulate_honeycomb(test2Dparams, multiprocess=False)

simulatehoneycomb: 0/10
simulatehoneycomb: 0.00 [s]

plt.clf()
plt.pcolor(sweepx,sweepy,test_dot_2.hcgs.sum(axis=2), shading='auto')
plt.colorbar()
plt.show()

plt.clf()
plt.pcolor(sweepx,sweepy,test_dot_2.honeycomb, shading='auto')
plt.colorbar()
plt.show()