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Author: Harald Schilly
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Description: Jupyter notebook example-energy-levels.ipynb

QuTiP example: Energy-levels of a quantum systems as a function of a single parameter

J.R. Johansson and P.D. Nation

For more information about QuTiP see http://qutip.org

In [1]:
%matplotlib inline import matplotlib.pyplot as plt
In [2]:
import numpy as np from numpy import pi
In [3]:
from qutip import *

Energy spectrum of three coupled qubits

In [4]:
def compute(w1list, w2, w3, g12, g13): # Pre-compute operators for the hamiltonian sz1 = tensor(sigmaz(), qeye(2), qeye(2)) sx1 = tensor(sigmax(), qeye(2), qeye(2)) sz2 = tensor(qeye(2), sigmaz(), qeye(2)) sx2 = tensor(qeye(2), sigmax(), qeye(2)) sz3 = tensor(qeye(2), qeye(2), sigmaz()) sx3 = tensor(qeye(2), qeye(2), sigmax()) idx = 0 evals_mat = np.zeros((len(w1list),2*2*2)) for w1 in w1list: # evaluate the Hamiltonian H = w1 * sz1 + w2 * sz2 + w3 * sz3 + g12 * sx1 * sx2 + g13 * sx1 * sx3 # find the energy eigenvalues of the composite system evals, ekets = H.eigenstates() evals_mat[idx,:] = np.real(evals) idx += 1 return evals_mat
In [5]:
w1 = 1.0 * 2 * pi # atom 1 frequency: sweep this one w2 = 0.9 * 2 * pi # atom 2 frequency w3 = 1.1 * 2 * pi # atom 3 frequency g12 = 0.05 * 2 * pi # atom1-atom2 coupling strength g13 = 0.05 * 2 * pi # atom1-atom3 coupling strength w1list = np.linspace(0.75, 1.25, 50) * 2 * pi # atom 1 frequency range
In [6]:
evals_mat = compute(w1list, w2, w3, g12, g13)
In [7]:
fig, ax = plt.subplots(figsize=(12,6)) for n in [1,2,3]: ax.plot(w1list / (2*pi), (evals_mat[:,n]-evals_mat[:,0]) / (2*pi), 'b') ax.set_xlabel('Energy splitting of atom 1') ax.set_ylabel('Eigenenergies') ax.set_title('Energy spectrum of three coupled qubits');