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

In [1]:

    

%pylab inline


    

    




Populating the interactive namespace from numpy and matplotlib

In [2]:

    

from qutip import *


    

In [3]:

    

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 = 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,:] = real(evals)

        idx += 1

    return evals_mat


    

In [4]:

    

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 = linspace(0.75, 1.25, 50) * 2 * pi # atom 1 frequency range


    

In [5]:

    

evals_mat = compute(w1list, w2, w3, g12, g13)


    

In [6]:

    

figure(figsize=(12,6))

for n in [1,2,3]:
    plot(w1list / (2*pi), (evals_mat[:,n]-evals_mat[:,0]) / (2*pi), 'b')

xlabel('Energy splitting of atom 1')
ylabel('Eigenenergies')
title('Energy spectrum of three coupled qubits');


    

In [7]:

    

from qutip.ipynbtools import version_table

version_table()


    

    
Out[7]:




Software
Version
Cython
0.20.1post0
QuTiP
3.0.0.dev-526f1d2
OS
posix [linux]
IPython
2.0.0
Numpy
1.8.1
matplotlib
1.3.1
Python
3.4.1 (default, Jun  9 2014, 17:34:49) 
[GCC 4.8.3]
SciPy
0.13.3
Wed Jun 25 14:28:49 2014 JST