```
# This file is part of QuTiP: Quantum Toolbox in Python.
#
# Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
# of its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
'''
This module provides functions that are useful for simulating the
three level atom with QuTiP. A three level atom (qutrit) has three states,
which are linked by dipole transitions so that 1 <-> 2 <-> 3.
Depending on there relative energies they are in the ladder, lambda or
vee configuration. The structure of the relevant operators is the same
for any of the three configurations::
Ladder: Lambda: Vee:
|two> |three>
-------|three> ------- -------
| / \ |one> /
| / \ ------- /
| / \ \ /
-------|two> / \ \ /
| / \ \ /
| / \ \ /
| / -------- \ /
-------|one> ------- |three> -------
|one> |two>
References
----------
The naming of qutip operators follows the convention in [1]_ .
.. [1] Shore, B. W., "The Theory of Coherent Atomic Excitation",
Wiley, 1990.
Notes
-----
Contributed by Markus Baden, Oct. 07, 2011
'''
__all__ = ['three_level_basis', 'three_level_ops']
from qutip.states import qutrit_basis
from numpy import array
[docs]def three_level_basis():
''' Basis states for a three level atom.
Returns
-------
states : array
`array` of three level atom basis vectors.
'''
# A three level atom has the same representation as a qutrit, i.e.
# three states
return qutrit_basis()
[docs]def three_level_ops():
''' Operators for a three level system (qutrit)
Returns
--------
ops : array
`array` of three level operators.
'''
one, two, three = qutrit_basis()
# Note that the three level operators are different
# from the qutrit operators. A three level atom only
# has transitions 1 <-> 2 <-> 3, so we define the
# operators seperately from the qutrit code
sig11 = one * one.dag()
sig22 = two * two.dag()
sig33 = three * three.dag()
sig12 = one * two.dag()
sig32 = three * two.dag()
return array([sig11, sig22, sig33, sig12, sig32], dtype=object)
```

© Copyright 2011 and later, P.D. Nation, J.R. Johansson.

Last updated on Dec 31, 2014.

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