error in the dephasing

[Manny]

Hi

I believe that the examples, both in the tutorials, and the manual, have errors when dealing with dephasing. 

In the manual for the 4.6.0 release (page 98), the dephasing operator is defined as:  np.sqrt(gamma2) * sz:

c_ops = [np.sqrt(gamma1) * sm, np.sqrt(gamma2) * sz] # relaxation and dephasing

  

There should be a factor of 2

 np.sqrt(gamma2/2) * sz 

so that the decay of the off diagonal elements is T2=1/gamma2

Since the Lindbladt operator for dephasing is sqrt(gamma/2)*sz

[Simon Cross]

Hi Manny,

I think I agree with you, but I'd like to confirm a few things.

Is the example you're referring to https://qutip.org/docs/latest/guide/dynamics/dynamics-time.html#running-string-based-time-dependent-problems-using-parfor ?

If so, this example is more of an illustration of how to make multiple calls to a solver in parallel rather than a discussion of a particular piece of physics, so I'm not that surprised that the definition of some constants absorbs a factor of 2.

If we update this, it would be nice to point readers to a standard reference so that they can look up the physics being demonstrated. Could you perhaps suggest one?

Yours sincerely,

Simon Cross

[Manny]

Hi Simon

Yes, that was the example i was refering too and also the tutorial:

• Master equation solver: Qubit dynamics

available here: https://qutip.org/tutorials.html;

Regarding a reference, honestly i was surprised how hard was to find one reference where they treat 2-level system dephasing.  My usual place to look this up would have being the book "Exploring the Quantum," but they don't treat dephasing explicitly when they derive the Lindblad equation (chapter 4). 

They first place  I found this was Andreas Wallraf paper: "Dynamics of dispersive single-qubit readout in circuit quantum electrodynamics", Eq. 4. 

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.80.043840

The other reference I found was in  the notes for the  MIT course "Quantum Theory of Radiation Interactions", chapter 8 of the notes. 

https://ocw.mit.edu/courses/nuclear-engineering/22-51-quantum-theory-of-radiation-interactions-fall-2012/lecture-notes/MIT22_51F12_Ch8.pdf

In  Example A: spin-1/2 dephasing, at the bottom of page 71. 

Thanks

Manuel