How to compute normalized second order correlation function

[Parvendra Kumar]

Dear Group Members,

I hope you are doing well. 

I am quite new to qutip, trying to learn and apply various functions of qutip for a two-level atom coupled to cavity. I would like to calculate the normalized second order correlation function of cavity field, which is given as:

g2(t, tau)=<adagger(t)adagger(t+tau)a(t+tau)a(t)>/(<adagger(t)a(t)>  <adagger(t+tau)a(t+tau)>)

The numerator part of g2 can be easily computed using "correlation_3op_2t" function of qutip. 

However, I am struggling to compute one of the denominator part of g2  " <adagger(t+tau)a(t+tau)>)" , the other one can be computed using me solver of qutip.

Please see if some one can spare his/her precious time to help me out.  

Thanks and Regards,

Parvendra Kumar

DU, India

  

[Dmbhm Esyan]

Check these examples and see if helps: 

https://qutip.org/docs/4.1/guide/guide-correlation.htmlQ

Also the lecture notes:

https://nbviewer.jupyter.org/github/jrjohansson/qutip-lectures/blob/master/Lecture-2B-Single-Atom-Lasing.ipynb

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[Joaquin Guimbaogaspar]

Dear Parvendra,

The term <adagger(t)a(t)> is equal to the cavity population term of the density matrix rho(cav) (i.e. The diagonal term corresponding the evoultion of number of photons). This means that for computing:

 <adagger(t)a(t)> <adagger(t+tau)a(t+tau)>

Yo can substitute by:

rho(cav)(t)*rho(cav)(t+tau)

You can extract the temporal array rho(cav)(t) from the solution of the master equation.

Joaquin

Enviado desde mi iPhone

El 4 jul 2021, a las 2:44, Dmbhm Esyan <haim...@gmail.com> escribió:



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[Parvendra Kumar]

Dear Joaquin Guimbaogaspar,

Thanks for your inputs. Based on your suggestions, I tried the following

rho=mesolve(H, psi0, tlist, c_ops, [])  # computation of rho(t)
rho1=mesolve(H, rho.states[0], taulist, c_ops, [a.dag()*a]).expect[0]  #computation of <adagger(t1+tau)a(t1+tau)>=Tr(adagger(t1+tau)a(t1+tau)rho(t1+tau))

But I have to do it manually for all the  t's in the tlist. But I'm not sure whether there is a way of computing rho(t+tau) using a for loop function or any other way.

Your further inputs are appreciated in this regard.

Regards,

Parvendra

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[Parvendra Kumar]

Thanks for your inputs.

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