Mean photon number in Qutip

[latifeh iri]

Hi all,

I have a question about mean photon number, For example for two level systems, if I have initially mean photon number equal (n), after absorption process, since photon is absorbed, How can I calculate mean photon number after absorption for coherent state? I would appreciate if anyone can give me suggestion about that.

Best,

[Leonardo Assis]

Hello,

For a coherent state, you can do the following:

1. Define your initial coherent state. 

2. Apply the annihilation operator.

3. Calculate the mean photon number for the new state.

The following code implement the steps above using qutip:

import qutip


# parameters
DIMENSION = 30 # dimension of Hilbert space
INITIAL_PHOTON_NUMBER = 2

# operators
an_dag = qutip.destroy(DIMENSION)
number = qutip.num(DIMENSION)

initial_state = qutip.coherent(DIMENSION, INITIAL_PHOTON_NUMBER)
final_state = an_dag*initial_state
final_state_normalised = final_state.unit()
mean_final = qutip.expect(number, final_state_normalised)

Note that since the coherent state is an eigenstate of the annihilation operator, the mean photon number will not be changed.

Nevertheless, you can use a similar code to see the effects of the annihilation operator to other states, such as Fock or thermal states.

You can find more info in this page in the QuTiP documentation.

Kind Regards,

Leonardo.

[latifeh iri]

Thank you so much for your response. I also have another question that I got stuck in it and couldn't find the reasonable result.

For the three level system interacting with one mode cavity, if I want to consider the changes in  detuning (delta), how can I see the differences in the probability plots.

I have delta here:

 wc = (E2 - E1 - delta1)
wc = (E2 - E3 - delta2)

and then I have tried to add it in the non-interaction Hamiltonian:

H0 = ((E2 - E1 - delta1)*a.dag()*a) + (E1 * sigma11.dag()*sigma11) + (E2 * sigma22.dag()*sigma22) + (E3 * sigma33.dag()*sigma33)

but for differences values of delta, there is nothing changed! I tried to add detuning part in the interaction Hamiltonian, so here I can see the changes in detuning and plots, but I think physics behind of that is wrong. (based on equation, adding detuning to the interaction part is not correct).

For example:

H1 = g1* (E2 - E1 - delta1) *sigma12*a.dag()

H2 = g1 * (E2 - E3 - delta2) *sigma12.dag()*a

Do you have any suggestion, how can I add the detuning part to see the changes?

Thank you so much in advance,

Best