optomechanics time evolution

[Akash Dixit]

Hey,

I'm working on trying to implement the optomechanical hamiltonian (shown in attached image). In principle I should see beam splitter dynamics at a rate of g_opt*(eps_0/omega_m).

Please see attached notebook for my attempted implementation. Currently I include no loss and start the system with no excitations, but still see unexpected dynamics. And of course when I start the system with 1 excitation (in either mode) I do not observe the expected beam splitter dynamics.

Any advice or help the community could provide would be much appreciated. I'm sure this issue is just a result on my lack of knowledge/experience with qutip.

Thanks,

Akash

[dixit...@gmail.com]

By significantly increase the bare coupling between microwave and mechanical mode and reducing the strength of the pump I am able to drive rabi oscillations. I can additionally reduce the coupling and see oscilation at slower rates. However, when I increase the drive strength, the simulation seems to mess up. I tried increasing the number of level in the microwave mode to accommodate the large drive, but this didn't seem to help. Thanks for any insight you might be able to provide.

Akash

[Simon Cross]

Hi Akash,

Could you describe what you mean by "the simulation seems to mess up".

Regards,

Simon

[dixit...@gmail.com]

Hey Simon,

Sorry for not providing more details. I am attaching two simulation with different bare coupling g and pump power. The swap rate between the mechanical and optical modes scales as sqrt(n_pump)*g and should be the same between the simulations. As you can see, the dynamics for simulation with the larger pump doesn't exhibit the swap behavior I expect. I've increased the number of levels for the opt mode in the large pump case to just ensure that its not a problem with accessing higher Fock levels.

Thanks,

Akash

[nwla...@gmail.com]

Dear Akash,

Just to chip in, it's been a while I played with this  opto-mechanics model, but looking at your second figure it looks like the optical mode is hitting the Fock-space cut-off.    During the dynamics the cavity photon occupation can reach values of something like <n> ~ (eps_opt/(omega_opt_d-omega_opt)**2)     which can be very large because of the driving.

To avoid the difficulty of simulating this, I think normally in these opto-mechanics models people do a RWA on the drive, and then linearize the interaction by displacing the optical mode around the drive strength, like b_opt -> a_opt + alpha,   where alpha =  eps_opt/2  (more or less something like that).  

I hope this helps...

all the best

neill