Timeline for Time evolution of a Gaussian State
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 30, 2021 at 16:47 | vote | accept | Ronan | ||
| Jun 30, 2021 at 15:58 | answer | added | Quantum Mechanic | timeline score: 2 | |
| Jun 30, 2021 at 15:31 | comment | added | Ronan | I am working in the rotating frame, so there are no $\hat{a}^\dagger \hat{a}$ and $\hat{b}^\dagger \hat{b}$ terms. So, what would be the infinitesimal effect of the beamsplitter term? Is it $\dot{\alpha}(t) = g (\beta(t)-\alpha(t))$ and $\dot{\beta}(t) = g (\alpha(t)-\beta(t))$? | |
| Jun 30, 2021 at 15:25 | comment | added | Sebastian Riese | But if you know the time-evolution of the individual terms and your ansatz is correct you can reduce the time-evolution to infinitesimal steps to obtain an ODE for $\alpha$ and $\beta$. (And in the end you can check whether your ansatz was correct by checking that your solution fulfils the Schrödinger equation.) | |
| Jun 30, 2021 at 15:22 | comment | added | Sebastian Riese | Is $\hat{H}$ the full Hamiltonian of the system or is it an "interaction" Hamiltonian and there are additional terms $\hbar \omega_a a^\dagger a$ and $\hbar \omega_b b^\dagger b$ in the full Hamiltonian. (Or are you working in the interaction picture and the operators carry the "free" time-dependency.) | |
| Jun 30, 2021 at 15:01 | history | asked | Ronan | CC BY-SA 4.0 |