Welcome to the Two-Level Laser Control Demonstration!
Developer: Nikolay Golubev
This interactive tool visualizes a simple approach for obtaining analytical laser pulses that drive a two-level system in an arbitrarily chosen way, relating any desired population-evolution path to a single resonant pulse.
The interface is organized into two main sections: the Control Panel and the Plot section. The Control Panel allows the parameters of the driving pulse and of the two-level system to be adjusted. As these parameters are modified, the Plot section updates to display the resulting laser pulse and envelope, alongside the time evolution of the level populations.
A detailed description of the underlying theory can be found in:
For additional interactive demonstrations and related projects, visit www.ngolubev.com!
Control Panel
Integration Parameters
This panel defines the initial and final times, $t_{\text{min}}$ and $t_{\text{max}},$ over which the time-dependent Schrödinger equation is numerically propagated.
Laser Pulse Parameters
These parameters shape the driving pulse: $t_0$ sets the time at which the population transfer is centered, and $\alpha$ controls how abruptly it occurs, with larger values producing a faster, more sudden transfer.
System Parameters
This panel defines the two-level system: $a_i$ and $a_f$ are the initial and final populations of lower energy level, $\mu$ is the transition dipole moment coupling the two levels, and $\omega_1,$ $\omega_2$ are the energies of levels $|1\rangle$ and $|2\rangle.$
Laser Pulse
This plot displays the electric field of the driving laser pulse together with its envelope as a function of time, showing the shape and timing of the control field.
Populations
This plot shows the time-dependent populations of the two quantum levels as they evolve under the driving pulse, compared against the prescribed target transfer curve $f(t).$