Welcome to the Stimulated Raman Adiabatic Passage (STIRAP) Learning Tool!
Developers: Brayton Bosuku, Miguel Alarcón, Nikolay Golubev
This interactive learning tool provides a visualization of a generalized fractional STIRAP scheme for controlling a coherent superposition of quantum states. STIRAP is a technique for transferring population from one quantum state to another through an intermediate state using a sequence of laser pulses. Unlike direct excitation, the process is designed so that the intermediate level remains only weakly populated, making the population transfer highly efficient and robust. In its generalized variant, STIRAP enables precise control over the relative contributions of the components of an existing quantum superposition by adjusting the shape, timing, and intensity of the control pulses.
The interface is organized into two main sections: the Control Panel and the Plot section. The Control Panel allows the parameters of the STIRAP protocol to be adjusted interactively. As these parameters are modified, the Plot section updates in real time to display the corresponding laser pulse sequence, the time evolution of the populations, and the resulting coherent superposition. This interactive layout enables users to explore how different pulse configurations influence the dynamics of the population transfer and the final quantum state.
A detailed description of the generalized fractional STIRAP protocol, its theoretical foundations, and its application to the coherent control of quantum dynamics in atomic systems can be found in the following reference:
For additional interactive demonstrations and related projects, visit www.ngolubev.com!
Control Panel
Energy Levels
This panel defines the three-level quantum system used in the STIRAP simulation. The energies of the three quantum levels can be adjusted to explore different level configurations and investigate how the energy spacing influences the interaction with the applied laser fields.
Population Controls
This panel specifies the initial and target population distributions between the states $|1\rangle$ and $|3\rangle$. By adjusting these populations, different initial conditions and target states can be prepared, allowing various population transfer pathways and coherent dynamics to be explored.
Laser Parameters
This panel controls the properties of the Pump and Stokes laser pulses that drive the population transfer. In the implemented scheme, each pulse is constructed as a combination of two time-delayed Gaussian pulses, referred to as the Left and Right Gaussian components, whose relative amplitudes are determined by the selected mixing angles. The available controls allow the detuning of the laser frequencies from resonance to be adjusted, set the duration of the Gaussian components, and specify the temporal positions of the left and right Gaussians, thereby defining the timing, overlap, and overall shape of the control fields.
Integration Parameters
This panel defines the initial and final times over which the time-dependent Schrödinger equation is numerically propagated.
This checkbox toggles the display of the exact numerical solution of the time-dependent Schrödinger equation together with the solution obtained using the rotating-wave approximation (RWA). The RWA is the approximation commonly used to derive the STIRAP equations, in which the rapidly oscillating terms of the laser-matter interaction are neglected while the near-resonant terms responsible for the population transfer are retained. Comparing the two solutions makes it possible to assess the validity of the RWA and identify the conditions under which it accurately describes the system dynamics.
Envelope and Pulse Functions
This plot displays both the envelopes and the corresponding electric fields of the Pump and Stokes laser pulses as functions of time. The envelopes define the temporal profiles of the pulses, while the oscillating fields represent the electromagnetic waves that drive the transitions between the quantum levels. Together, they illustrate the relative timing, duration, temporal overlap, and oscillatory behavior of the two control fields throughout the STIRAP sequence.
Angle
This plot shows the time evolution of the mixing angle, $\theta(t)=\arctan[\Omega_P(t)/\Omega_S(t)]$, which characterizes the relative strengths of the Pump and Stokes couplings. The gradual variation of this angle determines the adiabatic evolution of the quantum system and governs the transfer of population between the initial and target quantum levels while minimizing occupation of the intermediate level.
Energy-Level Diagram
This panel illustrates the three-level energy structure together with the Pump and Stokes laser couplings. The diagram provides a schematic representation of the optical transitions driven by the two laser fields and shows how the fields couple the quantum levels throughout the STIRAP process.
Populations
This plot displays the time-dependent populations of the quantum levels during the interaction with the Pump and Stokes pulses. It provides a direct visualization of the population transfer process, showing how the population evolves from the initial state to the target state while the occupation of the intermediate level remains strongly suppressed under adiabatic conditions.