Stimulated Raman adiabatic passage

In quantum optics, stimulated Raman adiabatic passage (STIRAP) is a process that permits transfer of a population between two applicable quantum states via at least two coherent electromagnetic (light) pulses.

[1][2] These light pulses drive the transitions of the three level Ʌ atom or multilevel system.

[3][4] The process is a form of state-to-state coherent control.

Consider the description of three level Ʌ atom having ground states

Suppose in the beginning the total population is in the ground state

Here the logic for transformation of the population from ground state

couple, afterward superposition of states

This process of transforming the population without populating the excited state is called the stimulated Raman adiabatic passage.

with the goal of transferring population initially in state

Allow the system to interact with two coherent radiation fields, the pump and Stokes fields.

Let the pump field couple only states

and the Stokes field couple only states

, for instance due to far-detuning or selection rules.

Denote the Rabi frequencies and detunings of the pump and Stokes couplings by

The energy ordering of the states is not critical, and here it is taken so that

Ʌ and V configurations can be realized by changing the signs of the detunings.

allows the Hamiltonian to be written in the more configuration independent form

denote the single and two-photon detunings respectively.

STIRAP is achieved on two-photon resonance

Focusing to this case, the energies upon diagonalization of

The first condition reveals that the critical two-photon resonance condition yields a dark state which is a superposition of only the initial and target state.

, the second condition can be used to express this dark state as

From this, the STIRAP counter-intuitive pulse sequence can be deduced.

which corresponds the presence of only the Stokes field (

case corresponds to the opposing limit of a strong pump field (

Practically, this corresponds to applying Stokes and pump field pulses to the system with a slight delay between while still maintaining significant temporal overlap between pulses; the delay provides the correct limiting behavior and the overlap ensures adiabatic evolution.

A population initially prepared in state

The pulse envelopes can take on fairly arbitrary shape so long as the time rate of change of the mixing angle is slow compared to the energy splitting with respect to the non-dark states.

This adiabatic condition takes its simplest form at the single-photon resonance condition

You can help Wikipedia by expanding it.This quantum mechanics-related article is a stub.