
Stimulated Raman adiabatic passage (STIRAP) is a process that permits transfer of a population between two applicable
quantum state
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
s via at least two coherent
electromagnetic (light) pulses.
These light pulses drive the transitions of the three level Ʌ
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, and ...
or multilevel system.
The process is a form of state-to-state
coherent control
Coherent control is a quantum mechanics-based method for controlling dynamic processes by light. The basic principle is to control quantum interference phenomena, typically by shaping the phase of laser pulses. The basic ideas have proliferated, f ...
.
Population transfer in three level Ʌ atom
Consider the description of three level Ʌ atom having
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
s
and
(for simplicity suppose that the energies of the ground states are the same) and
excited state
In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to a ...
. Suppose in the beginning the total population is in the ground state
. Here the logic for transformation of the population from ground state
to
is that initially the unpopulated states
and
couple, afterward superposition of states
and
couple to the state
. Thereby a state is formed that permits the transformation of the population into state
without populating the excited state
. This process of transforming the population without populating the excited state is called the stimulated
Raman adiabatic passage.
Three level theory
Consider states
,
and
with the goal of transferring population initially in state
to state
without populating state
. Allow the system to interact with two coherent radiation fields, the pump and Stokes fields. Let the pump field couple only states
and
and the Stokes field couple only states
and
, for instance due to far-detuning or
selection rules. Denote the
Rabi frequencies and
detunings of the pump and Stokes couplings by
and
. Setting the energy of state
to zero, the
rotating wave Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonian ...
is given by
The energy ordering of the states is not critical, and here it is taken so that
only for concreteness. Ʌ and V configurations can be realized by changing the signs of the detunings. Shifting the energy zero by
allows the Hamiltonian to be written in the more configuration independent form
Here
and
denote the single and two-photon detunings respectively. STIRAP is achieved on two-photon resonance
. Focusing to this case, the energies upon
diagonalization of
are given by
where
. Solving for the
eigenstate
, it is seen to obey the condition
The first condition reveals that the critical two-photon resonance condition yields a
dark state
In atomic physics, a dark state refers to a state of an atom or molecule that cannot absorb (or emit) photons. All atoms and molecules are described by quantum states; different states can have different energies and a system can make a transition ...
which is a superposition of only the initial and target state. By defining the mixing angle
and utilizing the normalization condition
, the second condition can be used to express this dark state as
From this, the STIRAP counter-intuitive pulse sequence can be deduced. At
which corresponds the presence of only the Stokes field (
), the dark state exactly corresponds to the initial state
. As the mixing angle is rotated from
to
, the dark state smoothly interpolates from purely state
to purely state
. The latter
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
will adiabatically follow the dark state and end up in state
without populating state
as desired. 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
where it can be expressed as
References
Quantum mechanics
Raman scattering
Raman spectroscopy
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