Stimulated Raman adiabatic passage

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.

Time evolution of state populations for counter-intuitive STIRAP pulse sequence demonstrating coherent transfer.

Population transfer in three level Ʌ atom

Consider the description of three level Ʌ atom having ground states and (for simplicity suppose that the energies of the ground states are the same) and excited state . 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.[5]

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 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 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

  1. Vitanov, Nikolay V.; Rangelov, Andon A.; Shore, Bruce W.; Bergmann, Klaas (2017). "Stimulated Raman adiabatic passage in physics, chemistry, and beyond". Reviews of Modern Physics. 89 (1): 015006. arXiv:1605.00224. Bibcode:2017RvMP...89a5006V. doi:10.1103/RevModPhys.89.015006. ISSN 0034-6861. S2CID 118612686.
  2. Bergmann, Klaas; Vitanov, Nikolay V.; Shore, Bruce W. (2015). "Perspective: Stimulated Raman adiabatic passage: The status after 25 years". The Journal of Chemical Physics. 142 (17): 170901. Bibcode:2015JChPh.142q0901B. doi:10.1063/1.4916903. ISSN 0021-9606. PMID 25956078.
  3. Unanyan, R.; Fleischhauer, M.; Shore, B.W.; Bergmann, K. (1998). "Robust creation and phase-sensitive probing of superposition states via stimulated Raman adiabatic passage (STIRAP) with degenerate dark states". Optics Communications. 155 (1–3): 144–154. Bibcode:1998OptCo.155..144U. doi:10.1016/S0030-4018(98)00358-7. ISSN 0030-4018.
  4. Schwager, Heike (2008). A quantum memory for light in nuclear spin of quantum dot (PDF). Max-Planck-Institute of Quantum Optics.
  5. Marte, P.; Zoller, P.; Hall, J. L. (1991). "Coherent atomic mirrors and beam splitters by adiabatic passage in multilevel systems". Physical Review A. 44 (7): R4118–R4121. Bibcode:1991PhRvA..44.4118M. doi:10.1103/PhysRevA.44.R4118. ISSN 1050-2947. PMID 9906446.


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