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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Adiabatic passage methods in cooling trapped molecular ions

Constantinos Lazarou, Matthias Keller, B. M. Garraway

Published Apr 30, 2010• 0 citations
Publisher

Abstract

Different adiabatic passage methods are applied as part of a state mapping scheme in multilevel trapped systems. The aim is to achieve full population transfer from the rotational states of a trapped molecular ion to its translational states. Our analysis is based on numerical simulations with the master equation. We discuss how the resolved sideband condition, and spontaneous emission have an adverse effect on the efficiency for stimulated Raman adiabatic passage. Use of adiabatic rapid passage techniques, with two-photon Raman transitions results in higher efficiencies that can exceed 97%.

DOI
10.1117/12.853854

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Different adiabatic passage methods are applied as part of a state mapping scheme in multilevel trapped systems. The aim is to achieve full population transfer from the rotational states of a trapped molecular ion to its translational states. Our analysis is based on numerical simulations with the master equation. We discuss how the resolved sideband condition, and spontaneous emission have an adverse effect on the efficiency for stimulated Raman adiabatic passage. Use of adiabatic rapid passage techniques, with two-photon Raman transitions results in higher efficiencies that can exceed 97%.
In this work, we investigate the theory for three different unidirectional population-transfer schemes in trapped multilevel systems which can be utilized to cool molecular ions. The approach we use exploits the laser-induced coupling between the internal and motional degrees of freedom so that the internal state of a molecule can be mapped onto the motion of that molecule in an external trapping potential. By sympathetically cooling the translational motion back into its ground state, the mapping process can be employed as part of a cooling scheme for molecular rotational levels. This step is achieved through a common mode involving a laser-cooled atom trapped alongside the molecule. For the coherent mapping, we will focus on adiabatic passage techniques which may be expected to provide robust and efficient population transfers. By applying far-detuned chirped adiabatic rapid passage pulses, we are able to achieve an efficiency of better than 9898%98 for realistic parameters and including spontaneous emission. Even though our main focus is on cooling molecular states, the analysis of the different adiabatic methods has general features which can be applied to atomic systems.
We explore theoretically the rovibrational dynamics of stimulated Raman adiabatic passage (STIRAP) in molecular electronic states including both the rotational and the vibrational degrees of freedom, with the LiH molecule as an example. By using a pure rovibrational state as initial state, we find that, under the condition of two-photon resonance, an efficient rovibrational population transfer can be achieved via STIRAP in molecular electronic states and the desired target state can be selected by adjusting laser-pulse parameters. Besides the interested rovibrational states, however, some unwanted rovibrational states may affect population transfer process, especially while the two-photon detuning is taken into account. By inspecting the evolution process of wave packet, we can easily search these unwanted rovibrational states and study their influences. Moreover, the effect of rotational temperature on the population transfer process is discussed using thermal mixed state as initial state.
We review and compare recent experiments and theoretical models demonstrating complete population transfer to selected states in atoms and molecules using (1) Stimulated Raman Adiabatic Rapid Passage (STIRAP) with temporally delayed but partially overlapping time dependent fundamental and Stokes fields and (2) Chirped Adiabatic Passage (CHIRAP) using frequency chirped field with the frequency swept through the resonance frequency of transitions. The transfer efficiency in these processes is unity when the adiabatic criteria are satisfied. Alignment and orientation of the initial and terminals levels of the transitions can be obtained using these methods. The dynamics involve the atomic or molecular internal angular momentum states because the Rabi frequencies for the transitions depend on the magnetic quantum numbers of the states. Full wavefunction and density matrix (necessary when spontaneous emission of the excited states plays a role) calculations are presented and adiabatic-following wavefunction and density matrix descriptions are advanced to explain unexpected experimental results.
We demonstrate experimentally how the process of stimulated Raman adiabatic passage (STIRAP) can be utilized for efficient coherent internal state transfer in single trapped and laser-cooled 40 Ca + ions. The transfer from the D 3/2 to the D 5/2 state, is detected by a fluorescence measurement revealing the population not transferred to the D 5/2 state. A coherent population transfer efficiency at the level of 95% in a set-up allowing for the internal state detection of individual ions in a string has been obtained.
This work explores the effect of spontaneous emission on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The approach uses adiabatic elimination of weakly coupled density matrix elements in the Liouville equation, from which a very accurate analytic approximation is derived. The loss of population transfer efficiency is found to decrease exponentially with the factor ${\ensuremath{\Omega}}_{0}^{2}∕\ensuremath{\Gamma}$, where $\ensuremath{\Gamma}$ is the spontaneous emission rate and ${\ensuremath{\Omega}}_{0}$ is the peak Rabi frequency. The transfer efficiency increases with the pulse delay and reaches a steady value. For large pulse delay and large spontaneous emission rate STIRAP degenerates into optical pumping.