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Physical Review A

Laser-driven population transfer in four-level atoms: Consequences of non-Abelian geometrical adiabatic phase factors

Razmik G. Unanyan, Bruce W. Shore, Klaas Bergmann

Published Apr 1, 1999• 228 citations
Publisher

Abstract

We analyze the influence of three pulsed laser fields interacting with a four-state atomic system for which there occur two degenerate population-trapping dressed states. We present a simple expression for the geometrical phase acquired by such an atom during a stimulated Raman adiabatic passage (STIRAP) process using a delay between Stokes and pump pulses, during which the two Rabi frequencies adiabatically traverse a closed path in the parameter space. We describe techniques that can produce (geometrical) state-vector phases that are independent of the longitudial velocity with which atoms move across a laser beam, and that are insensitive to radiative decay from the intermediate excited state. The geometrical phase can be changed by changing the relative delay of the pulses. The geometrical phase can be measured by observing the population in atomic states. We show that when the pump and Stokes pulses are properly timed, high population transfer from the initial state to the target state is achieved. In the adiabatic limit the robustness of the population transfer is equivalent to that of STIRAP.

DOI
10.1103/physreva.59.2910

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We analyze the influence of three pulsed laser fields interacting with a four-state atomic system for which there occur two degenerate population-trapping dressed states. We present a simple expression for the geometrical phase acquired by such an atom during a stimulated Raman adiabatic passage (STIRAP) process using a delay between Stokes and pump pulses, during which the two Rabi frequencies adiabatically traverse a closed path in the parameter space. We describe techniques that can produce (geometrical) state-vector phases that are independent of the longitudial velocity with which atoms move across a laser beam, and that are insensitive to radiative decay from the intermediate excited state. The geometrical phase can be changed by changing the relative delay of the pulses. The geometrical phase can be measured by observing the population in atomic states. We show that when the pump and Stokes pulses are properly timed, high population transfer from the initial state to the target state is achieved. In the adiabatic limit the robustness of the population transfer is equivalent to that of STIRAP.
The manipulation of population transfer and the creation of an arbitrary superposition between two atomic states in the framework of a closed inverse Y-type four-level system driven by a series of pulse pairs and an external control field is reported. It is shown that when the laser fields are tuned to resonance with respective transitions, the non-adiabatic coupling between two degenerate adiabatic states can be reduced tremendously and complete population transfer from the initial state to the target state can be achieved in a piecewise manner. Moreover, an arbitrary superposition between the initial state and target state can be created by suitably tuning the Rabi frequency of the control laser field, inter-pair time delay, pulse number or intra-pair time delay between the pump and Stokes pulses. This scheme combines stimulated Raman adiabatic passage and temporal coherent control, and may be useful for quantum information processing and control of chemical reactions.
Stimulated Raman scattering involving adiabatic passage (STIRAP) is a proven technique for population transfer in three-level systems with strong oscillator strengths. We show that the STIRAP process should also yield high transfer efficiencies when the densities of states near the intermediate and final levels are high, provided certain criteria for the experimentally controllable parameters are met. We also show that high transfer efficiencies may even be possible when the pump and Stokes lasers can access levels outside of the three-level system. The criteria are derived with an approach that emphasizes the adiabatic nature of the transfer process in an eigenvector of the interaction Hamiltonian that resembles a trapped state. The results are compared to density matrix calculations.
Abstract The population transfer of a NaH molecule from the ground state X 1 Σ + to the target state A 1 Σ + via stimulated Raman adiabatic passage (STIRAP) is investigated. The results show that the intensity, delay time and detuning have a significant effect on population transfer. A large population transfer is observed with increased pump and Stokes intensity, especially when the pump and Stokes intensity match. Population transfer also depends on the delay time between the pump laser pulse and the Stokes laser pulse. The detuning of the two pulses influences the population transfer. Efficient population transfer can be realized under the resonant or two-photon resonant condition.
Ongoing work aimed at developing highly efficient methods of populating a chosen sublevel of an energy level highlights the need to understand off-resonant effects in coherent excitation. This motivated us to re-examine some aspects of the theory of coherent excitation in a three-state system with a view to obtaining algebraic expressions for off-resonant eigenvalues and eigenvectors. Earlier work gives simple closed-form expressions for the eigenvalues this system, expressions applying even when the system is not on two-photon resonance. We present here expressions of similar simplicity for the components of the normalised eigenvectors. The analytic properties of these components explain the observed sensitivity of the stimulated-Raman-adiabatic-passage process (STIRAP) to the condition of two-photon resonance. None of the eigenstates is ‘trapped’ or ‘dark’ unless the system is on two-photon resonance; off resonance, all states have nonzero projections on the unperturbed intermediate state. A simple argument shows that no dressed state can be adiabatically connected to both the unperturbed initial and final states when the system is off two-photon resonance. That is, adiabatic transfer from initial to final state requires that these be degenerate before and after the STIRAP pulse sequence, and this implies zero two-photon detuning. However, substantial transfer probabilities are observed experimentally for very small two-photon detunings. We show that such systems are characterised by very sharp avoided crossings of two eigenvalues, and that the observed population transfer can be understood as an effect of non adiabatic transitions occurring at the avoided crossings.
The effect of the collisions on the control of coherent population transfer in a closed inverse YYY-type four-level system driven by three laser fields is investigated with the stimulated Raman adiabatic passage technique. An arbitrary coherent superposition between the initial state and target state can be created either by varying the Rabi frequency of the control laser field or by tuning the one-photon detunings of the pump and Stokes laser fields. When the three laser fields with nearly equal peak Rabi frequencies are each tuned to resonance with the respective transitions, the low transfer efficiency due to the nonadiabatic coupling between two degenerate adiabatic states could be enhanced dramatically with the increase of the collision-induced coherence decay rates to the value nearly comparable to the Rabi frequency of the control field. The enhanced transfer efficiency results from the collision-controlled electromagnetically induced transparency in the $\ensuremath{\Lambda}$-type three-level subsystem and electromagnetically induced absorption in the ladder-type three-level subsystem of the four-level system.
We present experimental demonstrations of a technique, based on multistate variants of the stimulated Raman adiabatic passage (STIRAP) process, that allows efficient and robust preparation of a preselected superposition of two or three degenerate states (magnetic sublevels of an atom) and the measurement of their relative amplitudes and phases. The experiments verify theoretical results described in the preceding paper. We perform our experiments with neon atoms in a supersonic beam: atoms in the metastable 3P0^{3}{P}_{0}3P0​ state are transferred to a superposition of the metastable 3P2^{3}{P}_{2}3P2​ magnetic sublevels, using four different linkage patterns. Because the preparation utilizes adiabatic passage, it is robust against small fluctuations of the Rabi frequencies and temporal shape of the coupling fields. The relative phases and the amplitude ratios of the components of the prepared superpositions are experimentally analyzed using a technique termed phase-to-population mapping. Phase-to-population mapping is based on laser-induced fluorescence after the atoms have undergone optical pumping cycles induced by an additional laser. The optical pumping process maps the superposition phases into populations of a subset of levels by means of a filtering laser field, and is robust against variations in the intensity and detuning of that field.