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Physical Review A

Numerical exploration of coherent excitation in three-level systems

H. A. Camp, M. H. Shah, M. L. Trachy, Oliver L. Weaver, Brett D DePaola

Published May 4, 2005• 11 citations
Publisher

Abstract

A great deal of effort has been applied to understanding population dynamics within a variety of coherent excitation schemes. The goal in such studies has been to understand the conditions necessary for efficient transfer of population from one state to another. While many theoretical treatments include the effects of natural lifetimes that are present in any given system, some neglect this important aspect when considering specific cases. Adiabatic approximations are also widely made. Additionally, it is often difficult to envision how the different parameters controlling efficient population transfer are interrelated or even which parameters are the most critical, especially when the decay lifetimes are taken into account. This work describes a numerical study of coherent excitation applied to a $^{87}\mathrm{Rb}$ ladder system where spontaneous decay rates are included, and adiabaticity is not assumed. A useful method is introduced to explore the interdependence of various excitation parameters. The efficiency of population transfer as a function of several experimentally controllable parameters is explored, and other general trends are summarized.

DOI
10.1103/physreva.71.053401

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A great deal of effort has been applied to understanding population dynamics within a variety of coherent excitation schemes. The goal in such studies has been to understand the conditions necessary for efficient transfer of population from one state to another. While many theoretical treatments include the effects of natural lifetimes that are present in any given system, some neglect this important aspect when considering specific cases. Adiabatic approximations are also widely made. Additionally, it is often difficult to envision how the different parameters controlling efficient population transfer are interrelated or even which parameters are the most critical, especially when the decay lifetimes are taken into account. This work describes a numerical study of coherent excitation applied to a 87Rb^{87}\mathrm{Rb}87Rb ladder system where spontaneous decay rates are included, and adiabaticity is not assumed. A useful method is introduced to explore the interdependence of various excitation parameters. The efficiency of population transfer as a function of several experimentally controllable parameters is explored, and other general trends are summarized.
This work explores the effect of spontaneous emission on coherence generation and population transfer in a three-level ladder atomic system driven by two pulses in counterintuitive order. With adiabatic evolution and the weak-dephasing approximation, we find that a large coherence and population transfer can be achieved even with spontaneous decay rate. The maximum coherence and population transfer decrease with the increase of spontaneous decay rate from the highest state to intermediate state. But this effect can be compensated by shortening the pulse width and enlarging the delay time. Results show that the coherence generation and population transfer never depend on the spontaneous decay rate from the intermediate state to ground state. The validity of the analytic solution is examined by numerical calculation.
It is possible to prepare atoms or molecules in a selected excited state, one efficient way is to transfer population by stimulated-Raman-adiabatic-passage, but must understand off-resonant effects in coherent excitation in order to improve the efficient of transfer. Here, consider the transfer of population in a three-level system of stimulated-Raman- adiabatic-passage with computer analysis. The transfer efficiency of two-photon resonant is worked out and the outcome demonstrates the possibility of complete transfer. Also analysis the effect of two-photon off-resonant, single-photon off-resonant and difference of laser's intension.
We present a detailed theory of a technique for the adiabatic control of the population flow through a preselected decaying excited level in a three-level ladder quantum system, as was experimentally demonstrated recently by Garcia-Fernandez et al. [Phys. Rev. Lett. 95, 043001 (2005)]. Specifically, we consider a three-state excitation chain of bound states, 1-2-3, of successively increasing excitation energy, in which probability loss via fluorescence occurs from states 2 and 3. We describe a laser excitation scheme that can, by adjustment of laser parameters, alter at will the relative fraction of population that, starting from state 1, is ultimately lost through states 2 and 3. We present analytical results for the conditions under which quasiadiabatic passage can take place.
High-fidelity fast and robust coherent population transfer is a major challenge in coherent quantum control. At present, all coherent population transfer approaches are based on a well-known adiabatic condition. In this work, we demonstrate that a more strict adiabatic condition can markedly improve the performance of the coherent population transfer approach. Based on this, we propose a coherent population transfer approach, which just needs only one control parameter and depends on the eigenvalues of the systems. Comparing to other approaches, we numerically demonstrate that our approach can provide a more robustness coherent population transfer without affecting the fidelity and speed. Moreover, this approach may be generalized to complex quantum systems where the exact expressions of eigenstates are difficult to obtain or the parameters of systems are difficult to simultaneously drive. In short, our idea provides a way to further improve the performance of coherent population transfer approaches.
We propose a new scheme for achieving the complete population transfer and the optimal coherence generation between the ground state and the Rydberg state in a four-level ladder system by combining the STIRAP or fractional STIRAP technique and the π pulse technique. We consider, in particular, two different situations where spontaneous emission from the two highest states are neglected or not. Our numerical calculations show that the time width and the delay time of the π pulse are two critical parameters for attaining the maximal population transfer and coherence generation in this scheme.
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.