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Physical Review A

Adiabatic representation for the coherent dynamics ofN-level systems in intense laser fields

T. T. Nguyen‐Dang, S. Manoli, Hakima Abou‐Rachid

Published May 1, 1991• 15 citations
Publisher

Abstract

The exact adiabatic representation scheme of Nguyen-Dang [J. Chem. Phys. 90, 2657 (1989)] is applied to time evolution of the general laser-driven two- and three-level systems. It leads to exact formal results that do not assume a specific shape of the pulse and do not invoke the rotating-wave approximation (RWA). These results are a generalization of the corresponding RWA results because the former depend on an effective pulse area that varies with the detuning and involves a Rabi frequency modulated by a phase cphi(t). In addition, the exact adiabatic representation scheme is applied to N-level systems exhibiting various dynamic symmetries and, as in the previous cases, leads to results that do not invoke the RWA and depend on an effective pulse area. Time-reversal analysis on two- and three-level systems leads to quantization of the effective pulse area for time-symmetric pulses. This quantization leads to localized asymptotic population distributions.

DOI
10.1103/physreva.43.5012

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Acta Physica Sinica•Jan 1, 2025•0 citations
The exact adiabatic representation scheme of Nguyen-Dang [J. Chem. Phys. 90, 2657 (1989)] is applied to time evolution of the general laser-driven two- and three-level systems. It leads to exact formal results that do not assume a specific shape of the pulse and do not invoke the rotating-wave approximation (RWA). These results are a generalization of the corresponding RWA results because the former depend on an effective pulse area that varies with the detuning and involves a Rabi frequency modulated by a phase cphi(t). In addition, the exact adiabatic representation scheme is applied to N-level systems exhibiting various dynamic symmetries and, as in the previous cases, leads to results that do not invoke the RWA and depend on an effective pulse area. Time-reversal analysis on two- and three-level systems leads to quantization of the effective pulse area for time-symmetric pulses. This quantization leads to localized asymptotic population distributions.
We apply reverse engineering to design laser pulse shapes for controlling the time evolution of strong-field transitions under environmental effects. Our effective two-state representation of the full quantum system involves dynamic Stark shifts and multiphoton Rabi frequency. Furthermore, the environment is modeled with dephasing and dissipative terms. Solving the master equation of the two-level density matrix inversely for the field, we obtain quasianalytic laser pulse shapes that simultaneously drive the populations and relative phase according to user-defined quantum pathways. The validity of the proposed scheme is demonstrated with the example of the $3s\ensuremath{\rightarrow}\ensuremath{\rightarrow}4s$ two-photon transition of atomic sodium by solving the master equation of the multilevel system that incorporates effects beyond the adiabatic elimination and the rotating wave approximation. Due to the open character of the system, the proposed control is not always possible. We explore these situations and point out the conditions for creating steady states with large coherence.
We reconsider the problem of a two-level system interacting with a radiation field in order to study some new features suggested by the actual experimental conditions. Pulse shape and duration effects are included in the formalism and the counter-rotating terms are retained. The criterion of validity of the rotating wave approximation (RWA) for pulsed fields is investigated; generalizing results well known in RWA, we establish some new formal results, including non-RWA contributions to all orders and for any pulse shape. The analysis is then carried out for fluctuating fields, by developing a method based on the theory of multiplicative stochastic differential equations. For short pulses, the non-Markovian character of the stochastic field parameters is expected to affect the process and, for broadband fields, the RWA has to be checked ab initio. Thus, a formalism is proposed which allows the study of both features. A wide range of numerical calculations are presented, clarifying the role of both intensity fluctuations and spectrum bandwidth in the case of a chaotic field, as well as their interplay with the pulse features.
A formalism for calculating Berry phases for nonadiabatic systems containing an additional adiabatic time dependence is developed. This is then applied to a two-level atom in a strong resonant polarized laser, where the laser polarization provides the adiabatic parameter. It is found that, when the laser polarization is kept constant, judicious polarization choices allow one to eliminate either the rotating-wave or non-rotating-wave part of the interaction. Furthermore, the adiabatic Berry phasor obtained when the laser polarization is varied is found to be complex. This can be compared to the case of purely adiabatic time-reversal even systems, which can only have real Berry phasors.
A rotating-wave approximation (RWA) is developed to describe the interaction of a two-level system, which has permanent dipole moments, with two pulsed lasers. The RWA expressions for the time-dependent populations of the molecular states are applied to model laser-molecule interactions and tested by comparison with exact results. The results are used to discuss the pulsed-laser phase control of molecular excitation through the interplay of competing one- and two-photon resonances involving the effects of a nonzero difference d between the permanent dipoles of the two states involved in the transition; the competition vanishes if d=0.d=0.d=0.
It is shown that any pulse with a time-asymmetric envelope and a constant non-zero detuning excites a two-level quantum system with a probability of nearly one-half provided the pulse is very asymmetric, adiabatic in the slowly rising part of its envelope, sudden in the steep part and the peak Rabi frequency is much greater than the detuning. Three particular cases are considered analytically: the asymmetric hyperbolic-secant, the Bambini-Berman and the exponential pulse, which illustrate the general conclusions. The results are applied to a special three-level 'vee' system whose two transitions are driven by two asymmetric laser pulses of the same Rabi frequencies and the same detunings. Analysis shows that if such a system is prepared initially in its ground state, effective population depletion of this state can be achieved, the results being quite insensitive to variations in the Rabi frequency and the detuning.
Coherent population transfer in quantum systems is of fundamental importance in many fields such as atomic and molecular collision dynamics, and information processing for qubit systems. Stimulated Raman nonadiabatic passage technique, when implemented in an externally driven three-level system, provides an efficient approach for realizing accelerated population transfer while maintaining robust quantum coherence, with no need of rotating wave approximation. However, previous protocols employ multiple pulses and imply that Rabi frequencies have a few oscillations during dynamical evolution. In this work, under the condition of two-photon resonance, we use a gauge transformation method to inversely design a Λ-configuration three-level system that can be solved exactly. By using SU(3) transformation, we establish the relationship between Schrödinger representation and gauge representation, where the effective Hamiltonian is an Abelian operator. Subsequently, we construct the desired Hamiltonian and further investigate its dynamic behavior. The result shows that by imposing appropriate boundary conditions on the control parameters, high-fidelity population transfer can be achieved in ideal evolution. In addition, for the practical case with pulse truncation and intermediate state decay, the fidelities of specific models can reach about 99.996% and 99.983%, respectively. Compared with other existing nonadiabatic quantum control schemes, the present scheme has the distinctive advantages. We achieve the required quantum control by applying only a few sets of Stokes and pump pulses without introducing any additional microwave field. This method does not exhibit Rabi oscillations in the dynamic process, nor does it produce singularities in the pulse itself.