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The Journal of Chemical Physics

Coherence transfer in three-level systems: Controlled violation of adiabaticity and antiparallel double resonant irradiation

Vladimir L. Ermakov, Geoffrey Bodenhausen

Published Jul 1, 1995• 6 citations
Publisher

Abstract

It is shown by theory and experiment how coherent superpositions of quantum states in three-level systems can be manipulated by irradiating two connected transitions with two resonant fields with suitably shaped time-dependent amplitudes and phases. Three variants are discussed in detail; (i) adiabatic coherence transfer (ACT) between two transitions, which may be either allowed or forbidden; (ii) nonadiabatic transfer of coherence to a nonirradiated transition by controlled violation of adiabaticity (CVA); (iii) coherence transfer to a nonirradiated transition by antiparallel double resonant irradiation (APDRI). A geometrical representation of these experiments gives a clear physical picture of the phenomena and provides a tool for the development of new methods. The principles are illustrated experimentally by applications to magnetic resonance of deuterium (I=1) in anisotropic phase at high magnetic field, but could also be applied to three level-systems in nuclear quadrupole resonance, optics, and other areas of spectroscopy.

DOI
10.1063/1.469651

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It is shown by theory and experiment how coherent superpositions of quantum states in three-level systems can be manipulated by irradiating two connected transitions with two resonant fields with suitably shaped time-dependent amplitudes and phases. Three variants are discussed in detail; (i) adiabatic coherence transfer (ACT) between two transitions, which may be either allowed or forbidden; (ii) nonadiabatic transfer of coherence to a nonirradiated transition by controlled violation of adiabaticity (CVA); (iii) coherence transfer to a nonirradiated transition by antiparallel double resonant irradiation (APDRI). A geometrical representation of these experiments gives a clear physical picture of the phenomena and provides a tool for the development of new methods. The principles are illustrated experimentally by applications to magnetic resonance of deuterium (I=1) in anisotropic phase at high magnetic field, but could also be applied to three level-systems in nuclear quadrupole resonance, optics, and other areas of spectroscopy.
In this thesis, quantum coherent control of dynamic properties of double-dark-resonance atomic systems is pursued in detail. First we show our scheme for creating atomic coherent superposition states via the technique of stimulated Raman adiabatic passage in a Lambda-type four-level system. With the application of a control field, it is found that the presence of double dark states leads to two arbitrary coherent superposition states with equal amplitude but inverse relative phases, even though the condition of multiphoton resonance is not met. The suitable manipulation of the control field and detunings enables the proposed scheme to create any coherent superposition states one desired. Then, in the above mentioned double-dark-resonant system, a scheme for giant enhancement of the Kerr nonlinearity is put forward. Compared with that generated in a single-dark-resonance system, the Kerr nonlinearity can be enhanced by several orders of magnitude with vanishing linear absorption. We attribute this dramatic enhancement to the interaction of dark resonances. As another possible means for enhancement of Kerr nonlinearity, spontaneously generated coherence is proposed. Meanwhile, a theoretical investigation is carried out in a five-level tripod system for obtaining a high efficiency double-channel four-wave-mixing process. By manipulating the intensity of the two coupling fields, the conversion efficiency of four-wave-mixing can be controlled.
Abstract Double resonance, resonance Raman and resonance fluorescence are discussed in terms of a superposition of adiabatic states. The adiabatic states are the instantaneous eigenstates of a two‐level Hamiltonian which includes the interaction with a near‐resonant coherent pulse and which has been transformed by a unitary transformation so that its only time‐dependence is that of the field envelope of the pulse. Resonance Raman results from spontaneous transitions to a third, lower state from the adiabatic following state which reduces to the initial (lower) state of the two‐level system in the absence of radiation. Resonance fluorescence is produced by spontaneous transition to the lower third state from the upper adiabatic state which reduces to the upper state of the two‐level system in the absence of radiation. Differential equations allowing the calculation of the probability amplitudes of the adiabatic states are given and a method of solving these equations by successive approximation is proposed. Saturation effects such as dynamic Stark shift and splitting (Autler—Townes effect) and optical nutation are interpreted in terms of perturbation of adiabatic energy levels and interference effects between adiabatic states. The possibility of observing optical nutation in a two‐level system by using time‐resolved double resonance experiments is suggested. Decay of the states of the two‐level system is taken into account leading to extended adiabaticity conditions which show that adiabatic following becomes possible even at resonance. For weak fields it is shown that adiabatic following at resonance can produce light scattering narrower than the linewidth as predicted by Heitler. The adiabatic states theory has also been extended to near‐resonance multiphoton interaction for systems that can be described by an effective two‐level Hamiltonian.
A new scheme is suggested to manipulate the probe transitions (and hence the optical properties of atomic vapors) via double-control destructive and constructive quantum interferences. The influence of phase coherence between the two control transitions on the probe transition is also studied. The most remarkable feature of the present scheme is that the optical properties (absorption, transparency and dispersion) of an atomic system can be manipulated using this double-control multi-pathway interferences (multiple routes to excitation). It is also shown that a four-level system will exhibit a two-level resonant absorption because the two control levels (driven by the two control fields) form a dark state (and hence a destructive quantum interference occurs between the two control transitions). However, the present four-level system will exhibit electromagnetically induced transparency to the probe field when the three lower levels (including the probe level and the two control levels) form a three-level dark state. The present scenario has potential applications in new devices (e.g. logic gates and sensitive optical switches) and new techniques (e.g. quantum coherent information storage).
The main goal of this PhD work is an experimental study of coherent excitation of atomic and molecular wavepackets, i.e. superpositions of many quantum eigenstates, by shaped femtosecond pulses. Approaches allowing nearly complete population transfer between quantum eigenstates were well studied in the past within the two level approximation. In this work we focus on adiabatic and non-adiabatic methods of population transfer beyond the two-level approximation. Excitation of multi-level target states is possible due to broad spectrum of an ultrashort pulse which contains frequencies needed for multiple transitions to different states in the final superposition. At the same time, the spectrum of an ultrashort pulse can be modified, or ``shaped'', in order to affect the excitation process and control the amplitudes in the final superposition. Both non-adiabatic and quasi-adiabatic methods were first implemented and studied in electronic wavepackets in alkali atoms. The non-adiabatic approach revealed features linked to the strong-field perturbations of the energy level structure of the quantum system. An adiabatic method was implemented for the first time on a femtosecond time scale, and was thoroughly characterized. The control over complex amplitudes in the target superposition was demonstrated as well as completeness of the population transfer. In the second part of this work, we focused on coherent control of rotational wavepackets in diatomic molecules. Rotational excitation by a periodic train of femtosecond pulses was investigated in the context of ``delta-kicked'' rotor - a paradigm system for studying quantum chaos, and the effect of quantum resonance was demonstrated for the first time in a system of true quantum rotors. Control of uni-directional molecular rotation was proposed and demonstrated with a novel ``chiral pulse train'' - a sequence of femtosecond pulses with polarization rotating from pulse to pulse by a predefined angle. All the developed techniques offer new tools in coherent control of atomic and molecular wavepackets on an ultrashort time scale.
Atomic mirrors and beam splitters based on adiabatic following by delayed laser pulses in a three-level Raman configuration are analyzed. We show that in a pure three-level system of two ground states and one excited state, laser pulses tuned precisely on resonance with the excited state do not produce any accumulated phase shifts due to ac Stark shifts even if the process is nonadiabatic. A numerical simulation suggests that multiple delayed laser pulses are attractive for precision interferometry since high transfer efficiencies (up to 98.7% per pulse for the cesium D1 line) and low ac Stark shifts are expected. A possible application to optical two-photon spectroscopy for an optical clock is discussed.
The controlled transfer of nuclear state population using two x-ray laser pulses is investigated theoretically. The laser pulses drive two nuclear transitions in a nuclear three-level system facilitating coherent population transfer via the quantum optics technique of stimulated Raman adiabatic passage. To overcome present limitations of the x-ray laser frequency, we envisage accelerated nuclei interacting with two copropagating or crossed x-ray laser pulses in a three-beam setup. We present a systematic study of this setup providing both pulse temporal sequence and laser pulse intensity for optimized control of the nuclear state population. The tolerance for geometrical parameters such as laser beam divergence of the three-beam setup as well as for the velocity spread of the nuclear beam are studied and a two-photon resonance condition to account for experimental uncertainties is deduced. This additional condition gives a less strict requirement for the experimental implementation of the three-beam setup. Present experimental state of the art and future prospects are discussed.