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Physical Review A

Efficiency and robustness of coherent population transfer with intense, chirped laser pulses

Vladimir S. Malinovsky, Jeffrey L. Krause

Published Mar 20, 2001• 61 citations
Publisher

Abstract

We discuss electronic population transfer in diatomic molecules. By analyzing time-dependent wave packets on electronic potential-energy surfaces, we investigate the efficiency and robustness of population transfer with intense, chirped laser pulses. Recently, the magnitude of the population transfer was observed to have a remarkable dependence on the sign of the chirp [J. Cao, C. J. Bardeen, and K. R. Wilson, Phys. Rev. Lett. 80, 1406 (1998)]. In this work we explain the reason for this asymmetry, and show how the frequency detuning, intensity, and chirp rate affect the results. In particular, we demonstrate efficient, robust population transfer for both positive and negative chirps. A Landau-Zener model of multiple avoided crossings is invoked to model the results.

DOI
10.1103/physreva.63.043415

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•Dec 13, 2000•20 citations
We discuss electronic population transfer in diatomic molecules. By analyzing time-dependent wave packets on electronic potential-energy surfaces, we investigate the efficiency and robustness of population transfer with intense, chirped laser pulses. Recently, the magnitude of the population transfer was observed to have a remarkable dependence on the sign of the chirp [J. Cao, C. J. Bardeen, and K. R. Wilson, Phys. Rev. Lett. 80, 1406 (1998)]. In this work we explain the reason for this asymmetry, and show how the frequency detuning, intensity, and chirp rate affect the results. In particular, we demonstrate efficient, robust population transfer for both positive and negative chirps. A Landau-Zener model of multiple avoided crossings is invoked to model the results.
We have studied the intense chirped pulse excitation of a molecule coupled with a dissipative environment taking into account electronic coherence effects. We considered a two-state electronic system with relaxation treated as a diffusion on electronic potential energy surfaces. This relaxation model enables us to trace continuously the transition from a coherent population transfer to incoherent one. An inhomogeneously broadened system with frozen nuclear motion is invoked to model a purely coherent transfer. We show that the type of population transfer (coherent or incoherent) strongly depends on the pulse chirp, its sign, and the detunings of the exciting pulse carrier frequency with respect to the frequency of the Franck-Condon transition. For positive chirped pulses and moderate detunings, relaxation does not hinder a coherent population transfer. Moreover, under these conditions the relaxation favors more efficient population transfer with respect to the “coherent” system with frozen nuclear motion.
Adiabatic passage induced by chirped laser pulses in three-level $\ensuremath{\Lambda}$ systems is investigated. Two different strategies for efficient population transfer (equal and opposite sign of the chirp) are analyzed. The role of detuning, crucial for the attempt to reduce the population of the intermediate state, is demonstrated. The scheme of adiabatic passage by laser pulses with chirps of different sign is not symmetric with respect to the sign of the one-photon detuning. Blue detuning results in a smaller transient population of the intermediate state than does red detuning. The results are explained on the basis of dressed states. Numerical results for a fully off-resonant adiabatic passage scheme, based on two pulses with the same sign of the chirps, are also considered. The robustness of the schemes in terms of the Rabi frequency, chirp rate, detuning, and time delay of the pulses is explored.
We have developed a simple and physically clear picture of adiabatic rapid passage (ARP) in molecules in solution by careful examination of all the conditions needed for ARP. The relaxation effects were considered in the framework of the Landau-Zener model for random crossing of levels. The model enables us to include into consideration non-Markovian Gaussian-correlated noise. It explains all the numerical results obtained in the first paper of the series [B. D. Fainberg and V. A. Gorbunov, J. Chem. Phys. 117, 7222 (2002)], in particular, that for positive chirp pulse excitation relaxation favors more efficient population transfer with respect to the relaxation-free system with frozen nuclear motion. We also relate parameters of non-Markovian Gaussian-correlated noise with irreversible dephasing time of an optical transition by calculating the photon echo signal attenuation.
Using the concept of light-induced potentials introduced by Garraway and Suominen [Phys. Rev. Lett. 80, 932 (1998)], we study alternative schemes of adiabatic population transfer in a diatomic molecule from the lowest vibrational level of the ground electronic state to the lowest vibrational level of a third electronic state via allowed optical transitions from the ground and third electronic states to a second electronic state. Our chirped-pulse rapid adiabatic passage scheme is implemented with short-duration optical pulses, and can be understood in terms of ``road design engineering'' of the light-induced time-dependent adiabatic potential upon which the dynamics occurs. We explicitly show that complete adiabatic vibronic population transfer occurs using chirped picosecond-duration pulses in the sodium dimer example.
We study the dynamics of two-photon nonresonant electronic excitation of diatomic molecules driven by chirped pulses. While the majority of the experimental results address the role of the chirp for fixed pulse bandwidth, we analyze the possibility of selective excitation for fixed time, as a function of the pulse bandwidth, depending on the sign of the chirp. With strong picosecond pulses and positive chirp it is shown that the dynamics always prepare the molecule in the ground vibrational level of the excited electronic state. The robustness of the dynamics inherits the properties of an effective Landau–Zener crossing. For negative chirp the final state is very sensitive to the specific pulse bandwidth. The dynamics of the system follow a complex convoluted behavior, and the final state alternates between low vibrational levels of the excited electronic state and excited vibrational levels of the ground potential, which become increasingly more excited with increasing bandwidth. The final electronic populations follow a double-period oscillatory behavior. We present a model based on sequential independent crossings which correlates the long-oscillation period with changes in the final vibrational state selected. We show that the short-oscillation period is related with nonadiabatic effects that give rise to fast dynamic Rabi flipping between the electronic states, providing only information of the field–molecule effective coupling. Although the short-oscillation period partially masks the expected results of the final populations, we show that it is still possible to retrieve information from the long-oscillation period regarding the frequencies of the electronic potentials. In order to do so, or in order to control the outcome of the dynamics, it is necessary to perform experiments scanning very different pulse bandwidths, and we propose a possible experimental implementation. All the numerical results of the paper are calculated for a model of the Na2 dimer.
A coherent mechanism of robust population inversion in atomic and molecular systems by a chirped field is presented. It is demonstrated that a field of sufficiently high chirp rate imposes a certain relative phase between a ground and excited state wavefunction of a two-level system. The value of the relative phase angle is thus restricted to be negative and close to 0 or −pi-\\pi−pi for positive and negative chirp, respectively. This explains the unidirectionality of the population transfer from the ground to the excited state. In a molecular system composed of a ground and excited potential energy surface the symmetry between the action of a pulse with a large positive and negative chirp is broken. The same framwork of the coherent mechanism can explain the symmetry breaking and the population inversion due to a positive chirped field.