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arXiv:quant-ph/0407026

Inducing complete population oscillations in systems with externally induced dipole moments

Duje Bonacci

Published Jul 4, 2004• 0 citations
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Abstract

A two level system is considered which has no static dipole moment, e.g. molecule $H_2$ in its ground electronic state. If strong enough external field is applied, it will dynamically distort such a system and supply it with time (and field) dependent dipole moment. Although it is impossible to do so in the undistorted system which has no coupling to the dipole component of the external field, having induced in it a dipole moment, the rotational and vibrational dynamics of such system can be manipulated using lasers. In this work, a system is considered in which the external perturbation dynamically induces the transition dipole moment between only two distinct levels. The aim of the work is to show how the driving pulse can be analytically designed, that will produce Rabi-like complete population oscillations between the two levels.

DOI
10.48550/arxiv.quant-ph/0407026

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A two level system is considered which has no static dipole moment, e.g. molecule H2H_2H2​ in its ground electronic state. If strong enough external field is applied, it will dynamically distort such a system and supply it with time (and field) dependent dipole moment. Although it is impossible to do so in the undistorted system which has no coupling to the dipole component of the external field, having induced in it a dipole moment, the rotational and vibrational dynamics of such system can be manipulated using lasers. In this work, a system is considered in which the external perturbation dynamically induces the transition dipole moment between only two distinct levels. The aim of the work is to show how the driving pulse can be analytically designed, that will produce Rabi-like complete population oscillations between the two levels.
The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.
Rabi oscillations is a key phenomenon among the variety of quantum optical effects that manifests itself in the periodic oscillations of a two-level system between the ground and excited states when interacting with electromagnetic field. Commonly, the rate of these oscillations scales proportionally with the magnitude of the electric field probed by the two-level system. Here, we investigate the interaction of light with a two-level quantum emitter possessing permanent dipole moments. The semi-classical approach to this problem predicts slowing down and even full suppression of Rabi oscillations due to asymmetry in diagonal components of the dipole moment operator of the two-level system. We consider behavior of the system in the fully quantized picture and establish the analytical condition of Rabi oscillations collapse. These results for the first time emphasize the behavior of two-level systems with permanent dipole moments in the few photon regime, and suggest observation of novel quantum optical effects.
Linearized version of the Riccati-type differential equation for the ratio of population amplitudes in a laserdriven two-level system is used to calculate analytically the induced electric dipole moment.The formula found for the dipole moment is valid for weak excitations by smooth-shape pulses of arbitrary off-resonant frequencies, i.e., those producing neither exact one-photon nor odd multiphoton resonances.For a given pulse shape, the formula allows to express the Fourier components of the induced dipole moment as functions of both laser frequency and intensity and to find the field-dependent refractive index of the system versus laser frequency.
It is theoretically shown that the tunnelling dynamics of light between two sinusoidally curved coupled optical waveguides of different sizes exactly mimics the population dynamics of a two-level system with nonzero diagonal dipole matrix elements subjected to an applied sinusoidal electric field, thus realizing an optical analogue of a two-level dipolar molecule in an external ac field. Some characteristic dynamical features, including multi-photon transitions, sinusoidal population oscillations built up in a series of stair steps or square-wave population oscillations, are reproduced in the optical waveguide system. Design parameters for their observation are given with reference to lithium-niobate optical waveguides.
The spectral and dynamic effects associated with a non-zero difference, d, between the permanent dipole moments of two molecular states involved in a transition, are investigated for a variety of electromagnetic field-molecule interactions. Both analytical and exact numerical techniques are used to solve the time-dependent Schrodinger equation and to obtain the temporal populations of the molecular states and the associated absorption spectra, for molecular interactions with a Gaussian pulsed, or one or two continuous wave (CW), laser(s).;Analytical rotating wave approximation results are derived for a single CW laser interacting with a two-level d {dollar}\\ne{dollar} 0 molecule with an excited state lifetime, and for a two-level d {dollar}\\ne{dollar} 0 molecule interacting with two CW lasers. A symmetry-adapted Riemann product integral method for exact calculations of pulsed laser-molecule interactions is developed and applied to specific problems. The Floquet technique for the treatment of periodic Hamiltonians is extended to accommodate the interaction of a molecule with two CW lasers.;The one-field RWA results are used to predict and interpret the effects of permanent dipoles on the temporal behaviour of the molecular states for a decaying two-level system interacting with a CW laser, and for a non-decaying two-level system interacting with a pulsed laser. It is shown that the excited state lifetime and the pulse duration can act as internal and external probes, respectively, of the temporal effects of permanent dipoles, relative to the often-studied d = 0 problem. The two-field analytical RWA solutions are used to help discuss and predict the effects of permanent dipole moments in two-laser multi-photon transitions. Several examples of multi-photon, two-colour, two-level resonance profiles, calculated in the RWA and by using exact Floquet techniques, are used to demonstrate how particular multi-photon transitions can be optimized, and to help quantify the conditions for the validity of the two-colour RWA. The effects of neighbouring energy levels on the transition of interest, for both probe and pump-probe laser-molecule interactions, are investigated using a series of three- to seven-level model molecular systems.
State-selective preparation and manipulation of discrete-level quantum systems such as atoms, molecules, or quantum dots is the ultimate tool for many diverse fields such as laser control of chemical reactions, atom optics, high-precision metrology, and quantum computing. Rabi oscillations are one of the simplest, yet potentially quite useful mechanisms for achieving such manipulation. Rabi theory establishes that in the two-level systems resonant drive leads to the periodic and complete population oscillations between the two system levels. In this paper an analytic optimization algorithm for producing Rabi-like oscillations in the general discrete many-level quantum system is presented.