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Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of driven two-level systems with permanent dipole moments: an optical realization

Stefano Longhi

Published Apr 5, 2006• 12 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/39/8/016

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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.
We theoretically investigate the dipolar molecular system driven by monochromatic periodic, linear, parabolic, and sech2{\mathrm{sech}}^{2}sech2 forms external fields, respectively. The two-level Hamiltonian model with nonzero diagonal dipole matrix elements is adopted to describe the population dynamics of the driven dipolar molecule, and the corresponding exact solutions are presented in terms of the confluent Heun equations without the generalized rotating-wave approximation. The analytic solutions derived here are valid in the whole parameter space.
Solutions of the time-dependent Schrödinger equation, in the semi-classical electric dipole approximation, are developed for the interaction of a two-level system, possessing both transition and diagonal dipole matrix elements, with applied static and sinusoidal electric fields. Exact solutions can only be obtained subject to conditions involving the orientations and strengths of the applied fields. These, and perturbative extensions, are used to discuss some of the features of multi-photon processes that depend on the existence of non-zero diagonal dipole matrix elements. Some of the results apply, in the limit of vanishing permanent moments, to the atomic two-level problem.
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.
An optical analogue of two-photon Rabi oscillations, occurring in a three-level atomic or molecular system coherently driven by two detuned laser fields, is theoretically proposed and experimentally demonstrated using three evanescently coupled optical waveguides realized on an active glass substrate. The optical analogue stems from the formal analogy between spatial propagation of light waves in the three-waveguide structure and the coherent temporal evolution of populations in a three-level atomic medium driven by two laser fields under two-photon resonance. In our optical experiment, two-photon Rabi oscillations are thus visualized as a slow spatial oscillatory exchange of light power between the two outer waveguides of the structure with a small excitation of the central waveguide.
The photon quantum dynamics in a damped single-mode quantized cavity field coupled with a resonantly driven two-level system possessing nonzero permanent dipoles is investigated here. The interacting subsystems are very different frequencies (microwave and optical domains) and, in this highly dispersive regime, the emitter couples to the resonator mode via its diagonal dipole moments only. As a result, this interaction regime is responsible for the cavity multiphoton quantum dynamics and photon conversion from optical to terahertz ranges, for instance. Furthermore, enhanced terahertz photon correlations occur as well.
Bare-state population inversion is demonstrated in a two-level system with all dipole matrix elements nonzero. A laser field is resonantly driving the sample whereas a second weaker and lower frequency coherent field additionally pumps it near resonance with the dynamically-Stark-splitted states. Due to existence of differing permanent dipole moments in the excited and ground bare states, quantum coherences among the involved dressed-states are induced leading to inversion in the steady-state. Furthermore, large refractive indices are feasible as well as the determination of the diagonal matrix elements via the absorption or emission spectra. The results apply to available biomolecular, spin or asymmetric quantum dot systems.