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Optics Express

Dynamic symmetry-breaking in a simple quantum model of magneto-electric rectification, optical magnetization, and harmonic generation

A. A. Fisher, Elizabeth F. Cloos, W. M. Fisher, Stephen Colby Rand

Published Jan 31, 2014• 14 citations
Publisher

Abstract

The state mixings necessary to mediate three new optical nonlinearities are shown to arise simultaneously and automatically in a 2-level atom with an ℓ = 0 ground state and an ℓ = 1 excited state that undergoes a sequence of electric and magnetic dipole-allowed transitions. The treatment is based on an extension of dressed state theory that includes quantized electric and magnetic field interactions. Magneto-electric rectification, transverse magnetization, and second-harmonic generation are shown to constitute a family of nonlinear effects that can take place regardless of whether inversion is a symmetry of the initial unperturbed system or not. Interactions driven jointly by the optical electric and magnetic fields produce dynamic symmetry-breaking that accounts for the frequency, the intensity dependence, and the polarization of induced magnetization in prior experiments. This strong field quantum model explains not only how a driven 2-level system may develop nonlinear dipole moments that are forbidden between or within its stationary states, but it also broadens the class of materials suitable for optical energy conversion applications and magnetic field generation with light so as to include all transparent dielectrics.

DOI
10.1364/oe.22.002910

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The state mixings necessary to mediate three new optical nonlinearities are shown to arise simultaneously and automatically in a 2-level atom with an ℓ = 0 ground state and an ℓ = 1 excited state that undergoes a sequence of electric and magnetic dipole-allowed transitions. The treatment is based on an extension of dressed state theory that includes quantized electric and magnetic field interactions. Magneto-electric rectification, transverse magnetization, and second-harmonic generation are shown to constitute a family of nonlinear effects that can take place regardless of whether inversion is a symmetry of the initial unperturbed system or not. Interactions driven jointly by the optical electric and magnetic fields produce dynamic symmetry-breaking that accounts for the frequency, the intensity dependence, and the polarization of induced magnetization in prior experiments. This strong field quantum model explains not only how a driven 2-level system may develop nonlinear dipole moments that are forbidden between or within its stationary states, but it also broadens the class of materials suitable for optical energy conversion applications and magnetic field generation with light so as to include all transparent dielectrics.
Abstract : In the third and final year of research on magneto-electric conversion of optical energy to electricity, several major project objectives were achieved in the areas of theory and experiment. This was chiefly the result of a breakthrough in understanding the reported enhancement of magneto-electric scattering and switching to computer codes based on Matlab to improve both the speed of computations and the time required to acquire data. On the theoretical front, a dressed state approach was successfully developed to analyze optical magnetization. The introduction of Matlab software resulted in significant speedup. Computational timescales for large matrix diagonalizations went from days to hours. Applied to atomistic models, these computations of induced dipole moments revealed that the family of nonlinearities of interest in this work arise from dynamic symmetry-breaking by the optical magnetic field.
Laser-atom interactions create atomic coherence and large nonlinear atomic polarization.\nWe investigate resonant laser-atom interactions to generate large nonlinearities\nand control them using magneto-optical fields. Coherent control of high-order\nsusceptibilities and magneto-optical rotation are demonstrated. Experiments are supported\nby theoretical studies that effectively describe the observed phenomena.\nIt is shown that a new coherent field, with polarization orthogonal to a weak\nsignal field, can be parametrically generated via an all-resonant four-wave-mixing\nprocess. This is demonstrated in a double-ladder system having two intermediate\nstates between a ground and an excited state. It is shown that the parametricgeneration\nprocess can be coherently controlled by coupling lasers and magnetic fields.\nIt is theoretically established that the underlying physics is a resonant three-photon\nprocess with a wide domain of control parameters.\nElectromagnetically induced transparency (EIT), where absorption of a weak\nprobe is suppressed via quantum interference, is demonstrated in a usual three-level\nladder system. It is observed that in contrast with EIT in a usual ladder system,\naddition of a second channel helps to suppress the absorption of two weak probe\nfields in the double-ladder system. The resulting enhancement of transmission in two\ndifferent channels is due to gain caused by three-photon processes.\nCoherent control is strongly limited by coherence lifetime, which is the inverse of\nthe dephasing rate. A lambda-system, having two ground states coupled to a common\nexcited state by lasers, can generate a new eigen (dark)-state that is transparent to incoming fields and hence suppresses fluorescence. However, ground-state dephasing\nperturbs the dark state. A new method for measuring the ground-state dephasing\nrate from fluorescence signals is proposed and a proof-of-principle experiment demonstrated.\nWhile two laser fields in a lambda-system are resonant with their respective\ntransitions, the atomic polarizations are very sensitive to an applied magnetic field.\nThis effect can be used for optical magnetometry. The degree of sensitivity of the\nmagnetometer is determined by two competing parameters–atomic density and laser\nintensity. It is shown experimentally that the optimal sensitivity reaches saturation,\nwhich is contrary to the idea that sensitivity increases indefinitely with an increase\nin the above parameters.
Nonlinear crystals are typically used when interaction of different frequencies of light is requested. In classical optics these nonlinear phenomena are used for second-harmonic generation, sum-frequency generation, optical parametric amplification and many other effects. In quantum optics, dealing with optical interaction on the level of individual photons, the most prominent process is spontaneous parametric down-conversion (SPDC),1 where the crystal is pumped by intensive laser light and the crystal can mediate the splitting of a pump photon to a photon pair. The two generated photons are typically called signal and idler. Influence of magnetic field on these nonlinear processes was not thoroughly tested yet. This topic deserves intensive study both from theoretical and experimental point of view, because the magnetic field can decrease the symmetry of the nonlinear crystal and so it may allow to use new types of phase-matching conditions. We started to test the SPDC process in BBO crystals. Nonlinear magneto-optic tensor of this material is not known and we can hardly predict it. According to our first theoretical derivations the efficiency of the nonlinear processes has to oscillate when rotating the magnetic-field orientation.
The effects of a static electric field on the nonlinear optical rectification, second- and third-harmonic generation in a quantum well described by Morse potential are theoretically investigated. Analytical expressions for the optical coefficients due to intersubband optical transitions with an applied electric field are extracted from the compact-density matrix approach and iterative scheme. Numerical results presented for a typical GaAs quantum well reveal the feasibility of control of optical transitions between the size-quantized subbands. In addition, we have to emphasize the fact that the optical response of the system is remarkably sensitive to the electric field and structural range parameter.
We analyze second harmonic generation in sodium vapor in a transverse magnetic field induced by the two-photon resonant excitation of the 3S-3D transition. The phenomenon is explained by the rotation of the two-photon induced quadrupole moment in the magnetic field. The analysis explains well the saturation of the intensity and rotation of the polarization of the second harmonic radiation in the higher magnetic field ≳0.5{\gtrsim}0.5≳0.5 kG. The collisional decay rate of the coherence of the E1 forbidden transition has been measured as an application of this SHG.