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Europhysics Letters (EPL)

Anisotropic nonlinear optics based on quantum interference

A. Kani, Harshawardhan Wanare

Published Nov 1, 2017• 2 citations
Publisher

Abstract

\n\nWeak coherent radiation interacting with multilevel atomic systems can excite a family of higher-order multiphoton transitions in contravention to conventional perturbative analysis. Monochromatic excitation leads to a strong anisotropic response arising from the interference of numerous underlying multiphoton pathways. The interference can be controlled through the polarization content of the input radiation. This anisotropic response is subnatural, quite unlike the anisotropy arising from spontaneous-emission–assisted optical pumping. Its sensitivity to external influences such as magnetic field suggests its utility in magnetometry. Specifically, we discover the presence of an elemental closed loop involving series of absorption and emission cycles that is central to the total response, and is universal to all atomic configurations. However, as not all atomic configurations support such anisotropy, we present a general classification of atomic transitions that exhibit anisotropic nonlinear response through quantum interference.\n

DOI
10.1209/0295-5075/120/33001

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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.

•Jan 1, 2008•0 citations
\n\nWeak coherent radiation interacting with multilevel atomic systems can excite a family of higher-order multiphoton transitions in contravention to conventional perturbative analysis. Monochromatic excitation leads to a strong anisotropic response arising from the interference of numerous underlying multiphoton pathways. The interference can be controlled through the polarization content of the input radiation. This anisotropic response is subnatural, quite unlike the anisotropy arising from spontaneous-emission–assisted optical pumping. Its sensitivity to external influences such as magnetic field suggests its utility in magnetometry. Specifically, we discover the presence of an elemental closed loop involving series of absorption and emission cycles that is central to the total response, and is universal to all atomic configurations. However, as not all atomic configurations support such anisotropy, we present a general classification of atomic transitions that exhibit anisotropic nonlinear response through quantum interference.\n
Atomic coherence effects arising from coherent light-atom interaction are conventionally known to be governed by quantum interference and optical pumping mechanisms. However, anisotropic nonlinear response driven by optical field involves another fundamental effect arising from closed-loop multiphoton transitions. This closed-loop phase dictates the tensorial structure of the nonlinear susceptibility as it governs the principal coordinate system in determining, whether the light field will either compete or cooperate with the external magnetic field stimulus. Such a treatment provides deeper understanding of all magneto-optical anisotropic response. The magneto-optical response in all atomic systems is classified using closed-loop phase. The role of quantum interference in obtaining electromagnetically induced transparency or electromagnetically induced absorption in multi-level systems is identified.
Suppression of photoionization, fluorescence, amplified spontaneous emission, and nonlinear optical conversion have all been reported in the presence of resonant multiphoton excitation.1 At first glance, the nonlinear phenomena manifesting this suppression and the order of the nonlinear processes appear to be quite distinct. In some cases, this suppression has been shown to result from a destructive interference (alternatively, a competition) between alternative excitation pathways to the resonant intermediate state.2
Quantum interference and coherence lead to many interesting phenomenon and applications in quantum optics. In this dissertation, we study the quantum coherent properties in the following systems and aspects. We first investigate the optical bistability in a combined cavity-cold atoms system. In such a system the atom-photon interaction provides an optical lattice to the atoms and affects the mechanical motion of the atoms while atoms induce a position dependent phase shift on the cavity field. This highly nonlinearity induces optical bistability of intra-cavity photon number with respect to the pumping light added along the cavity axis. We show that the presence of this bistability can be controlled by a second pumping field added perpendicular to the cavity axis. It is also found that the critical input intensity of switching from one branch of bistability to the other depends on the the way of the field being added. This behavior is similar to the anomalous switching of the dispersive optical bistability of atomic media in the cavity. We also study the effect of counter-rotating terms in the control of spontaneous emission. We make use of a unitary transformation method and investigate the effect of dynamic energy shifts on the spontaneous emission modification via quantum interference in a four-level atomic system. We show that the counter-rotating terms, which are normally neglected in the usual investigation of atomic systems, do produce a significant influence on the evolution of the atomic amplitudes and the emission spectrum. This effect of counter-rotating terms can be observed in the time scale of the decay rate even when the dipole moments of the two upper levels are orthogonal to each other. The effect of counter-rotating terms on the spontaneous emission in a 3-D anisotropic photonic crystal is also discussed. It is shown that the behavior of the emission is similar to the case making rotating wave approximation, i.e., the localized and propagating fields are also separated by two characteristic atomic transition frequencies. However, the two characteristic frequencies are shifted due to the full Lamb shift which is obtained with counter-rotating terms being included in the Hamiltonian. We also utilize the unitary transformation method to show how the Lamb shift in a multi-level atom can be controlled by a driving field. Finally, we propose a subwavelength atom localization scheme for an atom located in a standing-wave field. The strategy is based on the observation that the photon statistics of resonance fluorescence depends on the position-dependent Rabi frequency.
In recent years interest has significantly quickened in investigation of nonlinear optical and spectroscopic phenomena in such unique objects as Rydberg atoms (the atoms in the energy states near the ionization limit) and van der Waals complexes (dimers). These objects are characterized, in particular, by that their energy states are strongly degenerate due to a large value of angular (rotational) momentum. Here, the problem arises of adequate theoretical description of experimental results, especially when polarization peculiarities of nonlinear radiation processes are considered. The problem is caused by the existence of a huge number of quantum magnetic sublevels of energy states, which are, in the general case, coherently coupled to each other and take part in the radiation processes. Figure 1 gives a vivid presentation of the problem arising even in such a seemingly simple case when one need describe the radiation transitions caused by a strong monochromatic field between two energy levels with large values of the angular momentum J. If the field polarization is arbitrary, the whole set of the magnetic sublevels turn out to be coupled by radiative transitions. Formally, the problem becomes essentially multilevel. In this case not only the hope fades of solving it analytically using the traditional quantum-mechanical approach, but the problems of numerical solution grow abruptly with increasing quantum number J as well. On the other hand, as is often the case, every cloud has a silver lining. With large J we approach the situation when the rotational motion of particles can be described classically. It turns out that the transition from the quantum description of orientation states of the angular momentum to the classical one simplifies the problem radically: it reduces to the problem of radiation processes in the simplest model of nondegenerate states. In this case the rotational motion manifests itself in a dependence of the density matrix elements on orientation angles of the angular momentum as on a parameter.
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.