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Physical Review Letters

Nanoscale Stratification of Local Optical Fields in Low-Dimensional Atomic Lattices

A. E. Kaplan, S. N. Volkov

Published Sep 25, 2008• 18 citations
Publisher

Abstract

We predict nanoscale field and dipole patterns due to the broken uniformity of a laser-driven local field in 1D and 2D lattices. They may result in size-related resonances and large field enhancement, which in turn can give rise to low-intensity nonlinear optical effects, e.g., optical bistability, even in the ultimate case of a pair of coupled atoms. At certain, "magic" numbers and configurations of atoms in a lattice, the system may exhibit the self-induced cancellation of the suppression of a local field.

DOI
10.1103/physrevlett.101.133902

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Nanoscale Stratification of Local Field and Related Effects of Giant Resonances, “Magic Numbers” and Hystereses

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We predict nanoscale local-field patterns in self-interacting 1D and 2D lattices of two-level atoms. They result in giant size-related resonances, low-intensity optical bistability, and self-induced cancellation of resonant local-field suppression.

Frontiers in Optics•Jan 1, 2008•0 citations

Nano-stratification of local field and atomic bistability in low-dimensional structures

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Nano-scale strata due to broken uniformity of local field in strongly self-interacting low-dimensional structures are predicted. They result in giant field resonances and atomic optical bistability, including ultimate case of two coupled atoms.

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Nanoscale stratification of optical excitation in self-interacting one-dimensional arrays

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The major assumption of the Lorentz-Lorenz theory about uniformity of local fields and atomic polarization in dense material does not hold in finite groups of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett. 101, 133902 (2008)]. The uniformity is broken at subwavelength scale, where the system may exhibit strong stratification of local field and dipole polarization, with the strata period being much shorter than the incident wavelength. In this paper, we further develop and advance that theory for the most fundamental case of one-dimensional arrays, and study nanoscale excitation of so-called ``locsitons'' (local field excitations) and their standing waves (strata) that result in size-related resonances and related large field enhancement in finite arrays of atoms. The locsitons may have a whole spectrum of spatial frequencies, ranging from long waves, to an extent reminiscent of ferromagnetic domains, to supershort waves, with neighboring atoms alternating their polarizations, which are reminiscent of antiferromagnetic spin patterns. Of great interest is the different kind of ``hybrid'' mode of excitation, greatly departing from any magnetic analogies. We also study differences between Ising-type near-neighbor approximation and the case where each atom interacts with all other atoms in the array. We find an infinite number of ``exponential eigenmodes'' in the lossless system in the latter case. At certain ``magic'' numbers of atoms in the array, the system may exhibit self-induced (but linear in the field) cancellation of resonant local-field suppression. We also studied nonlinear modes of locsitons and found optical bistability and hysteresis in an infinite array for the simplest modes.

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Local field effects on the spatiotemporal dynamics of broad-area three-level lasers

J. Mompart, V. Ahufinger, R. Corbalán +3 more

Summary form only given. It is well known that in dense media the effective field acting on an atom/molecule is no longer the macroscopic field but the so-called local field, which is due to all external sources and to all dipole moments of the atoms/molecules within the sample except the one under consideration. The inclusion of the local field effects gives rise to the prediction of a large number of interesting phenomena in optical systems, such as spectral red shifts, mirrorless optical bistability, "piezophotonic" effects, and enhancement of inversionless gain and absorptionless index in lasing without inversion. As an example, a density of 10/sup 17/ atoms/cm/sup 3/ of sodium atoms is sufficient to give rise to a shift of about 1 GHz of the sodium D line. We analyze here the role of the local field effects on the spatiotemporal dynamics of broad-area homogeneously broadened three-level lasers. In these three-level systems, laser emission in one atomic transition is investigated while an external plane-wave driving laser couples an adjacent transition. Due to the interplay between atomic nonlinearities and light diffraction, the optical wavevector of the generated laser field develops a small component in the transverse plane, i.e., the emitted laser beam is slightly tilted with respect to the cavity-axis.

Conference on Lasers and Electro-Optics•Aug 29, 2005•0 citations
We predict nanoscale field and dipole patterns due to the broken uniformity of a laser-driven local field in 1D and 2D lattices. They may result in size-related resonances and large field enhancement, which in turn can give rise to low-intensity nonlinear optical effects, e.g., optical bistability, even in the ultimate case of a pair of coupled atoms. At certain, "magic" numbers and configurations of atoms in a lattice, the system may exhibit the self-induced cancellation of the suppression of a local field.
The major assumption of the Lorentz-Lorenz theory about uniformity of local fields and atomic polarization in dense material does not hold in finite groups of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett. 101, 133902 (2008)]. The uniformity is broken at subwavelength scale, where the system may exhibit strong stratification of local field and dipole polarization, with the strata period being much shorter than the incident wavelength. In this paper, we further develop and advance that theory for the most fundamental case of one-dimensional arrays, and study nanoscale excitation of so-called ``locsitons'' (local field excitations) and their standing waves (strata) that result in size-related resonances and related large field enhancement in finite arrays of atoms. The locsitons may have a whole spectrum of spatial frequencies, ranging from long waves, to an extent reminiscent of ferromagnetic domains, to supershort waves, with neighboring atoms alternating their polarizations, which are reminiscent of antiferromagnetic spin patterns. Of great interest is the different kind of ``hybrid'' mode of excitation, greatly departing from any magnetic analogies. We also study differences between Ising-type near-neighbor approximation and the case where each atom interacts with all other atoms in the array. We find an infinite number of ``exponential eigenmodes'' in the lossless system in the latter case. At certain ``magic'' numbers of atoms in the array, the system may exhibit self-induced (but linear in the field) cancellation of resonant local-field suppression. We also studied nonlinear modes of locsitons and found optical bistability and hysteresis in an infinite array for the simplest modes.
We study excitations of the local field (locsitons) in nanoscale two-dimensional (2D) lattices of strongly interacting resonant atoms and various unusual effects associated with them. Locsitons in low-dimensional systems and the resulting spatial strata and more complex patterns on a scale of just a few atoms were predicted by us earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett. 101, 133902 (2008)]. These effects present a radical departure from the classical Lorentz-Lorenz theory of the local field (LF), which assumes that the LF is virtually uniform on this scale. We demonstrate that the strata and patterns in the 2D lattices may be described as an interference of plane-wave locsitons, build an analytic model for such unbounded locsitons, and derive and analyze dispersion relations for the locsitons in an equilateral triangular lattice. We draw useful analogies between 1D and 2D locsitons but also show that the 2D case enables locsitons with the most diverse and unusual properties. Using the nearest-neighbor approximation, we find the locsiton frequency band for different mutual orientations of the lattice and the incident field. We demonstrate a formation of distinct vector locsiton patterns consisting of multiple vortices in the LF distribution and suggest a way to design finite 2D lattices that exhibit such patterns at certain frequencies. We illustrate the role of lattice defects in supporting localized locsitons and also demonstrate the existence of ``magic shapes,'' for which the LF suppression at the exact atomic resonance is canceled.
There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here we show theoretically that sub-Doppler-cooled two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonance saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all regimes of atomic bunching and simultaneously accounts for the backaction of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only limited regimes of atomic bunching. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices.
Summary form only given. It is well known that in dense media the effective field acting on an atom/molecule is no longer the macroscopic field but the so-called local field, which is due to all external sources and to all dipole moments of the atoms/molecules within the sample except the one under consideration. The inclusion of the local field effects gives rise to the prediction of a large number of interesting phenomena in optical systems, such as spectral red shifts, mirrorless optical bistability, "piezophotonic" effects, and enhancement of inversionless gain and absorptionless index in lasing without inversion. As an example, a density of 10/sup 17/ atoms/cm/sup 3/ of sodium atoms is sufficient to give rise to a shift of about 1 GHz of the sodium D line. We analyze here the role of the local field effects on the spatiotemporal dynamics of broad-area homogeneously broadened three-level lasers. In these three-level systems, laser emission in one atomic transition is investigated while an external plane-wave driving laser couples an adjacent transition. Due to the interplay between atomic nonlinearities and light diffraction, the optical wavevector of the generated laser field develops a small component in the transverse plane, i.e., the emitted laser beam is slightly tilted with respect to the cavity-axis.