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Physical Review A

Parity-time-antisymmetric atomic lattices without gain

Jin‐Hui Wu, M. Artoni, Giuseppe Carlo La Rocca

Published Mar 11, 2015• 77 citations
Publisher

Abstract

Lossy atomic photonic crystals can be suitably tailored so that the real and imaginary parts of the susceptibility are, respectively, an odd and an even function of position. Such a parity-time $(PT)$ space antisymmetry in the susceptibility requires neither optical gain nor negative refraction, but is rather attained by a combined control of the spatial modulation of both the atomic density and their dynamic level shift. These passive photonic crystals made of dressed atoms are characterized by a tunable unidirectional reflectionlessness accompanied by an appreciable degree of transmission. Interestingly, such peculiar properties are associated with non-Hermitian degeneracies of the crystal scattering matrix, which can then be directly observed through reflectivity measurements via a straightforward phase modulation of the atomic dynamic level shift and even off resonance.

DOI
10.1103/physreva.91.033811

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Lossy atomic photonic crystals can be suitably tailored so that the real and imaginary parts of the susceptibility are, respectively, an odd and an even function of position. Such a parity-time (PT)(PT)(PT) space antisymmetry in the susceptibility requires neither optical gain nor negative refraction, but is rather attained by a combined control of the spatial modulation of both the atomic density and their dynamic level shift. These passive photonic crystals made of dressed atoms are characterized by a tunable unidirectional reflectionlessness accompanied by an appreciable degree of transmission. Interestingly, such peculiar properties are associated with non-Hermitian degeneracies of the crystal scattering matrix, which can then be directly observed through reflectivity measurements via a straightforward phase modulation of the atomic dynamic level shift and even off resonance.
We study an ensemble of ultracold atoms trapped in the one-dimensional optical lattices under the N level configuration to examine the absorption and dispersion properties modulated into different ways along the lattice direction z. We find these trapped atoms with a Gaussian density distribution in each period may exhibit either symmetry χp(z)=χp*(-z) or antisymmetry χp(z)=-χp*(-z) of parity-time (PT) in terms of the probe susceptibility. Such intriguing twofold modulations of real (χ'p) and imaginary (χ″p) susceptibilities with a π/2 phase shift are attained by spatially modulating intensities or frequencies of one driving field in a suitable way. The PT-symmetric or PT-antisymmetric atomic lattices correspond in fact to complex photonic crystals and may be extended to develop functional devices like photonic diodes and transistors, a task impossible for real photonic crystals.
We experimentally demonstrate an anti-parity-time (anti-PTPTPT)-symmetric photonic lattice in thermal cesium atoms driven by two standing-wave laser fields. Such a lattice possesses anti-PTPTPT-symmetric susceptibility, of which the real (imaginary) part is an odd (even) function of position. By manipulating the intensities and phases of the two standing-wave fields, we experimentally observe unidirectional reflectionless propagation at the exceptional points. Our work provides a platform to study the scattering property of anti-PTPTPT-symmetric systems.
Two-dimensional (2D) optical lattices of driven cold atoms can provide a useful platform to construct 2D electromagnetically induced grating (EIG) with parity-time (PT) antisymmetry. This atomic grating is achieved by the spatial modulations of the atomic density and frequency detunings in the four-level double-Λ atomic system. Gain-assisted PT antisymmetry allows us to realize lop-sided Raman-Nath diffraction with high diffraction efficiency at the exception point. It is shown that the nontrivial phenomenon originates from non-Hermitian degeneracy of PT antisymmetry. Our scheme may provide the possibility for active all-optical control and conversion of the spatial beam in optics.
Abstract We propose a scheme for realizing exact parity-time ( P T ) antisymmetry of complex susceptibility in a wide range of probe detuning by considering a one-dimensional lattice of cold atoms driven into the simplest three-level Λ configuration. This is attained by modulating the intensity of a standing-wave coupling field with a proper phase shift to counteract the product of a single-photon detuning and a two-photon detuning. Such a dynamically controlled P T -antisymmetric lattice supports the integration of a few nontrivial scattering behaviors including unidirectional light reflectionless, asymmetric perfect absorption, and directional signal quenching. These behaviors, depending in particular on atomic densities and lattice lengths, facilitate the on-demand realization of unidirectional or bidirectional photon transport blockade.
Rb atomic system both experimentally and theoretically. Such an instantaneously reconfigurable anti-PT-symmetric photonic lattice is "written" by two one-dimensional coupling fields, which are arranged alternately along the x direction and can modulate the refractive index of the atomic vapor in a spatially periodical manner via controllable atomic coherence. By properly adjusting the relevant atomic parameters, the phase shift between two adjacent lattice channels occurs in the constructed non-Hermitian photonic system. Such a readily reconfigurable anti-PT-symmetric photonic lattice may open the door for demonstrating the discrete characteristics of the optical waves in periodic anti-PT-symmetric photonic systems.