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Optics Express

Investigation of P T- and P T-antisymmetry in two dimensional (2D) optical lattices

Muqaddar Abbas, Aqiba Khurshid, Ibrar Hussain, Ziauddin Ziauddin

Published Feb 12, 2020• 24 citations
Publisher

Abstract

A collection of cold rubidium atoms in three-level configuration trapped in two dimensional (2D) optical lattices is revisited. The trapped atoms are considered in the Gaussian density distribution and we study the realization of P T -, non- P T -, and P T -antisymmetry in 2D optical lattices. Such a fascinating modulation is achieved by spatially modulating the intensity of the driving field. Interestingly, control over P T - to non- P T -symmetry and vice versa in 2D optical lattices is achieved via a single knob such as microwave field, probe field and relative phase of optical and microwave fields. In addition, control over P T -antisymmetry to non- P T -symmetry and vice versa is also achieved via relative phase. The coherent control of P T - non- P T - and P T -antisymmetry in optical susceptibility of 2D atomic lattices can be extended to 2D optical devices including modulators, detectors, and the 2D atomic lattices can also be extended to photonic transistors and diodes.

DOI
10.1364/oe.384073

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A collection of cold rubidium atoms in three-level configuration trapped in two dimensional (2D) optical lattices is revisited. The trapped atoms are considered in the Gaussian density distribution and we study the realization of P T -, non- P T -, and P T -antisymmetry in 2D optical lattices. Such a fascinating modulation is achieved by spatially modulating the intensity of the driving field. Interestingly, control over P T - to non- P T -symmetry and vice versa in 2D optical lattices is achieved via a single knob such as microwave field, probe field and relative phase of optical and microwave fields. In addition, control over P T -antisymmetry to non- P T -symmetry and vice versa is also achieved via relative phase. The coherent control of P T - non- P T - and P T -antisymmetry in optical susceptibility of 2D atomic lattices can be extended to 2D optical devices including modulators, detectors, and the 2D atomic lattices can also be extended to photonic transistors and diodes.
A collection of cold rubidium atoms in three-level configuration trapped in one dimensional (1D) optical lattice is revisited. The trapped atoms are considered in the Gaussian density distribution and study the realization of P T -, non- P T - and P T anti-symmetry in optical susceptibility in 1D atomic lattices in a periodic structure. Such a fascinating modulation is achieved by spatially modulating the intensity of the driving field. Interestingly, a nonreciprocal optical propagation phenomenon is investigated. In this system, we have introduced a microwave that couples to the two ground states, spatial modulation of the coupling field, and the atomic density with Gaussian distribution in practice. With a proper detuning and coupling field Rabi frequencies, we can find the condition of P T -symmetry along with field propagation direction, and the novel properties of transmission and reflections have been discussed. The large difference of field reflections from the two ends of the atomic lattice medium shows strong evidence that the nonreciprocal behavior can be greatly enhanced by increasing the spatial modulation amplitude.
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.
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 physical scheme to realize optical lattices that are symmetric under a combination of parity and time ( ) reversal. The -symmetric structures can be constructed with periodical gain and loss profiles in a coherently prepared four-level N-type atomic system under the effects of cross-Kerr nonlinearity and Doppler broadening. The atoms are considered in the Gaussian density distribution loaded into the dipole traps of one- and two-dimensional optical lattices. The spatial modulation of the probe field susceptibility is achieved by a proper combination of standing wave strong control fields. With proper detunings and coupling field Rabi frequencies, we find the conditions of achieving -symmetry in optical lattices of nonlinear atoms. We show that the -symmetry can be realized when the cross-Kerr nonlinearity is significantly enhanced, and further demonstrate that it survives the Doppler broadening. Our model is based on experimentally observable and effectively controllable scheme which may find potential applications in optical information processing.
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.
Abstract We have proposed two schemes to exhibit   -antisymmetry in a four-level N-type atomic system interacting with two strong driving fields and a weak probe field. For both the schemes, the required spatially modulated coherence rendering   -antisymmetry is achieved by employing a double-channel Gaussian beam for one driving field with a single channel for the other driving field in different field configurations. In each scheme, for equal and opposite detunings of the double-channel Gaussian beam,   -antisymmetry can be obtained in the spatial domain. Such a way of control is unique to this model. Using the present method, it is possible to obtain   -antisymmetry for both the homogeneously and inhomogeneously broadened atoms.