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Optics Express

Three-color reflections in one-dimensional ordered and disordered atomic lattices with trapped N-type cold atoms

Maohua Wang, Tianming Li, Yan Zhang, Xiaoshan Pei, Hong Wei Yang

Published Aug 30, 2022• 1 citation
Publisher

Abstract

Investigating and controlling light propagation in one-dimensional (1D) ordered and disordered atomic lattices is critical both fundamentally and for applications. In this study, cold atoms are trapped in 1D optical lattice and driven to the four-level N configuration. In each period, the atoms exhibit a Gaussian density distribution with the average atomic density N 0 (1 + Δ k ). When the random number Δ k = 0 (the atomic density N k ( z )) corresponding to an ordered 1D atomic lattice, there are three reflection regions of high reflectivity located in two EIT windows and one large detuning range. However, the atomic density may increase ( N k + ( z ) with Δ k > 0) or decrease ( N k − ( z ) with Δ k < 0) owing to the imperfect manufacturing process or random distribution of atoms corresponding to a disordered atomic lattice. The results show that the width and height of reflections can be raised (reduced) by the increased (decreased) ratio of N k + ( z ) / N k ( z ) ( N k − ( z ) / N k ( z ) ) with the random distribution of lattice cells with N k + ( z ) ( N k − ( z ) ). When a cluster of disordered lattice cells with N k + ( z ) and N k − ( z )

DOI
10.1364/oe.463767

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Investigating and controlling light propagation in one-dimensional (1D) ordered and disordered atomic lattices is critical both fundamentally and for applications. In this study, cold atoms are trapped in 1D optical lattice and driven to the four-level N configuration. In each period, the atoms exhibit a Gaussian density distribution with the average atomic density N 0 (1 + Δ k ). When the random number Δ k = 0 (the atomic density N k ( z )) corresponding to an ordered 1D atomic lattice, there are three reflection regions of high reflectivity located in two EIT windows and one large detuning range. However, the atomic density may increase ( N k + ( z ) with Δ k > 0) or decrease ( N k − ( z ) with Δ k < 0) owing to the imperfect manufacturing process or random distribution of atoms corresponding to a disordered atomic lattice. The results show that the width and height of reflections can be raised (reduced) by the increased (decreased) ratio of N k + ( z ) / N k ( z ) ( N k − ( z ) / N k ( z ) ) with the random distribution of lattice cells with N k + ( z ) ( N k − ( z ) ). When a cluster of disordered lattice cells with N k + ( z ) and N k − ( z )
We extend a recent theoretical work [ Phys. Rev. A 101 , 053856 ( 2020 ) 10.1103/PhysRevA.101.053856 ] by replacing disorders characterized by varied atomic densities with defects characterized by vacant lattice cells to evaluate again three-color reflection in a one-dimensional optical lattice filled with cold 87Rb atoms. This is based on the consideration that trapped atoms may escape from some lattice cells and effects of vacant cells on light propagation are of major importance from both fundamental and applied research viewpoints. We consider two types of defective atomic lattices where vacant cells are randomly or continuously distributed among filled cells. Numerical results show that the wider reflection band in a large detuning region of negligible off-resonance absorption is quite sensitive to, while the narrower reflection bands in two near-resonant regions of electromagnetically induced transparency are rather robust against, the number of random vacant cells. In contrast, all three reflection bands exhibit strong robustness against the number of continuous vacant cells. Note, however, that both narrower reflection bands may become widened and exhibit a blue shift when continuous vacant cells appear in the front of our atomic lattice due to the joint contributions of Bragg scattering and quantum interference.
We investigate a four-level tripod atomic sample trapped, respectively, in a one-dimensional order and disorder (atom number fluctuation) optical lattice to achieve the tunable and robust three-color reflections in the regimes of zero absorption. Based on electromagnetically induced transparency (EIT) and the periodic modulation of the atom number density, there are three reflection regions of high probe reflectivity in different frequency ranges, respectively. Such three-color reflections arise from the double-EIT atomic structure in the optical lattice and can also be observed by the suppression of the density of photonic states. One of them appears in the large detuning range, and the other two locate in two EIT windows, respectively, which are relatively narrow and can be dynamically manipulated flexibly. It is worth noting that such reflection scheme has strong robustness, i.e., it is immune to the atom number fluctuation in the disorder structure. Our results have potential applications in all-optical networks with respect to fabricating efficient devices (such as reflectors and diodes) for manipulating multicolor photon flows.
Using the technique of electromagnetically induced transparency, three photonic bandgaps can be established and manipulated at any time due to the refraction modulated periodically by the one-dimensional optical lattice in a tripod atomic system which is trapped in a one-dimensional optical lattice with a Gaussian density distribution. Using the density-matrix equations to describe the interaction between laser and atoms and the transfer-matrix equation to describe the scattering of light waves in periodic media, we can obtain the steady reflection and transmission spectra. It can be found that the position and width as well as the reflectivity of the photonic band-gap could be tuned by changing the detunings and intensities of the coupling fields and the geometric Bragg detuning.
Based on the broken spatial symmetry, we propose a scheme for engineering a unidirectional photonic reflector using a one-dimensional atomic lattice with defective cells that have been specifically designed to be vacant. By trapping three-level atoms and driving them into the regime of electromagnetically induced transparency, and through the skillful design of the number and position of vacant cells in the lattice, numerical simulations demonstrate that a broad and high unidirectional reflection region can be realized within the EIT window. This proposed unidirectional reflector scheme provides a new platform for achieving optical nonreciprocity and has potential applications for designing optical circuits and devices of nonreciprocity at extremely low energy levels. Published by the American Physical Society 2024
We study photonic band gaps in a one-dimensional optical lattice of laser-cooled trapped atoms. We solve for the self-consistent equilibrium positions of the atoms, accounting for the backaction of the atoms on the trapping beams. This solution depends strongly on the sign of the trapping laser detuning. For red-detuned trapping lasers, the resulting lattice exhibits a one-dimensional photonic band gap for frequencies between the trapping laser frequency and the atomic resonance. For blue detuning the stop band extends symmetrically about resonance, typically for hundreds of atomic linewidths, except for the small region between atomic resonance and the lattice frequency, which is excluded. We calculate the reflection spectrum for a lattice of Cs atoms for various trapping laser detunings and interpret its behavior as a function of the lattice size and density. For a mean density of 1011{10}^{11}1011 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and 1000 planes, 55% reflection of a weak probe beam should be observed. We also consider Bragg scattering in a three-dimensional optical lattice as a means of probing the long-range order in the atomic density correlation function.
Assisted by the probe gain, we propose a scheme to realize the amplified unidirectional broadband reflection in a one-dimensional defective atomic lattice. In this system, some lattice cells are intentionally designed to prevent atom trapping and exhibit a periodic distribution, in order to break the spatial symmetry of light propagation and form a well reflection band. While the filled lattice cells of 87Rb^{87}\mathrm{Rb}87Rb atoms are driven into the closed three-level $\mathrm{\ensuremath{\Delta}}$-type configuaration, which can realize the amplification of the probe field. By optimizing parameters and reasonable settings, it is obvious that our scheme not only yields a flexible and adjustable broadband unidirectional reflection amplification, but also has reduced the requirement for probe gain and greatly shortened the length of defective atomic lattices.