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Physical Review A

Dynamically tunable three-color reflections immune to disorder in optical lattices with trapped cold Rb 87 atoms

Hong Wei Yang, Tinggui Zhang, Yan Zhang, Jin‐Hui Wu

Published May 26, 2020• 21 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.101.053856

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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.
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.
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 )
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.
Non-reciprocal reflections of optical signals are unusual yet fascinating to achieve the imminent applications of non-reciprocal photonic devices and circuits. The complete non-reciprocal reflection (unidirectional reflection) was recently found to be achievable in a homogeneous medium, if the real and imaginary parts of the probe susceptibility satisfy the spatial Kramers-Kronig (KK) relation. We propose a coherent four-level tripod model for realizing dynamically tunable two-color non-reciprocal reflections by applying two control fields with linearly modulated intensities. We found that, the unidirectional reflection can be obtained if the non-reciprocal frequency regions are located in the electromagnetically induced transparency (EIT) windows. This mechanism is to break the spatial symmetry by the spatial modulation of susceptibility to induce unidirectional reflections, the real and imaginary parts of the probe susceptibility are no longer required to satisfy the spatial KK relation.
We study an ensemble of cold atoms driven to the four-level double-$\ensuremath{\Lambda}$ configuration and trapped in the one-dimensional optical lattices for achieving dynamically controlled photonic band gaps (PBGs) via the balanced four-wave mixing interaction. Numerical results show that a pair of PBGs characterized by high platforms of probe reflectivities and reduced density of photonic states are established, simultaneously, on both probe transitions in one symmetric driving scheme. Such two-color PBGs can be easily manipulated in position and width by modulating, e.g., the balanced Rabi frequencies of two coupling fields and the Gaussian widths of atomic density distributions, to change the equal probe detunings fulfilling both Bragg conditions. Each two-color PBG as predicted in the coherent atomic lattices may be explored to attain robust light entanglement, even for single-probe photons, via an efficient frequency conversion during the nonlinearly correlated reflection.
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