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Optics Express

Coherent control of photonic band gaps through the relative phase using modified superradiance lattice

Muhammad Saeed, Atif Shabbir

Published Dec 8, 2023• 1 citation
Publisher

Abstract

We report photonic band gaps based on a modified superradiance lattice having reflectivity close to 100% for both the low and high-frequency ranges. We observe that tuning the relative phase between the coupling fields provides additional control over photonic band gaps. We notice that the relative phase can control three input channels of the probe field simultaneously and efficiently. This feature of relative phase over photonic band gaps provides potential in the field of quantum optics. Further, this scheme is experimentally more viable. Rubidium atoms 87 Rb can obtain low-frequency (infrared) photonic band gaps. On the other hand, rubidium atoms 85 Rb and beryllium ions Be 2+ can form high-frequency ultraviolet and soft X-ray photonic band gaps, achieving reflectivities of 80% and 96%, respectively. This scheme holds promise for constructing highly efficient optical switches and beam splitters.

DOI
10.1364/oe.506407

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We report photonic band gaps based on a modified superradiance lattice having reflectivity close to 100% for both the low and high-frequency ranges. We observe that tuning the relative phase between the coupling fields provides additional control over photonic band gaps. We notice that the relative phase can control three input channels of the probe field simultaneously and efficiently. This feature of relative phase over photonic band gaps provides potential in the field of quantum optics. Further, this scheme is experimentally more viable. Rubidium atoms 87 Rb can obtain low-frequency (infrared) photonic band gaps. On the other hand, rubidium atoms 85 Rb and beryllium ions Be 2+ can form high-frequency ultraviolet and soft X-ray photonic band gaps, achieving reflectivities of 80% and 96%, respectively. This scheme holds promise for constructing highly efficient optical switches and beam splitters.
Abstract We report that modified superradiance lattice (2023, Phys. Scr. 98 015 105) can be used to obtain high-frequency photonic band gaps which are controllable using low-frequency light. Here, we also notice that the maximum reflectivity of these photonic band gaps can be achieved via low-frequency light control. This maximum reflectivity remains constant for a certain range of probe detuning depending upon the strength of the control field. We also report that this can lead to experimental realization of the soft x-ray regime (high-frequency) via 61st-order low-frequency light using Be2+ ions, the corresponding reflectivity in this case is 96%. Therefore, one can construct controllable x-ray photonic band gaps which can further be used to devise optical switches, beam splitters, and frequency combs. Moreover, this scheme holds the promise of working efficiently in all types of other configurations where reflection of high-frequency light is needed using nth order low-frequency light.
We study a five-level $\text{quasi}\ensuremath{-}\ensuremath{\Lambda}$ system of cold atoms for achieving high-order photonic band gaps (PBGs) probed by an ultraviolet field in two cases where either an infrared or a visible control field works in the standing-wave configuration to induce one atomic grating. Transfer-matrix calculations for appropriate rubidium levels demonstrate that three fifth-order band gaps or two second-order band gaps can be generated near the probe resonance when the standing-wave control field is modulated to satisfy relevant Bragg conditions in the regime of electromagnetically induced transparency. These high-order PBGs, as characterized by homogeneous high reflectivities, can be dynamically tuned in positions and widths on demand and may be extended to develop efficient devices (like diodes and reflectors) for manipulating weak high-frequency light with strong low-frequency light.
We show that the momentum of light can be reversed via the atomic coherence created by another light with one or two orders of magnitude lower frequency. Both the backward retrieval of single photons from a timed Dicke state and the reflection of continuous waves by high-order photonic band gaps are analyzed. The required control field strength scales linearly with the nonlinearity order, which is explained by the dynamics of superradiance lattices. Experiments are proposed with 85Rb^{85}\mathrm{Rb}85Rb atoms and Be2+{\mathrm{Be}}^{2+}Be2+ ions. This holds promise for light-controllable x-ray reflectors.
The photonic band gap is a spectral range which cannot propagate in a periodic optical nanostructure, that is, the structure itself has a “forbidden band”. It has been successfully applied to the filters, amplifiers, mixers, etc. As is well known, dynamically tunable photonic band gaps in cold atomic lattices are of great importance in various research fields. However, the photonic band gaps of a traditional photonic crystal are non-tunable because the periodic structure is determined once the photonic crystal is grown. On the other hand, a majority of previous researches focused on improving the reflectivity of photonic band gap, which can only keep approaching to 1. Due to the action of the vacuum of the radiation field, near-degenerate lower level has an additional coherence term, the spontaneously generated coherence term. In this paper, we consider a three-level ∧-type atomic system driven by a strong coherent field, a weak coherent field and an incoherent pump, in which the two ground states are of hyperfine structure. The one-dimensional photonic band gaps are formed by cold atoms trapped in a one-dimensional-ordered optical lattice and this system may create two photonic band gaps (PBGs). The trapped cold atoms have a Gaussian density distribution in each period as determined by the optical potential depth and the average atomic temperature. We investigate in detail how the reflectivities of the two PBGs are influenced by the coherent effect of spontaneously generated coherence. Then, we find that the reflectivities of the two band gaps can be significantly improved by the spontaneously generated coherence. The reflectivities of such two band gaps can be dynamically manipulated by varying the intensity of incoherent driving field and the relative phase between the probe field and the coupling field, which cannot be realized in a conventional ∧-type atomic system. Besides, by adjusting the parameters appropriately, the reflectivities of these two band gaps can be higher than 1, which is because probe field gain stems from the spontaneously generated coherence. In the future, photonic transport properties can be investigated in the three-dimensional atomic lattices and this work is meaningful for the optical routing, photodiode and transistor.
Abstract We propose a scheme for generating frequency combs in an electromagnetically induced transparency—based superradiance lattice. When the probe frequency satisfies the m th-order resonance condition with the control field, 2 m + 1 discrete spectral components emerge, forming a frequency comb. The comb spacing and reflectivity are dynamically tunable via the control-field strength. The proposed scheme is experimentally feasible and enables the generation of low-frequency (infrared) combs using 87 Rb atoms. Moreover, high-frequency combs in the ultraviolet and x-ray regimes can be realized using 85 Rb atoms and Be 2 + ions, exhibiting appreciable reflectivity. These results establish a versatile platform for frequency-comb generation with potential applications in quantum optics and quantum information processing.
We report that frequency combs are generated within the superradiance lattice from low frequency (infrared) to high frequency (X-ray) range. Our observations reveal that the infrared frequency combs have a reflectivity approaching 95%, while the X-ray frequency combs exhibit approximately 55% reflectivity. We can control the width and amplitude of the spectral lines of these frequency combs by adjusting the control field intensity. This atomic scheme is experimentally viable. We can propose conducting experiments utilizing beryllium ions for X-rays and rubidium atoms for generating infrared frequency combs. This approach holds great promise for potential applications in quantum optics.