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Physical Review A

Tunable high-order photonic band gaps of ultraviolet light in cold atoms

Yan Zhang, Yi-Mou Liu, Xue-Dong Tian, Tai-Yu Zheng, Jin‐Hui Wu

Published Jan 20, 2015• 19 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.91.013826

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We study a five-level quasi\ensuremath−\ensuremathΛ\text{quasi}\ensuremath{-}\ensuremath{\Lambda}quasi\ensuremath−\ensuremathΛ 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 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.
We study a cold atomic sample coherently driven into the five-level triple-$\ensuremath{\Lambda}$ configuration for attaining a dynamically controlled triple photonic band-gap structure. Our numerical calculations show that three photonic band gaps with homogeneous reflectivities up to 9292%92 can be induced on demand around the probe resonance by a standing-wave driving field in the presence of spontaneously generated coherence. All these photonic band gaps are severely malformed with probe reflectivities declining rapidly to very low values when spontaneously generated coherence is gradually weakened. The triple photonic band-gap structure can also be attained in a five-level chain-$\ensuremath{\Lambda}$ system of cold atoms in the absence of spontaneously generated coherence, which however requires two additional traveling-wave fields to couple relevant levels.
By using the technique of electromagnetically induced transparency and solving density matrix equations for atoms and transfer matrix equations of fields, we study the steady optical properties of a four-level system of cold atoms driven by a traveling-wave field and a standing-wave field. It is found that a nearly perfect structure of double photonic band-gap can be generated with specific parameters. In particular, the reflectivity inside each photonic band-gap is homogeneous over 95%. It is convenient to modulate the positions and widths of both photonic band-gaps by changing intensities and frequencies of the driving fields. The double photonic band-gaps can be used to achieve all-optical routing and switching and therefore may have applications in all-optical information networks.
We illustrate a mechanism based on coherent optical nonlinearities to realize optically tunable photonic crystals built from media supporting electromagnetically induced transparency. These exhibit specific periodic patterns where a light probe can experience a fully developed photonic band-gap with negligible absorption. An analytical method based on a two-mode approximation is developed to study the optical response of such a periodically modulated medium driven into a regime of standing-wave electromagnetically induced transparency. A comparison with a transfer matrix approach and with techniques based on the coupled Maxwell–Liouville equations shows that our method is very accurate to describe the optical properties of such photonic metamaterials in the frequency region of interest. Nearly perfect reflectivities may be attained for ultracold 87Rb atoms samples which are seen to reflect with little loss and deformation light pulses whose frequency components are contained within the gap. When the same mechanism is implemented for inhomogeneously broadened optical transitions of nitrogen-vacancy centers in diamond, which is more amenable to device applications, fully developed photonic band-gap structures with negligible absorption, reflectivities very close to unity and sufficiently large bandwidths may also be attained. We further examine more flexible schemes based on four level systems under double driving conditions showing more accurate and efficient coherent optical control of the photonic band-gap. The remarkable experimental simplicity of the schemes that we presented is set to ease quantum nonlinear optics applications.
For the first time, to the best of our knowledge, we investigate the photonic band gap (PBG) structure through scanning the frequency detunings of the probe field, the dressing field, and the coupling field in the static and moving electromagnetically induced grating (EIG) field. When we scan the frequency detuning of the coupling field, the PBG structure and six-wave-mixing band gap signal (SWM BGS) appear at the right of the electromagnetically induced transparency (EIT) position. But the PBG structure and SWM BGS appear at the left of the EIT position in the case of scanning the probe field frequency detuning. Also, on the condition of scanning the probe field frequency detuning, the SWM BGS appears in two frequency ranges. Moreover, in the moving PBG structure, nonreciprocity of the SWM BGS can be obtained. Furthermore, the intensity, width, and location of the SWM BGS can be modulated through changing the frequency detunings and intensities of the probe field, the dressing field, and the coupling field; the sample length; and the frequency difference of coupling fields in EIG. Such a scheme could have potential applications in optical diodes, amplifiers, and quantum information processing.
We study both the steady and the dynamic optical response of cold atoms trapped in an optical lattice and driven to the three-level $\mathrm{\ensuremath{\Lambda}}$ configuration. These atoms are found to exhibit gain without population inversion when an incoherent pump is applied to activate spontaneously generated coherence. Gain-assisted double photonic band gaps characterized by reflectivities over 100% then grow up near the probe resonance due to the periodic distribution of the atomic density. These band gaps along with the neighboring allowed bands of transmissivities over 100% can be tuned by modulating the control field in amplitude, frequency, and, especially, phase. Consequently it is viable to realize a reflector, an amplifier, or a splitter when a weak incident light pulse is totally reflected in the photonic band gaps, totally transmitted in the allowed bands, or equally reflected and transmitted in the intersecting regions. Our results have potential applications in all-optical networks with respect to fabricating dynamically switchable devices for manipulating photon flows at low-light levels.