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arXiv:2308.09287 · Physical Review A

Localization-delocalization transition in an electromagnetically induced photonic lattice

Rui Tian, Shuai Li, Maksims Arzamasovs, Hong Gao, Yong-Chang Zhang, Bo Liu

Published Oct 16, 2023• 5 citations
arXivHTMLPDF

Abstract

We investigate the localization-delocalization transition (LDT) in an electromagnetically induced photonic lattice. A four-level tripod-type scheme in atomic ensembles is proposed to generate an effective photonic moir\'e lattice through the electromagnetically induced transparency (EIT) mechanism. By taking advantage of the tunable atomic coherence, we show that both periodic (commensurable) and aperiodic (incommensurable) structure can be created in such a photonic moir\'e lattice via adjusting the twist angle between two superimposed periodic patterns with square primitive. Furthermore, we also find that by tuning the amplitudes of these two superimposed periodic patterns, the localization-delocalization transition occurs for the light propagating in the aperiodic moir\'e lattice. Such localization is shown to link the fact that the flat bands of moir\'e lattice support quasi-nondiffracting localized modes and thus induce the localization of the initially localized beam. It would provide a promising approach to control the light propagation via the electromagnetically induced photonic lattice.

DOI
10.1103/physreva.108.043711

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We investigate the localization-delocalization transition (LDT) in an electromagnetically induced photonic lattice. A four-level tripod-type scheme in atomic ensembles is proposed to generate an effective photonic moir'e lattice through the electromagnetically induced transparency (EIT) mechanism. By taking advantage of the tunable atomic coherence, we show that both periodic (commensurable) and aperiodic (incommensurable) structure can be created in such a photonic moir'e lattice via adjusting the twist angle between two superimposed periodic patterns with square primitive. Furthermore, we also find that by tuning the amplitudes of these two superimposed periodic patterns, the localization-delocalization transition occurs for the light propagating in the aperiodic moir'e lattice. Such localization is shown to link the fact that the flat bands of moir'e lattice support quasi-nondiffracting localized modes and thus induce the localization of the initially localized beam. It would provide a promising approach to control the light propagation via the electromagnetically induced photonic lattice.
Electromagnetically induced optical (or photonic) lattices via atomic coherence in atomic ensembles have recently received great theoretical and experimental interest. We here conceive a way to generate electromagnetically induced moiré optical lattices — a twisted periodic pattern when two identical periodic patterns (lattices) are overlapped in a twisted angle ( θ ) — in a three-level coherent atomic gas working under electromagnetically induced transparency. We show that, changing the twisted angle and relative strength between the two constitutive sublattices, the moiré Bloch bands that are extremely flattened can always appear, resembling the typical flat-band and moiré physics found in other contexts. Dynamics of light propagation in the induced periodic structures demonstrating the unique linear localization and delocalization properties are also revealed. Our scheme can be implemented in a Rubidium atomic medium, where the predicted moiré optical lattices and flattened bands are naturally observable.
We propose a scheme to realize a transition from delocalization to localization of light waves via electromagnetically induced transparency. The system we suggested is a resonant cold atomic ensemble having NNN configuration, with a control field consisting of two pairs of laser beams with different cross angles, which produce an electromagnetically induced quasiperiodic waveguide (EIQPW) for the propagation of a signal field. By appropriately tuning the incommensurate rate or relative modulation strength between the two pairs of control-field components, the signal field can exhibit the delocalization-localization transition as it transports inside the atomic ensemble. The delocalization-localization transition point is determined and the propagation property of the signal field is studied in detail. Our work provides a way of realizing wave localization via atomic coherence, which is quite different from the conventional, off-resonant mechanism-based Aubry-Andre model, and the great controllability of the EIQPW also allows an easy manipulation of the delocalization-localization transition.
Photonic moiré lattices (PMLs), with unique twisted periodic patterns, provide a valuable platform for investigating strongly correlated materials, unconventional superconductivity, and the localization−delocalization transition. However, PMLs created either by the misorientation between lattice layers or by twisted van der Waals materials are typically non-tunable and inherently possess immutable refractive indices. Unlike those in the moiré lattices of twisted two-dimensional materials, our work reports a moiré lattice formed by overlapping two identical sublattices with twisted angles in an ultracold atomic ensemble. This photoinduced moiré lattice with two twisted sublattices exhibits high flexibility and rich periodicity through adjustable twisted angles. Our results indicate that both the absorption/dispersion coefficients and the transmission of the photoinduced moiré lattices can be effectively tuned by photon detuning and Rabi frequency, resulting in amplitude- and phase-type moiré lattices. Based on the Fraunhofer diffraction theory, we have demonstrated that the far-field diffraction efficiency can be adjusted via altering photon detuning, and the rotation angle serves as a control knob for modulating the diffracted intensity distribution, thereby optimizing the performance of the photonic lattice. It is also found that the operation domains of the moiré lattices with different rotation angles remain consistent, allowing for seamless conversion between various moiré period structures. Furthermore, a moiré lattice composed of three twisted sublattices is investigated, revealing that the diffraction energy is uniformly dispersed in a circular distribution, which provides excellent agility in the design of optical devices. Such tunable PML offer a powerful tool for studying light propagation control and the intriguing physics of twisted systems in atomic media.
We experimentally and theoretically demonstrate an electromagnetically induced binary photonic lattice with an instantaneously tunable flat band in a three-level85Rb atomic configuration. The transmitted binary patterns result from the diffraction of an injected Gaussian probe beam through the atomic vapor cell, in which the refractive index is modulated by a binary coupling field with alternating high- and low-intensity peaks under electromagnetically induced transparency. The binary coupling field is established by spatially superimposing two standing-wave fields whose periods differ by a factor of two. The transmitted patterns and the flat band can be readily modulated via controllable atomic coherence. Crucially, by tuning the Rabi frequencies to engineer the refractive index contrast, instantaneous switching of the flat band is achieved. This investigation provides a new method for producing tunable binary photonic lattices, which can serve as a promising platform for investigating the dynamical evolutions of wave packets.
We have experimentally demonstrated the realization of an instantaneously reconfigurable Lieb photonic lattice with a flatband in a three-level Λ-type rubidium atomic configuration. Such a coherently controllable Lieb photonic lattice is optically induced by a coupling field possessing a spatially periodic intensity distribution (generated via a spatial light modulator) under the condition of electromagnetically induced transparency. The incident weak Gaussian probe field can experience discrete diffraction and the observed probe beam at the output surface of the medium exhibits the same Lieb pattern, verifying the formation of the refractive index with a Lieb profile inside the atomic vapor cell. The potential wells and the band structure of the Lieb photonic lattice can be effectively manipulated by easily tuning the frequency of the involved laser beams. The current work can promisingly pave the way for exploring the exotic dynamics as well as tunable photonic devices in Lieb photonic lattices.
In this Letter, we have investigated experimentally the photonic realization of a moving lattice with an instantaneously tunable transverse velocity in a three-level Λ -type warm 85 R b atomic medium. The dynamic photonic lattice moving along the direction of its spatial periodicity was constructed by introducing a frequency difference (determining the velocity) between two coupling beams, whose interference pattern could optically induce a (spatial) periodic refractive index change inside the atomic vapor under electromagnetically induced transparency. When a Gaussian probe field is launched into this optically induced lattice, the output diffraction patterns can shift along the transverse direction, indicating dynamical features of induced photonic structures. The realization of this effectively controllable moving photonic lattice provides a new platform for guiding the transport of light.