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1. Utilizing phase delays of an integrated pixel-array structure to generate orbital-angular-momentum beams with tunable orders and a broad bandwidth

   https://doi.org/10.1364/OL.396447  

   Song, Hao ; Zhao, Zhe ; Zhang, Runzhou ; Song, Haoqian ; Zhou, Huibin ; Pang, Kai ; Du, Jing ; Li, Long ; Liu, Cong ; Su, Xinzhou ; et al ( July 2020 , Optics Letters)

   We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the$k$th input carrying a phase delay of$(k-<\#comment/>1)\mathrm{\Delta <\#comment/>}\mathrm{\phi <\#comment/>}$. The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay$\mathrm{\Delta <\#comment/>}\mathrm{\phi <\#comment/>}$; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., $l=\{-<\#comment/>1\},\{-<\#comment/>1,+1\},\{-<\#comment/>1,0,+1\}$, or$\{-<\#comment/>2,-<\#comment/>1,+1,+2\}$); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own$\mathrm{\Delta <\#comment/>}\mathrm{\phi <\#comment/>}$value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% for$l=-<\#comment/>1$), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for$l=\{-<\#comment/>1\}$to 122 nm for$l=\{-<\#comment/>2,-<\#comment/>1,+1,+2\}$), and (c) increased crosstalk within the C-band (from$-<\#comment/>23.7$to$-<\#comment/>13.2\mathrm{d}\mathrm{B}$when the tunable range increases from 2 to 4).

    

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2. Partons as unique ground states of quantum Hall parent Hamiltonians: The case of Fibonacci anyons

   https://doi.org/10.21468/SciPostPhys.15.2.043  

   Tanhayi Ahari, Mostafa ; Bandyopadhyay, Sumanta ; Nussinov, Zohar ; Seidel, Alexander ; Ortiz, Gerardo ( January 2023 , SciPost Physics)

   We present microscopic, multiple Landau level, (frustration-free and positive semi-definite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are parton-like and whose excitations display either Abelian or non-Abelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate S-duality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing parton-like states, specifically at filling factor\nu=2/3$\nu =2/3$. The emergent Entangled Pauli Principle (EPP), introduced in [Phys. Rev. B 98, 161118(R) (2018)] and which defines the “DNA” of the quantum Hall fluid, is behind the exact determination of the topological characteristics of the fluid, including charge and braiding statistics of excitations, and effective edge theory descriptions. When the closed-shell condition is satisfied, the densest (i.e., the highest density and lowest total angular momentum) zero-energy mode is a unique parton state. We conjecture that parton-like states generally span the subspace of many-body wave functions with the two-bodyM$M$-clustering property within any given number of Landau levels, that is, wave functions withM$M$th-order coincidence plane zeroes and both holomorphic and anti-holomorphic dependence on variables. General arguments are supplemented by rigorous considerations for theM=3$M=3$case of fermions in four Landau levels. For this case, we establish that the zero mode counting can be done by enumerating certain patterns consistent with an underlying EPP. We apply the coherent state approach of [Phys. Rev. X 1, 021015 (2011)] to show that the elementary (localized) bulk excitations are Fibonacci anyons. This demonstrates that the DNA associated with fractional quantum Hall states encodes all universal properties. Specifically, for parton-like states, we establish a link with tensor network structures of finite bond dimension that emerge via root level entanglement.

    

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3. Velocity-resolved Reverberation Mapping of NGC 3227

   https://doi.org/10.3847/1538-4357/ad08b8  

   Bentz, Misty C. ; Markham, Madison ; Rosborough, Sara ; Onken, Christopher A. ; Street, Rachel ; Valluri, Monica ; Treu, Tommaso ( December 2023 , The Astrophysical Journal)

   We describe the results of a new reverberation mapping program focused on the nearby Seyfert galaxy NGC 3227. Photometric and spectroscopic monitoring was carried out from 2022 December to 2023 June with the Las Cumbres Observatory network of telescopes. We detected time delays in several optical broad emission lines, with Hβhaving the longest delay at${\tau }_{\mathrm{cent}}={4.0}_{-0.9}^{+0.9}$days and Heiihaving the shortest delay with${\tau }_{\mathrm{cent}}={0.9}_{-0.8}^{+1.1}$days. We also detect velocity-resolved behavior of the Hβemission line, with different line-of-sight velocities corresponding to different observed time delays. Combining the integrated Hβtime delay with the width of the variable component of the emission line and a standard scale factor suggests a black hole mass of$M_{\mathrm{BH}}={1.1}_{-0.3}^{+0.2}\times {10}^7$M_⊙. Modeling of the full velocity-resolved response of the Hβemission line with the phenomenological codeCARAMELfinds a similar mass of$M_{\mathrm{BH}}={1.2}_{-0.7}^{+1.5}\times {10}^7$M_⊙and suggests that the Hβ-emitting broad-line region (BLR) may be represented by a biconical or flared disk structure that we are viewing at an inclination angle ofθ_i≈ 33° and with gas motions that are dominated by rotation. The new photoionization-based BLR modeling toolBELMACfinds general agreement with the observations when assuming the best-fitCARAMELresults; however,BELMACprefers a thick-disk geometry and kinematics that are equally composed of rotation and inflow. Both codes infer a radially extended and flattened BLR that is not outflowing.

    

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4. Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

   https://doi.org/10.1038/s41598-022-22812-x  

   Wijewardena, U. Kushan ; Nanayakkara, Tharanga R. ; Kriisa, Annika ; Reichl, Christian ; Wegscheider, Werner ; Mani, Ramesh G. ( November 2022 , Scientific Reports)

   Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting,$$g \mu _B B$$$g{\mu }_{B}B$, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in$$\nu$$$\nu$for the$$R_{xx}$$$R_{\mathrm{xx}}$minimum, e.g., from$$\nu = 11/7$$$\nu =11/7$to$$\nu = 8/5$$$\nu =8/5$, and a corresponding change in the$$R_{xy}$$$R_{\mathrm{xy}}$, e.g., from$$R_{xy}/R_{K} = (11/7)^{-1}$$$R_{\mathrm{xy}}/R_K={(11/7)}^{-1}$to$$R_{xy}/R_{K} = (8/5)^{-1}$$$R_{\mathrm{xy}}/R_K={(8/5)}^{-1}$, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the$$\nu = 4/3$$$\nu =4/3$and$$\nu = 7/5$$$\nu =7/5$resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of$$R_{xy}$$$R_{\mathrm{xy}}$at the$$R_{xx}$$$R_{\mathrm{xx}}$minima- the latter occurring for$$\nu = 4/3, 7/5$$$\nu =4/3,7/5$and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same$$\nu$$$\nu$and$$R_{xy}$$$R_{\mathrm{xy}}$, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

    

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5. Amplitude and phase sorting of orbital angular momentum states at low light levels

   https://doi.org/10.1364/OPTICA.409204  

   Ariyawansa, Ashan ; Figueroa, Edward J. ; Brown, Thomas G. ( January 2021 , Optica)

   We present a method of photon orbital angular momentum selection at very low light levels using spatial interference between a strong local oscillator field and a weak beam. By using Fourier phase recovery techniques familiar in classical interferometry, we can experimentally obtain a quantum-limited$Q$distribution with a standard deviation consistent with the quantum noise floor. Further, by projecting the complex Fourier peak on a Laguerre–Gauss basis, we can distinguish states of different orbital angular momentum with high fidelity for small numbers of counts per acquisition frame. The noise equivalent photoelectron count for this measurement is${10}^{-<\#comment/>5}$counts per pixel per frame.

    

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