Quantum-limit Chern topological magnetism in TbMn6Sn6.

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics1-15. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry14,15. However, quantum materials hosting ideal spin-orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking16-21. Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn6Sn6, that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn6Sn6, and may enable the observation of topological quantum phenomena in the RMn6Sn6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets.

Turbulence mitigation of four mode-division-multiplexed QPSK channels in a pilot-assisted self-coherent free-space optical link using a photodetector array and DSP-based channel demultiplexing.

In this Letter, we demonstrate turbulence mitigation of four mode-division-multiplexing (MDM) quadrature-phase-shift-keying (QPSK) channels in a pilot-assisted self-coherent free-space optical (FSO) link using a photodetector (PD) array and digital signal processing (DSP)-based channel demultiplexing. A Gaussian pilot beam is co-transmitted with four 1-Gbaud QPSK channels carried by four orbital angular momentum (OAM) modes. The pilot beam experiences similar turbulence-induced wavefront distortion to the data beams. At the receiver, the turbulence distortion is mitigated by its conjugate during the pilot-data mixing in a PD array. Subsequently, we demultiplex the four channels by applying in DSP a fixed matrix on the signals. Results show that our approach has <3-dB turbulence-induced power penalty at a 7% forward error correction (FEC) limit under a turbulence strength of 2w0/r0 = ∼4.4. The same turbulence can cause >18-dB penalties for a local oscillator (LO)-based coherent MDM system.

Adaptive-optics-based turbulence mitigation in a 400 Gbit/s free-space optical link by multiplexing Laguerre-Gaussian modes varying both radial and azimuthal spatial indices: publisher's note.

This publisher's note contains a correction to Opt. Lett.48, 6452 (2023)10.1364/OL.506270.

Experimental demonstration of an optics-based 4-PSK half-adder using nonlinear wave mixing.

We experimentally demonstrate an optics-based half-adder of two 4-phase-shift-keying (4-PSK) data channels using nonlinear wave mixing. The optics-based half-adder has two 4-ary phase-encoded inputs (i.e., SA and SB) and two phase-encoded outputs (i.e., Sum and Carry). The input quaternary base numbers {0,1,2,3} are represented by 4-PSK signals A and B with four phase levels. Along with the original signals A and B, the phase-conjugate signal copies A* and B*and phase-doubled signal copies A2 and B2 are also generated to form two signal groups SA(A, A*, A2) and SB(B, B*, B2). All of the above signals in the same signal group are (a) prepared in the electrical domain with a frequency spacing of Δf and (b) generated optically in the same IQ modulator. When combined with a pump laser, group SA mixes with group SB in a periodically poled lithium niobate nonlinear (PPLN) device. At the output of the PPLN device, both the Sum (A2B2) and the Carry (AB + A*B*) are simultaneously generated with four phase levels and two phase levels, respectively. In our experiment, the symbol rates can be varied between 5 Gbaud and 10 Gbaud. The experimental results show that (i) the measured conversion efficiency of two 5-Gbaud outputs is approximately -24 dB for Sum and approximately -20 dB for Carry, and (ii) the measured optical signal-to-noise ratio (OSNR) penalty of the 10-Gbaud Sum and Carry channels is <10 dB and <5 dB, compared with that of the 5-Gbaud channels at the BER of 3.8 × 10-3.

Space-time wave packets with reduced divergence and tunable group velocity generated in free space after multi-mode fiber propagation.

Previously, space-time wave packets (STWPs) have been generated in free space with reduced diffraction and a tunable group velocity by combining multiple frequency comb lines each carrying a single Bessel mode with a unique wave number. It might be potentially desirable to propagate the STWP through fiber for reconfigurable positioning. However, fiber mode coupling might degrade the output STWP and distort its propagation characteristics. In this Letter, we experimentally demonstrate STWP generation and propagation over 1-m graded-index multi-mode fiber. Fiber mode coupling is mitigated by pre-distortion according to the inverse matrix of the fiber mode coupling matrix. Measurement of the STWP at the fiber output shows that its group velocity can vary from 1.0042c to 0.9967c by tuning the wave number of the Bessel mode on each frequency. The measured time-averaged intensity profiles show that the beam radius remains similar after 150-mm free-space propagation after exiting the fiber.

Automatic turbulence mitigation for coherent free-space optical links using crystal-based phase conjugation and fiber-coupled data modulation.

There are various performance advantages when using temporal phase-based data encoding and coherent detection with a local oscillator (LO) in free-space optical (FSO) links. However, atmospheric turbulence can cause power coupling from the Gaussian mode of the data beam to higher-order modes, resulting in significantly degraded mixing efficiency between the data beam and a Gaussian LO. Photorefractive crystal-based self-pumped phase conjugation has been previously demonstrated to "automatically" mitigate turbulence with limited-rate free-space-coupled data modulation (e.g., <1 Mbit/s). Here, we demonstrate automatic turbulence mitigation in a 2-Gbit/s quadrature-phase-shift-keying (QPSK) coherent FSO link using degenerate four-wave-mixing (DFWM)-based phase conjugation and fiber-coupled data modulation. Specifically, we counter-propagate a Gaussian probe from the receiver (Rx) to the transmitter (Tx) through turbulence. At the Tx, we generate a Gaussian beam carrying QPSK data by a fiber-coupled phase modulator. Subsequently, we create a phase conjugate data beam through a photorefractive crystal-based DFWM involving the Gaussian data beam, the turbulence-distorted probe, and a spatially filtered Gaussian copy of the probe beam. Finally, the phase conjugate beam is transmitted back to the Rx for turbulence mitigation. Compared to a coherent FSO link without mitigation, our approach shows up to ∼14-dB higher LO-data mixing efficiency and achieves error vector magnitude (EVM) performance of <16% under various turbulence realizations.

Demonstration of optically-assisted reconfigurable average of two 20-Gbaud 4-phase-encoded data channels using nonlinear wave mixing.

Networks can play a key role in high-speed and reconfigurable arithmetic computing. However, two performance bottlenecks may arise when: (i) relying solely on electronics to handle computation for multiple data channels at high data rates, and (ii) the data streams input to a processing node (PN) are transmitted as phase-encoded signals over an optical network. We experimentally demonstrate the operation of optically-assisted reconfigurable average of two 4-phase-encoded data channels at 10- and 20-Gbaud rates. Our input signals are two streams of 2-bit numbers representing a binary floating-point format, and the operation results in 7-phase-encoded output signals represented by 3-bit numbers. The average operation is achieved in three stages: (1) phase encoding and division-using an optical modulator to encode the data streams; (2) summation-using a highly nonlinear fiber (HNLF); and (3) multicast-using a periodically poled lithium niobate (PPLN) waveguide to multicast back the result into the original signal wavelengths. The experimental results validate the concept, and the measured penalties indicate that: (i) the error vector magnitudes (EVMs) of optical signals increase at each stage and reach ∼18-21% for the final multicast results, and (ii) compared to the inputs, the optical signal-to-noise ratio (OSNR) penalty of output is ∼6.7 dB for the 10-Gbaud rate and ∼6.9 dB for the 20-Gbaud rate at a bit error rate (BER) of 3.8e-3.

Adaptive-optics-based turbulence mitigation in a 400†Git/s free-space optical link by multiplexing Laguerre-Gaussian modes varying both radial and azimuthal spatial indices.

In general, atmospheric turbulence can degrade the performance of free-space optical (FSO) communication systems by coupling light from one spatial mode to other modes. In this Letter, we experimentally demonstrate a 400 Gbit/s quadrature-phase-shift-keyed (QPSK) FSO mode-division-multiplexing (MDM) coherent communication link through emulated turbulence using four Laguerre Gaussian (LG) modes with different radial and azimuthal indices (L G 10, L G 11, L G -10, and L G -11). To mitigate turbulence-induced channel cross talk and power loss, we implement an adaptive optics (AO) system at the receiver end. A Gaussian beam at a slightly different wavelength is co-propagated with the data beams as the probe beam. We use a wavefront sensor (WFS) to measure the wavefront distortion of this probe beam, and this information is used to tune a spatial light modulator (SLM) to adaptively correct the four distorted data-beam wavefronts. Using this adaptive-optics approach, the power loss and cross talk are reduced by ∼10 and ∼18 dB, respectively.

Bond-breaking induced Lifshitz transition in robust Dirac semimetal VAI3.

Topological electrons in semimetals are usually vulnerable to chemical doping and environment change, which restricts their potential application in future electronic devices. In this paper, we report that the type-II Dirac semimetal [Formula: see text] hosts exceptional, robust topological electrons which can tolerate extreme change of chemical composition. The Dirac electrons remain intact, even after a substantial part of V atoms have been replaced in the [Formula: see text] solid solutions. This Dirac semimetal state ends at [Formula: see text], where a Lifshitz transition to p-type trivial metal occurs. The V-Al bond is completely broken in this transition as long as the bonding orbitals are fully depopulated by the holes donated from Ti substitution. In other words, the Dirac electrons in [Formula: see text] are protected by the V-Al bond, whose molecular orbital is their bonding gravity center. Our understanding on the interrelations among electron count, chemical bond, and electronic properties in topological semimetals suggests a rational approach to search robust, chemical-bond-protected topological materials.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies.

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LGℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

Utilizing multiplexing of structured THz beams carrying orbital-angular-momentum for high-capacity communications.

Structured electromagnetic (EM) waves have been explored in various frequency regimes to enhance the capacity of communication systems by multiplexing multiple co-propagating beams with mutually orthogonal spatial modal structures (i.e., mode-division multiplexing). Such structured EM waves include beams carrying orbital angular momentum (OAM). An area of increased recent interest is the use of terahertz (THz) beams for free-space communications, which tends to have: (a) larger bandwidth and lower beam divergence than millimeter-waves, and (b) lower interaction with matter conditions than optical waves. Here, we explore the multiplexing of THz OAM beams for high-capacity communications. Specifically, we experimentally demonstrate communication systems with two multiplexed THz OAM beams at a carrier frequency of 0.3 THz. We achieve a 60-Gbit/s quadrature-phase-shift-keying (QPSK) and a 24-Gbit/s 16 quadrature amplitude modulation (16-QAM) data transmission with bit-error rates below 3.8 × 10-3. In addition, to show the compatibility of different multiplexing approaches (e.g., polarization-, frequency-, and mode-division multiplexing), we demonstrate an 80-Gbit/s QPSK THz communication link by multiplexing 8 data channels at 2 polarizations, 2 frequencies, and 2 OAM modes.

Synthesis of near-diffraction-free orbital-angular-momentum space-time wave packets having a controllable group velocity using a frequency comb.

Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional (2D) space-time (ST) OAM wave packets (ℓ = +1, +2, or +3) with variable group velocities in free space by coherently combining multiple frequency comb lines, each carrying a unique Bessel mode. Introducing a controllable specific correlation between temporal frequencies and spatial frequencies of these Bessel modes, we experimentally generate and detect near-diffraction-free OAM wave packets with high mode purities (>86%). Moreover, the group velocity can be controlled from 0.9933c to 1.0069c (c is the speed of light in vacuum). These ST OAM wave packets might find applications in imaging, nonlinear optics, and optical communications. In addition, our approach might also provide some insights for generating other interesting ST beams.

Turbulence-resilient pilot-assisted self-coherent free-space optical communications using a photodetector array for bandwidth enhancement.

We experimentally demonstrate a 4-Gbit/s 16-QAM pilot-assisted, self-coherent, and turbulence-resilient free-space optical link using a photodetector (PD) array. The turbulence resilience is enabled by the efficient optoelectronic mixing of the data and pilot beams in a free-space-coupled receiver, which can automatically compensate for turbulence-induced modal coupling to recover the data's amplitude and phase. For this approach, a sufficient PD area might be needed to collect the beams while the bandwidth of a single larger PD could be limited. In this work, we use an array of smaller PDs instead of a single larger PD to overcome the beam collection and bandwidth response trade-off. In the PD-array-based receiver, the data and pilot beams are efficiently mixed in the aggregated PD area formed by four PDs, and the four mixing outputs are electrically combined for data recovery. The results show that: (i) either with or without turbulence effects (D/r0 = ∼8.4), the 1-Gbaud 16-QAM signal recovered by the PD array has a lower error vector magnitude than that of a single larger PD; (ii) for 100 turbulence realizations, the pilot-assisted PD-array receiver recovers 1-Gbaud 16-QAM data with a bit-error rate below 7% of the forward error correction limit; and (iii) for 1000 turbulence realizations, the average electrical mixing power loss of a single smaller PD, a single larger PD, and a PD array is ∼5.5 dB, ∼1.2 dB, and ∼1.6 dB, respectively.

Tunability of space-time wave packet carrying tunable and dynamically changing OAM value.

Space-time (ST) wave packets have gained much interest due to their dynamic optical properties. Such wave packets can be generated by synthesizing frequency comb lines, each having multiple complex-weighted spatial modes, to carry dynamically changing orbital angular momentum (OAM) values. Here, we investigate the tunability of such ST wave packets by varying the number of frequency comb lines and the combinations of spatial modes on each frequency. We experimentally generate and measure the wave packets with tunable OAM values from +1 to +6 or from +1 to +4 during a ∼5.2-ps period. We also investigate, in simulation, the temporal pulse width of the ST wave packet and the nonlinear variation of the OAM values. The simulation results show that: (i) a pulse width can be narrower for the ST wave packet carrying dynamically changing OAM values using more frequency lines; and (ii) the nonlinearly varying OAM value can result in different frequency chirps along the azimuthal direction at different time instants.

Demonstration of turbulence mitigation in a 200-Gbit/s orbital-angular-momentum multiplexed free-space optical link using simple power measurements for determining the modal crosstalk matrix.

We experimentally demonstrate turbulence mitigation in a 200-Gbit/s quadrature phase-shift keying (QPSK) orbital-angular-momentum (OAM) mode-multiplexed system using simple power measurements for determining the modal coupling matrix. To probe and mitigate turbulence, we perform the following: (i) sequentially transmit multiple probe beams at 1550-nm wavelength each with a different combination of Laguerre-Gaussian (LG) modes; (ii) detect the power coupling of each probe beam to LG0,0 for determining the complex modal coupling matrix; (iii) calculate the conjugate phase of turbulence-induced spatial phase distortion; (iv) apply this conjugate phase to a spatial light modulator (SLM) at the receiver to mitigate the turbulence distortion for the 1552-nm mode-multiplexed data-carrying beams. The probe wavelength is close enough to the data wavelength such that it experiences similar turbulence, but is far enough away such that the probe beams do not affect the data beams and can all operate simultaneously. Our experimental results show that with our turbulence mitigation approach the following occur: (a) the inter-channel crosstalk is reduced by ∼25 and ∼21 dB for OAM +1 and -2 channels, respectively; (b) the optical signal-to-noise ratio (OSNR) penalty is <1 dB for both OAM channels for a bit error rate (BER) at the 7% forward error correction (FEC) limit, compared with the no turbulence case.

Tunable optical second-order Volterra nonlinear filter using wave mixing and delays to equalize a 10-20 Gbaud 4-APSK channel.

We experimentally demonstrate a tunable optical second-order Volterra filter using wave mixing and delays. Wave mixing is performed in a periodically poled lithium niobate waveguide with the cascaded sum-frequency generation and difference-frequency generation processes. Compared to conventional optical tapped delay line structures, second-order taps are added through the wave mixing of two signal copies. We measure the frequency response of the filter by sending a frequency-swept sinusoidal wave as the input. The tap weights are tuned with a liquid-crystal-on-silicon waveshaper for different filter configurations. With the additional second-order taps, the filter is able to perform a nonlinear function. As an example, we demonstrate the compensation of a nonlinearly distorted 10-20 Gbaud 4-amplitude and phase shift keying signal.

Modal properties of a beam carrying OAM generated by a circular array of multiple ring-resonator emitters.

We investigate the modal properties of a beam carrying orbital angular momentum (OAM) generated by a circular array (ring) of multiple micro-ring emitters (rings) analytically and via simulation. In such a "ring-of-rings" structure, N emitters generate N optical vortex beams with the same OAM-order l0 at the same wavelength. The output beam is a coherent combination of the N vortex beams located at different azimuthal positions, having the same radial displacement. We derive an analytical expression for the output optical field and calculate the OAM-order power spectrum of the generated beam. The analytical expression and simulation results show that (1) the OAM spectrum of the output beam composes equidistant OAM spectral components, symmetrically surrounding l0 with a spacing equal to N; (2) the envelope of the OAM spectrum broadens with an increased radius of the circular array or the value of l0; and (3) the OAM components of the generated beam could be tuned either by changing the value of l0, corresponding to different spectrum envelopes, or by adding different linear phase delays to the micro-ring emitters, which does not affect the envelope of the OAM spectrum.

Demonstration of generating a 100 Gbit/s orbital-angular-momentum beam with a tunable mode order over a range of wavelengths using an integrated broadband pixel-array structure.

We experimentally generate an orbital-angular-momentum (OAM) beam with a tunable mode order over a range of wavelengths utilizing an integrated broadband pixel-array OAM emitter. The emitter is composed of a 3-to-4 coupler, four phase controllers, and a mode convertor. An optical input is split into four waveguides by the coupler. Subsequently, the four waveguide fields are coherently combined and transformed into a free-space OAM beam by the mode convertor. By tuning the phase delay Δφ between the four waveguides using the integrated phase controllers, the OAM order of the generated beam could be changed. Our results show that (a) a single OAM beam with a tunable OAM order (ℓ=-1 or ℓ=+1) is generated with the intermodal power coupling of <-11dB, and (b) in a wavelength range of 6.4 nm, a free-space link of a single 50 Gbaud quadrature-phase-shift-keying (QPSK) channel carried by the tunable OAM beam is achieved with a bit error rate below the forward-error-correction threshold. As proof of concept, a 400 Gbit/s OAM-multiplexed and WDM QPSK link is demonstrated with a ∼1-dB OSNR penalty compared with a single-beam link.

Simulation of near-diffraction- and near-dispersion-free OAM pulses with controllable group velocity by combining multiple frequencies, each carrying a Bessel mode.

Optical pulses carrying orbital angular momentum (OAM) have recently gained interest. In general, it might be beneficial to simultaneously achieve: (i) minimum diffraction, (ii) minimum dispersion, and (iii) controllable group velocity. Here, we explore via simulation the generation of near-diffraction-free and near-dispersion-free OAM pulses with arbitrary group velocities by coherently combining multiple frequencies. Each frequency carries a specific Bessel mode with the same topological charge (ℓ) but different kr (spatial frequency) values based on space-time correlations. Moreover, we also find that (i) both positive and negative group velocities could be achieved and continuously controlled from the subluminal to superluminal values and (ii) when the ℓ is varied from 0 to 10, the simulated value of the group velocity remains the same. However, as the ℓ value increases, the pulse duration becomes longer for a given number of frequency lines.

Rare Earth Engineering in RMn_{6}Sn_{6} (R=Gd-Tm, Lu) Topological Kagome Magnets.

Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn_{6}Sn_{6} manifest the quantum transport properties analogical to those in the quantum-limit Chern magnet TbMn_{6}Sn_{6}. The topological transport in the family, including quantum oscillations with nontrivial Berry phase and large anomalous Hall effect arising from Berry curvature field, points to the existence of Chern gapped Dirac fermions. Our observation demonstrates a close relationship between rare-earth magnetism and topological electron structure, indicating the rare-earth elements can effectively engineer the Chern quantum phase in kagome magnets.