Femtosecond Laser Direct Sau Ntawm Bloch Oscillations hauv Optical Floquet Lattices

Thaum lub Plaub Hlis 28, 2024, Prof. Shu Xuewen pab neeg ntawm Huazhong University of Science thiab Technology (HUST), koom tes nrog Prof. Sun Xiankai pab neeg ntawm Suav University of Hong Kong (CUHK), tau tshaj tawm cov kev tshawb fawb tshiab tshaj plaws ntawm kev soj ntsuam ntawm photonic. Floquet - Bloch oscillations.
Bloch oscillations yog ib qho classical coherent quantum thauj phenomenon tshwm sim raws li lub sij hawm oscillations ntawm quantum hais nyob rau hauv ib lub sij hawm muaj peev xwm teb nyob rau hauv qhov kev txiav txim ntawm ib tug siv tas li quab yuam. Raws li cov txiaj ntsig tseem ceeb ntawm lub cev, Bloch oscillations tau tshawb pom thiab tshawb fawb hauv ntau lub tshuab, xws li semiconductor superlattices, ultracold atoms, coupled waveguide arrays, thiab hluavtaws Dimension ntawm photonic lattices, thiab lwm yam. Kev tshawb fawb physics, tab sis kuj muab cov tswv yim tshiab thiab cov txheej txheem rau kev hloov pauv hloov pauv ntawm kev hloov pauv ntawm kev ua haujlwm nthwv dej. Txawm li cas los xij, cov kev tshawb fawb ntawm Bloch oscillation phenomenon tau tsom mus rau cov tshuab zoo li qub, thiab Bloch oscillation tshwm sim nyob rau hauv lub sij hawm uas tau tsav (Floquet) systems yuav tsum tau tshawb nrhiav ntxiv hauv qhov tob.

Fig. 1. (a) Schematic ntawm femtosecond laser direct-sau waveguide array. (b) Yees duab ntawm ntu ntu ntawm qhov kev sim npaj ua qauv. (c) Sab saum toj saib daim duab ntawm kev sim npaj ua qauv.
Txhawm rau daws qhov teeb meem no, txoj kev tshawb fawb no tshawb xyuas qhov tshwm sim ntawm Bloch oscillation phenomenon hauv Froché system siv ib qho ntawm ib sab ntawm bent waveguide array npaj los ntawm femtosecond laser direct sau, tawm tswv yim dav dav ntawm Bloch oscillation phenomenon nyob rau hauv optical Froché lattice, thiab sim visualizes thiab soj ntsuam qhov optical Froché-Bloch oscillation phenomenon. Raws li pom nyob rau hauv daim duab 1, lub bending trajectory ntawm lub waveguide nyob rau hauv lub array yog ib tug sib xyaw trajectory uas muaj xws li ncig bending superimposed ntawm lub sij hawm bending. Nyob rau yav tsaus ntuj-axis kwv yees, qhov sib npaug sib npaug piav qhia txog kev hloov pauv ntawm kev thauj mus los hauv lub zog ntawm cov kab lus waveguide no yog lej sib npaug rau Schrödinger equation piav txog lub sij hawm-dependent evolution ntawm electrons nyob rau hauv ib lub sij hawm muaj peev xwm teb nyob rau hauv qhov kev txiav txim ntawm ib tug siv hluav taws xob teb, cov kev taw qhia ntawm lub teeb thauj nyob rau hauv lub waveguide array yog sib npaug rau lub sij hawm lub sij hawm nyob rau hauv lub Schrödinger kab zauv. Lub curvature ntawm lub waveguide dabtsi yog khoov trajectory yog suav hais tias yog qhov sib npaug ntawm lub zog hluav taws xob ua haujlwm ntawm lub teeb xa hluav taws xob, qhov twg lub voj voog bending trajectory generates qhov sib npaug ntawm qhov hluav taws xob tsis tu ncua ua rau Bloch oscillations, thiab lub sij hawm bending trajectory generates qhov sib npaug lub sij hawm hluav taws xob teb. quab yuam qhia Frohnke kev hloov kho. Yog li, lub waveguide array ua rau kev soj ntsuam ntawm Bloch oscillation phenomenon nyob rau hauv ib qho optical Floquet lattice.

Daim duab 2. (a)-(d) Kev soj ntsuam kev soj ntsuam ntawm ib lub waveguide excitation. (e)-(h) Kev soj ntsuam kev soj ntsuam ntawm dav nqaj excitation.
Hauv txoj kev tshawb no, kev hloov pauv ntawm kev sib kis ntawm lub teeb tsis tu ncua hauv waveguide arrays tau pom thiab pom siv waveguide fluorescence microscopy. Daim duab 2 qhia txog kev ua pa thiab oscillation hom ntawm Bloch oscillation phenomenon nyob rau hauv lub optical Froquet lattice rau ib waveguide tshwm sim thiab dav beam tshwm sim, feem. Thaum lub sij hawm Floquet modulation tsis sib npaug rau ib qho sib npaug ntau ntawm Bloch oscillation lub sij hawm, Floquet dispersion yog tas li thiab sib npaug rau xoom, thiab optical Floquet-Bloch oscillations nrog lub sij hawm uas yog qhov tsawg tshaj plaws ntau yam ntawm Floquet modulation lub sij hawm thiab Bloch. Lub sijhawm oscillation tshwm sim. Nyob rau hauv tas li ntawd, lub Floquet dispersion tsis yog sib npaug rau 0, thiab kis tau tus mob ntawm lub teeb yog feem ntau characterized los ntawm diffuse diffraction. Tsis tas li ntawd, cov kws tshawb fawb theoretically thiab sim tau tshawb xyuas qhov cuam tshuam ntawm Flokay modulation tsis nyob rau ntawm qhov muag pom Flokay-Bloch oscillations, nthuav tawm qhov txawv txav ntawm qhov tshwm sim, suav nrog cov fractal spectral zog cuam tshuam nrog lub sijhawm Flokay modulation thiab fractional-order Flokay. tunneling zog txuam nrog Flokay modulation amplitude.

Fig. 3. (a) Fractal spectral zog ntawm optical Froquet-Bloch oscillations. (b) Fractional Order Floquet-Bloch tunneling zog ntawm optical Floquet-Bloch oscillations.
Kev soj ntsuam pom ntawm optical Floquet-Bloch oscillations nthuav tawm cov txheej txheem tshiab ntawm kev ua haujlwm nthwv dej evolution, uas yog qhov tseem ceeb hauv ob qho tib si kev tshawb fawb thiab kev siv tswv yim. Nyob rau hauv cov nqe lus ntawm kev tshawb fawb tseem ceeb, tus qauv theoretical thiab kev sim platform txhawb ntxiv kev tshawb nrhiav ntawm cov xwm txheej tshiab tshwm sim los ntawm kev sib cuam tshuam ntawm kev tsim thiab kev hloov kho ntawm Frohike-Bloch oscillations nrog binary lattices, non-Ermian lattices, thiab optical nonlinearities; thiab nyob rau hauv cov nqe lus ntawm kev siv tswv yim, qhov kho qhov muag Frohike-Bloch oscillations yog qhov tseem ceeb ntawm kev thauj khoom sib txuam, thiab yog li tuaj yeem ua tau zoo hauv kev siv, optical Floquet-Bloch oscillations yog qhov tseem ceeb ntawm kev thauj mus los sib xws, thiab yog li tuaj yeem txuas ntxiv mus rau ntau yam kev tshawb fawb. platforms xws li hluavtaws zaus-domain lattices, txias atoms, qhov chaw-lub sij hawm siv lead ua, thiab quantum taug kev, thiab yuav tsum tau siv rau realizing zaus conversion, precision ntsuas, thiab manipulation ntawm ntau yam yoj kis tau tus mob.