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Giant modulation of optical nonlinearity by Floquet engineering

A Publisher Correction to this article was published on 12 January 2022

This article has been updated


Strong periodic driving with light offers the potential to coherently manipulate the properties of quantum materials on ultrafast timescales. Recently, strategies have emerged to drastically alter electronic and magnetic properties by optically inducing non-trivial band topologies1,2,3,4,5,6, emergent spin interactions7,8,9,10,11 and even superconductivity12. However, the prospects and methods of coherently engineering optical properties on demand are far less understood13. Here we demonstrate coherent control and giant modulation of optical nonlinearity in a van der Waals layered magnetic insulator, manganese phosphorus trisulfide (MnPS3). By driving far off-resonance from the lowest on-site manganese dd transition, we observe a coherent on–off switching of its optical second harmonic generation efficiency on the timescale of 100 femtoseconds with no measurable dissipation. At driving electric fields of the order of 109 volts per metre, the on–off ratio exceeds 10, which is limited only by the sample damage threshold. Floquet theory calculations14 based on a single-ion model of MnPS3 are able to reproduce the measured driving field amplitude and polarization dependence of the effect. Our approach can be applied to a broad range of insulating materials and could lead to dynamically designed nonlinear optical elements.

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Fig. 1: Static SHG from MnPS3.
Fig. 2: Coherent drive-induced state modification.
Fig. 3: Driving photon energy dependence of RA SHG transients.
Fig. 4: Driving field amplitude and polarization dependence of SHG modulation.

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Data availability

All other data that support the findings of this study are available from the corresponding author on reasonable request. Source data are provided with this paper.

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We acknowledge discussions with X. Li, S. Chaudhary and G. Refael. This work was supported by ARO MURI grant number W911NF-16-1-0361. D.H. also acknowledges support for instrumentation from the David and Lucile Packard Foundation and from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-1733907). M.Y. acknowledges support by the Gordon and Betty Moore Foundation through grant GBMF8690 to UCSB and by the National Science Foundation under grant number NSF PHY-1748958. J.-G.P. was supported by the Leading Researcher Program of the National Research Foundation of Korea (grant number 2020R1A3B2079375).

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Authors and Affiliations



S.L. and J.-G.P. synthesized and characterized the MnPS3 crystals. J.-Y.S. and H.C. performed the optical measurements. M.Y., J.-Y.S. and L.B. performed the single-ion model based static and Floquet dynamical calculations. J.-Y.S., M.Y. and D.H. wrote the paper with input from all authors.

Corresponding author

Correspondence to D. Hsieh.

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The authors declare no competing interests.

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Peer review information Nature thanks thanks Liang Wu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 EDX measurements.

The EDX spectrum and the calculated atomic percentage measured at three different spots.

Extended Data Fig. 2 Magnetic susceptibility measurements.

The magnetic susceptibility measured with the magnetic field parallel to the ab plane and to the c* axis, which is the out-of-plane direction.

Extended Data Fig. 3 Optical absorption data.

The relationship between (KE)2 and E is plotted (green circles) to facilitate the linear fit (black curve). Inset shows the DOS of in-gap impurity states.

Extended Data Fig. 4 Linear coupling between SHG susceptibility and AFM order parameter.

The log-log plot of the critical behavior of \({\chi }_{{ijk}}^{{\rm{ED}}({\rm{c}})}\) (squares). Linear fits within two different temperature ranges are overlaid (lines).

Extended Data Fig. 5 Linear reflectivity transients.

ΔR/R with 1.55 eV probe and ħΩ = 0.66 eV taken at various driving a, amplitudes and b, polarizations.

Extended Data Fig. 6 Ruling out competition between SHG and SFG as the source of SHG suppression.

Driving field amplitude dependence of SFG intensity at various probe fluences.

Extended Data Fig. 7 SHG transients at higher temperatures.

Time-resolved SHG measured at a, 70 K and b, 90 K with ħΩ = 0.66 eV driving. \({E}_{{\rm{\max }}}^{{\rm{pu}}}\) = 109 V/m, θ = 90˚ and φ = 60˚.

Extended Data Fig. 8 Comparisons between RA patterns induced by resonant driving and static RA patterns at higher temperatures.

Upper panels show the time-resolved RA patterns taken at 10 K, and lower panels show the static RA patterns taken at higher temperatures. Identical fits to the crystal point group for each column are overlaid (black lines).

Extended Data Fig. 9 Drive amplitude dependence of long time SHG suppression.

The calculated (black) and experimental (blue) driving amplitude (ħΩ = 2.07 eV) dependence of ∆Imag/Imag plateau values. Experimental data are taken at t = 200 ps.

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Shan, JY., Ye, M., Chu, H. et al. Giant modulation of optical nonlinearity by Floquet engineering. Nature 600, 235–239 (2021).

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