Work Description

Date: 27 August, 2024

Dataset Title: Publically available repository for "Cavity Floquet Engineering

Dataset Creators: Lingxiao Zhou

Dataset Contact: lingxiaz@umich.edu

Funding: Army Research Office under Awards W911NF-17-1-0312, the Air Force Office of Scientific Research under Awards FA2386-21-1-4066, the National Science Foundation under Awards DMR 2132470, Office of Naval Research under Awards N00014-21-1-2770, and the Gordon and Betty Moore Foundation under Grant GBMF10694.

Key Points:
- The authors demonstrate enhancement by nearly two-orders of magnitude of the circular-polarized optical Stark effect in WSe₂ embedded into a Fabry Perot cavity.
- the effect is equivelent to 200 Tesla.
- Then the effect can be used to implement a XOR switch.

Research Overview:
Floquet engineering is a promising tool to manipulate quantum systems coherently. A wellknown example is the optical Stark effect, which has been used for optical trapping of atoms and breaking time-reversal symmetry in solids. However, as a coherent nonlinear optical effect, Floquet engineering typically requires high field intensities obtained in ultrafast pulses, severely limiting its use. Here, we show that cavity engineering of the vacuum modes can lead to orders-of-magnitude enhancement of the effective Floquet field. We demonstrate Floquet effects at an extremely low fluence of 450 photons/μm2 and, at higher fluences, up to 50 meV spin and valley splitting of WSe2 excitons, corresponding to an enormous time-reversal breaking, non-Maxwellian magnetic field of over 200 T. Utilizing such an optically-controlled magnetic field, we demonstrate an ultrafast, picojoule chirality XOR gate. These results suggest that cavity Floquet engineering may enable the creation of steady-state or quasi-equilibrium Floquet bands, strongly non-perturbative modifications of materials beyond the reach of other means, and application of Floquet engineering to a wide range of materials and applications.

Methodology:
1. Data collected by Princeton Instrument spectrometer, in the format of ".SPE".
2. Data collected by Throlab Image camera, in the format of ".TIFF".
3. Data collected by PARK AFM, in the format of ".TIFF".
4. Code for data analysis/simuation, Matlab and Mathematica script.

Instrument and/or Software specifications: Princeton Instrument spectrometer, Throlab Image camera, PARK AFM, Matlab and Mathematica

Files contained here:

(Fig1) Reflectance_spectrum Data_Code:
-experiment: SiNSiO2_DBR_reflectance, ZnSMgF2_DBR_reflectance, Whole_device_reflectance are three folders containing reflectance experiment data for SiNSiO2_DBR, ZnSMgF2_DBR, and the Whole_device. Under each folder, the ".spe" files are raw data, "R_contrast_fullregion.m" or "frameRC.m" will analyse data with the help of script "loadspe.m" (no need to run loadspe.m individually). The data is plotted in figure 1c.
-simulation: Two files are simulation script for figure 1c: Monlayer_TMDs_incavity.m simulates the whole device reflectance, SiN_SiO2_DBR_MgF2_ZnS_DBR.m simulates the reflectance of two DBRs. The last one, SiO2_TiO2_DBR_hBN.m, simulates the bare DBR enhancement vs hBN thickness as plotted in supplement as figure s1f.

(Fig_23) Optical Stark Effect Data (all):
-DBR_co: The experiment co-circular OSE data measured with bare DBR
-each sub folder: corresponding to a power scannning as its name
-BG folder: measured the all-reflected light background from pump and probe
-RC folder: single test reflected probe light when focused on sample (not used for data analysis, just a test during experiment)
-"****.spe": the probe reflectance scanning the time delay between pump and probe. main data.
-"pumpprobe.m": the script analysing the data. The first three sections ("%%") must be executed within the BG folder, and then following sections should be executed in the folder containing the series of "****.spe" files. By the contrast of background and sample we can extract the feature information.
-"loadspe.m": the script helps reading the raw data used in "pumpprobe.m", no need to run it individually.
-Help generate Figure 2b 2g s2

-enhanced_co: The experiment co-circular OSE data measured with cavity
-each sub folder: corresponding to a power scannning as its name
-BG folder: measured the all-reflected light background from pump and probe
-"****.spe": the probe reflectance scanning the time delay between pump and probe. main data.
-"pumpprobe.m": the script analysing the data. The first three sections ("%%") must be executed within the BG folder, and then following sections should be executed in the folder containing the series of "****.spe" files. By the contrast of background and sample we can extract the feature information.
-"loadspe.m": the script helps reading the raw data used in "pumpprobe.m", no need to run it individually.
-Help generate Figure 2a 2c 2d 2f 2h s2

-enhanced_cross: The experiment cross-circular OSE data measured with cavity
-each sub folder: corresponding to a power scannning as its name
-BG folder: measured the all-reflected light background from pump and probe
-"****.spe": the probe reflectance scanning the time delay between pump and probe. main data.
-"pumpprobe.m": the script analysing the data. The first three sections ("%%") must be executed within the BG folder, and then following sections should be executed in the folder containing the series of "****.spe" files. By the contrast of background and sample we can extract the feature information.
-"loadspe.m": the script helps reading the raw data used in "pumpprobe.m", no need to run it individually.
-Help generate Figure 2e 2f 2h s2

(Fig4) Maxshift estimate:
A numerical calculation script about potential largest OSE shift based on experiental measured light-matter coupling strength, two-photon and linear excitation efficiency.

Supplement:
-OSE induced cavity shift estimate code (sup): an analytical script to estimate how cavity mode shift once TMD has OSE. Generate figure S3

-Pump beam profile and DBR enhancement (sup) Generate figure S1:
-Beamshape (data): contains a image camera recording beam spatial profile
-DBR hBN AFM (data): contains a PARK AMF measured hBN thickness AFM data
-ML WSe2 on DBR RC (data): contains ML WSe2 information
-Pump pulse duration (data): contains time dependent data recording beam time profile

-Two-photon excitation Data (sup): contains a power-dependent Two-photon excitation data. TPL_intensity_extraction.m is the analysis code. Generate figure S4

Related publication(s):
Lingxiao Zhou, et al. Cavity-Floquet Engineering. Nature Communication (2024)

Use and Access:
This data set is made available under a Attribution-NonCommercial 4.0 International (CC BY-NC 4.0).

To Cite Data:
Lingxiao Zhou, et al. (2024). Cavity-Floquet Engineering. -Deep Blue. https://doi.org/10.7302/f6xv-d389
Lingxiao Zhou, et al. Cavity-Floquet Engineering. Nature Communication (2024)