DOI: 10.5061/dryad.4qrfj6qkc
title: Data from: Squeezed dual-comb spectroscopy

description: Laser spectroscopy and interferometry provide an unparalleled view into
 the fundamental nature of matter and the Universe through ultra-precise
 measurements of atomic transition frequencies and gravitational waves.
 Optical frequency combs have expanded metrology capabilities by
 phase-coherently bridging radio frequency and optical domains to enable
 traceable high-resolution spectroscopy across bandwidths greater than
 hundreds of terahertz. However, quantum mechanics limits the measurement
 precision achievable with laser frequency combs and traditional laser
 sources, ultimately impacting fundamental interferometry and spectroscopy.
 Squeezing the distribution of quantum noise to enhance measurement
 precision of either the amplitude or phase quadrature of an optical field
 leads to significant measurement improvements with continuous wave lasers.
 But experiments demonstrating true metrological advantage of broad
 bandwidth squeezing with optical frequency combs are much less developed.
 In this work, we generate bright amplitude-squeezed frequency comb light
 and apply it to molecular spectroscopy using interferometry that leverages
 the high-speed and broad spectral coverage of the dual-comb technique.
 Using the Kerr effect in nonlinear optical fiber, the amplitude quadrature
 of a frequency comb centered at 1560 nm is squeezed by &gt;3 dB over a
 2.5 THz of bandwidth that includes 2500 comb teeth spaced by 1 GHz.
 Interferometry with a second coherent state frequency comb yields
 mode-resolved spectroscopy of hydrogen sulfide gas with a signal-to-noise
 ratio nearly 3 dB beyond the shot noise limit, taking full metrological
 advantage of the amplitude squeezing when the electrical noise floor is
 considered. The quantum noise reduction leads to a two-fold quantum
 speedup in the determination of gas concentration, with impact for fast,
 broadband, and high signal-to-noise ratio measurements of multiple species
 in dynamic chemical and biological environments. Overall, this work
 solidifies the general understanding of quantum noise reduction in Fourier
 transform spectroscopy and motivates further exploration with squeezed
 states in the broad application space of frequency comb metrology.
description: # Data from: Squeezed dual-comb spectroscopy
 [https://doi.org/10.5061/dryad.4qrfj6qkc](https://doi.org/10.5061/dryad.4qrfj6qkc) ## Description of the data and file structure 1. “Raw DCS Data” Folder. The raw data for each of the three measurement cases and additional noise floor. The data stream in the preAcquisition_data.bin file in the Input_data subfolders. The data contains the four-channel stream of the interferogram with molecular absorption, the baseline interferogram, and the two beat notes between the squeezed and coherent comb with the CW laser, in that order. 2. “Processed DCS Data” folder. Contains the MATLAB data files with the phase- and self-corrected data. “FullSCData6_17_24_1112IGMs.mat” contains a stream of 1112 self-corrected IGMs for the “No Aux” (SNL), “Phase 1” (SQZ), and “Phase 2” (ANTI-SQZ) cases, with two streams for each case (Ch 1 and Ch 2, denoting the interferogram with absorption and baseline interferogram, respectively). “AvgSCData6_17_24_1112IGMs.mat” contains the averaged interferogram for each of these three cases and each channel. “NewAxesSCData6_17_24_1112IGMs.mat” contains the frequency scaling factor for each of the three cases, with ‘fs_new’, ‘fs_new1’, and ‘fs_new2’ corresponding to SNL, Phase1, and Phase2, respectively. It also contains fitting objects for each of the three measurement cases, as well as the fit and averaging data used in the corresponding figures. 3. “OSA Data” folder. The OSA spectra used in Figure 3B. Included in the “Scripts” folder is the “Plot_soliton” python script used to generate this figure. 4. “Single Squeezed Comb Data” folder. The single comb squeezing data in Figure 3E and Figure S3 are included along with the data used to generate Figure S2. Associated scripts are in the “Scripts” folder. 5. "Scripts" folder. Contains code to generate Figures 3B, 3E, 4, 5, S2, S3, S6, S7, S8. ### Files and variables #### File: QDCS\_Data.zip **Description:** Zipped datafile including Raw DCS Data, Processed DCS Data, OSA Data, Single Squeezed Comb Data. #### File: SSA3201X\_14.94mW\_146uW\_SNL\_00.0\_mW\_1 kHz\_1 kHz\_2024\_07\_11\_\_21\_58\_38.txt **Description:** Example of File in Single Squeezed Comb Data Folder. First Column is RF frequency in MHz. Second Column is RF power in dBm. #### File: squeezedcomb.csv **Description:** Example of File in OSA Data Folder. First Column after Header and empty rows is optical wavelength in nm. Second Column after header and empty rows is optical power in dBm. #### File: preAcquistion\_data.bin **Description:** Example of File in Raw DCS Data Folder under "Input_data" for each subfolder. Data is stream of arbitrary voltages from digitizer stored in binary format. Utilize InitialProcessing_loadRawData_H2S_10_29_2024.m for fast phase correction. Self correction is available online as selfCorrectIGMS.m from MathWorks File Exchange. #### File: FullSCData6\_17\_24\_1112IGMs.mat **Description:** Fast phase and self corrected interferograms. Data is matlab data file containing six waves: "Igm_SC_NoAuxChannel1", "Igm_SC_Phase1Channel1", "Igm_SC_Phase2Channel1", and the same with Channel 2. "No Aux" refers to SNL, "Phase 1" to SQZ, and "Phase 2" to ANTI-SQZ. Channel 1 contains the gas sample, and Channel 2 does not. Each wave is the interferogram stream containing 1112 individual interferograms and has units of arbitrary voltages from digitizer. #### File: AvgSCData6\_17\_24\_1112IGMs.mat **Description:** Chopped and averaged interferograms from FullSCData6_17_24_1112IGMs.mat, with the same naming convention for the six waves. Units of arbitrary voltages from digitizer. #### File: NewAxesSCData6\_17\_24\_1112IGMs.mat **Description:** .mat file containing three waves (‘fs_new', ‘fs_new1', ‘fs_new2') each containing a single number, corresponding to SNL, SQZ, and ANTI-SQZ, respectively. This number (in MHz) is the frequency scaling which allows one to convert from arbitrary frequency axis generated from Fourier transform to a frequency axis in real units. #### Files: 'NoAux\_correctfittingobject.mat', 'Phase1\_fittingobject.mat', & 'Phase2\_fittingobject.mat' **Description:** .mat file each containing 'obj', which is the full fitting object generated for SNL (NoAux), SQZ (Phase1), and ANTI-SQZ (Phase2), respectively. #### File: 'fullfittingoutput-10-22.mat' **Description:** .mat file containing the data used to analyze the shot noise as a function of power. Specifically, it contains data generated by fitting each of the 1112 interferograms individually. 'fit' contains the fit and resids contains the fit residuals. Both are arrays of size 1220 x 1112 x 3, with these dimensions corresponding to wavelength x IGM x (SNL / SQZ / ANTI-SQZ). 'obj' is a representative fitting object used to retrieve the fitting wavelength axis. 'lfitvals' contains the fit cell lengths, 'residsstd' contains the standard deviation of the fit residuals, and 'residsvar' the variance of the fit residuals. All three are of dimensions 1112 x 3, corresponding to IGM x (SNL / SQZ / ANTI-SQZ). #### File: fig5data.mat **Description:** .mat file containing the data and fits used to generate Figure 5. 'fitTPhase1' contains the squeezed data fit. 'Igm_SC_NoAuxChannel1_avg' contains the averaged IGM with absorption for SNL case. 'noaux' contains the fitting object for the SNL case. 'wvNoAux', 'wvPhase1', and 'wvPhase2' contain the wavelength axes for SNL, SQZ, and ANTI_SQZ data, respectively, in nm. 'measTNoAux', 'measTPhase1', and 'measTPhase2' contain the measured transmission data at each wavelength for SNL, SQZ, and ANTI_SQZ data, respectively. 'residNoAux', 'residPhase1', and 'residPhase2' contain the transmission fit residuals at each wavelength for SNL, SQZ, and ANTI_SQZ data, respectively. #### File: figS7fits.mat **Description:** .mat file containing the data and fits used to generate Figure S7. It contains two waves: 'nIGMsarray' and 'residsstd'. 'nIGMsarray' is the x-axis data of this figure, and includes the number of interferograms included to fit each data point. 'residsstd' is a 54x3 matlab array, with each column corresponding to SNL, SQZ, and ANTI-SQZ, respectively. It is the y-axis data for this plot and contains the standard deviation of the fit residuals. #### File: figS6generation.m **Description:** Matlab code which generates the mode-resolved dual comb spectra shown in Figure S6. Requires loading 'FullSCData6_17_24_1112IGMs.mat,' NewAxesSCData6_17_24_1112IGMs.mat', and 'NoAux_correctfittingobject.mat'. #### File: figS8generation.m **Description:** Matlab code which generates Figure S8. Requires loading 'NoAux_correctfittingobject.mat,' 'Phase1_fittingobject.mat,' 'Phase2_fittingobject.mat,' 'AvgSCData6_17_24_1112IGMs.mat', and 'fullfittingoutput-10-22.mat.' #### File: fig5generation.m **Description:** Matlab code which generates Figure 5. Requires loading 'fig5data.mat'. #### File: figS7generation.m **Description:** Matlab code which generates Figure S7. Requires loading 'figS7fits.mat'. #### File: Fermionics\_wideband\_squeezing.py **Description:** Python code which generates Figure 3E. Requires loading data from 'try3' folder under Fermionics_Wideband_Squeezing in Single Comb Squeezing Data. #### File: SNL\_Fermionics.oy **Description** Python code which generates Figure S2. Requires loading data from 'SNL_scan' folder under Fermionics_Wideband_Squeezing in Single Comb Squeezing Data. #### File: BDX\_wideband\_squeezing.py **Description** Python code which generates Figure S3. Requires loading data from BDX_Wideband_Squeezing in Single Comb Squeezing Data folder. #### File: Plot\_soliton.py **Description** Python code which generates Figure 3D. Requires loading data from OSA Data folder. #### File: InitialProcessing\_loadRawData\_H2S\_10\_29\_2024.m **Description** Matlab code which runs fast phase correction and generates Figure4. Requires loading data from Figure 4 folder in Raw DCS Data. Will need to change path names appropriately to match your downloaded data.