DOI: 10.5061/dryad.wm37pvn0j
title: Coherent acoustic frequency comb via floquet engineering of optical tweezer phonon lasers

description: Floquet engineering, featuring time-periodic control of various systems,
 has enabled observations of many exotic phenomena such as time crystals,
 breaking of reciprocity symmetry, and exceptional topology. Theoretically,
 a periodic drive can make the system inherit the time period and generate
 new harmonics or distort the band structure at the fundamental frequency.
 Here, by combining such a technique with levitated optomechanics, we
 present the first example of a coherent acoustic frequency comb with
 microsphere phonon lasers. This work shows that our technique offers the
 capability of flexibly controlling both the teeth number and the teeth
 spacing of the resulting coherent acoustic frequency comb. Particularly,
 we confirm that all Floquet-driven comb teeth can reach the truly coherent
 regime, i.e., satisfying all the characteristic features of phonon lasers.
 Our work provides a platform to drive the nonlinear phonon laser to a
 coherent acoustic frequency comb with truly coherent comb teeth.
description: # Coherent acoustic frequency comb via floquet engineering of optical
 tweezer phonon lasers Dataset DOI:
 [10.5061/dryad.wm37pvn0j](10.5061/dryad.wm37pvn0j) ## Description of the
 data and file structure Data for Figs.1-4 in  'Coherent Acoustic
 Frequency Comb via Floquet Engineering of Optical-tweezer Phonon
 Lasers'  ### Files and variables #### File: Fig1c.xlsx
 **Description:** **Fig. 1.** **Overview of the Floquet coherent acoustic
 frequency comb.** **c.** Power spectrum of phonons before and after the
 Floquet pump in experiment and simulation. #### File: Fig2a.xlsx
 **Description:** **Fig. 2.** **Coherent phonon lasing behaviors of the
 coherent acoustic frequency comb.** **a.** Evolutions of the coherent
 acoustic frequency comb. Measured phonon autocorrelations. #### File:
 Fig2b.xlsx **Description:** **Fig. 2.** **Coherent phonon lasing behaviors
 of the coherent acoustic frequency comb.** **b.** ***g***(2)(0) and at
 zero-time delay for **Ω+1,** and **2Ω+1** showing the phonon lasing
 behavior of the Floquet sidebands. The error bars denote the standard
 deviation of each measurement, consisting of 55 samples. #### File:
 Fig2c.xlsx **Description:** **Fig. 2.** **Coherent phonon lasing behaviors
 of the coherent acoustic frequency comb.** **c.** ***g***(3)(0) at
 zero-time delay for **Ω+1**, and **2Ω+1** showing the phonon lasing
 behavior of the Floquet sidebands. The error bars denote the standard
 deviation of each measurement, consisting of 55 samples. #### File:
 Fig3a.xlsx **Description: Fig. 3.** **Phase coherence of frequency
 combs.** **a.** Measured displacement the microsphere, showing a stable
 envelope state. #### File: Fig3b.xlsx **Description:**  **Fig. 3.**
 **Phase coherence of frequency combs.** **b.** Velocity of the
 microsphere, showing a stable envelope state. #### File: Fig3c.xlsx
 **Description:** **Fig. 3.** **Phase coherence of frequency combs.**
 **c.** Phase noise of the coherent acoustic frequency comb and the phonon
 laser. #### File: Fig4a.xlsx **Description:** **Fig. 4.** **Coherent
 acoustic frequency comb with Floquet engineering.** **a.** Three typical
 power spectra for different modulation frequencies Ωmod. #### File:
 Fig4c.xlsx **Description:** **Fig. 4.** **Coherent acoustic frequency comb
 with Floquet engineering.c.** The evolution of the power spectrum with
 increasing modulation depth *η*, showing the generation of new comb teeth
 around the phonon lasing modes Ω0, 2Ω0, 3Ω0 with Floquet engineering. ####
 File: Fig4d.xlsx **Description:** **Fig. 4.** **Coherent acoustic
 frequency comb with Floquet engineering.** **d.** The intensity of phonon
 power spectra of phonon lasing Ω0, Ω+1, and Ω+2, with varying modulation
 depth, indicating energy transfers from the fundamental mode to two
 sidebands. #### File: Fig4e.xlsx **Description:** **Fig. 4.** **Coherent
 acoustic frequency comb with Floquet engineering.** **e.** Phonon
 population &lt;*N*&gt; versus *η* for the sideband Ω+1. #### File:
 Fig4f.xlsx **Description:** **Fig. 4.** **Coherent acoustic frequency comb
 with Floquet engineering.**  **f.** Measured phonon autocorrelations
 ***g***(2)(0) at zero-time delay for Ω+1. #### File: Fig4g.xlsx
 **Description:**  **Fig. 4.** **Coherent acoustic frequency comb with
 Floquet engineering.**  **g.** Measured phonon autocorrelations
 ***g***(3)(0) at zero-time delay for Ω+1.