Coherent control of acoustic phonons in a silica fiber using a multi-GHz optical frequency comb

Multi-gigahertz mechanical vibrations stemming from interactions between light fields and matter, also known as acoustic phonons, have long been a subject of study. In recent years, specially designed functional devices have been developed to enhance the light-matter interaction strength, since the excitation of acoustic phonons by a continuous wave laser alone is insufficient. However, with such structure-dependent enhancements, the strength of the interaction cannot be aptly and instantly controlled. We propose a new technique to control the effective interaction strength, which is not via the material structure in the spatial domain, as with the above-mentioned specially designed functional devices, but through the structure of light in the time domain. Here we show the effective excitation and coherent control of acoustic phonons in a single-mode fiber using an optical frequency comb by tailoring the optical pulse train. We believe this work represents an important step towards"comb-matter interactions."


skyrmions, and that it will lead to increasingly flexible tools in combination with the aforementioned functional devices.
Research on the interaction between light fields and acoustic phonons in lattice media has greatly advanced over the past decade. It holds enormous potential in scientific studies and practical areas, where possible applications include the generation of ultra-low noise lasers 1 , optical frequency combs (OFCs) 2,3 , coherent control 4,5 , optical storage [6][7][8] , slow and fast light generation 9 , optical switching 10 , and Brillouin cooling 11 , to name of few. This light-matter interaction is caused by a permittivity change of a medium by an incident electric field. Due to the weak nature of the interaction, specially-designed photonic crystal fibers 5,[12][13][14] , suspended waveguides 15,16 or microresonators 1,6 , are devised to constrain both the optical fields and the acoustic modes, to improve the interaction strength. However, with such structure-dependent interaction enhancement, there is a lack of ability to control the interaction strength dynamically or rapidly. In optical fibers, Brillouin scattering is the main process involved in the generation of acoustic phonons and it requires long interaction lengths, like with cw or long pulsed (at least few nanoseconds) 17 lasers. Long pulses, however, are unsuitable for telecommunication applications that require fast and efficient control of the light-matter interaction.
We demonstrate here that if a second pulse is launched after a first one well within the lifetime of a given acoustic phonon, this acoustic phonon can be coherently enhanced or damped. To achieve this, we used the picosecond pulses from our own developed multi-GHz OFC which has its repetition rate set to the phonon resonance frequency (up to 16 GHz) 18 .
Enhancing and damping can be controlled by the pulse repetition rate or the time delay between the pulses, which make multi-GHz OFCs suitable for the effective and coherent excitation of acoustic phonons.
Brillouin scattering results from photon-phonon interactions through the electrostriction effect 19 . When an acoustic phonon satisfies the phase-matching condition, it scatters light in the counter-propagating backward direction (BWD). This is shown in Fig. 1 (a), as a cw (or long pulsed) laser beam propagates in the forward direction (FWD) with an angular frequency of (FWD optical, red line) and is coupled into an optical fiber, the beam is scattered by where represents the wavelength of the FWD optical wave and the concept is described in the dispersion diagram of Fig. 1 (b). In other words, the acoustic wave leads to a Brillouin gain and loss at the center frequencies of − and + , respectively, as shown in the gain profile in Fig. 1  To demonstrate coherent control of acoustic phonons, the repetition rate of the OFC was changed to 7.8 GHz (half the phonon resonance frequency), and a Michelson interferometer (MI) was inserted to produce double pulses as shown in Fig. 2 (d) (see Method for further details). Here, the pulse delay was normalized to the inverse of half the phonon resonance (128 ps). As depicted in Fig. 3 (a), the phonon amplitude can be accumulated when the interval of a series of optical pulses matches the phonon resonance, which is identical to the results of the previous experiment illustrated in Fig. 2. In contrast, when the delay is set to the inverse of 0.25 or 0.75 of the phonon resonance frequency, while the first pulse excites the phonon, the second pulse damps it (Fig. 3 (b)). As a result, the amplitude of the phonon is suppressed even if the fundamental repetition frequency of the OFC is matched to the phonon resonance frequency.  Fig. 3 (d) are enhanced when the pulse interval is 0, 0.5 or 1, which supports the concept as shown in Fig. 1 (e) and (f). In contrast, when the phonon is out of resonance, the optical spectrum does not change even though the pulse interval changes (Fig. 3 (e)).
In conclusion, we demonstrate coherent control of acoustic phonons in a standard singlemode fiber by a repetition-frequency-tailored multi-GHz OFC. Not only was the phonon amplitude coherently enhanced, but the acoustic phonon was also controlled by the optical pulse delay. Our new approach to control the effective interaction strength between photons and phonons, can be applied in various areas of science, especially in the field of telecommunications. In this letter, we focus on acoustic phonon experiments, but the result opens an entirely new optical scheme to manipulate (quasi) particles in the field of solid-state physics, where there are a myriad of intriguing elemental excitations such as optically accessible skyrmions 20 and magnons 21,22 . The technique could be extended to controlling multiple kinds of excitations simultaneously by combining other degrees of freedom of the OFC, such as the carrier-envelope offset frequency, the pulse duration or the chirp, to name a few. We believe applying OFCs to study and manipulate particles has great potential in the field of solid-state physics and that our work represents an important step in "comb-matter interactions" research.

The light source (multi-GHz OFC)
An OFC based on a Kerr-lens mode-locked Yb:Y2O3 ceramic laser with a repetition rate of 7.8/15.6 GHz was used. The center wavelength and pulse duration were 1080 nm (278 THz) and 152 fs, respectively. The repetition rate was stabilized to an analog signal generator via a phase-locked loop circuit and a piezo actuator mounted on one of the cavity mirrors. Other details of this OFC can be found in the reference 18 . Free-running fluctuations of the carrierenvelop offset and optical frequencies were negligible, and we did not apply any stabilization to them during the experiments.
The OFC output was spectrally filtered by a hand-made optical band-pass filter (OBPF) with a maximum frequency resolution of 2 GHz at the wavelength of 1080 nm. It is based on a multi-pass, high-resolution spectrograph 23 and it would let through four longitudinal modes, as shown in Fig. 2. (c). The filtered output was amplified by a three-stage optical amplifier (a cascade of one semiconductor optical amplifier followed by two Yb:fiber amplifiers) to a maximum average power of more than 100 mW. The output power could be tuned by a variable optical attenuator assembled in-house.

Preparation of the double pulse
The Michelson interferometer (MI) was used to generate double pulses. In one of the interferometer arms, a stepper-motorized mechanical stage was used to tune the pulse time interval between 0 and 160 ps. A piezo actuator and a noise source were used to scan the arm length in order to average out the spectral interference of the double pulse to achieve higher SNR. Without this piezo actuator, sub-wavelength stabilization of the interferometer's arm would be required, and the cost would be lengthy scan times and data averaging. While the use of a piezo actuator reduces the time resolution of the experiment to several hundreds of femtoseconds, such a high time resolution was not required for our measurements. The peakto-peak amplitude and the bandwidth were measured to be 3 µm and 300 Hz, respectively.

Photon-phonon interaction
The field distribution of the FWD and BWD optical modes in the fiber are expressed as  can be estimated from ( ) and ( ) . To calculate the simulated dashed line in Fig. 3(c), we solved these differential equations in MATLAB and as described in the supplemental information of reference 12 .