A chip-integrated coherent photonic-phononic memory

Controlling and manipulating quanta of coherent acoustic vibrations—phonons—in integrated circuits has recently drawn a lot of attention, since phonons can function as unique links between radiofrequency and optical signals, allow access to quantum regimes and offer advanced signal processing capabilities. Recent approaches based on optomechanical resonators have achieved impressive quality factors allowing for storage of optical signals. However, so far these techniques have been limited in bandwidth and are incompatible with multi-wavelength operation. In this work, we experimentally demonstrate a coherent buffer in an integrated planar optical waveguide by transferring the optical information coherently to an acoustic hypersound wave. Optical information is extracted using the reverse process. These hypersound phonons have similar wavelengths as the optical photons but travel at five orders of magnitude lower velocity. We demonstrate the storage of phase and amplitude of optical information with gigahertz bandwidth and show operation at separate wavelengths with negligible cross-talk.

modulator. The CW laser signal is carved into pulses by two intensity modulators connected to a short-pulse generator, allowing the generation of pulses with different amplitude levels and phase states. The pulses are amplified using erbium-doped fibre amplifiers (EDFA) and subsequently filtered by narrow bandwidth (0.5 nm) bandpass filters to reduce the effect of broadband white noise introduced by the amplification step. Additionally to the passive bandpass filter a nonlinear fibre loop is implemented in the write-and-read arm. The loop consists of 1 km standard singlemode fibre, a polarization controller and a 50/50 coupler to introduce some asymmetry in the two paths. This fibre loop is used for two reasons: firstly it allows only the pulses to be transmitted and efficiently suppresses any noise or coherent background present from the laser or amplifier respectively. Secondly, it improves the pulse shape by smoothing the edges of the pulses. After the loop a second EDFA amplifies the pulses again to reach the necessary peak power of several watts. Both paths lead to opposite sides of the photonic chip and are coupled to the waveguide using lensed fibres.
For the multi-wavelength measurement a second laser, 100 GHz apart from the first laser, is used and coupled into the data or write-and-read arm, respectively. The output from the chip (circulator port 3 in Supplementary Figure 1) is split with a 50 / 50 fibre coupler and sent to two narrowband filters to separate the two wavelength channels. Each filtered channel is then detected using two 12 GHz photodiodes connected to a dual channel oscilloscope. to achieve the highest amplitude read-out efficiency. Achieving record readout amplitude efficiencies comes with distortions in the pulse shape. However, there are applications, where the overall readout amplitude is more important than the pulse shape, such as simple on-off keying schemes.
In the same way one can increase the maximum retrieval time of the buffer by increasing the efficiency and therefore lifting the amplitude of the retrieved pulse above the noise floor. Higher input power increases the nonlinear process known as self phase modulation, chirping the pulses 2 .
The nonlinear loop in the setup therefore not only reduces the noise, but also allows for a more efficient readout amplitude through compression of the retrieved pulse. However the pulse shape is not maintained in this case. Besides using chirped pulses to improve the maximum retrieval ampli- tude, it was also shown theoretically that small amounts of chirp help to more efficiently excite the acoustic wave 3 . This can be understood by drawing an analogy to the McCall and Hahn area theorem for atomic two-level system 4 . Analogues to the π pulse in atomic resonances, a normalized pulse area of the write pulses can be defined and is given by 3 with the Brillouin gain coefficient g B , the speed of light c, the effective mode area A eff , the acoustic decay time τ B , the refractive index n and the time integral over the pulse envelope A(t). The maximum efficiency for exciting the acoustic wave is achieved when Θ = (m + 1/2)π with m being an integer number. However the data pulse cannot be transferred to the acoustic wave if the pulse area is an integer multiple of π. If the pulse area is a multiple of π the first half of the pulse will write the acoustic wave, while the second half retrieves it again. However, for a linear chirped pulse the beginning of the pulse has a different frequency as the end of the pulse. Therefore, only a certain part of the pulse resonantly excites the acoustic wave and importantly does not de-excite the acoustic wave.
Supplementary Note 4: Simulation method. To simulate the phase and amplitude response of our system we solved standard coupled mode equations as presented in Ref. [1] using an implicit fourth order Runge-Kutta method 5 . The slowly-varying envelope coupled mode equations for a forward travelling pump wave A P , a counterpropagating Stokes wave A S and an acoustic wave Q can be written in the following form 1 : The slowly varying envelopes A P , A S are normalized such that |A P/S | 2 is the power in watts, Q is the amplitude of the acoustic wave, n is the refractive index, c the speed of light, g 0 the Brillouin gain coefficient, A eff the effective mode area, τ B the acoustic lifetime and α the waveguide loss parameter.
The envelopes of the input data, write-and-read pulses are approximated to have Gaussian form 3 : with the parameter C giving the chirp rate in GHz / ns following the definition of Ref. [3] and τ being the FWHM. The parameters used for the amplitude simulations (Fig. 3b) are as follows: n = 2.4, g 0 = 0.715 · 10 −9 m/W, A eff = 1.5 · 10 −15 m 2 , τ B = 10.5 ns, α = 0.2 dB/cm. The FWHM of the data pulses is 500 ps and the peak power is varying in equidistant steps from 15 mW to 40 mW. The FWHM of the data pulses was 1 ns, the peak power 3.5 W and C = 0.88 GHz / ns. The temporal separation of the write and the read pulse was 3.5 ns. The parameters used for the phase simulations ( Fig. 3d) are the same as for the amplitude simulations with 40 mW of data power and two different phases 0 and π.