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Bragg mirror acoustic cavities : how to characterize an acoustic resonance at 20GHz ?

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In order to explore the quantum properties at a macroscopic scale, the acoustic oscillator must have a resonance frequency comparable to the environment thermal energy. The fabrication of resonators operating at a few dozen of GHz would allow to observe quantum effects on the movement of the oscillator at a few degrees Kelvin, temperatures that are nowadays easily reachable with a cryogenic system. For this purpose, semiconductor micropillar cavities seem to be promising devices. Investigations were conducted on the cavities optical properties, but only a few on the acoustic properties. Indeed, the characterization of mechanical modes at such high frequencies is difficult with the classical optomechanical techniques. It is within this framework that researchers from the INSP team « acoustique pour les nanosciences » have characterized planar and micropillar acoustic cavities at 20GHz using pump probe experiment with a resonant subharmonic excitation technique, thus making possible the measurement of quality factor as high as 27000.

GaAs/AlAs Bragg mirror cavities studied here were grown using molecular beam epitaxy, in the lab by Paola Atkinson. A GaAs spacer is surrounded by two GaAs/AlAs bilayer stacks, acting like acoustic mirrors at frequencies belonging to forbidden bands centered around 20GHz and its odd harmonics. This cavity confines both optical and acoustic modes because the acoustic and optical impedance contrasts between GaAs and AlAs are comparable. By etching micropillars from a planar cavity, one can obtain a confinement in the three spatial dimensions (fig 1 a).

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Figure 1
a) Micropillar cavity. b) Acoustic spectrum. c) Zoom on the forbidden band around the fundamental mode at 19,9 GHz, for an antiresonant (up) and for a resonant (bottom) repetition rate. d) acoustic mode resonance amplitude of a planar cavity as a function of the LASER repetition rate. Blue dots : experimental data, black line : Lorentzian adjustment.

We have conducted a passive characterization of such cavities through pump probe technique at low temperature, 20K. A pulsed femto-second LASER beam known as pump excites the cavity acoustic mode. A probe LASER beam is used to measure the sample acoustic spectrum (fig 1 b) on which the different Bragg mirror forbidden bands and the cavity resonance can be observed (fig 1c). However, this technique does not have the required frequency resolution to resolve the resonance thinner than our frequency step (fig1c, bottom).

In order to bypass this limitation, a subharmonic excitation technique was used : the pump beam repetition rate ( 80MHz) has been chosen to be equal to a subharmonic of the acoustic resonance frequency ( 20GHz). Each pump impulsion therefore excites resonantly the mode, and the acoustic resonance can be observed with a maximum amplitude (fig1c, bottom). Nonetheless, if the pump pulse train excites antiresonantly the mode, no acoustic resonance is observed (fig 1c, top). The dependence of the resonance amplitude as a function of the repetition rate (fig 1d) allows to obtain its characteristics, such as the resonance frequency fm, the mode lifetime, and therefore the quality factor Q.

We were able to measure the acoustic resonance at 20GHz of a planar cavity with 25 bilayer Bragg mirrors, and to determine its quality factor of 27000. This can give a Qfm product, which quantifies the decoupling of the mode from its environment, of 5.1014 Hz at 20K, which is comparable to state-of-the-art. This technique could be useful to characterize the micropillar acoustic modes and to determine If they can be used as optomechanical systems.

Reference
High spectral resolution of GaAs/AlAs phononic cavities by subharmonic resonant pump-probe excitation
Lagoin, C ; Perrin, B ; Atkinson, P ; Garcia-Sanchez, D
PHYSICAL REVIEW B Volume : 99 Issue : 6 Article Number : 060101
https://journals.aps.org/prb/abstra...

Contact
Bernard Perrin
Daniel Garcia
Camille Lagoin