Subterahertz phonon dynamics in acoustic nanocavities

Terahertz phonon engineering with van der Waals heterostructures

Phonon engineering at gigahertz frequencies forms the foundation of microwave acoustic filters1, acousto-optic modulators2 and quantum transducers3,4. Terahertz phonon engineering could lead to acoustic filters and modulators at higher bandwidth and speed, as well as quantum circuits operating at higher temperatures. Despite their potential, methods for engineering terahertz phonons have been limited due to the challenges of achieving the required material control at subnanometre precision and efficient phonon coupling at terahertz frequencies. Here we demonstrate the efficient generation, detection and manipulation of terahertz phonons through precise integration of atomically thin layers in van der Waals heterostructures. We used few-layer graphene as an ultrabroadband phonon transducer that converts femtosecond near-infrared pulses to acoustic-phonon pulses with spectral content up to 3 THz. A monolayer WSe2 is used as a sensor. The high-fidelity readout was enabled by the exciton-phonon coupling and strong light-matter interactions. By combining these capabilities in a single heterostructure and detecting responses to incident mechanical waves, we performed terahertz phononic spectroscopy. Using this platform, we demonstrate high-Q terahertz phononic cavities and show that a WSe2 monolayer embedded in hexagonal boron nitride can efficiently block the transmission of terahertz phonons. By comparing our measurements to a nanomechanical model, we obtained the force constants at the heterointerfaces. Our results could enable terahertz phononic metamaterials for ultrabroadband acoustic filters and modulators and could open new routes for thermal engineering.

Enhanced Photon-Phonon Interaction in WSe2 Acoustic Nanocavities

Acoustic nanocavities (ANCs) with resonance frequencies much above 1 GHz are prospective to be exploited in sensors and quantum operating devices. Nowadays, acoustic nanocavities fabricated from van der Waals (vdW) nanolayers allow them to exhibit resonance frequencies of the breathing acoustic mode up to f ∼ 1 THz and quality factors up to Q ∼ 103. For such high acoustic frequencies, electrical methods fail, and optical techniques are used for the generation and detection of coherent phonons. Here, we study experimentally acoustic nanocavities fabricated from WSe2 layers with thicknesses from 8 up to 130 nm deposited onto silica colloidal crystals. The substrate provides a strong mechanical support for the layers while keeping their acoustic properties the same as in membranes. We concentrate on experimental and theoretical studies of the amplitude of the optically measured acoustic signal from the breathing mode, which is the most important characteristic for acousto-optical devices. We probe the acoustic signal optically with a single wavelength in the vicinity of the exciton resonance and measure the relative changes in the reflectivity induced by coherent phonons up to 3 × 10-4 for f ∼ 100 GHz. We reveal the enhancement of photon-phonon interaction for a wide range of acoustic frequencies and show high sensitivity of the signal amplitude to the photoelastic constants governed by the deformation potential and dielectric function for photon energies near the exciton resonance. We also reveal a resonance in the photoelastic response (we call it photoelastic resonance) in the nanolayers with thickness close to the Bragg condition. The estimates show the capability of acoustic nanocavities with an exciton resonance for operations with high-frequency single phonons at an elevated temperature.

Probing gigahertz coherent acoustic phonons in TiO2 mesoporous thin films

Ultrahigh-frequency acoustic-phonon resonators usually require atomically flat interfaces to avoid phonon scattering and dephasing, leading to expensive fabrication processes, such as molecular beam epitaxy. Mesoporous thin films are based on inexpensive wet chemical fabrication techniques that lead to relatively flat interfaces regardless the presence of nanopores. Here, we report mesoporous titanium dioxide-based acoustic resonators with resonances up to 90 GHz, and quality factors from 3 to 7. Numerical simulations show a good agreement with the picosecond ultrasonics experiments. We also numerically study the effect of changes in the speed of sound on the performance of the resonator. This change could be induced by liquid infiltration into the mesopores. Our findings constitute the first step towards the engineering of building blocks based on mesoporous thin films for reconfigurable optoacoustic sensors.

Giant Photoelasticity of Polaritons for Detection of Coherent Phonons in a Superlattice with Quantum Sensitivity

The functionality of phonon-based quantum devices largely depends on the efficiency of the interaction of phonons with other excitations. For phonon frequencies above 20 GHz, generation and detection of the phonon quanta can be monitored through photons. The photon-phonon interaction can be enormously strengthened by involving an intermediate resonant quasiparticle, e.g., an exciton, with which a photon forms a polariton. In this work, we discover a giant photoelasticity of exciton-polaritons in a short-period superlattice and exploit it to detect propagating acoustic phonons. We demonstrate that 42 GHz coherent phonons can be detected with extremely high sensitivity in the time domain Brillouin oscillations by probing with photons in the spectral vicinity of the polariton resonance.

Role of scattering by surface roughness in the photoacoustic detection of hidden micro-structures

We present an experimental study in which we compare two different pump-probe setups to generate and detect high-frequency laser-induced ultrasound for the detection of gratings buried underneath optically opaque metal layers. One system is built around a high-fluence, low-repetition-rate femtosecond laser (1 kHz) and the other around a low-fluence, high-repetition-rate femtosecond laser (5.1 MHz). We find that the signal diffracted by the acoustic replica of the grating as a function of pump-probe time delay is very different for the two setups used. We attribute this difference to the presence of a constant background field due to optical scattering by interface roughness. In the low-fluence setup, the optical field diffracted by the acoustic replica is significantly weaker than the background optical field, with which it can destructively or constructively interfere. For the right phase difference between the optical fields, this can lead to a significant "amplification" of the weak field diffracted off the grating-shaped acoustic waves. For the high-fluence system, the situation is reversed because the field diffracted off the acoustic-wave-induced grating is significantly larger than the background optical field. Our measurements show that optical scattering by interface roughness must be taken into account to properly explain experiments on laser-induced ultrasound performed with high-repetition-rate laser systems and can be used to enhance signal strength.

Polariton-driven phonon laser

Efficient generation of phonons is an important ingredient for a prospective electrically-driven phonon laser. Hybrid quantum systems combining cavity quantum electrodynamics and optomechanics constitute a novel platform with potential for operation at the extremely high frequency range (30-300 GHz). We report on laser-like phonon emission in a hybrid system that optomechanically couples polariton Bose-Einstein condensates (BECs) with phonons in a semiconductor microcavity. The studied system comprises GaAs/AlAs quantum wells coupled to cavity-confined optical and vibrational modes. The non-resonant continuous wave laser excitation of a polariton BEC in an individual trap of a trap array, induces coherent mechanical self-oscillation, leading to the formation of spectral sidebands displaced by harmonics of the fundamental 20 GHz mode vibration frequency. This phonon "lasing" enhances the phonon occupation five orders of magnitude above the thermal value when tunable neighbor traps are red-shifted with respect to the pumped trap BEC emission at even harmonics of the vibration mode. These experiments, supported by a theoretical model, constitute the first demonstration of coherent cavity optomechanical phenomena with exciton polaritons, paving the way for new hybrid designs for quantum technologies, phonon lasers, and phonon-photon bidirectional translators.

Hartman effect for spin waves in exchange regime

Hartman effect for spin waves tunnelling through a barrier in a thin magnetic film is considered theoretically. The barrier is assumed to be created by a locally increased magnetic anisotropy field. The considerations are focused on a nanoscale system operating in the exchange-dominated regime. We derive the formula for group delay τ_gr of a spin wave packet and show that τ_gr saturates with increasing barrier width, which is a signature of the Hartman effect predicted earlier for photonic and electronic systems. In our calculations, we consider the general boundary conditions which take into account different strength of exchange coupling between the barrier and its surrounding. As a system suitable for experimental observation of the Hartman effect we propose a CoFeB layer with perpendicular magnetic anisotropy induced by a MgO overlayer.

A Topological View on Optical and Phononic Fabry–Perot Microcavities through the Su–Schrieffer–Heeger Model

Advances in nanofabrication technologies have enabled the study of acoustic wave phenomena in the technologically relevant GHz–THz range. First steps towards applying concepts from topology in nanophononics were made with the proposal of a new topological acoustic resonator, based on the concept of band inversion. In topology, the Su–Schrieffer–Heeger (SSH) model is the paradigm that accounts for the topological properties of many one-dimensional structures. Both the classical Fabry–Perot resonator and the reported topological resonators are based on Distributed Bragg Reflectors (DBRs). A clear and detailed relation between the two systems, however, is still lacking. Here, we show how a parallelism between the standard DBR-based acoustic Fabry–Perot type cavity and the SSH model of polyacetylene can be established. We discuss the existence of surface modes in acoustic DBRs and interface modes in concatenated DBRs and show that these modes are equivalent to Fabry–Perot type cavity modes. Although it is not possible to assign topological invariants to both acoustic bands enclosing the considered minigap in the nanophononic Fabry–Perot case, the existence of the confined mode in a Fabry–Perot cavity can nevertheless be interpreted in terms of the symmetry inversion of the Bloch modes at the Brillouin zone edge.

Spectral control of elastic dynamics in metallic nano-cavities

We show how the elastic response of metallic nano-cavities can be tailored by tuning the interplay with an underlying phononic superlattice. In particular, we exploit ultrafast optical excitation in order to address a resonance mode in a tungsten thin film, grown on top of a periodic MgO/ZrO₂ multilayer. Setting up a simple theoretical model, we can explain our findings by the coupling of the resonance in the tungsten to an evanescent surface mode of the superlattice. To demonstrate a second potential benefit of our findings besides characterization of elastic properties of multilayer samples, we show by micromagnetic simulation how a similar structure can be utilized for magneto-elastic excitation of exchange-dominated spin waves.

Picosecond optomechanical oscillations in metal-polymer microcavities

We experimentally study mechanical vibrations in planar Fabry-Perot microcavities made of metallic mirrors and a polymer spacer, using broadband pump-probe spectroscopy. These acoustic waves oscillate at a picosecond time-scale and result in spectral oscillations of the cavity transmission spectrum. We find that the oscillations are initiated at the metal mirrors and that their temporal dynamics match the elastic modes of the polymer layer, indicating that mechanical momentum is transferred within the structure. Such structures combine the strong optical absorption of metals with the elasticity and the processability of polymers, which open the road to a new class of optomechanical devices.

Multiple Quantum Wells for PT-Symmetric Phononic Crystals

We demonstrate that the parity-time symmetry for sound is realized in laser-pumped multiple-quantum-well structures. Breaking of the parity-time symmetry for the phonons with wave vectors corresponding to the Bragg condition makes the structure a highly selective acoustic wave amplifier. Single-mode distributed feedback phonon lasing is predicted for structures with realistic parameters.

Optical tracking of picosecond coherent phonon pulse focusing inside a sub-micron object

By means of an ultrafast optical technique, we track focused gigahertz coherent phonon pulses in objects down to sub-micron in size. Infrared light pulses illuminating the surface of a single metal-coated silica fibre generate longitudinal-phonon wave packets. Reflection of visible probe light pulses from the fibre surface allows the vibrational modes of the fibre to be detected, and Brillouin optical scattering of partially transmitted light pulses allows the acoustic wavefronts inside the transparent fibre to be continuously monitored. We thereby probe acoustic focusing in the time domain resulting from generation at the curved fibre surface. An analytical model, supported by three-dimensional simulations, suggests that we have followed the focusing of the acoustic beam down to a ~150-nm diameter waist inside the fibre. This work significantly narrows the lateral resolution for focusing of picosecond acoustic pulses, normally limited by the diffraction limit of focused optical pulses to ~1 μm, and thereby opens up a new range of possibilities including nanoscale acoustic microscopy and nanoscale computed tomography.

Ultracompact interference phonon nanocapacitor for storage and lasing of coherent terahertz lattice waves

We introduce a novel ultracompact nanocapacitor of coherent phonons formed by high-finesse interference mirrors based on atomic-scale semiconductor metamaterials. Our molecular dynamics simulations show that the nanocapacitor stores coherent monochromatic terahertz lattice waves, which can be used for phonon lasing-the emission of coherent phonons. Either one- or two-color phonon emission can be realized depending on the geometry of the nanodevice. The two-color regime of the interference phonon nanocapacitor originates from the different incidence-angle dependence of the transmission of longitudinal and transverse phonons at the respective interference antiresonances. Coherent phonon storage can be achieved by an adiabatic cooling the nanocapacitor initially thermalized at room temperature or by the pump-probe optical technique. The linewidth narrowing and the computed relative phonon participation number confirm strong phonon confinement in the ultracompact interference nanocavity by an extremely small amount of resonance defects. The emission of coherent terahertz acoustic beams from the nanocapacitor can be realized by applying a tunable reversible stress, which shifts the frequencies of the interference antiresonances.

Observing backfolded and unfolded acoustic phonons by broadband optical light scattering

We use broadband time domain Brillouin scattering to observe coherently generated phonon modes in bulk and nanolayered samples. We transform the measured transients into a frequency-wavevector diagram and compare the resulting dispersion relations to calculations. The detected oscillation amplitude depends on the occupation of phonon modes induced by the pump pulse. For nanolayered samples with an appropriately large period, the whole wavevector range of the Brillouin zone becomes observable by broadband optical light scattering. The backfolded modes vanish, when the excitation has passed the nanolayers and propagates through the substrate underneath.

Nonlinear ultrafast acoustics at the nano scale

Pulsed femtosecond lasers can generate acoustic pulses propagating in solids while displaying either diffraction, attenuation, nonlinearity and/or dispersion. When acoustic attenuation and diffraction are negligible, shock waves or solitons can form during propagation. Both wave types are phonon wavepackets with characteristic length scales as short as a few nanometer. Hence, they are well suited for acoustic characterization and manipulation of materials on both ultrafast and ultrashort scales. This work presents an overview of nonlinear ultrasonics since its first experimental demonstration at the beginning of this century to the more recent developments. We start by reviewing the main properties of nonlinear ultrafast acoustic propagation based on the underlying equations. Then we show various results obtained by different groups around the world with an emphasis on recent work. Current issues and directions of future research are discussed.

Towards GHz-THz cavity optomechanics in DBR-based semiconductor resonators

Resonators based on acoustic distributed Bragg reflectors (DBRs) were optimized to work in the GHz-THz regime, and grown by molecular beam epitaxy. We show that in structures made of GaAlAs alloys a simultaneous optimal confinement of light in the visible range and phonons in the tens of GHz range can be achieved. We report time resolved differential optical reflectivity experiments performed with fs-ps laser pulses. The experimental results are in excellent agreement with simulations based on standard transfer matrix methods. The resonant behavior of the photoelastic coefficient is discussed. The perfect optic-acoustic mode overlapping, added to a strongly enhanced coupling mechanism, implies that these DBR-based cavities could be the base of highly efficient optomechanical resonators.

Generation and detection of gigahertz acoustic oscillations in thin membranes

Single crystalline membranes are a perfect model system for the study of coherent acoustic phonon generation and decay in the time domain. Coherent acoustical modes are excited and detected in thin single-crystalline silicon and gallium arsenide membranes with femtosecond pulses in the ultraviolet and infrared wavelength region using the asynchronous optical sampling technique. The measured acoustic spectra are compared with each other and are discussed in terms of different generation and detection mechanisms. A clear dependence of the generated spectra on the absorption length of the pump and probe pulses is observed. It is shown that a short absorption length for the pump pulse leads to the generation of coherent high frequency phonons up to several 100 GHz frequencies. Membranes are demonstrated to be useful as broadband acoustic cavities and can help to disentangle details of high frequency phonon dynamics. Two-layer membrane systems offer additional insight into energy transfer in the GHz frequency range and adhesion properties.

Semiconductor superlattices: a tool for terahertz acoustics

The properties of optical to acoustic transduction of semiconductor superlattices have been explored for several years in the sub terahertz frequency range. Using femtosecond laser pulses focused on these structures, acoustic modes are excited with a frequency related to the periodicity of the structure stacking. We have shown that these acoustic waves can be extracted and can propagate in the underlying substrate. We study superlattices ability to be quasi monochromatic generators. On the other hand, superlattices have been found to be very sensitive and selective detectors. We present a set of experimental results concerning the generation, propagation over large distances and detection of acoustic waves at high frequencies, up to the challenging 1 THz by picosecond ultrasonics experiments in transmission geometry.

Electrical manipulation of crystal symmetry for switching transverse acoustic phonons

We experimentally explore the use of a novel device where lateral electric fields can be applied to break the translational symmetry within the isotropic plane and hence change the selection rules to allow normally forbidden transverse acoustic (TA) phonon generations. The ultrafast screening of the lateral electric field by the photocarriers relieves shear strain in the structure and switches on the propagating TA waves. The amplitude and on-state time of the TA mode can be modulated by the external field strength and size of the laterally biased region. The observed frequency shift with an external bias as well as the strong geometrical dependence confirm the role of the asymmetric potential distribution in electrically manipulating the crystal symmetry to control modal behavior of acoustic phonons.

Tunneling times of acoustic phonon packets through a distributed Bragg reflector

The longwave phenomenological model is used to make simple and precise calculations of various physical quantities such as the vibrational energy density, the vibrational energy, the relative mechanical displacement, and the one-dimensional stress tensor of a porous silicon distributed Bragg reflector. From general principles such as invariance under time reversal, invariance under space reflection, and conservation of energy density flux, the equivalence of the tunneling times for both transmission and reflection is demonstrated. Here, we study the tunneling times of acoustic phonon packets through a distributed Bragg reflector in porous silicon multilayer structures, and we report the possibility that a phenomenon called Hartman effect appears in these structures.

Dynamics of a vertical cavity quantum cascade phonon laser structure

Driven primarily by scientific curiosity, but also by the potential applications of intense sources of coherent sound, researchers have targeted the phonon laser (saser) since the invention of the optical laser over 50 years ago. Here we fabricate a vertical cavity structure designed to operate as a saser oscillator device at a frequency of 325 GHz. It is based on a semiconductor superlattice gain medium, inside a multimode cavity between two acoustic Bragg reflectors. We measure the acoustic output of the device as a function of time after applying electrical pumping. The emission builds in intensity reaching a steady state on a timescale of order 0.1 μs. We show that the results are consistent with a model of the dynamics of a saser cavity exactly analogous to the models used for describing laser dynamics. We also obtain estimates for the gain coefficient, steady-state acoustic power output and efficiency of the device.

Phonon lasers are the acoustic equivalent to optical lasers. Here Maryam and colleagues study the dynamics of semiconductor phonon lasers operating in the terahertz frequency regime, and show that these dynamics are similar to that of comparable optical lasers.

Gigahertz coherent guided acoustic phonons in AlN/GaN nanowire superlattices

The generation of guided acoustic phonons in the GHz range in GaN/AlN superlattices grown atop a GaN nanowire is presented. Combined with a femtosecond laser, ultrafast pump-probe spectroscopy allows the generation and detection of guided acoustic phonons at different frequencies in the nanowire superlattices. The capability of the nanowire superlattices to be excellent detectors of acoustic phonons at specific frequencies is then used to observe the strong dispersion, as a result of nanoconfinement, of guided acoustic phonons after their propagation in the nanowire. The generation of high frequency coherent guided acoustic phonons could be useful not only to realize an acoustic transducer with a nanolateral size but also as a source to understand the thermal behavior of nanowires.

Acoustic spectroscopy of DNA in the gigahertz range

We find a parametric resonance in the gigahertz range of DNA dynamics, generated by pumping hypersound. The resonance may be accompanied by the formation of localized phonon modes due to the random structure of elastic modulii of DNA.

Bloch oscillations of THz acoustic phonons in coupled nanocavity structures

Nanophononic Bloch oscillations and Wannier-Stark ladders have been recently predicted to exist in specifically tailored structures formed by coupled nanocavities. Using pump-probe coherent phonon generation techniques we demonstrate that Bloch oscillations of terahertz acoustic phonons can be directly generated and probed in these complex nanostructures. In addition, by Fourier transforming the time traces we had access to the proper eigenmodes in the frequency domain, thus evidencing the related Wannier-Stark ladder. The observed Bloch oscillation dynamics are compared with simulations based on a model description of the coherent phonon generation and photoelastic detection processes.

Enhancement and inhibition of coherent phonon emission of a Ni film in a BaTiO3/SrTiO3 cavity

We report pump-probe time resolved reflectivity experiments in a hybrid air-Ni metal-BaTiO(3)/SrTiO(3) oxide mirror phonon cavity. We demonstrate that the generated coherent acoustic phonon spectra of the impulsively excited metallic film can be inhibited or enhanced in the phonon cavity with respect to a Ni film directly grown on a SrTiO(3) substrate. The experiments are compared with simulations that highlight the role of the phonon density of states in the coherent acoustic emission, extending concepts at the base of the optical Purcell effect to the field of phononics.

Coherent terahertz sound amplification and spectral line narrowing in a stark ladder superlattice

The bias voltage applied to a weakly coupled n-doped GaAs/AlAs superlattice increases the amplitude of the coherent hypersound oscillations generated by a femtosecond optical pulse. This bias-induced amplitude increase and experimentally observed spectral narrowing of the superlattice phonon mode with a frequency 441 GHz provides the evidence for hypersound amplification by stimulated emission of phonons in a system where the inversion of the electron populations for phonon-assisted transitions exists.

Lifetime of THz acoustic nanocavity modes

We present an ultrahigh resolution Raman study of the lifetime of 1 THz acoustic phonons confined in nanocavities. We demonstrate that the cavity Q factor can be controlled by design. Anharmonicity contributes only marginally to limit the cavity phonon lifetime, even at room temperature, while thickness fluctuations in the scale of 1/10 of a unit cell are the main limitation for the performance of THz phonon cavities.

Hypersonic modes in nanophononic semiconductors

Frequency gaps and negative group velocities of hypersonic phonon modes in periodically arranged composite semiconductors are presented. Trends and criteria for phononic gaps are discussed using a variety of atomic-level theoretical approaches. From our calculations, the possibility of achieving semiconductor-based one-dimensional phononic structures is established. We present results of the location and size of gaps, as well as negative group velocities of phonon modes in such structures. In addition to reproducing the results of recent measurements of the locations of the band gaps in the nanosized Si/Si{0.4}Ge{0.6} superlattice, we show that such a system is a true one-dimensional hypersonic phononic crystal.

Selective optical generation of coherent acoustic nanocavity modes

Femtosecond pump-probe experiments on a Ga0.85In0.15As nanocavity enclosed by two Ga(0.85)In(0.15)As/AlAs phonon Bragg mirrors reveal selective generation of terahertz confined acoustic modes and regular folded phonons. Selective generation of the confined modes alone is achievable for laser excitation at certain energies below the mirror absorption edges, corresponding to electronic transitions within the cavity layer only. Calculations based on the photoelastic effect explain the experimental results. Decay times of cavity and regular modes evidence longer decay times and anharmonic effects for the cavity mode.