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arXiv:2008.10361 · Applied Physics Letters

Generation of coherent phonons via a cavity enhanced photonic lambda scheme

Jeremy Bourhill, Natália C. Carvalho, Maxim Goryachev, Serge Galliou, Michael Edmund Tobar

Published Oct 19, 2020• 6 citations
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Abstract

We demonstrate the generation of coherent phonons in a quartz bulk acoustic wave (BAW) resonator through the photoelastic properties of the crystal, via coupling to a microwave cavity enhanced by a photonic lambda scheme. This is achieved by imbedding a single crystal BAW resonator between the post and the adjacent wall of a microwave re-entrant cavity resonator. This 3D photonic lumped LC resonator at the same time acts as the electrode of a BAW phonon resonator and allows the direct readout of coherent phonons via the linear piezoelectric response of the quartz. A microwave pump, ωp, is tuned to the cavity resonance ω0, while a probe frequency, ωprobe, is detuned and varied around the red and blue detuned values with respect to the BAW phonon frequency, Ωm. The pump and probe power dependence of the generated phonons unequivocally determines the process to be electrostrictive, with the phonons produced at the difference frequency between the pump and the probe, with no back action effects involved. Thus, the phonons are created without threshold and can be considered analogous to a passive coherent population trapped maser scheme.

DOI
10.1063/5.0023624

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We demonstrate the generation of coherent phonons in a quartz bulk acoustic wave (BAW) resonator through the photoelastic properties of the crystal, via coupling to a microwave cavity enhanced by a photonic lambda scheme. This is achieved by imbedding a single crystal BAW resonator between the post and the adjacent wall of a microwave re-entrant cavity resonator. This 3D photonic lumped LC resonator at the same time acts as the electrode of a BAW phonon resonator and allows the direct readout of coherent phonons via the linear piezoelectric response of the quartz. A microwave pump, ωp, is tuned to the cavity resonance ω0, while a probe frequency, ωprobe, is detuned and varied around the red and blue detuned values with respect to the BAW phonon frequency, Ωm. The pump and probe power dependence of the generated phonons unequivocally determines the process to be electrostrictive, with the phonons produced at the difference frequency between the pump and the probe, with no back action effects involved. Thus, the phonons are created without threshold and can be considered analogous to a passive coherent population trapped maser scheme.
A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10¹⁸ Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.
We demonstrate that Bulk Acoustic Wave (BAW) quartz resonator cooled down to millikelvin temperatures are excellent building blocks for hybrid quantum systems with extremely long coherence times. Two overtones of the longitudinal mode at frequencies of 15.6 and 65.4 MHz demonstrate a maximum f.Q product of 7.8×1016 Hz. With this result, the Q-factor in such devices near the quantum ground state can be four orders of magnitude better than previously attained in other mechanical systems. Tested quartz resonators possess the ultra low acoustic losses crucial for electromagnetic cooling to the phonon ground state.
Transverse bulk phonons in a multimode integrated quantum acoustic device are excited and characterized via their free-space coupling to a three-dimensional (3D) microwave cavity. These bulk acoustic modes are defined by the geometry of the Y-cut lithium niobate substrate in which they reside and couple to the cavity electric field via a large dipole antenna, with an interaction strength on the order of the cavity linewidth. Using finite element modeling, we determine that the bulk phonons excited by the cavity field have a transverse polarization with a shear velocity matching previously reported values. We demonstrate how the coupling between these transverse acoustic modes and the electric field of the 3D cavity depends on the relative orientation of the device dipole, with a coupling persisting to room temperature. Our study demonstrates the versatility of 3D microwave cavities for mediating contact-less coupling to quantum, and classical, piezoacoustic devices.
Circuit quantum acoustodynamics systems have emerged as a promising platform for quantum information by coupling superconducting qubits to mechanical resonators, with their long-lived mechanical modes serving as quantum memories. We demonstrate suspended quartz phononic crystal resonators at 100 MHz with millisecond lifetimes at 8 K. With a contactless electrode geometry suppressing both two-level system losses and other electrode-induced energy dissipation, we evaluate the piezoelectric coupling rate between the mechanical modes and fluxonium qubits (resonant coupling) and transmon qubits (parametric coupling mediated by a Josephon-junction-based three-wave mixer). We further discuss multi-period defect geometries for enhancing these coupling rates.
Detecting coherent phonons pose different challenges compared to coherent photons due to the much stronger interaction between phonons and matter.This is especially true for high frequency heat carrying phonons, which are intrinsic lattice vibrations experiencing many decoherence events with the environment, and are thus generally assumed to be incoherent.Two photon interference techniques, especially coherent population trapping (CPT) and electromagnetically induced transparency (EIT), have led to extremely sensitive detection, spectroscopy and metrology.Here, we propose the use of two photon interference in a three-level system to sense coherent phonons.Unlike prior works which have treated phonon coupling as damping, we account for coherent phonon coupling using a full quantum-mechanical treatment.We observe strong asymmetry in absorption spectrum in CPT and negative dispersion in EIT susceptibility in the presence of coherent phonon coupling which cannot be accounted for if only pure phonon damping is considered.Our proposal has application in sensing heat carrying coherent phonons effects and understanding coherent bosonic multi-pathway interference effects in three coupled oscillator systems.Phonons are packets of vibrational energy that shares many similarities with its bosonic cousin photons.Advances in nanofabrication has enabled many parallels between the development of photon and phonon control.Parallel developments in passive control techniques include photonic [1] versus phonoic crystals [2], optical [3] versus acoustic metamaterials [4] etc. Development in active manipulation of electromagnetic waves through light-matter interaction have led to creation of nanoscale optical emitters [5] and gates [6] and similar progress have been made in controlling phonons using their interaction with matter especially in the realms of optomechanics [7] and phononic devices [8,9].Phonons span a vast frequency range and while techniques to control and sense lower frequency coherent phonons have been well-developed [10-19], heat carrying coherent terahertz acoustic phonons have been harder to measure directly due to the small wavelength and numerous scattering mechanism at these small wavelengths [20].In the past, THz crystal phonons have been generated and detected in low temperature experiments with defect doped crystals [21-24], with experimental evidence of coherent phonon generation [25][26][27].At the same time, interpretation of non-equilibrium phonon transport, with the advancement of nanoscale electrical heating and ultrafast optical pump-probe techniques, have allowed us to infer phonon coherence from broadband thermal conductivity measurements [28][29][30][31][32].There have been also interest of using defect-based techniques as a thermal probe using perturbation to energy levels due to changes in temperature [33].Furthermore, surface deflection techniques with ultrafast optics have also been used to generate phonons close to THz frequencies in materials [34][35][36][37].Defect-based techniques are attractive compared to both thermal conductivity measurement and deflection techniques due to its ability to directly access atomic length scales where THz phonon wavelength resides.Also, the energy levels in the excited state [21,38,39] and ground state [25,40] electron manifold of these defects can match the phonon energy precisely, resulting in a narrow band phonon detector.In light of the success of defect-based optical absorption techniques in coupling directly to high frequency phonons, we propose the use of two photon interference to measure the coherence properties of these phonons.
We propose a tunable phonon laser prototype with a large trapped ion array, where some of the ions are effectively pinned by optical tweezers, thus isolating a subset of ions that mimics an acoustic cavity used as a phonon lasing resonator. The cavity loss can then be controlled by the tweezer strength and the ``wall thickness'', the number of pinned ions for isolation. We pump the resonator by applying blue-sideband lasers, and investigate the lasing dynamics of the ``cavity'' motional modes such as threshold behavior, population distribution, the second-order coherence, and linewidth narrowing. This scheme can be generalized to multimode resonators, for which we report the mode competition phenomenon and lasing mode multistability. Our work provides an excellent platform for acoustic quantum state manipulation, paving the way towards phonon-mediated quantum computing, communications, and metrology.