Session B52: Optomechanics and Hybrid Systems I: Novel Systems

Exploring the Macroscopic Quantum Physics of Motion with Superfluid He-4

We demonstrate the use of superfluid helium-4 as an extremely low loss optomechanical element. We form an optomechanical system with a cylindrical niobium superconducting TE$_{011}$ resonator whose 40 cm$^3$ inner cylindrical cavity is filled with $^4$He. Coupling is realized via the variations in permittivity resulting from the density profile of the acoustic modes. Acoustic losses in helium-4 below 500 mK are governed by the intrinsic nonlinearity of sound, leading to an attenuation which drops as T$^4$, indicating the possibility of quality factors (Q) over 10$^{10}$ at 10 mK. In our lowest loss mode, we demonstrate this T$^4$ law at temperatures down to 50 mK, realizing an acoustic Q of 1.35*10$^8$ at 8.1 kHz. When coupled with a low phase noise microwave source, we expect this system to be utilized as a probe of macroscopic quantized motion, for precision measurements to search for fundamental physical length scales, and as a continuous gravitational wave detector. Our estimates suggest that a resonant superfluid acoustic system could exceed the sensitivity of current broad-band detectors for narrow-band sources such as pulsars.\\ \\ De Lorenzo, L. A. and Schwab, K. C., \emph{New J. Phys.} \textbf{16}, 113020 (2014).   

Mechanical Resonance and Damping Properties of Gallium Nitride Nanowires in Selected-Area Growth Arrays Measured via Optical Bragg Scattering

We report the use of optical Bragg scattering to measure the mechanical resonance frequencies and quality factors (Q) of gallium nitride (GaN) nanowires (NWs) in selected-area growth arrays. The GaN NWs are grown by catalyst-free molecular beam epitaxy on silicon (111) wafers. Hexagonal arrays of approximately 100 GaN NWs with pitch spacings of 400 - 1000 nm have been prepared. The NWs contained in such arrays have diameters ranging from 100-300 nm and lengths from 3 - 10 $\mu$m. A diode laser operating at 640 nm and 2 mW of optical power is used to perform Bragg scattering homodyne detection to passively read out the thermally induced Brownian mechanical motion of the NWs. The first order cantilever-mode mechanical resonance frequencies of these NWs have been measured to be between 2 - 12 MHz. We find that the optical readout via Bragg scattered light allows the simultaneous detection of all lowest order mechanical resonances in a given array. Q factors ranging from 1,000 - 12,000 have been seen at room temperature and $10^{-5}$ Torr pressures. Qs as high as 25,000 have been seen at temperatures of 80 K. These results show that the narrow mechanical resonances observed in freely-grown GaN NWs can also be seen in NWs prepared via selected-area growth.   

Ultra-thin superconducting film coated silicon nitride nanowire resonators for low-temperature applications

We demonstrate fabrication of high stress silicon nitride nanowire resonators with a thickness and width of less than 50 nm intended to be used as probes for the study of superfluid $^{3}$He. The resonators are fabricated as doubly-clamped wires/beams using a combination of electron-beam lithography and wet/dry etching techniques. We demonstrate the ability to suspend (over a trench of depth \textasciitilde 8 \textmu m) wires with a cross section as small as 30 nm, covered with a 20 nm superconducting film, and having lengths up to 50 \textmu m. Room temperature resonance measurements were carried out by driving the devices using a piezo stage and detecting the motion using an optical interferometer. The results show that metalizing nano-mechanical resonators not only affects their resonant frequencies but significantly reduce their quality factor (Q). The devices are parametrically pumped by modulating the system at twice its fundamental resonant frequency, which results in observed amplification of the signal. The wires show self-oscillation with increasing modulation strength. The fabricated nanowire resonators are intended to be immersed in the superfluid $^{3}$He. By tracking the resonant frequency and the Q of the various modes of the wire versus temperature, we aim to probe the superfluid gap structure.   

Optomechanics with superfluid He4 thin films

Cavity optomechanics focuses on the interaction between confined light and a mechanical degree of freedom. Vibrational modes of superfluid helium-4 have recently been identified as an attractive mechanical element for cavity optomechanics, thanks to their ultra-low dissipation arising from superfluid’s viscosity free flow. Here we propose and demonstrate an approach to superfluid optomechanics based on femtogram thin films of superfluid helium condensed on the surface of a microscale microtoroid optical whispering gallery mode resonator. Excitations within the film, known as third sound, manifest as surface waves with a restoring force provided by the van der Waals interaction. We experimentally probe the thermodynamics of these superfluid excitations in real-time, and demonstrate both laser cooling and amplification of the thermal motion. In addition, we propose and demonstrate an entirely new approach to optical forcing based on the atomic recoil of superfluid helium-4. This technique utilizes the thermomechanical effect of superfluids, whereby frictionless fluid flow is generated in response to a local heat source. Using this technique, we achieve superfluid forces on a microtoroid mechanical mode an order of magnitude greater than the equivalent radiation pressure force.   

Strong coupling and parametric amplification in mechanical modes of graphene

We demonstrate strong dynamical coupling and parametric amplification in mechanical modes of a graphene drum using an all electrical configuration. Low tension in the system allows large electrostatic tunability of the modes thus enabling dynamic pumping experiments. In the strong coupling regime a red detuned pump gives rise to new eigenmodes having highly tunable mode splitting (cooperativity \textasciitilde 60) with coherent energy transfer. The coupling is also used to amplify the modes under the action of a blue detuned pump. In addition, self-oscillations and parametric amplification of the fundamental vibrational mode is demonstrated with a gain of nearly 3. The low mass and high frequency of these atomically thin resonators could prove useful for studying mode coupling in the quantum regime.   

Observation of vacuum-enhanced electron spin resonance of optically levitated nanodiamonds

Electron spins of diamond nitrogen-vacancy (NV) centers are important quantum resources for nanoscale sensing and quantum information. Combining such NV spin systems with levitated optomechanical resonators will provide a hybrid quantum system for many novel applications. Here we optically levitate a nanodiamond and demonstrate electron spin control of its built-in NV centers in low vacuum. We observe that the strength of electron spin resonance (ESR) is enhanced when the air pressure is reduced. To better understand this novel system, we also investigate the effects of trap power and measure the absolute internal temperature of levitated nanodiamonds with ESR after calibration of the strain effect. Our results show that optical levitation of nanodiamonds in vacuum not only can improve the mechanical quality of its oscillation, but also enhance the ESR contrast, which pave the way towards a novel levitated spin-optomechanical system for studying macroscopic quantum mechanics. The results also indicate potential applications of NV centers in gas sensing.   

Piezo-optomechanical circuits

Coherent links between the optical, radio frequency (RF), and mechanical domains are critical for applications ranging from quantum state transfer between the RF and optical domains to signal processing in the acoustic domain for microwave photonics. We develop such a piezo optomechanical circuit platform in GaAs, in which localized and interacting 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. GaAs allows us to exploit the photoelastic effect to engineer cavities with strong optomechanical coupling (g$_{\mathrm{0}}$/2$\pi \approx $1.1 MHz) and the piezoelectric effect to couple RF fields to mechanical motion through surface acoustic waves, which are routed on-chip using phononic crystal waveguides. This platform enables optical readout of electrically-injected mechanical states with an average coherent intracavity phonon number as small as $\approx $0.05 and the ability to drive mechanical motion with equal facility through either the optical or electrical channel. This is used to demonstrate a novel acoustic wave interference effect in which optically-driven motion is completely cancelled by electrically-driven motion, and vice versa. As an application of this, we present time-domain measurements of optically-controlled acoustic pulse propagation.   

Magneto-optical coupling in whispering gallery mode resonators

We demonstrate that yttrium iron garnet microspheres support optical whispering gallery modes similar to those in non-magnetic dielectric materials. The direction of the ferromagnetic moment tunes the resonant optical frequency via the Voigt effect, dependent on the angle of the magnetization with respect to the plane of the whispering gallery mode. This parametric coupling of the magnetization to the optical mode may enable analogous experiments to those performed in cavity optomechanics. In addition, the Faraday effect couples the two ordinarily linear polarized modes, split by the geometrical birefringence due to the boundary conditions at the surface. This results in a polarization rotation of the light emitted from the cavity. Our results extend recent work on the strong coupling of microwave photons to magnetization dynamics into the optical domain. An understanding of the magneto-optical coupling in whispering gallery modes, where the propagation direction rotates with respect to the magnetization, is fundamental to the emerging field of cavity optomagnonics. [arXiv:1510.06661].   

Quartz-superconductor quantum electromechanical system

Quartz bulk acoustic wave oscillators support mechanical modes with very high resonance frequencies and extremely high quality factors. As such, they provide an appealing platform for quantum optics experiments with phonons, gravitational wave detection, and tests of quantum mechanics. We propose to cool and measure the motion of a quartz oscillator using a transmon, with the coupling mediated by a tuneable superconducting LC circuit. The mechanical motion ($\sim$250MHz) is resonantly coupled to the LC circuit ($\sim$250MHz) by a piezoelectric interaction, the LC circuit is coupled to the transmon ($\sim$8GHz) via sideband transitions, and there is a smaller direct coupling between the quartz oscillator and the transmon. By driving the transmon on its red sideband, the mechanical and electrical oscillators may be cooled close to their quantum ground state. By observing the fluorescence of the qubit, the occupations of the oscillators may be determined via the motional sidebands they induce. A minimal model of this system consists of a qubit coupled to two oscillators, which are themselves mutually coupled. The steady-state of the system and the qubit fluorescence spectrum are evaluated analytically using a perturbative projection operator technique, and verified numerically.   

Single photon frequency conversion and channelization based on microwave piezo-optomechanical devices.

Cavity optomechanics holds very promising potentials for quantum information processing, as it provides both a convenient method to manipulate photons and a platform to bridge different quantum system. Especially, the integration of microwave devices with cavity optomechanics draws great interest as such a hybrid platform can provide strong electrical actuation, ultra-sensitive optical readout, and parametric mechanical signal amplification simultaneously in a single device. This hybrid platform enables great functionalities in manipulating photons, and builds direct link between microwave photon and optical photon, which is important for future quantum network. Aluminum nitride (AlN) is ideal for such hybrid platform. Besides low optical and mechanical loss, AlN possesses strong piezoelectric effect, which gives rise to strong coupling between microwave cavities and mechanical resonators. We will present our recent progress in developing integrated AlN hybrid platform for photon manipulation, such as optical amplification and absorption, cascaded optical delay, single photon frequency shifting, etc.   

Displacement linear detection down to thermal fluctuations of a silicon nitride membrane with self-mixing technique

Active optomechanical systems exploit the interaction between photons and mechanical vibrations inside a laser cavity. A compound cavity made of a laser diode and an external vibrating reflector is a suitable platform, due to its ease of construction and coupling modulation. Here we use it as a linear displacement detector, by studying the motion of a silicon nitride suspended membrane as the external mirror of a near infrared laser diode. The membrane vibrations cause fluctuations in the laser optical power, which are collected by a photodiode and measured with a spectrum analyzer. The dynamics of the membrane driven by a piezo actuator was investigated in a homodyne configuration. The high Q-factor ($\sim$ $10^5$ at low pressure) of the fundamental mechanical mode at $74$ kHz enabled direct measurement of thermal motion at room temperature, which holds an average displacement of $20$ pm. Therefore, compound cavity systems can be employed as table-top, cost-effective displacement linear detectors. Furthermore, nonlinear optomechanical interactions could be observed, with new possibilities in the study of non-Markovian quantum properties at the mesoscale.   

Microwave cavity piezo-opto-mechanical resonators based on film thickness modes operating beyond 10 GHz

Micromechanical resonators, which support and confine microwave frequency phonons on a scale comparable to optical wavelength, provide a valuable intermediate platform facilitating interactions among electrical, optical, and mechanical domains. High-frequency mechanical resonances ease the refrigeration conditions for reaching quantum mechanical ground state and also hold promise for practical device applications. However, efficient actuation of the highly stiff mechanical motions above gigahertz frequencies remains a challenging task. Here, we demonstrate a high-performance piezo-opto-mechanical resonator operating at 10.4 GHz by exploiting the acoustic thickness mode of an aluminum nitride micro-disk. In contrast to the in-plane mechanical modes, the thickness mode can be easily scaled to high frequencies with low mechanical and optical dissipations. A high $f \cdot Q$ product of $1.9\times10^{13}$?Hz is achieved in ambient air at room temperature. Moreover, strong piezo-electro-mechanical coupling can be achieved by coupling the thickness mode with a microwave resonator, making it possible for coherent signal conversion. The thickness mode-based piezo-opto-mechanical resonators can be expected to serve as essential elements for advanced hybrid information networks.   

Slot-mode optomechanical crystals with enhanced coupling and multimode functionality

A number of cavity optomechanics applications involve multiple interacting optical and mechanical modes. A key challenge in such systems is developing multimode platforms with both flexibility in the optical and mechanical designs and interactions as strong as those shown in single-mode systems. We thus present slot-mode optomechanical crystals, in which photonic and phononic crystal nanobeams separated by a narrow slot couple optomechanically. We pattern these beams to confine a low-loss optical mode in the slot and a mechanical breathing mode at the center of the mechanical beam. This structure has large optomechanical coupling rates and great design flexibility toward multimode systems. We demonstrate this in Si$_{\mathrm{3}}$N$_{\mathrm{4}}$ slot-mode devices, with 980 nm optical modes coupling to mechanical modes at 3.4 GHz, 1.8 GHz, and 400 MHz. We use Si$_{\mathrm{3}}$N$_{\mathrm{4}}$ tensile stress to shrink slot widths to 24 nm, greatly enhancing optomechanical coupling. Finally, with this platform, we develop multimode systems with three-beam geometries, in which two different mechanical modes couple to one optical mode and two different optical modes couple to one mechanical mode.   

Nonlinearly Coupled Superconducting Lumped Element Resonators

We study SQUID-mediated tunable coupling between two superconducting on-chip resonators in the microwave frequency range. In this circuit QED implementation, we employ lumped-element type resonators, which consist of Nb thin film structured into interdigitated finger shunt capacitors and meander inductors. A SQUID, functioning as flux dependent and intrinsically nonlinear inductor, is placed as a coupling element together with an interdigitated capacitor between the two resonators (cf. A. Baust \textit{et al.}, Phys. Rev. B \textbf{91} 014515 (2015)). We perform a spectroscopic measurement in a dilution refrigerator and find the linear photon hopping rate between the resonators to be widely tunable as well as suppressible for an appropriate choice of parameters, which is made possible due to the interplay of inductively and capacitively mediated coupling. Vanishing linear coupling promotes nonlinear effects ranging from onsite- to cross-Kerr interaction. A dominating cross-Kerr interaction related to this configuration is notable, as it induces a unique quantum state. In the course of analog quantum simulations, such elementary building blocks can serve as a precursor for more complex geometries and thus pave the way to a number of novel quantum phases of light   

Microwave Reentrant Cavities for Quantum Devices

A microwave reentrant cavity is a device able to provide a very sensitive high-Q microwave mode. Its design can be highly advantageous for electromechanical devices and quantum measurements. In this sense, a tuneable device based on a narrow-gap superconducting reentrant cavity is under development. The resonant frequency is able to be fine-tuned over a range larger than 500 MHz at 10 mK with an electrical Q-factor of 10$^5$. Such a cavity could possibly accommodate a transmon qubit to control and manipulate its quantum state. We are also working on the investigation of bulk acoustic wave (BAW) resonators in microwave reentrant cavities. BAW resonators offer a promising way to process quantum information through the coupling between microwaves and acoustic phonons. Thus, we are developing a device able to excite phonons through non-linearities and the piezoelectricity of the plano-convex quartz crystal. We will detail our experiments that work towards cooling gram scale phonon resonances to the quantum ground state.