Session S38: Mechanical Systems

Quantum Coherence of Optomechanical Systems in the Single-photon Strong Coupling Regime

Optomechanical systems with ultrastrong coupling could demonstrate nonlinear optical effects such as photon blockade. The system-bath couplings in these systems play an essential role in observing these effects. In this work, we use a dressed-state master equation approach to study the quantum coherence of an optomechanical system. In this approach, the system-bath couplings are decomposed in terms of the eigenbasis of the optomechanical system, where the mechanical state is displaced by finite photon occupation. Compared with the standard master equation often seen in the literature, our master equation includes photon-number-dependent terms that induce dephasing. We calculate cavity dephasing, second-order photon correlation, and two-cavity entanglement using the dressed-state master equation. At high temperature, our master equation predicts faster decay of the quantum coherence than with the standard master equation. The second-order photon correlation derived with our master equation shows less antibunching than that with the standard master equation.   

Design and modeling of electro-optomechanical devices for microwave to optical quantum state transfer

A transducer that could transfer quantum information between the microwave and optical domains would connect the information processing and storage power of superconducting qubits with the long distance communication power of light in optical fibers. Electro-optomechanical structures, which parametrically couple mechanical vibration to both optical and microwave resonantors, have emerged as promising candidates for realizing such a transducer. Following on the recent demonstration of bidirectional and efficient conversion of classical information between the microwave and optical domains [1], we report on the design of improved electro-optomechnical transducers. These new transducers are designed to operate with higher conversion bandwidth and in a dilution refrigerator, thereby reaching the regime of quantum transduction.\\[4pt] [1] R.W. Andrews, R.W. Peterson, T.P. Purdy, K. Cicak, R.W. Simmonds, C.A. Regal, K.W. Lehnert, Nat. Phys. 10, 321-326 (2014)   

Improving integration of high-Q silicon nitride membrane resonators into electro-opto-mechanical devices for hybrid quantum systems

Macroscopic high-stress silicon nitride membranes can be implemented as ultra-high-quality-factor mechanical resonators operating in the quantum regime with average phonon occupancy below one quantum. Mechanical motion of these resonators can be engineered to simultaneously couple both to (THz) light in free-space optical cavities and to microwave (GHz) fields in superconducting circuits. Exploiting this parametric coupling to realize quantum information transfer between these domains entails construction of devices with challenging requirements. These devices must integrate the membranes with superconducting circuits operating at cryogenic temperatures in proximity of free space optical photons while meeting demands for various quantum and coupling requirements. Here we show how to construct such ``hybrid quantum devices'' by microfabricating and assembling chip-based structures that can be inserted into high-finesse optical cavities compatible with low temperatures. We include an overview of recent fabrication improvements of membranes mechanically isolated from environment by phononic band-gap crystals.   

Coherent mechanically-mediated state transfer between a superconducting qubit and a cavity

We study coherent state transfer between a superconducting qubit and a cavity coupled via a nanomechanical resonator. There are two major challenges relating to state transfer of such systems. First, the duration of the protocol needs to be shorter than the shortest time-scale associated with dissipation (qubit relaxation, mechanical damping, cavity decay\ldots). This constraint implies that most of the well-known adiabatic transfer protocols cannot be used as is. Second, a fast double swap protocol, where the state of the qubit is first transfered to the mechanical degree of freedom and then to the cavity, is the most sensible scheme to mechanical dissipation. Here, we present some protocols that take into account both constraints and optimize the fidelity of the coherent state transfer.   

Phonon mechanisms of nonlinear decay and dephasing of mesoscopic vibrational systems

The frequencies and the decay rates of mesoscopic oscillators depend on vibration amplitudes. Nonlinear decay has been seen recently in various nano- and micro-mechanical systems. Here we consider a microscopic mechanism of nonlinear decay, the nonlinear coupling of the vibrational mode of interest, for example, a flexural mode, to other vibrations. Typically, the modes of interest have low eigenfrequencies $\omega_0$. Their decay comes from the coupling to acoustic-phonon type vibrations with much higher frequency and density of states. Thus, nonlinear decay requires quartic anharmonic coupling or cubic anharmonicity in the higher order. We find the decay rate for the inverse lifetime of the involved phonons, which is determined by the internal nonlinearity and the boundary scattering, being either much larger or smaller than $\omega_0$. The results extend the thermo-elastic, Akhiezer, and Landau-Rumer decay theory to nonlinear decay of mesoscopic modes and make specific predictions on the temperature and frequency dependence of the decay rate for different types of systems. We show that nonlinear decay is invariably accompanied by dephasing. We also show that in nano-electro-mechanical systems the decay rate can be electrostatically controlled.   

Spectra of mesoscopic oscillators with dispersive mode-mode coupling

Mesoscopic vibrational systems typically have several nonlinearly coupled modes with different frequencies and with long lifetime. Examples are provided by flexural modes of carbon nanotubes, graphene sheets, and nanobeams. We consider the power spectrum of one of these modes, which we call an oscillator. Thermal fluctuations of the amplitudes of the modes coupled to the oscillator lead to fluctuations of its frequency and thus to the broadening of its spectrum. However, the coupling-induced broadening is partly masked by the broadening due to the oscillator decay. We show that the mode coupling can be easily identified from the change of the spectrum due to weak resonant driving. Despite the coupling-induced frequency fluctuations being non-Gaussian, it is possible to average over them in a path-integral formulation and thus to find the power spectrum. The shape of the spectrum depends on the interrelation between the nonlinear coupling strength and the decay rates of the modes. The characteristic features of the spectrum are analyzed in the limiting cases. We also find that the spectral effect of the internal nonlinearity of the oscillator differs substantially from the effect of mode-mode coupling.   

Improving the cooling performance of a mechanical resonator with two-level-system defects

We study cooling performance of a realistic mechanical resonator containing defects. The normal cooling method through an optomechanical system does not work efficiently due to those defects. We show by employing periodical $\sigma_z$ pulses, we can eliminate the interaction between defects and their surrounded heat baths up to the first order of time. Compared with the cooling performance of no $\sigma_z$ pulses case, much better cooling results are obtained. Moreover, this pulse sequence has an ability to improve the cooling performance of the resonator with different defects energy gaps and different defects damping rates.   

Determination of effective mechanical properties of a double-layer beam by means of a nano-electromechanical transducer

In the field of optomechanics, the light field in an optical resonator dynamically interacts with a mechanical degree of freedom, enabling cooling and amplification of mechanical motion. This concept of light matter interaction can be transferred to the microwave (MW) regime combining superconducting MW circuits with nanometer-sized mechanical beams, establishing the class of circuit nano-electromechanics. To taylor the mechanical properties of a vibrational element, double and multi-layer systems are of particular interest, e.g. the combination of highly tensile stressed SiN and metallic layers allow to increase the mechanical resonance frequency while maintaining a capacitive coupling scheme. Here, we investigate the mechanical properties of a doubly-clamped, double-layer nanobeam embedded into an electromechanical system. The nanobeam consists of a highly pre-stressed silicon nitride and a superconducting niobium layer. By measuring the mechanical displacement spectral density both in the linear and the nonlinear Duffing regime, we determine the pre-stress and the effective Young's modulus of the nanobeam corroborating the analytical double-layer model expectations.   

Circuit Electromechanics with a Non-Metallized Nano- beam

In the field of cavity optomechanics, a motional degree of freedom is coupled to an optical cavity. This approach can be transferred to the solid state environment by combining a superconducting microwave cavity with a nanomechanical resonator. Typically, metallized mechanical resonators are used, coupling capacitively to the microwave cavity. In contrast, non-metallized nanomechanical beams provide higher quality factors and have therefore been employed e.\,g.~for mechanical sensing devices. Here, we present an approach to integrate a pure, i.\,e.~non-metallized nanobeam, into a nano-electromechanical device, which is based on the dielectric coupling between a superconducting coplanar waveguide microwave resonator and a tensile-stressed silicon nitride nanobeam. By making use of the Duffing nonlinearity of the strongly driven beam, we calibrate the amplitude spectrum of the mechanical motion and determine the electromechanical vacuum coupling. We find a quality factor of $480{,}000$ at a resonance frequency of $14\,\mathrm{MHz}$ and 0.5\,K. We deduce a vacuum coupling of $11.5\,\mathrm{mHz}$, which is in quantitative agreement with finite element based model calculations.   

Temporal and spectral mode conversion of microwave signals with a mechanical resonator

Microwave fields are a powerful means for carrying information between separate quantum devices. Different devices, however, typically emit and capture fields with distinct frequencies and temporal envelopes. This spectral and temporal mismatch presents a challenge when wiring these elements into a fully functional information processing network. Here we show that this mismatch can be overcome by using an electromechanical circuit to arbitrarily alter the temporal envelope and center frequency of microwave signals, while at the same time acting as a storage medium. We demonstrate a protocol that shifts the frequency of 7 GHz microwave signals by 250 MHz, and converts an exponentially decaying temporal envelope into a Gaussian envelope. To characterize our signal conditioner in the quantum regime, we inject signals with a few quanta of energy to extract the total added noise and storage lifetime of the conditioner.   

Reservoir engineering in microwave cavity optomechanics

Microwave cavity optomechanics is an architecture in which a freely suspended membrane modulates the frequency of a superconducting microwave resonant circuit. The resulting parametric interactions influence both the mechanical degree of freedom and the microwave light emerging from the cavity. Even at cryogenic temperatures, the mechanical oscillator resonating at 10 MHz is typically dominated by its thermal reservoir, washing out any quantum behavior. However, in the presence of coherent drives to the cavity, the bare mechanical properties can be overwhelmed by the strong opto-mechanical interactions from the light field. By choosing wisely the frequency and amplitude of the drives, one can engineer the environment seen by the mechanical oscillator, a technique known as ``reservoir engineering''. From an experimentalist point of view, I will discuss how using two-tone driving schemes, we exploit correlations in the vacuum noise to: (1) eliminate the backaction imparted on the mechanical quadrature being measured, a technique so-called Back-Action Evasion, or (2) strongly couple the mechanical mode to a squeezed microwave bath.   

Microwave electromechanics on suspended piezoelectric membranes

Nanomechanical resonators with microwave frequency resonances have been operated in the quantum regime, and are attractive for hybrid electro- and opto-mechanical schemes. We characterize a class of electromechanical devices using propagating phonons in two dimensions, operating at frequencies compatible with both superconducting qubits and optomechanical resonators. We use interdigitated transducers on suspended aluminum nitride membranes to launch and detect traveling acoustic waves. We demonstrate resonances localized to the transducers, as well as transmission across membranes and extended resonances in the acoustic cavities formed by the edges of the suspended membranes. We compare these measurements to analytic as well as finite-element models to determine key parameters, including the electromechanical coupling and propagation loss.   

Building a quantum interface between microwave and optical photons

In previous work\footnote{Bochmann, et al. \textit{Nature Physics} \textbf{9}, 712 (2013)}, we have shown that optomechanical resonators fabricated out of piezoelectric materials may provide a means for coherent transduction between microwave and optical frequency photons. Electrical microwave signals are efficiently converted to microwave phonons, and these phonons in turn modulate the optical response of an optomechanical crystal. In this talk, we will describe new designs we are pursuing in this same direction, with simplified fabrication and a predicted much greater electrical-to-optical coupling strength. We will outline the current device design, simulations, fabrication, and preliminary measurements.   

Improving the quality factor of microwave-frequency mechanical resonators

Piezoelectric micromechanical resonators at gigahertz frequencies have been operated in the quantum limit, with quantum control and measurement achieved using superconducting qubits. However, experiments to date have been limited by mechanical dissipation, due to a combination of internal and radiative losses. In this talk, we explore an alternative resonator design, using a hybrid combination of low-loss single crystal silicon with an electromechanical transducer based on aluminum nitride, a strong piezoelectric. We can measure gigahertz-frequency mechanical modes that are among the overtones of the hybrid structure. We describe the resonator design and fabrication, including finite-element simulations, as well as measurements of the mechanical response.   

Antibunching and unconventional photon blockade with Gaussian squeezed states

There is considerable interest in both the circuit QED\footnote{D. Bozyigit, \textit{et al.}, Nat. Phys. \textbf{7}, 154-158 (2011).} and optomechanics,\footnote{J. D. Cohen, \textit{et al.} arXiv:1410.1047.} experiments in using the measured intensity fluctuations of a bosonic field as a direct signature of a nonclassical state. Although these nonclassical signatures, such as antibunching, are usually observed in strongly nonlinear systems, they also have been reported with Gaussian states in linear systems.\footnote{N. B. Grosse, \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 153603 (2007).} To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing if a field is non-Gaussian based on intensity correlations measurement.\footnote{M.-A. Lemonde, N. Didier, A. A. Clerk, arXiv:1410.6510.} With these results in hands, we shed light on the so-called \textit{unconventional photon blockade} effect predicted in a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing that it is a particular realization of optimized Gaussian amplitude squeezing.