Massive Resonators Research Articles

Detecting single gravitons with quantum sensing

The quantization of gravity is widely believed to result in gravitons – particles of discrete energy that form gravitational waves. But their detection has so far been considered impossible. Here we show that signatures of single graviton exchange can be observed in laboratory experiments. We show that stimulated and spontaneous single-graviton processes can become relevant for massive quantum acoustic resonators and that stimulated absorption can be resolved through continuous sensing of quantum jumps. We analyze the feasibility of observing the exchange of single energy quanta between matter and gravitational waves. Our results show that single graviton signatures are within reach of experiments. In analogy to the discovery of the photo-electric effect for photons, such signatures can provide the first experimental clue of the quantization of gravity.

Laser cooling a membrane-in-the-middle system close to the quantum ground state from room temperature

Many protocols in quantum science and technology require initializing a system in a pure quantum state. In the context of the motional state of massive resonators, this enables studying fundamental physics at the elusive quantum–classical transition, and measuring force and acceleration with enhanced sensitivity. Laser cooling has been a method of choice to prepare mechanical resonators in the quantum ground state, one of the simplest pure states. However, to overcome the heating and decoherence by the thermal bath, this usually has to be combined with cryogenic cooling. Here, we laser-cool an ultracoherent, soft-clamped mechanical resonator close to the quantum ground state directly from room temperature. To this end, we implement the versatile membrane-in-the-middle setup with one fiber mirror and one phononic crystal mirror, which reaches a quantum cooperativity close to unity already at room temperature. We furthermore introduce a powerful combination of coherent and measurement-based quantum control techniques, which allows us to mitigate thermal intermodulation noise. The lowest occupancy we reach is 30 phonons, limited by measurement imprecision. Doing away with the necessity for cryogenic cooling should further facilitate the spread of optomechanical quantum technologies.

Coiled Phononic Crystal with Periodic Rotational Locking: Subwavelength Bragg Band Gaps

Phononic crystals (PnC) are spatially periodic materials with band gaps that form by Bragg scattering of elastic waves. Within the frequency range of a band gap, wave propagation is not admitted. A long-standing limitation of this class of materials is that the wavelength for band-gap formation must be on the order of the unit-cell size. This restricts the presence of band gaps to relatively high frequencies for a given lattice spacing. Locally resonant metamaterials, on the other hand, enable the opening of low-frequency, subwavelength band gaps through resonance hybridization. However, their band gaps are characteristically narrow and require large or massive local resonators to form. Here, we break both limitations using beam-based PnCs by (1) locking the rotation degree of freedom at the edges of the primitive unit cell, and (2) coiling the PnC by applying full beam-axis rotations at the locked locations. These respective kinematic and geometric transformations convert a conventional beam PnC from its extended form with a nominal lattice constant to an extremely compact coiled configuration with a greatly reduced lattice constant. With the periodic rotational locking, the band gaps remain intact and are still large, and in fact increase noticeably in size. With the subsequent coiling, the band gaps remain based on Bragg scattering and are quantitatively conserved except now appearing at lower frequencies as dictated by the ratio of the extended-to-coiled lattice constants. This ratio defines a coiling factor, which is a measure of the reduction in the PnC unit-cell length in the direction of wave transmission while maintaining the band structure of its original extended form except for the favorable changes induced by the periodic rotational locking. A coiling factor of $\ensuremath{\beta}$ lowers, by construction, the location of the normalized central frequency of any given band gap by a factor of $\ensuremath{\beta}$. The only limitation is the need for lateral space to accommodate the coiling of the beam segments. The vibration behavior of a finite version of the coiled structure is experimentally tested demonstrating a matching band-gap response, despite the reduction in length, to that obtained by finite-element analysis of the extended rotationally locked version. This concept creates effectively subwavelength Bragg band gaps. It clears the path for PnCs to serve in applications that are orders-of-magnitude smaller in scale than are currently possible, while featuring band gaps that are significantly larger than those generated by locally resonant metamaterials.

Qubit-photon bound states in superconducting metamaterials

We study quantum features of electromagnetic radiation propagating in the one-dimensional superconducting quantum metamaterial comprised of an infinite chain of charge qubits placed within two-stripe massive superconductive resonators. The Quantum-mechanical model is derived assuming weak fields and that, at low temperatures, each qubit is either unoccupied ($N=0$) or occupied by a single Cooper pair ($N=1$). Based on this assumption we demonstrate the emergence of two bands of single-photon-qubit bound states with the energy lying within (lower branch) or outside (higher) the photon continuum. The emergence of bound states may cause radiation trapping which could be of interest for the control of photon transport in these systems.

Stochastic analysis of locally resonant linear and hysteretic metamaterials for seismic isolation of process equipment

Periodic metafoundations have proven to inherit valuable properties from wave propagating in phononic periodic structures in the very low-frequency regime. Therefore, finite locally resonant metafoundations (LRMs) represent a novel type of seismic isolation for ultralow-frequency applications. In this context, it is still unknown the impact that massive resonators with varying frequencies or devices with hysteretic behavior can entail on the whole system performance. For this purpose, we develop and optimize two finite locally resonant multiple degrees of freedom (MDoF) metafoundations in this paper: i) a foundation endowed with resonators, linear springs and linear viscous dampers tuned to multiple frequencies; and ii) a foundation equipped with fully nonlinear hysteretic dampers. Both are optimized considering the stochastic nature of ground motion, modelled with a modified Kanai-Tajimi filter in the stationary frequency domain, and a massive MDoF superstructure, chosen to be a fuel storage tank. In order to take all of the above-mentioned effects into account, we establish a procedure based on nonlinear programming that is able to optimize any number of parameters. More precisely, to optimize the nonlinear behavior of damper devices we employ a Bouc-Wen hysteretic model. Therefore, we reduce the nonlinear differential equations of Bouc-Wen models to a system of linear equations through the stochastic (equivalent) linearization technique. Moreover, we test the optimized systems against natural seismic records both with linear and nonlinear time history analyses. To investigate the role of hysteresis on the nonlinear band structure, we derive linearized and nonlinear dispersion relationships for the uncoupled periodic metafoundation. Finally, we obtain further detailed information on the nonlinear wave propagation by means of a spectro-spatial analysis.

Vibration mitigation of an MDoF system subjected to stochastic loading by means of hysteretic nonlinear locally resonant metamaterials

In this paper, we intend to mitigate absolute accelerations and displacements in the low-frequency regime of multiple-degrees-of-freedom fuel storage tanks subjected to stochastic seismic excitations. Therefore, we propose to optimize a finite locally resonant metafoundation equipped with massive resonators and fully nonlinear hysteretic devices. The optimization process takes into account the stochastic nature of seismic records in the stationary frequency domain; the records are modelled with the power spectral density S0 and modified with a Kanai–Tajimi filter. Moreover, the massive superstructure of a fuel storage tank is also considered in the optimization procedure. To optimize the nonlinear behaviour of dampers, we use a Bouc–Wen hysteretic model; the relevant nonlinear differential equations are reduced to a system of linear equations through the stochastic equivalent linearization technique. The optimized system is successively verified against natural seismic records by means of nonlinear transient time history analyses. Finally, we determine the dispersion relations for the relevant periodic metafoundation.

Single-Photon Cooling in Microwave Magnetomechanics.

Cavity optomechanics, where photons are coupled to mechanical motion, provides the tools to control mechanical motion near the fundamental quantum limits. Reaching single-photon strong coupling would allow to prepare the mechanical resonator in non-Gaussian quantum states. Preparing massive mechanical resonators in such states is of particular interest for testing the boundaries of quantum mechanics. This goal remains however challenging due to the small optomechanical couplings usually achieved with massive devices. Here we demonstrate a novel approach where a mechanical resonator is magnetically coupled to a microwave cavity. We measure a single-photon coupling of g_{0}/2π∼3 kHz, an improvement of one order of magnitude over current microwave optomechanical systems. At this coupling we measure a large single-photon cooperativity with C_{0}≳10, an important step to reach single-photon strong coupling. Such a strong interaction allows us to cool the massive mechanical resonator to a third of its steady state phonon population with less than two photons in the microwave cavity. Beyond tests for quantum foundations, our approach is also well suited as a quantum sensor or a microwave to optical transducer.

Synthesizing multi-phonon quantum superposition states using flux-mediated three-body interactions with superconducting qubits

Massive mechanical resonators operating at the quantum scale can enable a large variety of applications in quantum technologies as well as fundamental tests of quantum theory. Of crucial importance in that direction is both their integrability into state-of-the-art quantum platforms as well as the ability to prepare them in generic quantum states using well-controlled high-fidelity operations. Here, we propose a scheme for controlling a radio-frequency mechanical resonator at the quantum scale using two superconducting transmon qubits that can be integrated on the same chip. Specifically, we consider two qubits coupled via a capacitor in parallel to a superconducting quantum interference device (SQUID), which has a suspended mechanical beam embedded in one of its arms. Following a theoretical analysis of the quantum system, we find that this configuration, in combination with an in-plane magnetic field, can give rise to a tuneable three-body interaction in the single-photon strong-coupling regime, while enabling suppression of the stray qubit-qubit coupling. Using state-of-the-art parameters and qubit operations at single-excitation levels, we numerically demonstrate the possibility of ground-state cooling as well as high-fidelity preparation of mechanical quantum states and qubit-phonon entanglement, i.e. states having negative Wigner functions and obeying non-classical correlations. Our work significantly extends the quantum control toolbox of radio-frequency mechanical resonators and may serve as a promising architecture for integrating such mechanical elements with transmon-based quantum processors.

Proposal to test quantum wave-particle superposition on massive mechanical resonators

We present and analyze a proposal for a macroscopic quantum delayed-choice experiment with massive mechanical resonators. In our approach, the electronic spin of a single nitrogen-vacancy impurity is employed to control the coherent coupling between the mechanical modes of two carbon nanotubes. We demonstrate that a mechanical phonon can be in a coherent superposition of wave and particle, thus exhibiting both behaviors at the same time. We also discuss the mechanical noise tolerable in our proposal and predict a critical temperature below which the morphing between wave and particle states can be effectively observed in the presence of environment-induced fluctuations. Furthermore, we describe how to amplify single-phonon excitations of the mechanical-resonator superposition states to a macroscopic level, via squeezing the mechanical modes. This approach corresponds to the phase-covariant cloning. Therefore, our proposal can serve as a test of macroscopic quantum superpositions of massive objects even with large excitations. This work, which describes a fundamental test of the limits of quantum mechanics at the macroscopic scale, would have implications for quantum metrology and quantum information processing.

Heralded entangled coherent states between spatially separated massive resonators

We put forward an experimentally feasible scheme for heralded entanglement generation between two distant macroscopic mechanical resonators. The protocol exploits a hybrid quantum device, a qubit interacting with a mechanical resonator as well as a cavity mode, for each party. The cavity modes interfere on a beam-splitter followed by suitable heralding detections which post-select a hybrid entangled state with success probability 1/2. Subsequently, by local measurements on the qubits a mechanical entangled coherent state can be achieved. The mechanical entanglement can be further verified via monitoring the entanglement of the qubit pair. The setup is envisioned as a test bench for sensing gravitational effects on the quantum dynamics of gravitationally coupled massive objects. As a concrete example, we illustrate the implementation of our protocol using the current circuit QED architectures.

Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems

Cooling macroscopic objects is of importance for both fundamental and applied physics. Here we study the optomechanical cooling in a hybrid system which consists of a cloud of atoms coupled to a cavity optomechanical system. On one hand, the asymmetric Fano or electromagnetically induced transparency resonance is explored and the steady-state cooling limits of resonators with frequency ${\ensuremath{\omega}}_{\mathrm{m}}$ are analytically obtained, permitting ground-state cooling of massive low-frequency resonators beyond the resolved sideband limit. On the other hand, due to the excitation-saturation effect, the validity of cooling requires the number of atoms to be much larger than the number of steady-state excitations, which is proportional to ${\ensuremath{\omega}}_{\mathrm{m}}^{\ensuremath{-}2}$. Thus, this limitation plays a minor role in cooling higher-frequency resonators, but becomes important for macroscopic lower-frequency resonators. Under such limitation on the number of atoms, the optimal parameters are quantified. Our study can be a guideline for both theoretical and experimental study of cooling macroscopic objects in atom-optomechanical hybrid systems.

Asteroseismology of Red-Giant Stars as a Novel Approach in the Search for Gravitational Waves

AbstractStars are massive resonators that may be used as gravitational-wave (GW) detectors with isotropic sensitivity. New insights on stellar physics are being made possible by asteroseismology, the study of stars by the observation of their natural oscillations. The continuous monitoring of oscillation modes in stars of different masses and sizes (e.g., as carried out by NASA's Kepler mission) opens the possibility of surveying the local Universe for GW radiation. Red-giant stars are of particular interest in this regard. Since the mean separation between red giants in open clusters is small (a few light years), this can in principle be used to look for the same GW imprint on the oscillation modes of different stars as a GW propagates across the cluster. Furthermore, the frequency range probed by oscillations in red giants complements the capabilities of the planned eLISA space interferometer. We propose asteroseismology of red giants as a novel approach in the search for gravitational waves.

A Helium Cryostat for Investigating the Properties of Massive Solid Resonators with Deep Cooling

A helium cryostat for investigating the properties of massive solid acoustic and optical resonators (of the order of tens of kilograms) for cooling to helium temperatures is modernized and tested. A complete cycle of cooling from room temperature to nitrogen and helium temperatures is carried out. The dynamics of the acoustic characteristics of the model of a gravitational detector at different stages of cooling is tracked. The operating parameters of the new cryostat (the heat inflow and the consumption of coolant) are investigated. Optical inputs were mounted for cryogenic investigations of models with cryogenic mirrors.

Optomechanically-induced-transparency cooling of massive mechanical resonators to the quantum ground state

Ground state cooling of massive mechanical objects remains a difficult task restricted by the unresolved mechanical sidebands. We propose an optomechanically-induced-transparency cooling scheme to achieve ground state cooling of mechanical motion without the resolved sideband condition in a pure optomechanical system with two mechanical modes coupled to the same optical cavity mode. We show that ground state cooling is achievable for sideband resolution $\omega_{m}/\kappa$ as low as 0.003. This provides a new route for quantum manipulation of massive macroscopic devices and high-precision measurements.

Strong Coupling and Long-Range Collective Interactions in Optomechanical Arrays

We investigate the collective optomechanics of an ensemble of scatterers inside a Fabry-Pérot resonator and identify an optimized configuration where the ensemble is transmissive, in contrast to the usual reflective optomechanics approach. In this configuration, the optomechanical coupling of a specific collective mechanical mode can be several orders of magnitude larger than the single-element case, and long-range interactions can be generated between the different elements since light permeates throughout the array. This new regime should realistically allow for achieving strong single-photon optomechanical coupling with massive resonators, realizing hybrid quantum interfaces, and exploiting collective long-range interactions in arrays of atoms or mechanical oscillators.

Active feedback cooling of massive electromechanical quartz resonators

We present a general active feedback cooling scheme for massive electromechanical quartz resonators. We cool down two kinds of macrosized quartz tuning forks and find several characteristic constants for this massive quartz-resonator feedback cooling, in good agreement with theoretical calculations. When combined with conventional cryogenic techniques and low-noise devices, one may reach the quantum sensitivity for macroscopic sensors. This may be useful for high sensitivity measurements and for quantum information studies.

Observation of strong coupling between a micromechanical resonator and an optical cavity field

Achieving coherent quantum control over massive mechanical resonators is a current research goal. Nano- and micromechanical devices can be coupled to a variety of systems, for example to single electrons by electrostatic or magnetic coupling, and to photons by radiation pressure or optical dipole forces. So far, all such experiments have operated in a regime of weak coupling, in which reversible energy exchange between the mechanical device and its coupled partner is suppressed by fast decoherence of the individual systems to their local environments. Controlled quantum experiments are in principle not possible in such a regime, but instead require strong coupling. So far, this has been demonstrated only between microscopic quantum systems, such as atoms and photons (in the context of cavity quantum electrodynamics) or solid state qubits and photons. Strong coupling is an essential requirement for the preparation of mechanical quantum states, such as squeezed or entangled states, and also for using mechanical resonators in the context of quantum information processing, for example, as quantum transducers. Here we report the observation of optomechanical normal mode splitting, which provides unambiguous evidence for strong coupling of cavity photons to a mechanical resonator. This paves the way towards full quantum optical control of nano- and micromechanical devices.

Micromachined ultrasound transducers with improved coupling factors from a CMOS compatible process

For medical high frequency acoustic imaging purposes the reduction in size of a single transducer element for one-dimensional and even more for two-dimensional arrays is more and more limited by fabrication and cabling technology. In the fields of industrial distance measurement and simple object recognition low cost phased arrays are lacking. Both problems can be solved with micromachined ultrasound transducers (MUTs). A single transducer is made of a large number of microscopic elements. Because of the array structure of these transducers, groups of elements can be built up and used as a phased array. By integrating parts of the sensor electronics on chip, the cabling effort for arrays can be reduced markedly. In contrast to standard ultrasonic technology, which is based on massive thickness resonators, vibrating membranes are the radiating elements of the MUTs. New micromachining technologies have emerged, allowing a highly reproducible fabrication of electrostatically driven membranes with gap heights below 500 nm. A microelectronic BiCMOS process was extended for surface micromechanics (T. Scheiter et al., Proceedings 11th European Conference on Solid-State Transducers, Warsaw, Vol. 3, 1997, pp. 1595–1598). Additional process steps were included for the realization of the membranes which form sealed cavities with the underlying substrate. Membrane and substrate are the opposite electrodes of a capacitive transducer. The transducers can be integrated monolithically on one chip together with the driving, preamplifying and multiplexing circuitry, thus reducing parasitic capacities and noise level significantly. Owing to their low mass the transducers are very well matched to fluid loads, resulting in a very high bandwidth of 50–100% (C. Eccardt et al., Proceedings Ultrasonics Symposium, San Antonio, Vol. 2, 1996, pp. 959–962; P.C. Eccardt et al., Proceedings of the 1997 Ultrasonics Symposium, Toronto, Vol. 2, 1997, pp. 1609–1618). In the following it is shown how the BiCMOS process has been modified to meet the demands for ultrasound generation and reception. Bias and driving voltages have been reduced down to the 10 V range. The electromechanical coupling is now almost comparable with that for piezoelectric transducers. The measurements exhibit sound pressures and bandwidths that are at least comparable with those of conventional piezoelectric transducer arrays.