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Register a new userMechanical cat states in graphene resonators
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We study the quantum dynamics of a symmetric nanomechanical graphene resonator with degenerate flexural modes. Applying voltage pulses to two back gates, flexural vibrations of the membrane can be selectively actuated and manipulated. For graphene, nonlinear response becomes important already for amplitudes comparable to the magnitude of zero point fluctuations. We show, using analytical and numerical methods, that this allows for creation of cat-like superpositions of coherent states as well as superpositions of coherent cat-like non-product states.
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Generating non-classical states in macroscopic systems is a long standing challenge. A promising platform in the context of this quest are novel hybrid systems based on magnetic dielectrics, where photons can couple strongly and coherently to magnetic excitations, although a non-classical state therein is yet to be observed. We propose a scheme to generate a magnetization cat state, i.e. a quantum superposition of two distinct magnetization directions, using a conventional setup of a macroscopic ferromagnet in a microwave cavity. Our scheme uses the ground state of an ellipsoid shaped magnet, which displays anisotropic quantum fluctuations akin to a squeezed vacuum. The magnetization collapses to a cat state by either a single-photon or a parity measurement of the microwave cavity state. We find that a cat state with two components separated by $sim5hbar$ is feasible and briefly discuss potential experimental setups that can achieve it.
We report radio frequency (rf) electrical readout of graphene mechanical resonators. The mechanical motion is actuated and detected directly by using a vector network analyzer, employing a local gate to minimize parasitic capacitance. A resist-free doubly clamped sample with resonant frequency ~ 34 MHz, quality factor ~ 10000 at 77 K, and signal-to-background ratio of over 20 dB is demonstrated. In addition to being over two orders of magnitude faster than the electrical rf mixing method, this technique paves the way for use of graphene in rf devices such as filters and oscillators.
Graphene is an attractive material for nanomechanical devices because it allows for exceptional properties, such as high frequencies and quality factors, and low mass. An outstanding challenge, however, has been to obtain large coupling between the motion and external systems for efficient readout and manipulation. Here, we report on a novel approach, in which we capacitively couple a high-Q graphene mechanical resonator ($Q sim 10^5$) to a superconducting microwave cavity. The initial devices exhibit a large single-photon coupling of $sim 10$ Hz. Remarkably, we can electrostatically change the graphene equilibrium position and thereby tune the single photon coupling, the mechanical resonance frequency and the sign and magnitude of the observed Duffing nonlinearity. The strong tunability opens up new possibilities, such as the tuning of the optomechanical coupling strength on a time scale faster than the inverse of the cavity linewidth. With realistic improvements, it should be possible to enter the regime of quantum optomechanics.
Carbon nanotubes and graphene allow fabricating outstanding nanomechanical resonators. They hold promise for various scientific and technological applications, including sensing of mass, force, and charge, as well as the study of quantum phenomena at the mesoscopic scale. Here, we have discovered that the dynamics of nanotube and graphene resonators is in fact highly exotic. We propose an unprecedented scenario where mechanical dissipation is entirely determined by nonlinear damping. As a striking consequence, the quality factor Q strongly depends on the amplitude of the motion. This scenario is radically different from that of other resonators, whose dissipation is dominated by a linear damping term. We believe that the difference stems from the reduced dimensionality of carbon nanotubes and graphene. Besides, we exploit the nonlinear nature of the damping to improve the figure of merit of nanotube/graphene resonators.
Graphene and carbon nanotubes represent the ultimate size limit of one and two-dimensional nanoelectromechanical resonators. Because of their reduced dimensionality, graphene and carbon nanotubes display unusual mechanical behavior; in particular, their dynamics is highly nonlinear. Here, we review several types of nonlinear behavior in resonators made from nanotubes and graphene. We first discuss an unprecedented scenario where damping is described by a nonlinear force. This scenario is supported by several experimental facts: (i) the quality factor varies with the amplitude of the motion as a power law whose exponent coincides with the value predicted by the nonlinear damping model, (ii) hysteretic behavior (of the motional amplitude as a function of driving frequency) is absent in some of our resonators even for large driving forces, as expected when nonlinear damping forces are large, and (iii) when we quantify the linear damping force (by performing parametric excitation measurements) we find that it is significantly smaller than the nonlinear damping force. We then review parametric excitation measurements, an alternative actuation method which is based on nonlinear dynamics. Finally, we discuss experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling can be made so strong that the associated force acting on the nanotube becomes highly nonlinear with displacement and velocity. Overall, graphene and nanotube resonators hold promise for future studies on classical and quantum nonlinear dynamics.
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