We analyze the quantum dynamics of a micromechanical resonator capacitively coupled to a Cooperpair box. With appropriate quantum state control of the Cooper box, the resonator can be driven into a superposition of spatially separated states. The Cooper box can also be used to probe the decay of the resonator superposition state due to environmental decoherence. DOI: 10.1103/PhysRevLett.88.148301 PACS numbers: 85.85. +j, 03.65.Yz Micromechanical resonators with fundamental vibrational mode frequencies in the range 10 MHz -1 GHz can now be fabricated [1,2]. Applications include fast, ultrasensitive force and displacement detectors [3], electrometers [4,5], and radio frequency signal processors [6]. Advances in the development of micromechanical devices also raise the fundamental question of whether mechanical systems containing macroscopic numbers of atoms will exhibit quantum behavior. Because of their size, quantum behavior in micromechanical systems will be strongly influenced by interactions with the environment and the existence of an experimentally accessible quantum regime will depend on the rate at which decoherence occurs [7].In this Letter, we analyze an experimentally implementable scheme to create and detect superpositions of macroscopically distinct quantum states in a micromechanical resonator, and furthermore measure their decoherence rates, by entangling the resonator with a Cooper box [8][9][10]. The key advantage over optomechanical schemes [7,11] is the demonstrated coherent control of the Cooper box quantum charge state [9], together with the strong (controllable) coupling which can be achieved between the Cooper box state and the motional degree of freedom of a micron-sized mechanical oscillator. Cooper box-based schemes have also been proposed for creating macroscopic quantum state superpositions in superconducting islands [12] and superconducting resonators [13].A Cooper box consists of a small superconducting island weakly linked to a superconducting reservoir [8 -10]. The state of the Cooper box is determined by the balance between its Coulomb charging energy, and the strength of the Cooper-pair tunneling between the island and reservoir. Using an external gate, the Cooper box can be driven into either of two states of definite Cooper-pair number or a linear superposition of the two states [9]. Cooper boxes are being explored as possible candidates for qubits in future quantum computing devices since they act as readily controllable two-level quantum systems [10,14].The electrostatic interaction between a conducting cantilever and a nearby Cooper box causes a displacement in the cantilever whose sign depends on which of the two charge states the Cooper box is in. When the Cooper box is prepared in a superposition of charge states, it and the cantilever become entangled and the cantilever is driven into a superposition of spatially separated states. If the coupling is strong enough, then the separation between the states in the superposition can become larger than their quantum positio...

Surprisingly, when biasing near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK. These measurements have implications for nanomechanical readout of quantum information devices and the limits of ultra-sensitive force microscopy, e.g. single nuclear spin magnetic resonance force microscopy. Furthermore, we anticipate the use of these backaction effects to prepare ultra-cold and quantum states of mechanical structures, which would not be accessible with existing technology.In practice, these back-action impulses arise from the quantized and stochastic nature of the fundamental particles utilized in the measuring device. For example, in high precision optical interferometers such as the LIGO gravitational wave detector 4 or in the single-spin force microscope 5 , the position of a test mass is monitored by reflecting laser-light off of the measured object and interfering this light with a reference beam at a detector. The measured signal is the arrival rate of photons, and one might say that the optical "conductance" of the interferometer is modulated by the position of the measured object. Back-action forces which stochastically drive the measured object result from the random impact and momentum transfer of the discrete photons. This mechanical effect of light is thought to provide the ultimate limit to the position and force sensitivity of an optical interferometer. Although this photon "ponderomotive" noise has not yet been detected during the measurement of a macroscopic object 6 , these back-action effects are clearly observed and carefully utilized in the cooling of dilute atomic vapors to nanoKelvin temperatures.In the experiments reported here, we study an SSET which is capacitively coupled to a voltage-biased (V NR ), doubly-clamped nanomechanical resonator (Fig. 1). Like the interferometer, the conductance of the SSET is a very sensitive probe of the resonator's position, whereas the particles transported in this case are a mixture of single andCooper-paired electrons. We have recently shown the SSET to be nearly a quantumlimited position detector 7 , however reaching the best sensitivity will ultimately be limited by the back-action of the charged particles 3 , which could not be observed in previous experiments because of insufficient SSET-resonator coupling.The back-action force of the SSET results in three measurable effects on the resonator: a frequency shift, a damping rate, and position fluctuations. The frequency shift and damping rate are caused by the in-phase and small out-of phase response in the average electrostatic force between the SSET and resonator, as the resonator oscillates. .MHz is clearly visible, and accurately fits a simple harmonic oscillator response function, on top of a white power spectrum due to an ultra-low noise microwave preamplifier used to read out the SSET with microwave reflectometry 8 .For low SSET-nanoresonator coupling strengths, and the SSET biased close to the Josephson Quasiparticle Peak (JQP) 9 , T NR simply follows T ...

Using the approach of Fradkin and Vasiliev (1987), an action is constructed in 2+1 spacetime dimensions describing interacting massless fields of all integer and half-integer spins s>or=3/2. The action is associated with an infinite-dimensional superalgebra, denoted shs(1, 2)(+)shs(1,2). Truncation to the spin 3/2-spin 2 sector gives the (1,1) type anti-de Sitter (AdS) supergravity theory corresponding to osp(1,2; R)(+)osp(1,2; R). Various properties of the D=3 higher-spin theory, and its relevance to the higher-spin problem in four dimensions, are discussed.

The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg's uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.

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