Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.

We derive simple models for the dynamics of a single atom coupled to a cavity field mode in the absorptive bistable parameter regime by projecting the time evolution of the state of the system onto a suitably chosen nonlinear low-dimensional manifold, which is found by use of local tangent space alignment. The output field from the cavity is detected with a homodyne detector allowing observation of quantum jumps of the system between states with different average numbers of photons in the cavity. We find that the models, which are significantly faster to integrate numerically than the full stochastic master equation, largely reproduce the dynamics of the system, and we demonstrate that they are sufficiently accurate to facilitate feedback control of the state of the system based on the predictions of the models alone.

We propose a trap for confining cold neutral atoms in a microscopic ring using a magnetoelectrostatic potential. The trapping potential is derived from a combination of a repulsive magnetic field from a hard drive atom mirror and the attractive potential produced by a charged disk patterned on the hard drive surface. We calculate a trap frequency of ͓29.7, 42.6, 62.8͔ kHz and a depth of ͓16. Traps are a standard tool for the study and manipulation of cold neutral atoms, allowing the investigation of fundamental quantum dynamics as well as providing a basis for quantum information processing. The manipulation of trapped atoms on "atom chips" allows the implementation of many different atom optics elements for trapping, waveguiding, interferometry, etc. [1,2]. Most atom chips use micronsized current-carrying wires to generate the magnetic trapping fields. We propose to construct a magnetoelectrostatic ring trap, consisting of a hard drive atom mirror that provides a repulsive force on low-field seeking atoms [3] and electric pads that attract polarizable atoms via the Stark effect [4-6]. Schmiedmayer and Hinds and Hughes have proposed a range of such traps, including large-area two-dimensional traps, wire-based waveguides, and quantum-dot-like single state traps. Such traps could be used to construct beam splitters or to implement collisional quantum gates [7]. Here we propose a ring trap for cold neutral atoms constructed from a conducting disk placed above the atom mirror surface, which produces a trap with a deep ring potential around the edge of the disk.Let us first examine the trapping potential from a charged conducting disk above a hard drive atom mirror. The hard drive's sinusoidal pattern of magnetization results in a repulsive potential-for atoms in weak-field seeking states-in the form of a decaying exponential [8]The amplitude depends on the remnant magnetization of the mirror, B 0 , as well as the magnetic sublevel m F and Landé g F -factor of the atomic ground state. The decay length is proportional to the periodicity a of the magnetization pattern.A small externally applied magnetic field perpendicular to the magnetization of the hard disk eliminates zones of zero magnetic field which would allow Majorana spin-flip losses. The atom's low velocity allows the spin adiabatically to follow the magnetic field and thus the trapping potential depends only on the field magnitude.In order to create a trap, the repulsive force from the mirror is balanced by an attractive force due to the dc Stark effect. The atomic potential due to an electric field iswhere we assume that we are working with atoms such as cesium or rubidium which possess only a scalar polarizability in the ground state. A charged conducting disk creates high electric fields near its edge, resulting in a strong shortrange attractive potential. The mirror is made out of an etched hard drive whose aluminum substrate is grounded. The boundary conditions consist of a ground at the mirror surface, and a constant potential on the surface of the thi...