M. P. Blencowe

Cooling a nanomechanical resonator with quantum back-action

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radio-frequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latters position; back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK—an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these back-action effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.

Entanglement and Decoherence of a Micromechanical Resonator via Coupling to a Cooper-Pair Box

We analyze the quantum dynamics of a micromechanical resonator capacitively coupled to a Cooper-pair 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.

Quantum energy flow in mesoscopic dielectric structures

We investigate the phononic energy-transport properties of mesoscopic, suspended dielectric wires. The Landauer formula for the thermal conductance is derived and its universal aspects discussed. We then determine the variance of the energy current in the presence of a steady-state current flow. In the final part, some initial results are presented concerning the nature of the temperature fluctuations of a mesoscopic electron-gas thermometer due to the absorption and emission of wire phonons. @S0163-1829~99!02707-1#

Supermembranes and the signature of spacetime

Abstract We consider extended objects with s space and t time world-volume dimensions moving in a spacetime with S ⩾ s space and T ⩾ t time dimensions. The requirements of spacetime supersymmetry and world-volume fermionic gauge invariance severely restrict the possible values of S and T . If we furthermore insist that the transverse group SO( S − s , T − t ) be compact to avoid ghosts, then t = T . The results may be interpreted as a set of superconformal field theories with s + t ⩽6 and N ⩽8 whose superconformal groups are in one-to-one correspondence with those in Nahms classification. Although the choice t = T = 1 is not uniquely singled out, it does seem to play a preferred role.

Classical dynamics of a nanomechanical resonator coupled to a single-electron transistor

We analyze the dynamics of a nanomechanical resonator coupled to a single-electron transistor (SET) in the regime where the resonator behaves classically. A master equation is derived describing the dynamics of the coupled system which is then used to obtain equations of motion for the average charge state of the SET and the average position of the resonator. We show that the action of the SET on the resonator is very similar to that of a thermal bath, as it leads to a steady-state probability distribution for the resonator which can be described by mean values of the resonator position, a renormalized frequency, an effective temperature, and an intrinsic damping constant. Including the effects of extrinsic damping and finite temperature, we find that there remain experimentally accessible regimes where the intrinsic damping of the resonator still dominates its behavior. We also obtain the average current through the SET as a function of the coupling to the resonator.

Intrinsic noise of a micromechanical displacement detector based on the radio-frequency single-electron transistor

We investigate the tunneling shot noise limits on the sensitivity of a micromechanical displacement detector based on a metal junction, radio-frequency single-electron transistor (rf SET). In contrast with the charge sensitivity of the rf-SET electrometer, the displacement sensitivity improves with increasing gate voltage bias and, with a suitably optimized rf SET, displacement sensitivities of 10−6 A/Hz may be possible.

Analogue Hawking Radiation in a dc-SQUID Array Transmission Line

We propose the use of a superconducting transmission line formed from an array of direct-current superconducting quantum interference devices for investigating analogue Hawking radiation. Biasing the array with a space-time varying flux modifies the propagation velocity of the transmission line, leading to an effective metric with a horizon. Being a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as backreaction and analogue space-time fluctuations on the Hawking process.

Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor

We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor (SSET) in the vicinity of Josephson quasi-particle (JQP) and double Josephson quasi-particle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonances the dynamics of the resonator are given by a Fokker–Planck equation, i.e. the SSET behaves effectively as an equilibrium heat bath, characterized by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending on the gate and drain–source voltage bias points with respect to the superconducting resonance, the SSET can also give rise to an instability in the mechanical resonator marked by negative damping and temperature within the appropriate Fokker–Planck equation. Furthermore, sufficiently close to a resonance, we find that the Fokker–Planck description breaks down. We also point out that there is a close analogy between coupling of a nanomechanical resonator to an SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers.

Quantum squeezing of mechanical motion for micron-sized cantilevers

Abstract We show that substantial quantum squeezing of mechanical motion can be achieved for micron-sized cantilever devices using available techniques.

Probing the quantum coherence of a nanomechanical resonator using a superconducting qubit: I. Echo scheme

We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximized and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states, this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a suitable control pulse to the qubit allows its population to be inverted resulting in a reversal of the resonator dynamics. However, the resonators interactions with its environment mean that the dynamics is not completely reversible. We show that this irreversibility is largely due to the decoherence of the mechanical resonator and can be inferred from appropriate measurements on the qubit alone. Using estimates for the parameters involved based on a specific realization of the system, we show that it should be possible to carry out this scheme with existing device technology.