Iterative solutions to the steady-state density matrix for optomechanical systems.

We present a sparse matrix permutation from graph theory that gives stable incomplete lower-upper preconditioners necessary for iterative solutions to the steady-state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance.

Universal quantum fluctuations of a cavity mode driven by a Josephson junction.

We analyze the quantum dynamics of a superconducting cavity coupled to a voltage-biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.

A macroscopic mechanical resonator driven by mesoscopic electrical back-action.

Systems with coupled mechanical and optical or electrical degrees of freedom have fascinating dynamics that, through macroscopic manifestations of quantum behaviour, provide new insights into the transition between the classical and quantum worlds. Of particular interest is the back-action of electrons and photons on mechanical oscillators, which can lead to cooling and amplification of mechanical motion. Furthermore, feedback, which is naturally associated with back-action, has been predicted to have significant consequences for the noise of a detector coupled to a mechanical oscillator.

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.

Sensitivity and linearity of superconducting radio-frequency single-electron transistors: effects of quantum charge fluctuations.

We have investigated the effects of quantum fluctuations of quasiparticles on the operation of superconducting radio-frequency single-electron transistors (rf-SETs) for large values of the quasiparticle cotunneling parameter alpha = 8EJ/Ec, where EJ and Ec are the Josephson and charging energies. We find that, for alpha > 1, subgap rf-SET operation is still feasible despite quantum fluctuations that wash out quasiparticle tunneling thresholds. Surprisingly, such rf-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.

Real-time detection of electron tunnelling in a quantum dot.

Nanostructures in which strong (Coulomb) interactions exist between electrons are predicted to exhibit temporal electronic correlations. Although there is ample experimental evidence that such correlations exist, electron dynamics in engineered nanostructures have been observed directly only on long timescales. The faster dynamics associated with electrical currents or charge fluctuations are usually inferred from direct (or quasi-direct) current measurements.