Charge noise at Cooper-pair resonances

We analyze the charge dynamics of a superconducting single-electron transistor (SSET) in the regime where charge transport occurs via Cooper-pair resonances. Using an approximate description of the system Hamiltonian, in terms of a series of resonant doublets, we derive a Born-Markov master equation describing the dynamics of the SSET. The average current displays sharp peaks at the Cooper-pair resonances and we find that the charge noise spectrum has a characteristic structure which consists of a series of asymmetric triplets of peaks. The strongest feature in the charge noise spectrum is the triplet of peaks centered at zero frequency which has a peak spacing equal to the level separation within the doublets and is similar to the triplet in the spectrum of a driven, damped, two-level system. We also explore the back-action that the SSET charge noise would have on an oscillator coupled to the island charge, measurement of which provides a way of probing the charge noise spectrum.Comment: 14 pages, 7 figure

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.Comment: 5 pages, 4 figure

Probing the Quantum Coherence of a Nanomechanical Resonator Using a Superconducting Qubit: II. Implementation

We describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding, companion paper (Armour A D and Blencowe M P 2008 New. J. Phys. 10 095004). The implementation is based on the circuit quantum electrodynamics (QED) set-up, with the addition of a mechanical degree of freedom formed out of a suspended, doubly-clamped segment of the superconducting loop of a dc SQUID located directly opposite the centre conductor of a coplanar waveguide (CPW). The relative merits of two SQUID based qubit realizations are addressed, in particular a capacitively coupled charge qubit and inductively coupled flux qubit. It is found that both realizations are equally promising, with comparable qubit–mechanical resonator mode as well as qubit–microwave resonator mode coupling strengths

Noise properties of two single electron transistors coupled by a nanomechanical resonator

We analyze the noise properties of two single electron transistors (SETs) coupled via a shared voltage gate consisting of a nanomechanical resonator. Working in the regime where the resonator can be treated as a classical system, we find that the SETs act on the resonator like two independent heat baths. The coupling to the resonator generates positive correlations in the currents flowing through each of the SETs as well as between the two currents. In the regime where the dynamics of the resonator is dominated by the back-action of the SETs, these positive correlations can lead to parametrically large enhancements of the low frequency current noise. These noise properties can be understood in terms of the effects on the SET currents of fluctuations in the state of a resonator in thermal equilibrium which persist for times of order the resonator damping time.Comment: Accepted for publication in Phys. Rev.

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 the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised 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 a nanomechanical resonator to a SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers