Energy Spectrum and Exact Cover in an Extended Quantum Ising Model

We investigate an extended version of the quantum Ising model which includes beyond-nearest neighbour interactions and an additional site-dependent longitudinal magnetic field. Treating the interaction exactly and using perturbation theory in the longitudinal field, we calculate the energy spectrum and find that the presence of beyond-nearest-neighbour interactions enhances the minimal gap between the ground state and the first excited state, irrespective of the nature of decay of these interactions along the chain. The longitudinal field adds a correction to this gap that is independent of the number of qubits. We discuss the application of our model to implementing specific instances of 3-satisfiability problems (Exact Cover) and make a connection to a chain of flux qubits.Comment: 9 pages, 3 figures, published versio

Resonant multiple Andreev reflections in mesoscopic superconducting junctions

We investigate the properties of subharmonic gap structure (SGS) in superconducting quantum contacts with normal-electron resonances. We find two distinct new features of the SGS in resonant junctions which distinguish them from non-resonant point contacts: (i) The odd-order structures on the current-voltage characteristics of resonant junctions are strongly enhanced and have pronounced peaks, while the even-order structures are suppressed, in the case of a normal electron resonance being close to the Fermi level. (ii) Tremendous current peaks develop at $eV=\pm 2E_0$ where $E_0$ indicates a distance of the resonance to the Fermi level. These properties are determined by the effect of narrowing of the resonance during multiple Andreev reflections and by overlap of electron and hole resonances.Comment: 13 pages, 10 figure

Suppression and enhancement of the critical current in multiterminal S/N/S mesoscopic structures

We analyse the measured critical current $I_{m\text{}}$ in a mesoscopic 4-terminal S/N/S structure. The current through the S/N interface is shown to consist not only of the Josephson component $I_{c}\sin \phi ,$ but also a phase-coherent part $I_{sg}\cos \phi$ of the subgap current. The current $I_{m}$ is determined by the both components $I_{c}$ and $I_{sg},$ and depends in a nonmonotonic way on the voltage $V$ between superconductors and normal reservoirs reaching a maximum at $V\cong \Delta /e$. The obtained theoretical resultas are in qualitative agreement with recent experimental data.Comment: 4 page, 3 figures. To be puplished in PRB Rapid co

Quantum dynamics of a driven three-level Josephson-atom maser

Recently, a lasing effect has been observed in a superconducting nano-circuit where a Cooper pair box, acting as an artificial three-level atom, was coupled to a resonator. Motivated by this experiment, we analyze the quantum dynamics of a three-level atom coupled to a quantum-mechanical resonator in the presence of a driving on the cavity within the framework of the Lindblad master equation. As a result, we have access to the dynamics of the atomic level populations and the photon number in the cavity as well as to the output spectrum. The results of our quantum approach agree with the experimental findings. The presence of a fluctuator in the circuit is also analyzed. Finally, we compare our results with those obtained within a semiclassical approximation.Comment: 6 pages, 6 figure

Nonequilibrium Josephson effect in mesoscopic ballistic multiterminal SNS junctions

We present a detailed study of nonequilibrium Josephson currents and conductance in ballistic multiterminal SNS-devices. Nonequilibrium is created by means of quasiparticle injection from a normal reservoir connected to the normal part of the junction. By applying a voltage at the normal reservoir the Josephson current can be suppressed or the direction of the current can be reversed. For a junction longer than the thermal length, $L\gg\xi_T$, the nonequilibrium current increases linearly with applied voltage, saturating at a value equal to the equilibrium current of a short junction. The conductance exhibits a finite bias anomaly around $eV \sim \hbar v_F/L$. For symmetric injection, the conductance oscillates $2\pi$-periodically with the phase difference $\phi$ between the superconductors, with position of the minimum ($\phi=0$ or $\pi$) dependent on applied voltage and temperature. For asymmetric injection, both the nonequilibrium Josephson current and the conductance becomes $\pi$-periodic in phase difference. Inclusion of barriers at the NS-interfaces gives rise to a resonant behavior of the total Josephson current with respect to junction length with a period $\sim \lambda_F$. Both three and four terminal junctions are studied.Comment: 21 pages, 19 figures, submitted to Phys. Rev.

Single-artificial-atom lasing using a voltage-biased superconducting charge qubit

We consider a system composed of a single artificial atom coupled to a cavity mode. The artificial atom is biased such that the most dominant relaxation process in the system takes the atom from its ground state to its excited state, thus ensuring population inversion. A recent experimental manifestation of this situation was achieved using a voltage-biased superconducting charge qubit. Even under the condition of `inverted relaxation', lasing action can be suppressed if the `relaxation' rate is larger than a certain threshold value. Using simple transition-rate arguments and a semiclassical calculation, we derive analytic expressions for the lasing suppression condition and the state of the cavity in both the lasing and suppressed-lasing regimes. The results of numerical calculations agree very well with the analytically derived results. We start by analyzing a simplified two-level-atom model, and we then analyze a three-level-atom model that should describe accurately the recently realized superconducting artificial-atom laser.Comment: 21 pages in preprint format, 6 figure

Decoherence, Autler-Townes effect, and dark states in two-tone driving of a three-level superconducting system

We present a detailed theoretical analysis of a multi-level quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as the Autler-Townes splitting, which has been recently demonstrated experimentally [M. A. Sillanpaa et al., Phys. Rev. Lett. 103, 193601 (2009)] in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.Comment: 16 pages, 8 figure

Excess Noise in Biased Superconducting Weak Links

Non-equilibrium excess noise of a short quasi one-dimensional constriction between two superconductors is considered. A general expression for the current-current correlation function valid for arbitrary temperatures and bias voltages is derived. This formalism is applied to a current-carrying quantum channel with perfect transparency. Contrary to a transparent channel separating two normal conductors, a weak link between two superconductors exhibits a finite level of noise. The source of noise is fractional Andreev scattering of quasiparticles with energies $|E|$ greater than the half-width $\Delta$ of the superconducting gap. For high bias voltages, $V \gg \Delta /e$, the relation between the zero-frequency limit of the noise spectrum, $S(0)$, and the excess current $I_{\text{exc}}$ reads $S(0)=(1/5)|e|I_{\text{exc}}$. As $\Delta \rightarrow 0$ both the excess noise and the excess current vanish linearly in $\Delta$, %$\propto \Delta$, their ratio being constant.Comment: 8 pages (Latex), 1 figur