Dephasing of solid-state qubits at optimal points

Motivated by recent experiments with Josephson-junction circuits, we analyze the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We study the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. For 1/f noise strong higher-order effects influence the evolution.Comment: minor corrections and clarification

Measuring fermion parity correlations and relaxation rates in 1D topological superconducting wires

Zero energy Majorana fermion states (Majoranas) can arise at the ends of a semiconducting wire in proximity with a superconductor. A first generation of experiments has detected a zero bias conductance peak in these systems that strongly suggests these Majoranas do exist; however, a definitive demonstration of the long-ranged entanglement that is crucial for potential applications in quantum computing has yet to be carried out. This work discusses two possible measurement schemes to detect this long-ranged entanglement in a wire system with two coupled pairs of Majoranas, by varying the coupling between one pair while measuring the fermion parity of the second pair. First, in a system with two coupled pairs of Majoranas, we discuss how varying the coupling of one pair in time, while measuring temporal fermion parity correlations of the second pair, allows for an experimental probe of long-ranged Majorana entanglement. Second, we show that the power spectrum of the charge noise (fermion parity noise) of one pair contains signatures of these correlations, as well as allowing one to infer the parity relaxation rate

Depinning of disordered bosonic chains

We consider one-dimensional bosonic chains with a repulsive boson-boson interaction that decays exponentially on large length-scales. This model describes transport of Cooper-pairs in a Josepshon junction array, or transport of magnetic flux quanta in quantum-phase-slip ladders, i.e. arrays of superconducting wires in a ladder-configuration that allow for the coherent tunnelling of flux quanta. In the low-frequency, long wave-length regime these chains can be mapped to an effective model of a one-dimensional elastic field in a disordered potential. The onset of transport in these systems, when biased by external voltage, is described by the standard depinning theory of elastic media in disordered pinning potentials. We numerically study the regimes that are of relevance for quantum-phase-slip ladders. These are (i) very short chains and (ii) the regime of weak disorder. For chains shorter than the typical pinning length, i.e., the Larkin length, the chains reach a saturation regime where the depinning voltage does not depend on the decay length of the repulsive interaction. In the regime of weak disorder we find an emergent correlation length-scale that depends on the disorder strength. For arrays shorter than this length the onset of transport is similar to the clean arrays, i.e., is due to the penetration of solitons into the array. We discuss the depinning scenarios for longer arrays in this regime.Comment: 11 pages, 6 figure

Spin-spin correlators in Majorana representation

In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion) correlators need to be calculated. We discuss applications to the analysis of the dynamics of a spin coupled to a dissipative environment and of a quantum detector performing a continuous measurement of a qubit's state

Dephasing of qubits by transverse low-frequency noise

We analyze the dissipative dynamics of a two-level quantum system subject to low-frequency, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-frequency noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent oscillations under the influence of both low- and high-frequency fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing

Quantum-Limited Position Detection and Amplification: A Linear Response Perspective

Using standard linear response relations, we derive the quantum limit on the sensitivity of a generic linear-response position detector, and the noise temperature of a generic linear amplifier. Particular emphasis is placed on the detector's effective temperature and damping effects; the former quantity directly determines the dimensionless power gain of the detector. Unlike the approach used in the seminal work of Caves [Phys. Rev. D, 26, 1817 (1982)], the linear-response approach directly involves the noise properties of the detector, and allows one to derive simple necessary and sufficient conditions for reaching the quantum limit. Our results have direct relevance to recent experiments on nanoelectromechanical systems, and complement recent theoretical studies of particular mesoscopic position detectors.Comment: 9 pages; minor typos correcte

Density matrix purification due to continuous quantum measurement

We consider the continuous quantum measurement of a two-level system, for example, a single-Cooper-pair box measured by a single-electron transistor or a double-quantum dot measured by a quantum point contact. While the approach most commonly used describes the gradual decoherence of the system due to the measurement, we show that when taking into account the detector output, we get the opposite effect: gradual purification of the density matrix. The competition between purification due to measurement and decoherence due to interaction with the environment can be described by a simple Langevin equation which couples the random evolution of the system density matrix and the stochastic detector output. The gradual density matrix purification due to continuous measurement may be verified experimentally using present-day technology. The effect can be useful for quantum computing.Comment: 2 pages, 1 figure; submitted to LT'2