Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps

We solve the two-particle s-wave scattering problem for ultracold atom gases confined in arbitrary quasi-one-dimensional trapping potentials, allowing for two different atom species. As a consequence, the center-of-mass and relative degrees of freedom do not factorize. We derive bound-state solutions and obtain the general scattering solution, which exhibits several resonances in the 1D scattering length induced by the confinement. We apply our formalism to two experimentally relevant cases: (i) interspecies scattering in a two-species mixture, and (ii) the two-body problem for a single species in a non-parabolic trap.Comment: 22 pages, 3 figure

Applying voltage sources to a Luttinger liquid with arbitrary transmission

The Landauer approach to transport in mesoscopic conductors has been generalized to allow for strong electronic correlations in a single-channel quantum wire. We describe in detail how to account for external voltage sources in adiabatic contact with a quantum wire containing a backscatterer of arbitrary strength. Assuming that the quantum wire is in the Luttinger liquid state, voltage sources lead to radiative boundary conditions applied to the displacement field employed in the bosonization scheme. We present the exact solution of the transport problem for arbitrary backscattering strength at the special Coulomb interaction parameter g=1/2.Comment: 9 pages REVTeX, incl 2 fig

Interaction-induced harmonic frequency mixing in quantum dots

We show that harmonic frequency mixing in quantum dots coupled to two leads under the influence of time-dependent voltages of different frequency is dominated by interaction effects. This offers a unique and direct spectroscopic tool to access correlations, and holds promise for efficient frequency mixing in nano-devices. Explicit results are provided for an Anderson dot and for a molecular level with phonon-mediated interactions.Comment: 4 pages, 2 figures, accepted for publication in Phys.Rev.Let

Charge qubit entanglement in double quantum dots

We study entanglement of charge qubits in a vertical tunnel-coupled double quantum dot containing two interacting electrons. Exact diagonalization is used to compute the negativity characterizing entanglement. We find that entanglement can be efficiently generated and controlled by sidegate voltages, and describe how it can be detected. For large enough tunnel coupling, the negativity shows a pronounced maximum at an intermediate interaction strength within the Wigner molecule regime.Comment: revised version of the manuscript, as published in EPL, 7 pages, 4 figure

Electron injection in a nanotube with leads: finite frequency noise-correlations and anomalous charges

The non-equilibrium transport properties of a carbon nanotube which is connected to Fermi liquid leads, where electrons are injected in the bulk, are computed. A previous work which considered an infinite nanotube showed that the zero frequency noise correlations, measured at opposite ends of the nanotube, could be used to extract the anomalous charges of the chiral excitations which propagate in the nanotube. Here, the presence of the leads have the effect that such-noise cross-correlations vanish at zero frequency. Nevertheless, information concerning the anomalous charges can be recovered when considering the spectral density of noise correlations at finite frequencies, which is computed perturbatively in the tunneling amplitude. The spectrum of the noise cross-correlations is shown to depend crucially on the ratio of the time of flight of quasiparticles traveling in the nanotube to the ``voltage'' time which defines the width of the quasiparticle wave-packets injected when an electron tunnels. Potential applications toward the measurement of such anomalous charges in non-chiral Luttinger liquids (nanotubes or semiconductor quantum wires) are discussed.Comment: 11 pages, 5 figure

Transport theory of carbon nanotube Y junctions

We describe a generalization of Landauer-B\"uttiker theory for networks of interacting metallic carbon nanotubes. We start with symmetric starlike junctions and then extend our approach to asymmetric systems. While the symmetric case is solved in closed form, the asymmetric situation is treated by a mix of perturbative and non-perturbative methods. For N>2 repulsively interacting nanotubes, the only stable fixed point of the symmetric system corresponds to an isolated node. Detailed results for both symmetric and asymmetric systems are shown for N=3, corresponding to carbon nanotube Y junctions.Comment: submitted to New Journal of Physics, Focus Issue on Carbon Nanotubes, 15 pages, 3 figure

Coulomb drag shot noise in coupled Luttinger liquids

Coulomb drag shot noise has been studied theoretically for 1D interacting electron systems, which are realized e.g. in single-wall nanotubes. We show that under adiabatic coupling to external leads, the Coulomb drag shot noise of two coupled or crossed nanotubes contains surprising effects, in particular a complete locking of the shot noise in the tubes. In contrast to Coulomb drag of the average current, the noise locking is based on a symmetry of the underlying Hamiltonian and is not limited to asymptotically small energy scales.Comment: 4 pages Revtex, accepted for publication in PR

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform

The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of $0.9\pm0.03\%$ and $1.3\pm0.4\%$ fidelity for the CZ and the iSWAP gate, respectively. We argue that spurious $ZZ$-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.Comment: 24 pages, including supplementary informatio