Tunable ohmic environment using Josephson junction chains

We propose a scheme to implement a tunable, wide frequency-band dissipative environment using a double chain of Josephson junctions. The two parallel chains consist of identical SQUIDs, with magnetic-flux tunable inductance, coupled to each other at each node via a capacitance much larger than the junction capacitance. Thanks to this capacitive coupling, the system sustains electromagnetic modes with a wide frequency dispersion. The internal quality factor of the modes is maintained as high as possible, and the damping is introduced by a uniform coupling of the modes to a transmission line, itself connected to an amplification and readout circuit. For sufficiently long chains, containing several thousands of junctions, the resulting admittance is a smooth function versus frequency in the microwave domain, and its effective dissipation can be continuously monitored by recording the emitted radiation in the transmission line. We show that by varying in-situ the SQUIDs' inductance, the double chain can operate as tunable ohmic resistor in a frequency band spanning up to one GHz, with a resistance that can be swept through values comparable to the resistance quantum R_q = (h/4e^2) ~ 6.5 k{\Omega}. We argue that the circuit complexity is within reach using current Josephson junction technology.Comment: 11 pages, 9 figure

Ground-state cooling of a carbon nanomechanical resonator by spin-polarized current

We study the nonequilibrium steady state of a mechanical resonator in the quantum regime realized by a suspended carbon nanotube quantum dot contacted by two ferromagnets. Because of the spin-orbit interaction and/or an external magnetic field gradient, the spin on the dot couples directly to the flexural eigenmodes. Accordingly, the nanomechanical motion induces inelastic spin flips of the tunneling electrons. A spin-polarized current at finite bias voltage causes either heating or active cooling of the mechanical modes. We show that maximal cooling is achieved at resonant transport when the energy splitting between two dot levels of opposite spin equals the vibrational frequency. Even for weak electron-resonator coupling and moderate polarizations we can achieve ground-state cooling with a temperature of the leads, for instance, of $T=10\omega$

Charge-vibration interaction effects in normal-superconductor quantum dots

We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency $\omega$. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime $\omega <\Delta$, with the superconducting energy gap $\Delta$, and for sharp resonant transmission through the dot. When the energy $\varepsilon_0$ of the dot's level is close to the Fermi energy $\mu$, i.e. $|\varepsilon_0-\mu|\ll \Delta$, inelastic Andreev reflections dominate up to voltage $eV\gtrsim\Delta$. The inelastic quasiparticle tunneling becomes the leading process when the dot's level is close to the gap $|\varepsilon_0-\mu|\sim \Delta \pm \omega$. In both cases, the inelastic tunneling processes appear as sharp and prominent peaks - not broadened by temperature - in the $I$-$V$ characteristic and pave the way for inelastic spectroscopy of vibrational modes even at temperatures $T \gg \omega$. We also found that inelastic Andreev reflections as well as quasiparticle tunneling induce a strong nonequilibrium state of the oscillator. In different ranges on the dot's level, we found that the current produces: (i) ground-state cooling of the oscillator with phonon occupation $n\ll 1$, (ii) accumulation of energy in the oscillator with $n\gg 1$ and (iii) a mechanical instability which is a precursor of self-sustained oscillations. We show that ground-state cooling is achieved simultaneously for several modes of different frequencies. Finally, we discuss how the nonequilibrium vibrational state can be detected by the asymmetric behavior of the inelastic current peaks respect to the gate voltage

Control of vibrational states by spin-polarized transport in a carbon nanotube resonator

We study spin-dependent transport in a suspended carbon nanotube quantum dot in contact with two ferromagnetic leads and with the dot's spin coupled to the flexural mechanical modes. The spin-vibration interaction induces spin-flip processes between the two energy levels of the dot. This interaction arises from the spin-orbit coupling or a magnetic field gradient. The inelastic vibration-assisted spin flips give rise to a mechanical damping and, for an applied bias voltage, to a steady nonequilibrium occupation of the harmonic oscillator. We analyze these effects as function of the energy-level separation of the dot and the magnetic polarization of the leads. Depending on the magnetic configuration and the bias-voltage polarity, we can strongly cool a single mode or pump energy into it. In the latter case, we find that within our approximation, the system approaches eventually a regime of mechanical instability. Furthermore, owing to the sensitivity of the electron transport to the spin orientation, we find signatures of the nanomechanical motion in the current-voltage characteristic. Hence, the vibrational state can be read out in transport measurements

Finite frequency current noise in the Holstein model

We investigate the effects of local vibrational excitations in the nonsymmetrized current noise $S(\omega)$ of a nanojunction. For this purpose, we analyze a simple model - the Holstein model - in which the junction is described by a single electronic level that is coupled to two metallic leads and to a single vibrational mode. Using the Keldysh Green's function technique, we calculate the nonsymmetrized current noise to the leading order in the charge-vibration interaction. For the noise associated to the latter, we identify distinct terms corresponding to the mean-field noise and the vertex correction. The mean-field result can be further divided into an elastic correction to the noise and in an inelastic correction, the second one being related to energy exchange with the vibration. To illustrate the general behavior of the noise induced by the charge-vibration interaction, we consider two limit cases. In the first case, we assume a strong coupling of the dot to the leads with an energy-independent transmission whereas in the second case we assume a weak tunneling coupling between the dot and the leads such that the transport occurs through a sharp resonant level. We find that the noise associated to the vibration-charge interaction shows a complex pattern as a function of the frequency $\omega$ and of the transmission function or of the dot's energy level. Several transitions from enhancement to suppression of the noise occurs in different regions, which are determined, in particular, by the vibrational frequency. Remarkably, in the regime of an energy-independent transmission, the zero order elastic noise vanishes at perfect transmission and at positive frequency whereas the noise related to the charge-vibration interaction remains finite enabling the analysis of the pure vibrational-induced current noise

Decoherence and relaxation of topological states in extended quantum Ising models

We study the decoherence and the relaxation dynamics of topological states in an extended class of quantum Ising chains which can present a manyfold ground state subspace. The leading interaction of the spins with the environment is assumed to be the local fluctuations of the transverse magnetic field. By deriving the Lindblad equation using the many-body states, we investigate the relation between decoherence, energy relaxation and topology. In particular, in the topological phase and at low temperature, we analyze the dephasing rates between the different degenerate ground states

Nonequilibrium Andreev bound states population in short superconducting junctions coupled to a resonator

Inspired by recent experiments, we study a short superconducting junction of length $L\ll \xi$ (coherence length) inserted in a dc-SQUID containing an ancillary Josephson tunnel junction. We evaluate the nonequilibrium occupation of the Andreev bound states (ABS) for the case of a conventional junction and a topological junction, with the latter case of ABS corresponding to a Majorana mode. We take into account small phase fluctuations of the Josephson tunnel junction, acting as a damped LC resonator, and analyze the role of the distribution of the quasiparticles of the continuum assuming that these quasiparticles are in thermal distribution with an effective temperature different from the environmental temperature. We also discuss the effect of strong photon irradiation in the junction leading to a nonequilibrium occupation of the ABS. We systematically compare the occupations of the bound states and the supercurrents carried by these states for conventional and topological junctions.Comment: 20 pages, 9 figures; added references, corrected typos, edited the tex

Quantum phase transition with dissipative frustration

We study the quantum phase transition of the one-dimensional phase model in the presence of dissipative frustration, provided by an interaction of the system with the environment through two non-commuting operators. Such a model can be realized in Josephson junction chains with shunt resistances and resistances between the chain and the ground. Using a self-consistent harmonic approximation, we determine the phase diagram at zero temperature which exhibits a quantum phase transition between an ordered phase, corresponding to the superconducting state, and a disordered phase, corresponding to the insulating state with localized superconducting charge. Interestingly, we find that the critical line separating the two phases has a non monotonic behavior as a function of the dissipative coupling strength. This result is a consequence of the frustration between (i) one dissipative coupling that quenches the quantum phase fluctuations favoring the ordered phase and (ii) one that quenches the quantum momentum (charge) fluctuations leading to a vanishing phase coherence. Moreover, within the self-consistent harmonic approximation, we analyze the dissipation induced crossover between a first and second order phase transition, showing that quantum frustration increases the range in which the phase transition is second order. The non monotonic behavior is reflected also in the purity of the system that quantifies the degree of correlation between the system and the environment, and in the logarithmic negativity as entanglement measure that encodes the internal quantum correlations in the chain

Interplay of magneto-elastic and polaronic effects in electronic transport through suspended carbon-nanotube quantum dots

We investigate the electronic transport through a suspended carbon-nanotube quantum dot. In the presence of a magnetic field perpendicular to the nanotube and a nearby metallic gate, two forces act on the electrons: the Laplace and the electrostatic force. They both induce coupling between the electrons and the mechanical transverse oscillation modes. We find that the difference between the two mechanisms appears in the cotunneling current

Quantum Phase-Slip Junction Under Microwave Irradiation

We consider the dynamics of a quantum phase-slip junction (QPSJ) -- a dual Josephson junction -- connected to a microwave source with frequency $\omega_\textrm{mw}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e \omega_\textrm{mw} / \pi$ in the current-voltage (I-V) characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the I-V characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of these fluctuations are governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aimed at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.Comment: 12 pages, 9 figures, comments and suggestions would be greatly appreciate