Spin-Boson Quantum Phase Transition in Multilevel Superconducting Qubits.

Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices.

Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits.

Electromagnetic fields possess zero point fluctuations which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain, these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by zero point fluctuations in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modeling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about thirty environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits.

Direct Probe of the Seebeck Coefficient in a Kondo-Correlated Single-Quantum-Dot Transistor.

We report on the first measurement of the Seebeck coefficient in a tunnel-contacted and gate-tunable individual single-quantum dot junction in the Kondo regime, fabricated using the electromigration technique. This fundamental thermoelectric parameter is obtained by directly monitoring the magnitude of the voltage induced in response to a temperature difference across the junction, while keeping a zero net tunneling current through the device. In contrast to bulk materials and single molecules probed in a scanning tunneling microscopy (STM) configuration, investigating the thermopower in nanoscale electronic transistors benefits from the electric tunability to showcase prominent quantum effects. Here, striking sign changes of the Seebeck coefficient are induced by varying the temperature, depending on the spin configuration in the quantum dot. The comparison with numerical renormalization group (NRG) calculations demonstrates that the tunneling density of states is generically asymmetric around the Fermi level in the leads, both in the cotunneling and Kondo regimes.

Fate of Spinons at the Mott Point.

Gapless spin liquids have recently been observed in several frustrated Mott insulators, with elementary spin excitations-"spinons"-reminiscent of degenerate Fermi systems. However, their precise role at the Mott point, where charge fluctuations begin to proliferate, remains controversial and ill understood. Here we present the simplest theoretical framework that treats the dynamics of emergent spin and charge excitations on the same footing, providing a new physical picture of the Mott metal-to-insulator transition at half filing. We identify a generic orthogonality mechanism leading to strong damping of spinons, arising as soon as the Mott gap closes. Our results indicate that spinons should not play a significant role within the high-temperature quantum critical regime above the Mott point-in striking agreement with all available experiments.

Diagrammatic approach for the high-temperature regime of quantum Hall transitions.

We use a general diagrammatic formalism based on a local conductivity approach to compute electronic transport in continuous media with long-range disorder, in the absence of quantum interference effects. The method allows us then to investigate the interplay of dissipative processes and random drifting of electronic trajectories in the high-temperature regime of quantum Hall transitions. We obtain that the longitudinal conductance σ(xx) scales with an exponent κ=0.767±0.002 in agreement with the value κ=10/13 conjectured from analogies to classical percolation. We also derive a microscopic expression for the temperature-dependent peak value of σ(xx), useful to extract κ from experiments.

Numerical renormalization group at marginal spectral density: application to tunneling in Luttinger liquids.

Many quantum mechanical problems (such as dissipative phase fluctuations in metallic and superconducting nanocircuits or impurity scattering in Luttinger liquids) involve a continuum of bosonic modes with a marginal spectral density diverging as the inverse of energy. We construct a numerical renormalization group in this singular case, with a manageable violation of scale separation at high energy, capturing reliably the low energy physics. The method is demonstrated by a nonperturbative solution over several energy decades for the dynamical conductance of a Luttinger liquid with a single static defect.

Universal transport signatures in two-electron molecular quantum dots: gate-tunable Hund's rule, underscreened Kondo effect and quantum phase transitions.

We review here some universal aspects of the physics of two-electron molecular transistors in the absence of strong spin-orbit effects. Several recent quantum dot experiments have shown that an electrostatic backgate could be used to control the energy dispersion of magnetic levels. We discuss how the generally asymmetric coupling of the metallic contacts to two different molecular orbitals can indeed lead to a gate-tunable Hund's rule in the presence of singlet and triplet states in the quantum dot. For gate voltages such that the singlet constitutes the (non-magnetic) ground state, one generally observes a suppression of low voltage transport, which can yet be restored in the form of enhanced cotunneling features at finite bias. More interestingly, when the gate voltage is controlled to obtain the triplet configuration, spin S = 1 Kondo anomalies appear at zero bias, with non-Fermi liquid features related to the underscreening of a spin larger than 1/2. Finally, the small bare singlet-triplet splitting in our device allows fine-tuning with the gate between these two magnetic configurations, leading to an unscreening quantum phase transition. This transition occurs between the non-magnetic singlet phase, where a two-stage Kondo effect occurs, and the triplet phase, where the partially compensated (underscreened) moment is akin to a magnetically 'ordered' state. These observations are put theoretically into a consistent global picture by using new numerical renormalization group simulations, tailored to capture sharp finite-voltage cotunneling features within the Coulomb diamonds, together with complementary out-of-equilibrium diagrammatic calculations on the two-orbital Anderson model. This work should shed further light on the complicated puzzle still raised by multi-orbital extensions of the classic Kondo problem.

Observation of the underscreened Kondo effect in a molecular transistor.

We present the first quantitative experimental evidence for the underscreened Kondo effect, an incomplete compensation of a quantized magnetic moment by conduction electrons, as originally proposed by Nozières and Blandin. The device consists of an even charge spin S=1 molecular quantum dot, obtained by electromigration of C60 molecules into gold nanogaps and operated in a dilution fridge. The persistence of logarithmic singularities in the low temperature conductance is demonstrated by a comparison to the fully screened configuration obtained in odd charge spin S=1/2 Coulomb diamonds. We also discover an extreme sensitivity of the underscreened Kondo resonance to the magnetic field that we confirm on the basis of numerical renormalization group calculations.

Quantum phase transition in a single-molecule quantum dot.

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, is believed to govern many of the fascinating properties of strongly correlated systems such as heavy-fermion compounds or high-temperature superconductors. In contrast to bulk materials with very complex electronic structures, artificial nanoscale devices could offer a new and simpler means of understanding quantum phase transitions. Here we demonstrate this possibility in a single-molecule quantum dot, where a gate voltage induces a crossing of two different types of electron spin state (singlet and triplet) at zero magnetic field. The quantum dot is operated in the Kondo regime, where the electron spin on the quantum dot is partially screened by metallic electrodes. This strong electronic coupling between the quantum dot and the metallic contacts provides the strong electron correlations necessary to observe quantum critical behaviour. The quantum magnetic phase transition between two different Kondo regimes is achieved by tuning gate voltages and is fundamentally different from previously observed Kondo transitions in semiconductor and nanotube quantum dots. Our work may offer new directions in terms of control and tunability for molecular spintronics.

Nanoscale dynamical mean-field theory for molecules and mesoscopic devices in the strong-correlation regime.

We develop a nanoscale dynamical mean-field theory (nano-DMFT) to deal with strong Coulomb interaction effects in physical systems that are intermediate in size between atoms and bulk materials, taking into account the tunneling into nearby electrodes. Focusing on a simplified treelike geometry, the usual DMFT loop simply stops when the finite lattice is fully covered, starting with an initial seed provided by the electronic environment at the boundary. To illustrate this nano-DMFT, we investigate the disappearance of the quasiparticle weight in a correlated nano object near the Mott transition. In contrast to thermally driven classical phase transitions, quantum effects lead to unexpected oscillations of the order parameter, related to the interference of coherent renormalized quasiparticles. This behavior also implies a spatially inhomogeneous Mott localization process at the nanoscale.

Kondo effect in bosonic spin liquids.

In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature. In contrast, impurity moments coupled to spin-1 bulk bosons, such as triplet excitations in paramagnets, are only partially screened, even at the bulk quantum critical point. We argue that this difference is not due to the quantum statistics of the host particles but instead related to the structure of the impurity-host coupling, by demonstrating that frustrated magnets with bosonic spinon excitations can display a bosonic version of the Kondo effect. However, the Bose statistics of the bulk implies distinct behavior, such as a weak-coupling impurity quantum phase transition, and perfect screening for a range of impurity spin values. We discuss implications of our results for the compound Cs2CuCl4, as well as possible extensions to multicomponent bosonic gases.