By coupling a superconducting weak link to a microwave resonator, recent experiments probed the spectrum and achieved the quantum manipulation of Andreev states in various systems. However, the quantitative understanding of the response of the resona
tor to changes in the occupancy of the Andreev levels, which are of fermionic nature, is missing. Here, using Bogoliubov-de Gennes formalism to describe the weak link and a general formulation of the coupling to the resonator, we calculate the shift of the resonator frequency as a function of the levels occupancy and describe how transitions are induced by phase or electric field microwave drives. We apply this formalism to analyze recent experimental results obtained using circuit-QED techniques on superconducting atomic contacts and semiconducting nanowire Josephson junctions.
Spectral properties of a quantum circuit are efficiently read out by monitoring the resonance frequency shift it induces in a microwave resonator coupled to it. When the two systems are strongly detuned, theory attributes the shift to an effective re
sonator capacitance or inductance that depends on the quantum circuit state. At small detuning, the shift arises from the exchange of virtual photons, as described by the Jaynes-Cummings model. Here we present a theory bridging these two limits and illustrate, with several examples, its necessity for a general description of quantum circuits readout.
We study the transport through a molecular junction exhibiting interference effects. We show that these effects can still be observed in the presence of molecular vibrations if Coulomb repulsion is taken into account. In the Kondo regime, the conduct
ance of the junction can be changed by several orders of magnitude by tuning the levels of the molecule, or displacing a contact between two atoms, from nearly perfect destructive interference to values of the order of 2e 2 /h expected in Kondo systems. We also show that this large conductance change is robust for reasonable temperatures and voltages for symmetric and asymmetric tunnel couplings between the source-drain electrodes and the molecular orbitals. This is relevant for the development of quantum interference effect transistors based on molecular junctions.
We have performed microwave spectroscopy of Andreev states in superconducting weak links tailored in an InAs-Al (core-full shell) epitaxially-grown nanowire. The spectra present distinctive features, with bundles of four lines crossing when the super
conducting phase difference across the weak link is 0 or $pi.$ We interpret these as arising from zero-field spin-split Andreev states. A simple analytical model, which takes into account the Rashba spin-orbit interaction in a nanowire containing several transverse subbands, explains these features and their evolution with magnetic field. Our results show that the spin degree of freedom is addressable in Josephson junctions, and constitute a first step towards its manipulation.
Historically, the Natural Language Processing area has been given too much attention by many researchers. One of the main motivation beyond this interest is related to the word prediction problem, which states that given a set words in a sentence, on
e can recommend the next word. In literature, this problem is solved by methods based on syntactic or semantic analysis. Solely, each of these analysis cannot achieve practical results for end-user applications. For instance, the Latent Semantic Analysis can handle semantic features of text, but cannot suggest words considering syntactical rules. On the other hand, there are models that treat both methods together and achieve state-of-the-art results, e.g. Deep Learning. These models can demand high computational effort, which can make the model infeasible for certain types of applications. With the advance of the technology and mathematical models, it is possible to develop faster systems with more accuracy. This work proposes a hybrid word suggestion model, based on Naive Bayes and Latent Semantic Analysis, considering neighbouring words around unfilled gaps. Results show that this model could achieve 44.2% of accuracy in the MSR Sentence Completion Challenge.
The low temperature properties of single level molecular quantum dots including both, electron-electron and electron-vibration interactions, are theoretically investigated. The calculated differential conductance in the Kondo regime exhibits not only
the zero bias anomaly but also side peaks located at bias voltages which coincide with multiples of the energy of vibronic mode $V sim hbarOmega/e$. We obtain that the evolution with temperature of the two main satellite conductance peaks follows the corresponding one of the Kondo peak when $hbarOmega gg k_B T_K$, being $ T_K$ the Kondo temperature, in agreement with recent transport measurements in molecular junctions. However, we find that this is no longer valid when $ hbarOmega$ is of the order of a few times $k_B T_K$.
Coherent control of quantum states has been demonstrated in a variety of superconducting devices. In all these devices, the variables that are manipulated are collective electromagnetic degrees of freedom: charge, superconducting phase, or flux. Here
, we demonstrate the coherent manipulation of a quantum system based on Andreev bound states, which are microscopic quasiparticle states inherent to superconducting weak links. Using a circuit quantum electrodynamics setup we perform single-shot readout of this Andreev qubit. We determine its excited state lifetime and coherence time to be in the microsecond range. Quantum jumps and parity switchings are observed in continuous measurements. In addition to possible quantum information applications, such Andreev qubits are a testbed for the physics of single elementary excitations in superconductors.
We calculate the spectral density and occupations of a system of two capacitively coupled quantum dots, each one connected to its own pair of conducting leads, in a regime of parameters in which the total coupling to the leads for each dot $Gamma_i$
are different. The system has been used recently to perform pseudospin spectroscopy by controlling independently the voltages of the four leads. For an odd number of electrons in the system, $Gamma_1=Gamma_2$, equal dot levels $E_1=E_2$ and sufficiently large interdot repulsion $U_{12}$ the system lies in the SU(4) symmetric point of spin and pseudospin degeneracy in the Kondo regime. In the more realistic case $Gamma_1 eq Gamma_2$, pseudospin degeneracy is broken and the symmetry is reduced to SU(2). Nevertheless we find that the essential features of the SU(4) symmetric case are recovered by appropriately tuning the level difference $delta=E_2-E_1$. The system behaves as an SU(4) Kondo one at low energies. Our results are relevant for experiments which look for signatures of SU(4) symmetry in the Kondo regime of similar systems.
We describe and characterize a microwave setup to probe the Andreev levels of a superconducting atomic contact. The contact is part of a superconducting loop inductively coupled to a superconducting coplanar resonator. By monitoring the resonator ref
lection coefficient close to its resonance frequency as a function of both flux through the loop and frequency of a second tone we perform spectroscopy of the transition between two Andreev levels of highly transmitting channels of the contact. The results indicate how to perform coherent manipulation of these states.
We calculate the nonequilibrium conductance of a system of two capacitively coupled quantum dots, each one connected to its own pair of conducting leads. The system has been used recently to perform pseudospin spectroscopy by controlling independentl
y the voltages of the four leads. The pseudospin is defined by the orbital occupation of one or the other dot. Starting from the SU(4) symmetric point of spin and pseudospin degeneracy in the Kondo regime, for an odd number of electrons in the system, we show how the conductance through each dot varies as the symmetry is reduced to SU(2) by a pseudo-Zeeman splitting, and as bias voltages are applied to any of the dots. We analize the expected behavior of the system in general, and predict characteristic fingerprint features of the SU(4) to SU(2) crossover that have not been observed so far.
