Tunneling of Cooper pairs across voltage biased asymmetric single-Cooper-pair transistors

We analyze tunneling of Cooper pairs across voltage biased asymmetric single-Cooper-pair transistors. Also tunneling of Cooper pairs across two capacitively coupled Cooper-pair boxes is considered, when the capacitive coupling and Cooper pair tunneling are provided by a small Josephson junction between the islands. The theoretical analysis is done at subgap voltages, where the current-voltage characteristics depend strongly on the macroscopic eigenstates of the island(s) and their coupling to the dissipative environment. As the environment we use an impedance which satisfies Re[Z]<<R_Q and a few LC-oscillators in series with Z. The numerically calculated I-V curves are compared with experiments where the quantum states of mesoscopic SQUIDs are probed with inelastic Cooper pair tunneling. The main features of the observed I-V data are reproduced. Especially, we find traces of band structure in the higher excited states of the Cooper-pair boxes as well as traces of multiphoton processes between two Cooper-pair boxes in the regime of large Josephson coupling.Comment: 9 pages, 9 figures, Revtex

Effects of quasiparticle tunneling in a circuit-QED realization of a strongly driven two-level system

We experimentally and theoretically study the frequency shift of a driven cavity coupled to a superconducting charge qubit. In addition to previous studies, we here also consider drive strengths large enough to energetically allow for quasiparticle creation. Quasiparticle tunneling leads to the inclusion of more than two charge states in the dynamics. To explain the observed effects, we develop a master equation for the microwave dressed charge states, including quasiparticle tunneling. A bimodal behavior of the frequency shift as a function of gate voltage can be used for sensitive charge detection. However, at weak drives the charge sensitivity is significantly reduced by non-equilibrium quasiparticles, which induce transitions to a non-sensitive state. Unexpectedly, at high enough drives, quasiparticle tunneling enables a very fast relaxation channel to the sensitive state. In this regime, the charge sensitivity is thus robust against externally injected quasiparticles and the desired dynamics prevail over a broad range of temperatures. We find very good agreement between theory and experiment over a wide range of drive strengths and temperatures.Comment: 25 pages, 7 figure

Dynamic parity recovery in a strongly driven Cooper-pair box

We study a superconducting charge qubit coupled to an intensive electromagnetic field and probe changes in the resonance frequency of the formed dressed states. At large driving strengths, exceeding the qubit energy-level splitting, this reveals the well known Landau-Zener-Stuckelberg (LZS) interference structure of a longitudinally driven two-level system. For even stronger drives we observe a significant change in the LZS pattern and contrast. We attribute this to photon-assisted quasiparticle tunneling in the qubit. This results in the recovery of the qubit parity, eliminating effects of quasiparticle poisoning and leads to an enhanced interferometric response. The interference pattern becomes robust to quasiparticle poisoning and has a good potential for accurate charge sensing.Comment: 5 pages, 4 figure

Generating Two Continuous Entangled Microwave Beams Using a dc-Biased Josephson Junction

We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absence of a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions to prove the entanglement. The experimental results are found in quantitative agreement with theory, proving that the low-frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, estimate the entanglement flux at their output, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications

Josephson transistors interacting with dissipative environment

Abstract The quantum-mechanical effects typical for single atoms or molecules can be reproduced in micrometer-scale electric devices. In these systems the essential component is a small Josephson junction (JJ) consisting of two superconductors separated by a thin insulator. The quantum phenomena can be controlled in real time by external signals and have a great potential for novel applications. However, their fragility on uncontrolled disturbance caused by typical nearby environments is a drawback for quantum information science, but a virtue for detector technology. Motivated by this we have theoretically studied transistor kind of devices based on single-charge tunneling through small JJs. A common factor of the research is the analysis of the interplay between the coherent Cooper-pair (charge carriers in the superconducting state) tunneling and incoherent environmental processes. In the first work we calculate the current due to incoherent Cooper-pair tunneling through a voltage-biased small JJ in series with large JJs and compare the results with recent experiments. We are able to reproduce the main experimental features and interpret these as traces of energy levels and energy bands of the mesoscopic device. In the second work we analyze a similar circuit (asymmetric single-Cooper-pair transistor) but under the assumption that the Cooper-pair tunneling is mainly coherent. This predicts new resonant transport voltages in the circuit due to higher-order processes. However, no clear traces of most of them are seen in the experiments, and similar discrepancy is present also in the case of the symmetric circuit. We continue to study this problem by modeling the interplay between the coherent and incoherent processes more accurately using a density-matrix approach. By this we are able to demonstrate that in typical conditions most of these resonances are indeed washed out by strong decoherence caused by the environment. We also analyze the contribution of three typical weakly interacting dissipative environments: electromagnetic environment, spurious charge fluctuators in the nearby insulating materials, and quasiparticles. In the last work we model the dynamics of a current-biased JJ perturbed by a smaller JJ using a similar density-matrix approach. We demonstrate that the small JJ can be used also as a detector of the energy-band dynamics in a current biased JJ. The method is also used for modeling the charge transport in the Bloch-oscillating transistor

Resonance inversion in a superconducting cavity coupled to artificial atoms and a microwave background

We demonstrate how heating of an environment can invert the line shape of a driven cavity. We consider a superconducting coplanar cavity coupled to multiple artificial atoms. The measured cavity transmission is characterized by Fano-type resonances with a shape that is continuously tunable by bias current through nearby (magnetic flux) control lines. In particular, the same dispersive shift of the microwave cavity can be observed as a peak or a dip. We find that this Fano-peak inversion is possible due to a tunable interference between a microwave transmission through a background, with reactive and dissipative properties, and through the cavity, affected by bias-current induced heating. The background transmission occurs due to crosstalk with the multiple control lines. We show how such background can be accounted for by a Jaynes- or Tavis-Cummings model with modified boundary conditions between the cavity and transmission-line microwave fields. A dip emerges when cavity transmission is comparable with background transmission and dissipation. We find generally that resonance positions determine system energy levels, whereas resonance shapes give information on system fluctuations and dissipation

Bright On-Demand Source of Antibunched Microwave Photons Based on Inelastic Cooper Pair Tunneling

International audienceSingle-photon generation is an important proof of the underlying quantum nature of a physical process and a ubiquitous tool for scientific exploration, with applications ranging from spectroscopy and metrology to quantum computing. In the microwave regime, emission of antibunched radiation has so far relied on coherent control of Josephson qubits requiring precisely calibrated microwave pulses. In this work, we experimentally demonstrate the operation of a bright on-demand source of quantum microwave radiation driven by a simple dc voltage bias across a Josephson junction. Our source is based on photon emission into a microwave resonator through inelastic Cooper pair tunneling regulated by a high-impedance RC circuit preventing simultaneous tunnel events. It is characterized by its normalized second-order correlation function of g(2)(0)≈0.43 corresponding to antibunching in the single-photon regime. Our device can be triggered, and its in situ tunable emission rate exceeds those obtained with current microwave single-photon sources by more than 1 order of magnitude