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We have observed photon-assisted Cooper-pair tunneling in an atomic-scale Josephson junction formed between a superconducting Nb tip and a superconducting Nb sample in a scanning tunneling microscope (STM) at 30 mK. High-resolution tunneling spectroscopy data show a zero-bias conduction peak and other sharp sub-gap peaks from coupling of the STM junction to resonances in the electromagnetic environment. The sub-gap peaks respond to incident microwave radiation by splitting into multiple peaks with the position and height depending on the frequency and amplitude of the microwaves. The inter-peak spacing shows that the charge carriers are Cooper pairs, rather than quasiparticles, and the power dependence reveals that the current originates from photon-assisted phase-incoherent tunneling of pairs, rather than the more conventional phase-coherent tunneling of pairs that yields Shapiro steps., Comment: 7 pages, 8 figures

This paper describes a simple microwave apparatus to measure the Hall effect in semiconductor wafers. The advantage of this technique is that it does not require contacts on the sample or the use of a resonant cavity. Our method consists of placing the semiconductor wafer into a slot cut in an X-band (8 - 12 GHz) waveguide series tee, injecting microwave power into the two opposite arms of the tee, and measuring the microwave output at the third arm. A magnetic field applied perpendicular to the wafer gives a microwave Hall signal that is linear in the magnetic field and which reverses phase when the magnetic field is reversed. The microwave Hall signal is proportional to the semiconductor mobility, which we compare for calibration purposes with d. c. mobility measurements obtained using the van der Pauw method. We obtain the resistivity by measuring the microwave reflection coefficient of the sample. This paper presents data for silicon and germanium samples doped with boron or phosphorus. The measured mobilities ranged from 270 to 3000 cm2 /(V-sec)., Comment: 29 pages,10 figures, 1 table

We report a reproducible technique for the fabrication of sharp superconducting Nb tips for scanning tunneling microscopy (STM) and scanning tunneling spectroscopy. Sections of Nb wire with 250 $\mu$m diameter are dry etched in an SF$_6$ plasma in a Reactive Ion Etcher. The gas pressure, etching time and applied power are chosen to produce a self-sharpening effect to obtain the desired tip shape. The resulting tips are atomically sharp, with radii of less than 100 nm, and generate good STM images and spectroscopy on single crystal samples of Au(111), Au(100), and Nb(100), as well as a doped topological insulator Bi$_2$Se$_3$ at temperatures ranging from 30 mK to 9 K., Comment: See supplemental file for conductance map linked to Fig. 5(b)

We describe the design, construction, and performance of an ultra-low temperature, high-field scanning tunneling microscope (STM) with two independent tips. The STM is mounted on a dilution refrigerator and operates at a base temperature of 30 mK with magnetic fields of up to 13.5 T. We focus on the design of the two-tip STM head, as well as the sample transfer mechanism, which allows \textit{in situ} transfer from an ultra high vacuum (UHV) preparation chamber while the STM is at 1.5 K. Other design details such as the vibration isolation and rf-filtered wiring are also described. Their effectiveness is demonstrated via spectral current noise characteristics and the root mean square roughness of atomic resolution images. The high-field capability is shown by the magnetic field dependence of the superconducting gap of $\text{Cu}_x\text{Bi}_2\text{Se}_3$. Finally, we present images and spectroscopy taken with superconducting Nb tips with the refrigerator at 35 mK that indicate that the effective temperature of our tips/sample is approximately 184 mK, corresponding to an energy resolution of 16 $\mu$eV.

We present the experimental evidence for the presence of spinodal decomposition of the magnetic ions in the Ge/1-x-y/Cr/x/Eu/y/Te samples with chemical composition varying in the range of 0.015 < x < 0.057 and 0.003 < y < 0.042. The ferromagnetic transition at temperatures 50 < T < 57 K was observed, independent of the chemical composition. The long-range carrier mediated itinerant magnetic interactions seem to be responsible for the observed ferromagnetic order. The magnetic irreversibility with coercive field H/C/ = 5?63 mT and the saturation magnetization M/S/

We present the studies of magnetic properties of Ge/1-x/Cr/x/Te diluted magnetic semiconductor with changeable chemical composition 0.016 \leq x \leq 0.061. A spin-glass state (at T \leq 35 K) for x = 0.016 and 0.025 and a ferromagnetic phase (at T < 60 K) for x \geq 0.030 are observed. The long range carrier-mediated magnetic interactions are found to be responsible for the observed magnetic ordering for x < 0.045, while for x \geq 0.045 the spinodal decomposition of Cr ions leads to a maximum and decrease of the Curie temperature, TC, with increasing x. The calculations based on spin waves model are able to reproduce the observed magnetic properties at a homogeneous limit of Cr alloying, e.g. x < 0.04, and prove that carrier mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is responsible for the observed magnetic states. The value of the Cr-hole exchange integral, Jpd, estimated via fitting of the experimental results with the theoretical model, is in the limits 0.77...0.88 eV., Comment: 8 pages, 7 figures

We describe a thin-film superconducting Nb microwave resonator, tunable to within 0.3 ppm of the hyperfine splitting of $^{87}$Rb at $f_{Rb}=6.834683$ GHz. We coarsely tuned the resonator using electron-beam lithography, decreasing the resonance frequency from 6.8637 GHz to 6.8278 GHz. For \emph{in situ} fine tuning at 15 mK, the resonator inductance was varied using a piezoelectric stage to move a superconducting pin above the resonator. We found a maximum frequency shift of about 8.7 kHz per 60-nm piezoelectric step and a tuning range of 18 MHz., Comment: accepted in AIP Advances

We present a scheme to couple trapped $^{87}$Rb atoms to a superconducting flux qubit through a magnetic dipole transition. We plan to trap atoms on the evanescent wave outside an ultrathin fiber to bring the atoms to less than 10 $\mu$m above the surface of the superconductor. This hybrid setup lends itself to probing sources of decoherence in superconducting qubits. Our current plan has the intermediate goal of coupling the atoms to a superconducting LC resonator., Comment: 6 pages, 8 figures, Quantum Optics V (QOV V) conference proceedings

We report spectroscopic measurements of discrete two-level systems (TLSs) coupled to a dc SQUID phase qubit with a 16 \mu\m2 area Al/AlOx/Al junction. Applying microwaves in the 10 GHz to 11 GHz range, we found eight avoided level crossings with splitting sizes from 10 MHz to 200 MHz and spectroscopic lifetimes from 4 ns to 160 ns. Assuming the transitions are from the ground state of the composite system to an excited state of the qubit or an excited state of one of the TLS states, we fit the location and spectral width to get the energy levels, splitting sizes and spectroscopic coherence times of the phase qubit and TLSs. The distribution of splittings is consistent with non-interacting individual charged ions tunneling between random locations in the tunnel barrier and the distribution of lifetimes is consistent with the AlOx in the junction barrier having a frequency-independent loss tangent. To check that the charge of each TLS couples independently to the voltage across the junction, we also measured the spectrum in the 20-22 GHz range and found tilted avoided level crossings due to the second excited state of the junction and states in which both the junction and a TLS were excited.

We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase qubit with a 100 um^2 area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states., Comment: 14 pages, 9 figures; minor corrections, updated references

We analyze the behavior of a dc Superconducting Quantum Interference Device (SQUID) phase qubit in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias leads. Ignoring dissipation, we find the two-dimensional Hamiltonian of the system and use numerical methods and a cubic approximation to solve Schrodinger's equation for the eigenstates, energy levels, tunneling rates, and expectation value of the currents in the junctions. Using these results, we investigate how well this design provides isolation while preserving the characteristics of a phase qubit. In addition, we show that the expectation value of current flowing through the isolation junction depends on the state of the qubit and can be used for non-destructive read out of the qubit state., Comment: 38 pages, 7 figures

We report measurements of Rabi oscillations and spectroscopic coherence times in an Al/AlOx/Al and three Nb/AlOx/Nb dc SQUID phase qubits. One junction of the SQUID acts as a phase qubit and the other junction acts as a current-controlled nonlinear isolating inductor, allowing us to change the coupling to the current bias leads in situ by an order of magnitude. We found that for the Al qubit a spectroscopic coherence time T2* varied from 3 to 7 ns and the decay envelope of Rabi oscillations had a time constant T' = 25 ns on average at 80 mK. The three Nb devices also showed T2* in the range of 4 to 6 ns, but T' was 9 to 15 ns, just about 1/2 the value we found in the Al device. For all the devices, the time constants were roughly independent of the isolation from the bias lines, implying that noise and dissipation from the bias leads were not the principal sources of dephasing and inhomogeneous broadening., Comment: 5 figures. Accepted to Physical Review B

We report measurements of spectroscopic linewidth and Rabi oscillations in three thin-film dc SQUID phase qubits. One device had a single-turn Al loop, the second had a 6-turn Nb loop, and the third was a first order gradiometer formed from 6-turn wound and counter-wound Nb coils to provide isolation from spatially uniform flux noise. In the 6 - 7.2 GHz range, the spectroscopic coherence times for the gradiometer varied from 4 ns to 8 ns, about the same as for the other devices (4 to 10 ns). The time constant for decay of Rabi oscillations was significantly longer in the single-turn Al device (20 to 30 ns) than either of the Nb devices (10 to 15 ns). These results imply that spatially uniform flux noise is not the main source of decoherence or inhomogenous broadening in these devices., Comment: 4 pages, 5 figures, accepted for publication in IEEE Trans. Appl. Supercond

Rabi oscillations have been observed in many superconducting devices, and represent prototypical logic operations for quantum bits (qubits) in a quantum computer. We use a three-level multiphoton analysis to understand the behavior of the superconducting phase qubit (current-biased Josephson junction) at high microwave drive power. Analytical and numerical results for the ac Stark shift, single-photon Rabi frequency, and two-photon Rabi frequency are compared to measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions. Good agreement is found between theory and experiment., Comment: 4 pages, 4 figures, accepted for publication in IEEE Trans. Appl. Supercond

We have investigated the fidelity and speed of single-shot current-pulse measurements of the three lowest energy states of the dc SQUID phase qubit. We apply a short (2ns) current pulse to one junction of a Nb/AlOx/Nb SQUID that is in the zero voltage state at 25 mK and measure if the system switches to the finite voltage state. By plotting the switching rate versus pulse size we can determine average occupancy of the levels down to 0.01%, quantify small levels of leakage, and find the optimum pulse condition for single-shot measurements. Our best error rate is 3% with a measurement fidelity of 94%. By monitoring the escape rate during the pulse, the pulse current in the junction can be found to better than 10 nA on a 0.1 ns time scale. Theoretical analysis of the system reveals switching curves that are in good agreement with the data, as well as predictions that the ultimate single-shot error rate for this technique can reach 0.4% and the fidelity 99.2%.

The temperature dependence of the magnetic specific heat has been studied experimentally and theoretically in the semimagnetic semiconductor Pb_{1-x}Eu_{x}Te for x=0.027 and x=0.073, over the temperature range from 0.5 K to 10 K, in magnetic fields up to 2 T. There was a maximum in the magnetic specific heat between 1 and 3 K even in zero and low magnetic fields; this maximum shifted toward higher temperatures with increasing magnetic field. The experimental data have been analyzed in the framework of a model in which we assume that the ground states of europium ions are split even without an external magnetic field. We present arguments which support this assumption and we show that it is possible to find a physical mechanism leading to the splitting which can explain the experimental results., Comment: 11 pages, 7 figures, submitted to Physical Review B

Prototype Josephson-junction based qubit coherence times are too short for quantum computing. Recent experiments probing superconducting phase qubits have revealed previously unseen fine splittings in the transition energy spectra. These splittings have been attributed to new microscopic degrees of freedom (microresonators), a previously unknown source of decoherence. We show that macroscopic resonant tunneling in the extremely asymmetric double well potential of the phase qubit can have observational consequences that are strikingly similar to the observed data., Comment: 4 pages (3 figures); accepted version

We study the quantum mechanical behavior of a macroscopic, three-body, superconducting circuit. Microwave spectroscopy on our system, a resonator coupling two large Josephson junctions, produced complex energy spectra well explained by quantum theory over a large frequency range. By tuning each junction separately into resonance with the resonator, we first observe strong coupling between each junction and the resonator. Bringing both junctions together into resonance with the resonator, we find spectroscopic evidence for entanglement between all three degrees of freedom and suggest a new method for controllable coupling of distant qubits, a key step toward quantum computation., Comment: 4 pages, 3 figures

Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we propose two fundamental two-qubit quantum logic gates. Each of these gates, when supplemented by single-qubit operations, is sufficient for universal quantum computation. Numerical solutions of the time-dependent Schroedinger equation demonstrate that these operations can be performed with good fidelity., Comment: 4 pages, 5 figures, revised for publication

The zero-voltage state of a Josephson junction biased with constant current consists of a set of metastable quantum energy levels. We probe the spacings of these levels by using microwave spectroscopy to enhance the escape rate to the voltage state. The widths of the resonances give a measurement of the coherence time of the two states involved in the transitions. We observe a decoherence time shorter than that expected from dissipation alone in resonantly isolated 20 um x 5 um Al/AlOx/Al junctions at 60 mK. The data is well fit by a model including dephasing effects of both low-frequency current noise and the escape rate to the continuum voltage states. We discuss implications for quantum computation using current-biased Josephson junction qubits, including the minimum number of levels needed in the well to obtain an acceptable error limit per gate., Comment: 4 pages, 6 figures

We show that two capacitively-coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits., Comment: 4 pages, 6 figures. Slightly Revised and final accepted version

Science missions targeting the detection of organics from jet plumes originating from icy moons (i.e. Europa and Enceladus) will employ next-generation, state-of-the-art mass spectrometers to measure the composition of icy moon plume effluents and exospheres. During fly-bys, as mass spectrometers make their scientific measurements, molecular emissions from the spacecraft can interact with the local exosphere and associated jet plumes from the sub-surface oceans of the icy moons. Spacecraft-induced molecular effluents collide with molecules from the ambient exosphere, and a fraction of the spacecraft emissions are returned to the spacecraft and its complement of science instruments. The rate at which emitted molecules are returned to the spacecraft by collisions with other molecules (e.g. in Europa’s exosphere) is the return flux. The return flux of molecular emission from spacecraft sources is a major contributor to contaminant deposition onto the complement of contamination-sensitive instruments. Characterization of return flux is critical to the definition of requirements for materials outgassing for the spacecraft and its instruments, and for the definition of thruster operations.