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We report the observation of Electromagnetically Induced Transparency (EIT) of a mechanical field, where a superconducting artificial atom is coupled to a 1D-transmission line for surface acoustic waves. An electromagnetic microwave drive is used as the control field, rendering the superconducting transmon qubit transparent to the acoustic probe beam. The strong frequency dependence of the acoustic coupling enables EIT in a ladder configuration due to the suppressed relaxation of the upper level. Our results show that superconducting circuits can be engineered to interact with acoustic fields in parameter regimes not readily accessible to purely electromagnetic systems.

Artificial atoms coupled to surface acoustic waves (SAWs) have played a crucial role in the recent development of circuit quantum acoustodynamics (cQAD). In this paper, we have investigated the interaction of an artificial atom and SAWs beyond the weak coupling regime, focusing on the role of the interdigital transducer (IDT) that enables the coupling. We find a parameter regime in which the IDT acts as a cavity for the atom, rather than an antenna. In other words, the atom forms its own cavity. Similar to an atom coupled to an explicit cavity, this regime is characterized by vacuum-Rabi splitting, as the atom hybridizes with the phononic vacuum inside the IDT. This hybridization is possible because of the interdigitated coupling, which has a large spatial extension, and the slow propagation speed of SAWs. We work out a criterion for entering this regime from a model based on standard circuit-quantization techniques, taking only material parameters as inputs. Most notably, we find this regime hard to avoid for an atom on top of a strong piezoelectric material, such as LiNbO$_3$. The SAW-coupled atom on top of LiNbO$_3$ can thus be regarded as an atom-cavity-bath system. On weaker piezoelectric materials, the number of IDT electrodes need to be large in order to reach this regime., 11 pages, 5 figures

We study the radio-frequency single-electron transistor (rf-SET) as a readout device for charge qubits. We measure the charge sensitivity of an rf-SET to be $6.3\ensuremath{\mu}e/\sqrt{\mathrm{Hz}}$ and evaluate the backaction of the rf-SET on a single Cooper-pair box. This allows us to compare the needed measurement time with the mixing time of the qubit imposed by the measurement. We find that the mixing time can be substantially longer than the measurement time, which would allow readout of the state of the qubit in a single shot measurement.

We studied a mesoscopic cross-like normal metal structure connected to two superconducting (S) and two normal (N) reservoirs. We observed the Josephson effect under unusual conditions when there is no current through one of the two S/N interfaces. The potential difference between the S reservoirs was zero unless the voltage applied between S and N reservoirs exceeded a critical value although the electric potential in the N wire connecting the superconductors varied in a nonmonotonic way. The observed effects are discussed theoretically., Comment: 5 pages, 4 figures, to be published in PRB Rapid Communication

One-dimensional (1D) arrays of small-capacitance Josephson junctions demonstrate a sharp transition, from Josephson-like behavior to the Coulomb blockade of Cooper-pair tunneling, as the effective Josephson coupling between nearest neighbors is tuned with an externally applied magnetic field. Comparing the zero-bias resistance of three arrays with 255, 127, and 63 junctions, we observe a critical behavior where the resistance, extrapolated to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$, is independent of length at a critical magnetic field. Comparison is made with a theory of this $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ quantum phase transition, which maps to the 2D classical $\mathrm{XY}$ model.

The effect of the electromagnetic environment on Coulomb blockade devices can be estimated through a simple horizon model where the interaction length is determined by the Heisenberg uncertainty principle. The advantage of this horizon model can be demonstrated in a device with two tunnel junctions in parallel where a cutoff voltage related to physical dimensions is observed. This model also explains the characteristics of single junctions and single-electron tunneling (SET) transistors. Several Al/AlO${}_{x}$/Al devices of various geometries were measured and the effective Coulomb barrier has been investigated through the offset voltage defined as ${V}_{\mathrm{off}}\ensuremath{\equiv}V\ensuremath{-}IdV/dI$. We have also used ${V}_{\mathrm{off}}$ to determine the capacitances of SET transistors, from which we determined microstrip capacitance as a function of island size.

We show, in the context of single-photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarizability model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single-photon applications. Our results are presented in the context of a transmon in a one-dimensional microwave waveguide, but the conclusions also apply to optical systems.

One-dimensional arrays of small-capacitance Josephson junctions exhibit a current-voltage curve that is characterized by a zero-current state for bias voltage below a threshold voltage {ital V}{sub {ital t}}. The threshold voltages can be modulated with an external magnetic field {ital B}, which tunes effective Josephson coupling between adjacent electrodes of the array. The dependance of {ital V}{sub {ital t}} on {ital B} is well explained by a model where {ital V}{sub {ital t}} is the injection voltage for a Cooper-pair charge soliton. {copyright} {ital 1996 The American Physical Society.}

We have studied the superconductor-insulator (SI) phase transition for two-dimensional (2D) arrays of small Josephson junctions in a weak magnetic field. The data were analyzed within the context of the theory of the magnetic-field-tuned SI transition in 2D superconductors. We show resistance scaling curves over several orders of magnitude for the 2D arrays. The critical exponent ${\mathit{z}}_{\mathit{B}}$ is determined to be 1.05, in good agreement with the theory. Moreover, the transverse (Hall) resistance at the critical field is found to be very small in comparison to the longitudinal resistance.

We have embedded an artificial atom, a superconducting transmon qubit, in an open transmission line and investigated the strong scattering of incident microwave photons (∼6GHz). When an input coherent state, with an average photon number N 1 is on resonance with the artificial atom, we observe extinction of up to 99.6% in the forward propagating field. We use two-tone spectroscopy to study scattering from excited states and we observe electromagnetically induced transparency (EIT). We then use EIT to make a single-photon router, where we can control to what output port an incoming signal is delivered. The maximum on-off ratio is around 99% with a rise and fall time on the order of nanoseconds, consistent with theoretical expectations. The router can easily be extended to have multiple output ports and it can be viewed as a rudimentary quantum node, an important step towards building quantum information networks. © 2011 American Physical Society., We acknowledge financial support from the Swedish Research Council, the Wallenberg foundation and from the EU through the European Research Council and the integrated project SOLID. B. P. acknowledges CSIC JAEPREDOC2009, FIS2009-10061, and QUITEMAD S2009- ESP-1594.

In highly resistive superconducting tunnel junctions, excess subgap current is usually observed and is often attributed to microscopic "pinholes" in the tunnel barrier. We have studied the subgap current in superconductor-insulator-superconductor (SIS) and superconductor-insulator-normal-metal (SIN) junctions. In Al/AlOx/Al junctions, we observed a decrease of 2 orders of magnitude in the current upon the transition from the SIS to the SIN regime, where it then matched theory. In Al/AlOx/Cu junctions, we also observed generic features of coherent diffusive Andreev transport in a junction with a homogenous barrier. We use the quasiclassical Keldysh-Green function theory to quantify single- and two-particle tunneling and find good agreement over 2 orders of magnitude in transparency. We argue that our observations rule out pinholes as the origin of the excess current., 4 pages, 4 figures

We report the observation of photon generation in a microwave cavity with a time-dependent boundary condition. Our system is a microfabricated quarter-wave coplanar waveguide cavity. The electrical length of the cavity is varied using the tunable inductance of a superconducting quantum interference device. It is measured in the quantum regime, where the temperature is significantly less than the resonance frequency (~ 5 GHz). When the length is modulated at approximately twice the static resonance frequency, spontaneous oscillations of the cavity field are observed. Time-resolved measurements of the dynamical state of the cavity show multiple stable states. The behavior is well described by theory. Connections to the dynamical Casimir effect are discussed., 5 pages, 3 Figures

We have systematically measured the shot noise in a single electron transistor (SET) as a function of bias and gate voltages. By embedding a SET in a resonance circuit we have been able to measure its shot noise at the resonance frequency 464 MHz, where the 1/f noise is negligible. We can extract the Fano factor which varies between 0.5 and 1 depending on the amount of Coulomb blockade in the SET, in very good agreement with the theory., Comment: 4 figures

We have fabricated and investigated submicron-size (0.01 and 0.04 μm 2 ) Pb-alloy single Josephson junctions attached to high-resistance thin-film NiCr or Cr leads which providethe necessary conditions for a strong charging erect. When the Josephson coupling energy is less than the charging energy, we find a novel shape of the current-voltage curves, with a Coulomb gap at small voltages, and a current peak at larger voltages. A theory based on the concept of incoherent Cooper-pair tunneling has explained the data well

We directly observe low-temperature non-equilibrium quasiparticle tunneling in a pair of charge qubits based on the single Cooper-pair box. We measure even- and odd-state dwell time distributions as a function of temperature, and interpret these results using a kinetic theory. While the even-state lifetime is exponentially distributed, the odd-state distribution is more heavily weighted to short times, implying that odd-to-even tunnel events are not described by a homogenous Poisson process. The mean odd-state dwell time increases sharply at low temperature, which is consistent with quasiparticles tunneling out of the island before reaching thermal equilibrium., Comment: Replaced Figure 1 with color version, corrected more typos. Version submitted to PRB

The time correlation of tunneling events has been predicted to occur in ultrasmall tunnel junctions: a periodic tunneling with a frequency determined by the current f=I/e. To test the predictions, we have fabricated one-dimensional arrays of Al/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{O}}_{\mathit{y}}$/Al tunnel junctions with areas down to 0.006 \ensuremath{\mu}${\mathrm{m}}^{2}$ corresponding to capacitances of \ensuremath{\sim}0.2 fF. Each array contained between 15 and 53 junctions. Current-voltage characteristics were measured at temperatures between 0.05 and 4.2 K. We observed phase locking of single-electron-tunneling oscillations to external microwaves in the frequency range 0.7\char21{}5 GHz. The phase locking manifested itself as peaks in the differential resistance at bias currents I=nef (n=\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2), corresponding to multiples of the microwave frequency. Numerical simulations show good agreement with our experimental results.

We study the influence of dissipation on the switching current statistics of moderately damped Josephson junctions. Different types of both low- and high-${T}_{c}$ junctions with controlled damping are studied. The damping parameter of the junctions is tuned in a wide range by changing temperature, magnetic field, and gate voltage and introducing a ferromagnetic layer or in situ capacitive shunting. A paradoxical collapse of switching current fluctuations with increasing $T$ occurs in all studied junctions. The phenomenon critically depends on dissipation in the junction and is explained by the interplay of two counteracting consequences of thermal fluctuations, which, on one hand, assist in premature switching into the resistive state and, on the other hand, help in retrapping back to the superconducting state. This is one of the rare examples of anticorrelation between temperature and the amplitude of fluctuations of a physically measurable quantity.

We study thermal fluctuation phenomena in small Bi-2212 intrinsic Josephson junctions. Being able to measure switching currents of a single intrinsic junction, we observe that its statistics can be very well described by thermal activation from a periodic Josephson potential with the sinusoidal current-phase relation. This is a direct evidence for the dc-intrinsic Josephson effect and confirmation of the tunneling nature of interlayer transport in strongly anisotropic high-temperature superconductors. Furthermore, the fluctuation-free critical current, extracted from the analysis of switching current statistics, exhibits a temperature dependence typical for superconductor-insulator-superconductor tunnel junctions.

We report an experimental observation of the backaction of a single-electron transistor (SET) measuring the Coulomb staircase of a single-electron box. As current flows through the SET, the charge state of the SET island fluctuates. These fluctuations capacitively couple to the box and cause changes in the position, width, and asymmetry of the Coulomb staircase. A sequential tunneling model accurately recreates these effects, confirming this mechanism of the backaction of a SET. This is a first step toward understanding the effects of quantum measurement on solid-state qubits.

The escape rate from the zero voltage state in a superconducting Josephson junction (JJ) is determined by the temperature, but it saturates at low temperature due to macroscopic quantum tunneling (MQT). Complications due to $d$-wave symmetry in a high temperature superconductor, like low energy quasiparticles and an unconventional current-phase relation, may influence the escape rate. We report, for the first time to our knowledge, the observation of MQT in a ${\mathrm{Y}\mathrm{B}\mathrm{a}}_{2}{\mathrm{C}\mathrm{u}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ grain boundary biepitaxial JJ. This proves that dissipation can be significantly reduced by a proper junction configuration, which is of significance for quantum coherence.

We have measured the fully 2e periodic Coulomb staircase of a single Cooper pair box (SCB) in superconducting quantum interference design geometry, using a radio-frequency single-electron transistor. We have determined the energies of the SCB with microwave spectroscopy and compared the calculated shape of the Coulomb staircases to the measured staircases. We find excellent agreement as the Josephson coupling energy is tuned by an external magnetic field.

Measurements of the magnetic susceptibility, specific heat, and electrical resistivity of ${\mathrm{U}}_{2}$${\mathrm{Zn}}_{17}$ reveal a magnetic phase transition of this compound at 9.70 K. Details of the specific heat indicate that the ordering occurs among electrons whose energy spectrum shows an anomalously large density of states at the Fermi energy. This result is of interest with regard to the occurrence of superconductivity in similar systems.