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Super-resolved interferometric phase measurements in the RF domain have been demonstrated by estimating the Parity operator through quadrature measurements, saturating the information theoretic Cramer-Rao bound. We achieved 600-fold improvement over the Rayleigh limit with 56dB SNR.

The kinetic inductance (KI) of superconducting devices can be exploited for reducing the footprint of linear elements as well as for introducing nonlinearity to the circuit. We characterize the linear and nonlinear properties of a multimode resonator fabricated from amorphous tungsten silicide (WSi) with a fundamental frequency of \(f_1 = 172\) MHz. We show how the multimode structure of the device can be used to extract the different quality factors and to aid the nonlinear characterization. In the linear regime the footprint is reduced by a factor of \(\sim 2.9\) with standard lateral dimensions with no significant degradation of the internal quality factor compared to a similar Al device . In the nonlinear regime we observe self positive frequency shifts at low powers which can be attributed to saturation of tunneling two-level systems. The cross mode nonlinearities are described well by a Kerr model with a self-Kerr coefficient in the order of \(|K_{11}|/2\pi \approx 1.5\times10^{-7}\) Hz/photon. These properties together with a reproducible fabrication process make WSi a promising candidate for creating linear and nonlinear circuit QED elements., Comment: 7pages, 5 figures (+supplementary with 4 pages and 2 figures)

As quantum physics (QP) requires substantial mathematical knowledge, a thorough elementarization by reduction of complexity or with help of visualizations is needed without neglecting the goal of deeper understanding. First, we present how the visualization of the Dirac formalism could contribute to a deeper understanding of the central concepts of QP. Then, we present two teaching/learning proposals (TLP) for high school students based on the Dirac notation. Both approaches show how suitable strategies can improve student understanding of topics rooted in math and indicate significant success of the students in understanding, interpreting and implementation of the basic concepts of QP. The first approach presented here uses the concept of “wavity” or “wave-particle-duality” in the context of Dirac notation. The second approach emphasizes the measurement process and, on this basis, moves on to discuss the quantum state. It is asked whether and how it is possible to use the formal structure of these concepts to support students in interpreting them. In an inquiry-based teaching–learning sequence on high school level, educational strategies for consolidating the grasp of quantum concepts through math were developed and implemented in teaching experiments conducted in the framework of design-based research. Results of data analysis in both cases show that the adopted strategies are largely successful.

Superconducting quantum circuits are typically operated at low temperatures (mK), necessitating cryogenic low-noise, wide-band amplifiers for signal readout ultimately also compatible with room temperature electronics. While existing implementations partly meet these criteria, they suffer from certain limitations, such as rippled transmission spectra or limited dynamic range, some of which are caused by the lack of proper impedance matching. We develop a MIcrostrip Kinetic Inductance Travelling Wave Amplifier (MI-KITWA), exploiting the nonlinear kinetic inductance of tungsten-silicide for wave-mixing of the signal and a pump, and engineer the impedance to $50 \Omega$, while decreasing the phase velocity, with benefit for the amplification. Despite losses, pumping on our device amplifies the signal by 15 dB over a 2 GHz bandwidth., Comment: 5 pages + supplemental material

Superconducting quantum circuits, typically operated below -100dBm, require low-noise amplifiers with large dynamic range and wide bandwidth. Our microstrip kinetic inductance travelling wave parametric amplifier answers these requirements with up to 20 dB amplification.

The distribution of magnetic field in a finite thin-walled Nb superconducting cylinder in an axial magnetic field is analyzed. Both current density and magnetic field exhibit strong maximum in the cylinder edges. This triggers a giant flux jump in the hollow cylinder when a slowly increasing external magnetic field reaches a threshold value. Experimentally measured flux jumps were observed in a wide range of external fields, even below Hc1 of the Nb film. The field at which the jumps appear is temperature dependent. It was found that with increasing the wall thickness the singularity of the current density and magnetic field on the edges decreases, which explains the absence of giant jumps in a sample with thick walls in fields below Hc1.

Control over the vortex potential at the nanoscale in a superconductor is a subject of great interest for both fundamental and technological reasons. Many methods for achieving artificial pinning centers have been demonstrated, for example, with magnetic nanostructures or engineered imperfections, yielding many intriguing effects. However, these pinning mechanisms do not offer dynamic control over the strength of the patterned vortex potential because they involve static nanostructures created in or near the superconductor. Dynamic control has been achieved with scanning probe methods on the single vortex level but these are difficult so scale up. Here, we show that by applying controllable nanopatterned current injection, the superconductor can be locally driven out of equilibrium, creating an artificial vortex potential that can be tuned by the magnitude of the injected current, yielding a unique vortex channeling effect.

Penetration of magnetic flux into hollow superconducting cylinders is investigated by magnetic moment measurements. The magnetization curves of a flat and a nanopatterned thin-walled superconducting Nb cylinders with a rectangular cross section are reported for the axial field geometry. In the nanopatterned sample, a row of micron-sized antidots (holes) was milled in the film along the cylinder axis. Magnetic moment jumps are observed for both samples at low temperatures for magnetic fields not only above H c 1 , but also in fields lower than H c 1 , i. e., in the vortex-free regime. The positions of the jumps are not reproducible and they change from one experiment to another, resembling vortex lattice instabilities usually observed for magnetic fields larger than H c 1 . At temperatures above 0.66 T c and 0.78 T c the magnetization curves become smooth for the patterned and the as-prepared sample, respectively. The magnetization curve of a reference flat Nb film in the parallel field geometry does not exhibit jumps in the entire range of accessible temperatures.

Observation of resonance modes is the most straightforward way of studying mechanical oscillations because these modes have maximum response to stimuli. However, a deeper understanding of mechanical motion can be obtained by also looking at modal responses at frequencies in between resonances. Here, an imaging of the modal responses for a nanomechanical drum driven off resonance is presented. By using the frequency modal analysis, these shapes are described as a superposition of resonance modes. It is found that the spatial distribution of the oscillating component of the driving force, which is affected by both the shape of the actuating electrode and inherent device properties such as asymmetry and initial slack, greatly influences the modal weight or participation. This modal superposition analysis elucidates the dynamics of any nanomechanical system through modal weights. This aids in optimizing mode‐specific designs for force sensing and integration with other systems., Nanomechanical motion in between resonances are imaged and then described as superposition of resonance modes. The modal weight behavior allows for the elucidation of the dynamics of any nanomechanical system such as the spatial distribution of the oscillating driving force. This analysis demonstrates that spatial imaging of mechanical motion is more than just a visualization tool.

This study presents a new approach to teaching quantum physics in high-school physics courses facing the extremely deficient and fragmented treatment of quantum mechanics at present. The suggested curriculum adopts the paradigm of discipline-culture in representing physics knowledge. In accordance, the curriculum is structured in nucleus-body-periphery emphasizing the principles (nucleus), their illustration (body) and their contrast with the classical postulates (periphery). Thus, the proposed curriculum presents quantum physics as a structured physics theory, unlike most curricula in the world. The results of an experimental application show a positive impact on students’ conceptual knowledge and students’ nature-of-science understanding.

We measure the dynamics of magnetic field penetration into thin-walled superconducting niobium cylinders. It is shown that magnetic field penetrates through the wall of a cylinder in a series of giant jumps with amplitude 1 - 2 mT and duration of less than a microsecond in a wide range of magnetic fields, including the vortex free region. Surprisingly, the jumps take place when the total current in the wall, not the current density, exceeds a critical value. In addition, there are small jumps and/or smooth penetration, but their contribution reaches only ≃ 20 % of the total penetrating flux. The number of jumps decreases with increased temperature. Thermomagnetic instabilities cannot explain the experimental observations.

We create an optical frequency, polarization independent, narrow band-pass filter of 1.3 GHz (3 dB bandwidth), using the steep dispersion near the Rubidium D1 atomic transitions within a prism-shaped vapor cell. This enables us to clean the amplified spontaneous emission from a laser by more than 3 orders of magnitude. Such a filter could find uses in fields such as quantum information processing and Raman spectroscopy., 5 pages, 5 figures

Atomic sized two-level systems (TLSs) in amorphous dielectrics are known as a major source of loss in superconducting devices. In addition, individual TLS are known to induce large frequency shifts due to strong coupling to the devices. However, in the presence of a broad ensemble of TLSs these shifts are symmetrically canceled out and not observed in a typical single-tone spectroscopy experiment. We introduce a two-tone spectroscopy on the normal modes of a pair of coupled superconducting coplanar waveguide resonators to reveal this effect. Together with an appropriate saturation model this enables us to extract the average single-photon Rabi frequency of dominant TLSs to be $\Omega_0/2\pi \approx 79 $ kHz. At high photon numbers we observe an enhanced frequency shift due to nonlinear kinetic inductance when using the two-tone method and estimate the value of the nonlinear coefficient as $K/2\pi \approx -1\times 10^{-4}$ Hz/photon. Furthermore, the life-time of each resonance can be controlled (increased) by pumping of the other mode as demonstrated both experimentally and theoretically., Comment: 6 pages, 4 figures + supplementary (with 18 pages and 5 figures)

Multiple bosons undergoing coherent evolution in a coupled network of sites constitute a so-called quantum walk system. The simplest example of such a two-particle interference is the celebrated Hong-Ou-Mandel interference. When scaling to larger boson numbers, simulating the exact distribution of bosons has been shown, under reasonable assumptions, to be exponentially hard. We analyze the feasibility and expected performance of a globally connected superconducting resonator based quantum walk system, using the known characteristics of state-of-the-art components. We simulate the sensitivity of such a system to decay processes and to perturbations and compare with coherent input states.

We propose a novel method to couple two distant Nitrogen-Vacancy based qubits, based on the fabrication of a superconducting thin film with nano-structures. We report on the theoretical results for such a structure.

The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in $3+1$ dimensions onto a multilevel superconducting Josephson circuit. Resonant drives determine the particle mass and momentum, and the quantum state represents the internal spinor dynamics which are cast in the language of multilevel quantum optics. Zitterbewegung and wave-packet dynamics are reproduced. The degeneracy of the Dirac spectrum corresponds to a degeneracy of bright and dark states within the system, and particle spin and helicity are employed to interpret the multilevel dynamics. We also simulate the Schwinger mechanism of electron-positron pair production by introducing an analogous electric field as a doubly degenerate Landau-Zener problem. All proposed measurements can be performed well within typical decoherence times. This work opens an avenue for experimental study of the Dirac equation and provides a tool for control of complex dynamics in multilevel systems.

Motivated by recent observations of chiral-induced magnetization and spin-selective transport we studied the effect of chiral molecules on conventional BCS superconductors. By applying scanning tunneling spectroscopy, we demonstrate that the singlet-pairing s-wave order parameter of Nb is significantly altered upon adsorption of chiral polyalanine alpha-helix molecules on its surface. The tunneling spectra exhibit zero-bias conductance peaks embedded inside gaps or gap-like features, suggesting the emergence of unconventional triplet-pairing components with either d-wave or p-wave symmetry, as corroborated by simulations. These results may open a way for realizing simple superconducting spintroinics devices., 12 pages and 5 figures

Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau&ndash, Zener&ndash, St&uuml, ckelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O ( 2 n ) , which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.

Defects in Josephson junctions are considered a nuisance when it comes to using superconducting circuits as building blocks for a quantum-information processor. But if the interaction between the circuit and defects is accurately controlled—as has been demonstrated now—the imperfections might be useful, serving as memory elements.

When incorporated in quantum sensing protocols, quantum error correction can be used to correct for high frequency noise, as the correction procedure does not depend on the actual shape of the noise spectrum. As such, it provides a powerful way to complement usual refocusing techniques. Relaxation imposes a fundamental limit on the sensitivity of state of the art quantum sensors which cannot be overcome by dynamical decoupling. The only way to overcome this is to utilize quantum error correcting codes. We present a superconducting magnetometry design that incorporates approximate quantum error correction, in which the signal is generated by a two qubit Hamiltonian term. This two-qubit term is provided by the dynamics of a tunable coupler between two transmon qubits. For fast enough correction, it is possible to lengthen the coherence time of the device beyond the relaxation limit.

Bogoliubov theory for excitations in Bose-Einstein condensates was formulated over 50 years ago to qualitatively explain strongly interacting superfluids. Quantitative experimental verification of this theory came with the long-awaited realization of gaseous, weakly interacting condensates. This Colloquium reviews recent experimental advances in the study of Bogoliubov bulk excitations in Bose-Einstein condensates, obtained using two-photon Bragg scattering.

When quantum systems are shifted faster than their transition and coupling time scales, their susceptibility is dramatically modified. We measure the optical susceptibility of a strongly modulated electromagnetically induced transparency system. Time vs detuning plots for different pump modulation frequencies reveal a transition between an adiabatic regime where a series of smooth pulses are created and a nonadiabatic regime where a strong transient oscillating response is added. Applying a magnetic field lifts the hyperfine level degeneracy, revealing an interference effect between the different magnetic level transients. We explore the dynamics of the magnetic and nonmagnetic cases and discuss their coherent nature. We finally combine the global phase of the transmitted pulses with the transient interference to achieve broadband magnetic sensing without losing the sensitivity of a single electromagnetically induced transparency line.

We report the results of an experimental study of the dc and ac magnetic properties of superconducting Nb thin-walled cylinders in parallel to the axis magnetic fields. The magnetization curves at various temperatures are measured. Surprisingly, at 4.5 K, for magnetic fields much lower than ${H}_{c1}$, avalanchelike jumps of the magnetization are observed. The position of the jumps is not reproducible and changes from one experiment to another, resembling vortex lattice instabilities usually observed for magnetic fields larger than ${H}_{c1}$. At temperatures larger than 6.5 K, the measured magnetization curves become smooth. ac response is measured in constant and swept dc magnetic fields. A phenomenological model that describes the ac response of the surface superconducting states is proposed. This model assumes that the observed ac response in dc fields larger than ${H}_{c2}$ is due to the relaxation of surface superconducting states with nonzero current in the walls to the state with zero current, and the existence of a critical current below which this relaxation is absent.

Multi-level control of quantum coherence exponentially reduces communication and computation resources required for a variety of applications of quantum information science. However, it also introduces complex dynamics to be understood and controlled. These dynamics can be simplified and made intuitive by employing group theory to visualize certain four-level dynamics in a 'Bell frame' comprising an effective pair of uncoupled two-level qubits. We demonstrate control of a Josephson phase qudit with a single multi-tone excitation, achieving successive population inversions between the first and third levels and highlighting constraints imposed by the two-qubit representation. Furthermore, the finite anharmonicity of our system results in a rich dynamical evolution, where the two Bell-frame qubits undergo entangling-disentangling oscillations in time, explained by a Cartan gate decomposition representation. The Bell frame constitutes a promising tool for control of multi-level quantum systems, providing an intuitive clarity to complex dynamics.

We propose a scheme that utilizes the collective enhancement of a photonic mode inside an atomic ensemble together with a proper Zeeman manifold in order to achieve a heralded polarization entangled Bell state. The entanglement is between two photons that are separated in time and can be used as a post selected deterministic source for applications such as quantum repeaters where a subsequent entanglement swapping measurement is employed. We present a detailed analysis of the practical limitation of the scheme., Comment: 6 pages, 5 figures

Relaxation of the Larmor magnetic moment by spin-exchange collisions has been shown to diminish for high alkali densities, resulting from the linear part of the collisional interaction. In contrast, we demonstrate both experimentally and theoretically the elimination of spin-exchange relaxation of high magnetic moments (birefringence) in alkali vapor. This elimination originates from the nonlinear part of the spin-exchange interaction, as a scattering process of the Larmor magnetic moment. We find counter-intuitively that the threshold magnetic field is the same as in the Larmor case, despite the fact that the precession frequency is twice as large.

Through periodic index modulation, we create two different types of photonic structures in a heated rubidium vapor for controlled reflection, transmission and diffraction of light. The modulation is achieved through the use of the AC Stark effect resulting from a standing-wave control field. The periodic intensity structures create translationally invariant index profiles analogous to photonic crystals in spectral regions of steep dispersion. Experimental results are consistent with modeling., Comment: 6 pages, 6 figures

A dynamic photonic band gap is created in hot vapor for controlled reflection, transmission or storage of light. A Stark-shifting laser sets up a standing wave which creates a rapidly reconfigurable periodic index contrast.

We investigate the performance of inhomogeneously broadened spin ensembles as quantum memories under continuous dynamical decoupling. The role of the continuous driving field is twofold: firstly, it decouples individual spins from magnetic noise; secondly, and more importantly, it suppresses and reshapes the spectral inhomogeneity of spin ensembles. We show that a continuous driving field, which itself may also be inhomogeneous over the ensemble, can considerably enhance the decay of the tails of the inhomogeneous broadening distribution. This fact enables a spin-ensemble-based quantum memory to exploit the effect of cavity protection and achieve a much longer storage time. In particular, for a spin ensemble with a Lorentzian spectral distribution, our calculations demonstrate that continuous dynamical decoupling has the potential to improve its storage time by orders of magnitude for the state-of-the-art experimental parameters., publishedVersion

The analysis of wave-packet dynamics may be greatly simplified when viewed in phase-space. While harmonic oscillators are often used as a convenient platform to study wave-packets, arbitrary state preparation in these systems is more challenging. Here, we demonstrate a direct measurement of the Wigner distribution of complex photon states in an anharmonic oscillator - a superconducting phase circuit, biased in the small anharmonicity regime. We test our method on both non-classical states composed of two energy eigenstates and on the dynamics of a phase-locked wavepacket. This method requires a simple calibration, and is easily applicable in our system out to the fifth level., Comment: 5 figures, 1 table and supplementary material

The superconducting critical temperature, ${T}_{C}$, of thin Nb films is significantly modified when gold nanoparticles (NPs) are chemically linked to the Nb film, with a consistent enhancement when using 3 nm long disilane linker molecules. The ${T}_{C}$ increases by up to 10% for certain linker length and NP size. No change is observed when the nanoparticles are physisorbed with nonlinking molecules. Electron tunneling spectra acquired on the linked NPs below ${T}_{C}$ typically exhibit zero-bias peaks. We attribute these results to a pairing mechanism coupling electrons in the Nb and the NPs, mediated by the organic linkers.

Planar spirals offer a highly scalable geometry appropriate for wireless power transfer via strongly coupled inductive resonators. We numerically derive a set of geometric scale and material independent coupling terms, and analyze a simple model to identify design considerations for a variety of different materials. We use our model to fabricate integrated planar resonators of handheld sizes, and optimize them to achieve high Q factors, comparable to much larger systems, and strong coupling over significant distances with approximately constant efficiency., Comment: ISSN 1567-1739

An array of optical vortices is being used as a probe in an electromagnetically induced transparency experiment in warm Rubidium vapor. Scanning the two photon detuning reveals a change in the rotation angle and the distance between the vortices. We observe both positive (free-space like) enhanced rotation, and negative (contra free-space) rotation of the array.

We present a fabrication scheme and testing results for epitaxial sub-micrometer Josephson junctions. The junctions are made using a high-temperature (1170 K) 'via process' yielding junctions as small as 0.8 µm in diameter by use of optical lithography. Sapphire (Al2O3) tunnel-barriers are grown on an epitaxial Re/Ti multilayer base-electrode. We have fabricated devices with both Re and Al top-electrodes. While room temperature (295 K) resistance versus area data are favorable for both types of top-electrodes, the low-temperature (50 mK) data show that junctions with the Al top-electrode have a much higher subgap resistance. The microwave loss properties of the junctions have been measured by use of superconducting Josephson junction qubits. The results show that high subgap resistance correlates with improved qubit performance.

We measure the state dynamics of a tunable anharmonic quantum system, the Josephson phase circuit, under the excitation of a frequency-chirped drive. At small anharmonicity, the state evolves like a wavepacket - a characteristic response in classical oscillators; in this regime we report exponentially enhanced lifetimes of highly excited states, held by the drive. At large anharmonicity, we observe sharp steps, corresponding to the excitation of discrete energy levels. The continuous transition between the two regimes is mapped by measuring the threshold of these two effects., Comment: 4 pages, 4 figures. Supplementary material

We measure the lifetime ($T_{1}$) and coherence ($T_{2}$) of two-level defect states (TLSs) in the insulating barrier of a Josephson phase qubit and compare to the interaction strength between the two systems. We find for the average decay times a power law dependence on the corresponding interaction strengths, whereas for the average coherence times we find an optimum at intermediate coupling strengths. We explain both the lifetime and the coherence results using the standard TLS model, including dipole radiation by phonons and anti-correlated dependence of the energy parameters on environmental fluctuations., 4 pages, 4 figures and supplementary material (3 pages, 2 figures, 1 table)

Parametric excitation of a Bose-Einstein condensate (BEC) can be realized by periodically changing the interaction strength between the atoms. Above some threshold strength, this excitation modulates the condensate density. We show that when the condensate is trapped in a potential well of irregular shape, density waves can be strongly concentrated ("scarred") along the shortest periodic orbits of a classical particle moving within the confining potential. While single-particle wave functions of systems whose classical counterpart is chaotic may exhibit rich scarring patterns, in BEC, we show that nonlinear effects select mainly those scars that are locally described by stripes. Typically, these are the scars associated with self retracing periodic orbits that do not cross themselves in real space. Dephasing enhances this behavior by reducing the nonlocal effect of interference.

We demonstrate in a superconducting qubit the conditional recovery (uncollapsing) of a quantum state after a partial-collapse measurement. A weak measurement extracts information and results in a nonunitary transformation of the qubit state. However, by adding a rotation and a second partial measurement with the same strength, we erase the extracted information, canceling the effect of both measurements. The fidelity of the state recovery is measured using quantum process tomography and found to be above 70% for partial-collapse strength less than 0.6.

We demonstrate new experimental procedures for measuring small errors in a superconducting quantum bit (qubit). By carefully separating out gate and measurement errors, we construct a complete error budget and demonstrate single qubit gate fidelities of 0.98, limited by energy relaxation. We also introduce a new metrology tool-- Ramsey interference error filter-that can measure the occupation probability of the state |2> which is outside the computational basis, down to 10{-4}, thereby confirming that our quantum system stays within the qubit manifold during single qubit logic operations.

Superconducting quantum circuits must be designed carefully to avoid dissipation from coupling to external control circuitry. Here we introduce the concept of current transformation to quantify coupling to the environment. We test this theory with an experimentally-determined impedance transformation of $\sim 10^5$ and find quantitative agreement better than a factor of 2 between this transformation and the reduced lifetime of a phase qubit coupled to a tunable transformer. Higher-order corrections from quantum fluctuations are also calculated with this theory, but found not to limit the qubit lifetime. We also illustrate how this simple connection between current and impedance transformation can be used to rule out dissipation sources in experimental qubit systems., 4 pages, 4 figures

The microwave performance of amorphous dielectric materials at very low temperatures and very low excitation strengths displays significant excess loss. Here, we present the loss tangents of some common amorphous and crystalline dielectrics, measured at low temperatures (T < 100 mK) with near single-photon excitation energies, using both coplanar waveguide (CPW) and lumped LC resonators. The loss can be understood using a two-level state (TLS) defect model. A circuit analysis of the half-wavelength resonators we used is outlined, and the energy dissipation of such a resonator on a multilayered dielectric substrate is considered theoretically., 4 pages, 3 figures, submitted to Applied Physics Letters