Quantum superposition of macroscopic persistent-current states

Legget-Garg inequality for a two-mode entangled bosonic system

We discuss a model of two nonlinear quantum oscillators mutually coupled by linear interaction and continuously driven by external coherent excitation. For such a system, we analyze temporal correlations. We examine the violation of the Leggett-Garg inequality analysing various scenarios of measurements. These scenarios are based on the projection onto different Bell states. We show that the possibility of violation of the Leggett-Garg inequalities is associated with the use of different projectors.

Metasurface-Based Optical Logic Operators Driven by Diffractive Neural Networks

In this paper, a novel optical logic operator based on the multifunctional metasurface driven by all-optical diffractive neural network is reported, which can perform four principal quantum logic operations (Pauli-X, Pauli-Y, Pauli-Z, and Hadamard gates). The two ground states| 0 ⟩ $|0 \rangle $ and| 1 ⟩ $|1 \rangle $  are characterized by two orthogonal linear polarization states. The proposed spatial- and polarization-multiplexed all-optical diffractive neural network only contains a hidden layer physically mapped as a metasurface with simple and compact unit cells, which dramatically reduces the volume and computing resources required for the system. The designed optical quantum operator is proven to achieve high fidelities for all four quantum logical gates, up to 99.96% numerically and 99.88% experimentally. The solution will facilitate the construction of large-scale optical quantum computing systems and scalable optical quantum devices.

Geometric Phase of a Transmon in a Dissipative Quantum Circuit

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.

Generation of Schrödinger Cat States in a Hybrid Cavity Optomechanical System

We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom-cavity-oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb-Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation.

Peculiarities of Electron Wave Packet Dynamics in Planar Nanostructures in the Presence of Magnetic and Electric Fields

Currently, spatially localized electron densities and currents are considered to be candidates for use in the encoding of quantum information. For this reason, the control of their temporal dynamics is an important task. In this work, the spatiotemporal evolution of an electron wave packet in planar nanostructure in the presence of transverse magnetic and lateral electric fields is investigated by direct analytical solution of the non-stationary Schrödinger equation. Methods to control and manage the dynamics of the spatially localized electron density distribution are developed. The production of photon-like quantum states of electrons opens up opportunities for applications similar to quantum optical and quantum information technologies but implemented with charge carriers. Quantum control of the trajectory of the electron wave packet, accompanied by dramatic suppression of its spreading, is demonstrated. This study discovered methods to manage spatially localized electron behavior in a nanostructure that allows a controllable charge quantum transfer and gives rise to new prospects for quantum nanoelectronics technology.

Enhanced Coherence in Superconducting Circuits via Band Engineering

In superconducting circuits interrupted by Josephson junctions, the dependence of the energy spectrum on offset charges on different islands is 2e periodic through the Aharonov-Casher effect and resembles a crystal band structure that reflects the symmetries of the Josephson potential. We show that higher-harmonic Josephson elements described by a cos(2φ) energy-phase relation provide an increased freedom to tailor the shape of the Josephson potential and design spectra featuring multiplets of flat bands and Dirac points in the charge Brillouin zone. Flat bands provide noise-insensitive energy levels, and consequently, engineering band pairs with flat spectral gaps can help improve the coherence of the system. We discuss a modified version of a flux qubit that achieves, in principle, no decoherence from charge noise and introduce a flux qutrit that shows a spin-1 Dirac spectrum and is simultaneously quite robust to both charge and flux noise.

Entanglement Dynamics Induced by a Squeezed Coherent Cavity Coupled Nonlinearly with a Qubit and Filled with a Kerr-Like Medium

An analytical solution for a master equation describing the dynamics of a qubit interacting with a nonlinear Kerr-like cavity through intensity-dependent coupling is established. A superposition of squeezed coherent states is propped as the initial cavity field. The dynamics of the entangled qubit-cavity states are explored by negativity for different deformed function of the intensity-dependent coupling. We have examined the effects of the Kerr-like nonlinearity and the qubit-cavity detuning as well as the phase cavity damping on the generated entanglement. The intensity-dependent coupling increases the sensitivity of the generated entanglement to the phase-damping. The stability and the strength of the entanglement are controlled by the Kerr-like nonlinearity, the qubit-cavity detuning, and the initial cavity non-classicality. These physical parameters enhance the robustness of the qubit-cavity entanglement against the cavity phase-damping. The high initial cavity non-classicality enhances the robustness of the qubit-cavity entanglement against the phase-damping effect.

Circulator function in a Josephson junction circuit and braiding of Majorana zero modes

We propose a scheme for the circulator function in a superconducting circuit consisting of a three-Josephson junction loop and a trijunction. In this study we obtain the exact Lagrangian of the system by deriving the effective potential from the fundamental boundary conditions. We subsequently show that we can selectively choose the direction of current flowing through the branches connected at the trijunction, which performs a circulator function. Further, we use this circulator function for a non-Abelian braiding of Majorana zero modes (MZMs). In the branches of the system we introduce pairs of MZMs which interact with each other through the phases of trijunction. The circulator function determines the phases of the trijunction and thus the coupling between the MZMs to gives rise to the braiding operation. We modify the system so that MZMs might be coupled to the external ones to perform qubit operations in a scalable design.

Analysis of a multiple-quantum-dots embedded ring structure for potential optically-controlled quantum switch or spin filter

We theoretically study the average current through a ring embedded with multiple quantum dots in each arm subjected to a time-dependent external field. A current resonance band can be observed in a six-quantum-dot system. In the presence of a time-dependent external field, mutual transformation occurs between the resonance band and antiresonance band, indicating an effective optically-controlled quantum switch can be realized in a wider quantum dot's energy regime. As the Zeeman effect is introduced, the conversion between 100 and - 100% for spin polarization [Formula: see text] can be realized by adjusting the frequency of time-dependent external field, suggesting a physical scheme of an optically-controlled spin filter. The present work sheds lights onto the design and quantum computation of future nano-devices.

Observation of half-quantum flux in the unconventional superconductor β-Bi2Pd

Magnetic flux quantization is one of the defining properties of a superconductor. We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting β-Bi₂Pd thin films. The half-quantum fluxoid manifests itself as a π phase shift in the quantum oscillation of the superconducting critical temperature. This result verifies unconventional superconductivity of β-Bi₂Pd and is consistent with a spin-triplet pairing symmetry. Our findings may have implications for flux quantum bits in the context of quantum computing.

Probing Quantum Criticality and Symmetry Breaking at the Microscopic Level

We report on an experimental study of the Lipkin-Meshkov-Glick model of quantum spins interacting at infinite range in a transverse magnetic field, which exhibits a ferromagnetic phase transition in the thermodynamic limit. We use dysprosium atoms of electronic spin J=8, subjected to a quadratic Zeeman light shift, to simulate 2J=16 interacting spins 1/2. We probe the system microscopically using single magnetic sublevel resolution, giving access to the spin projection parity, which is the collective observable characterizing the underlying Z_{2} symmetry. We measure the thermodynamic properties and dynamical response of the system, and we study the quantum critical behavior around the transition point. In the ferromagnetic phase, we achieve coherent tunneling between symmetry-broken states, and we test the link between symmetry breaking and the appearance of a finite order parameter.

Unipolar magnetic field pulses as an advantageous tool for ultrafast operations in superconducting Josephson "atoms"

A theoretical approach to the consistent full quantum description of the ultrafast population transfer and magnetization reversal in superconducting meta-atoms induced by picosecond unipolar pulses of a magnetic field is developed. A promising scheme based on the regime of stimulated Raman Λ-type transitions between qubit states via upper-lying levels is suggested in order to provide ultrafast quantum operations on the picosecond time scale. The experimental realization of a circuit-on-chip for the discussed ultrafast control is presented.

Noise as Data: Nucleation of Electrochemically Generated Nanobubbles

Single-entity electrochemistry aims to expand the toolkit for probing matter at the nanometer scale. Originally focused largely on electrochemically active systems, these methods are increasingly turning into versatile probes complementary to optical, electrical, or mechanical methods. Recent studies of the nucleation, structure, and stability of gas nanobubbles, which exploit electrochemistry at nanoelectrodes as generation and stabilization mechanisms, are prototypical examples. These measurements illustrate the interplay between advances in electrochemical methods and strategies for extracting microscopic information from the results.

Symmetry-Broken Many-Body Excited States of the Gaseous Atomic Double-Well Bose-Einstein Condensate

Macroscopic, many-body self-trapped and quantum superposition states of the gaseous double-well Bose-Einstein condensate (BEC) are investigated within the context of a multiconfigurational bosonic self-consistent field theory based upon underlying spatially symmetry-broken one-body wave functions. To aid in the interpretation of our results, an approximate model is constructed in the extreme Fock state limit, in which self-trapped and superposition states emerge in the many-body spectrum, striking a delicate balance between the degree of symmetry breaking, the effects of the condensate's mean field, and that of atomic correlation. It is found, in both the model and full theory, that the superposition state lies energetically below its related self-trapped counterpart even when many configurations are involved. Noticeably different spatial density profiles are associated with each type of excited state, thus providing a rigorous justification for approximate descriptions of high-lying excited states of the BEC.

Nonclassicality of the Harmonic-Oscillator Coherent State Persisting up to the Macroscopic Domain

Can the most "classical-like" of all quantum states, namely the Schrödinger coherent state of a harmonic oscillator, exhibit nonclassical behavior? We find that for an oscillating object initially in a coherent state, merely by observing at various instants which spatial region the object is in, the Leggett-Garg inequality (LGI) can be violated through a genuine negative result measurement, thereby repudiating the everyday notion of macrorealism. This violation thus reveals an unnoticed nonclassicality of the very state which epitomizes classicality within the quantum description. It is found that for any given mass and oscillator frequency, a significant quantum violation of LGI can be obtained by suitably choosing the initial peak momentum of the coherent state wave packet. It thus opens up potentially the simplest way (without coupling with any ancillary quantum system or using nonlinearity) for testing whether various recently engineered and sought after macroscopic oscillators, such as feedback cooled thermal trapped nanocrystals of ∼10^{6}-10^{9}  amu mass, are indeed bona fide nonclassical objects.

Vacuum induced transparency and photon number resolved Autler-Townes splitting in a three-level system

We study the absorption spectrum of a probe field by a Λ-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler-Townes splitting (ATS). We also find that the parameter changing from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum in the parameter regime of vacuum induced ATS when the mean photon number of the quantized control field is changed from zero (vacuum) to a finite number. However, there is no photon number resolved spectrum in the parameter regime of VIT even that the quantized control field contains the finite number of photons. Finally, we further discuss possible experimental realization.

Quantum information processing with superconducting circuits: a review

During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

Macroscopic Superpositions as Quantum Ground States

We study the question of what kind of a macroscopic superposition can(not) naturally exist as a ground state of some gapped local many-body Hamiltonian. We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian provided that its ground state is a superposition of two well-distinguishable macroscopic "semiclassical" states. For a large class of macroscopic superposition states we show that the gap vanishes in the macroscopic limit. This in turn shows that preparation of such states by simple cooling to the ground state is not experimentally feasible and requires a different strategy. Our approach is very general and can be used to rule out a variety of quantum states, some of which do not even exhibit macroscopic quantum properties. Moreover, our methods and results can be used for addressing quantum marginal related problems.

Superconducting Qubits as Mechanical Quantum Engines

We propose the equivalence of superconducting qubits with a pistonlike mechanical quantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.

Stationary nano-SQUID: theoretical investigation and feasibility analysis

The standard operation of a dc SQUID leads to oscillatory electric fields that emit electromagnetic radiation. We estimate the effect that this radiation could have on the measured sample. A stationary SQUID could be advantageous if the oscillation contribution to back action on the measured sample has to be avoided. We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows across the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime, i.e. the densities of normal current and of supercurrent become functions of position only, independent of time. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The influence of thermal noise was estimated. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.

Tuneable on-demand single-photon source in the microwave range

An on-demand single-photon source is a key element in a series of prospective quantum technologies and applications. Here we demonstrate the operation of a tuneable on-demand microwave photon source based on a fully controllable superconducting artificial atom strongly coupled to an open-ended transmission line. The atom emits a photon upon excitation by a short microwave π-pulse applied through a control line. The intrinsically limited device efficiency is estimated to be in the range 65–80% in a wide frequency range from 7.75 to 10.5 GHz continuously tuned by an external magnetic field. The actual demonstrated efficiency is also affected by the excited state preparation, which is about 90% in our experiments. The single-photon generation from the single-photon source is additionally confirmed by anti-bunching in the second-order correlation function. The source may have important applications in quantum communication, quantum information processing and sensing.

Microwave single photon sources are important for quantum applications, but their design often incorporates a resonator that fixes the frequency of the emitted photon. Here, the authors demonstrate a tuneable on-demand photon source based on an artificial atom asymmetrically coupled to two transmission lines.

Macroscopic Quantum Superposition in Cavity Optomechanics

Quantum superposition in mechanical systems is not only key evidence for macroscopic quantum coherence, but can also be utilized in modern quantum technology. Here we propose an efficient approach for creating macroscopically distinct mechanical superposition states in a two-mode optomechanical system. Photon hopping between the two cavity modes is modulated sinusoidally. The modulated photon tunneling enables an ultrastrong radiation-pressure force acting on the mechanical resonator, and hence significantly increases the mechanical displacement induced by a single photon. We study systematically the generation of the Yurke-Stoler-like states in the presence of system dissipations. We also discuss the experimental implementation of this scheme.

Correlated Emission Lasing in Harmonic Oscillators Coupled via a Single Three-Level Artificial Atom

A single superconducting artificial atom can be used for coupling electromagnetic fields up to the single-photon level due to an easily achieved strong coupling regime. Bringing a pair of harmonic oscillators into resonance with the transitions of a three-level atom converts atomic spontaneous processes into correlated emission dynamics. We present the experimental demonstration of two-mode correlated emission lasing in harmonic oscillators coupled via a fully controllable three-level superconducting quantum system (artificial atom). The correlation of emissions with two different colors reveals itself as equally narrowed linewidths and quenching of their mutual phase diffusion. The mutual linewidth is more than 4 orders of magnitude narrower than the Schawlow-Townes limit. The interference between the different color lasing fields demonstrates that the two-mode fields are strongly correlated.

Dissipative dynamics in a quantum bistable system: crossover from weak to strong damping

The dissipative dynamics of a quantum bistable system coupled to a Ohmic heat bath is investigated beyond the spin-boson approximation. Within the path-integral approach to quantum dissipation, we propose an approximation scheme which exploits the separation of time scales between intra- and interwell (tunneling) dynamics. The resulting generalized master equation for the populations in a space localized basis enables us to investigate a wide range of temperatures and system-environment coupling strengths. A phase diagram in the coupling-temperature space is provided to give a comprehensive account of the different dynamical regimes.

Magnetic reversal dynamics of a quantum system on a picosecond timescale

We present our approach for a consistent, fully quantum mechanical description of the magnetization reversal process in natural and artificial atomic systems by means of short magnetic pulses. In terms of the simplest model of a two-level system with a magnetic moment, we analyze the possibility of a fast magnetization reversal on the picosecond timescale induced by oscillating or short unipolar magnetic pulses. We demonstrate the possibility of selective magnetization reversal of a superconducting flux qubit using a single flux quantum-based pulse and suggest a promising, rapid Λ-scheme for resonant implementation of this process. In addition, the magnetization reversal treatment is fulfilled within the framework of the macroscopic theory of the magnetic moment, which allows for the comparison and explanation of the quantum and classical behavior.

Two-dimensional lattice gauge theories with superconducting quantum circuits

A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

Flux qubits with long coherence times for hybrid quantum circuits

We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the 6-20  μs range and a pure dephasing time comprised between 3 and 10  μs. This significant improvement over previous works opens the way to the coherent coupling of a flux qubit to individual spins.

Experimental realization of Josephson junctions for an atom SQUID

We report the creation of a pair of Josephson junctions on a toroidal dilute gas Bose-Einstein condensate (BEC), a configuration that is the cold atom analog of the well-known dc superconducting quantum interference device (SQUID). We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. The junctions and toroidal trap are created with the painted potential, a time-averaged optical dipole potential technique which will allow scaling to more complex BEC circuit geometries than the single atom-SQUID case reported here. Since rotation plays the same role in the atom SQUID as magnetic field does in the dc SQUID magnetometer, the device has potential as a compact rotation sensor.

Loschmidt echo and the many-body orthogonality catastrophe in a qubit-coupled Luttinger liquid

We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behavior: the steady state exponent after quenching back and forth n times between 2 LLs (bang-bang protocol) is 2n times bigger than that of the adiabatic overlap and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup consisting of a hybrid system containing cold atoms and a flux qubit coupled to a Feshbach resonance is proposed to measure the Loschmidt echo using rf spectroscopy or Ramsey interferometry.

Charge relaxation in a single-electron Si/SiGe double quantum dot

We measure the interdot charge relaxation time T1 of a single electron trapped in an accumulation mode Si/SiGe double quantum dot. The energy level structure of the charge qubit is determined using photon assisted tunneling, which reveals the presence of a low-lying excited state. We systematically measure T1 as a function of detuning and interdot tunnel coupling and show that it is tunable over four orders of magnitude, with a maximum of 45  μs for our device configuration.

Magnetic flux noise in dc SQUIDs: temperature and geometry dependence

The spectral density S(Φ)(f) = A(2)/(f/1 Hz)(α) of magnetic flux noise in ten dc superconducting quantum interference devices (SQUIDs) with systematically varied geometries shows that α increases as the temperature is lowered; in so doing, each spectrum pivots about a nearly constant frequency. The mean-square flux noise, inferred by integrating the power spectra, grows rapidly with temperature and at a given temperature is approximately independent of the outer dimension of a given SQUID. These results are incompatible with a model based on the random reversal of independent, surface spins.

Strong-coupling BCS models of Josephson qubits

The strong-coupling version of the BCS theory for superconductors is used to derive microscopic models for all types of small Josephson junctions--charge qubit, flux qubit and phase qubit. Applied to Josephson qubits it yields a more complicated structure of the lowest-lying energy levels than that obtained from phenomenological models based on quantization of the Kirchhoff equations. In particular, highly degenerate levels emerge, which act as probability sinks for the qubit. The alternative formulae concerning spectra of superconducting qubits are presented and compared with the experimental data. In contrast to the existing theories those formulae contain microscopic parameters of the model. In particular, for the first time, the density of Cooper pairs at zero temperature is estimated for an Al-based flux qubit. Finally, the question whether small Josephson junctions can be treated as macroscopic quantum systems is briefly discussed.

Are cloned quantum states macroscopic?

We study quantum states produced by optimal phase covariant quantum cloners. We argue that cloned quantum superpositions are not macroscopic superpositions in the spirit of Schrödinger's cat, despite their large particle number. This is indicated by calculating several measures for macroscopic superpositions from the literature, as well as by investigating the distinguishability of the two superposed cloned states. The latter rapidly diminishes when considering imperfect detectors or noisy states and does not increase with the system size. In contrast, we find that cloned quantum states themselves are macroscopic, in the sense of both proposed measures and their usefulness in quantum metrology with an optimal scaling in system size. We investigate the applicability of cloned states for parameter estimation in the presence of different kinds of noise.

Heralded state preparation in a superconducting qubit

We demonstrate high-fidelity, quantum nondemolition, single-shot readout of a superconducting flux qubit in which the pointer state distributions can be resolved to below one part in 1000. In the weak excitation regime, continuous measurement permits the use of heralding to ensure initialization to a fiducial state, such as the ground state. This procedure boosts readout fidelity to 93.9% by suppressing errors due to spurious thermal population. Furthermore, heralding potentially enables a simple, fast qubit reset protocol without changing the system parameters to induce Purcell relaxation.

Measurements of quasiparticle tunneling dynamics in a band-gap-engineered transmon qubit

We have engineered the band gap profile of transmon qubits by combining oxygen-doped Al for tunnel junction electrodes and clean Al as quasiparticle traps to investigate energy relaxation due to quasiparticle tunneling. The relaxation time T1 of the qubits is shown to be insensitive to this band gap engineering. Operating at relatively low-E(J)/E(C) makes the transmon transition frequency distinctly dependent on the charge parity, allowing us to detect the quasiparticles tunneling across the qubit junction. Quasiparticle kinetics have been studied by monitoring the frequency switching due to even-odd parity change in real time. It shows the switching time is faster than 10  μs, indicating quasiparticle-induced relaxation has to be reduced to achieve T1 much longer than 100  μs.

Periodic magnetoresistance oscillations induced by superconducting vortices in single crystal Au nanowires

We show in this paper that it is possible to induce superconducting vortices in a gold nanowire connected to superconducting electrodes. The gold nanowire acquires superconductivity by the proximity effect. The differential magnetoresistance of the nanowire beyond a critical magnetic field shows uniform oscillations with increasing field with a period of Φ(0)/(2πr(2)) (Φ(0) = h/2e is the superconducting flux quantum, r = 35 nm is the radius of the nanowire). Our analysis indicates that these periodic oscillations are the signatures of the sequential generation and moving of vortices across the gold nanowire.

Long-range superharmonic Josephson current

We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an odd number of Cooper pairs cannot have a long-range propagation when there is only one spin-active region. When the temperature is much lower than the Thouless energy, the coherent transport of two Cooper pairs becomes the dominant process and the superharmonic current-phase relation is obtained (I ∝ sin2ϕ).

Quantification of macroscopic quantum superpositions within phase space

Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a harmonious manner: the degree of quantum coherence and the effective size of the physical system that involves the superposition. It enjoys remarkably good analytical and algebraic properties. It turns out to be the most general and inclusive measure ever proposed that it can be applied to any types of multipartite states and mixed states represented in phase space.

Tuned transition from quantum to classical for macroscopic quantum states

The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with basis states having persistent currents of 1  μA carried by a million pairs of electrons. By tuning the tunnel barrier between these states we see a crossover from quantum to classical. Released from nonequilibrium, the system exhibits spontaneous coherent oscillations. For high barriers the lifetime of the states increases dramatically while the tunneling period approaches the phase coherence time and the oscillations fade away.

Lyapunov decoherence rate in classically chaotic systems

We provide a path integral treatment of the decoherence process induced by a heat bath on a single particle whose dynamics is classically chaotic and show that the decoherence rate is given by the Lyapunov exponent. The loss of coherence is charaterized by the purity, which is calculated semiclassically within diagonal approximation, when the particle initial state is a single Gaussian wave packet. The calculation is performed for weak dissipation and in the high-temperature limit. This situation allows us to simplify the heat bath description to a single random potential. Although the dissipative term is neglected in such approach, the fluctuating one can be treated phenomenologically to fit with the above regime. Our results are therefore valid for times shorter than the inverse of the dissipation rate.

Stable macroscopic quantum superpositions

We study the stability of superpositions of macroscopically distinct quantum states under decoherence. We introduce a class of quantum states with entanglement features similar to Greenberger-Horne-Zeilinger (GHZ) states, but with an inherent stability against noise and decoherence. We show that in contrast to GHZ states, these so-called concatenated GHZ states remain multipartite entangled even for macroscopic numbers of particles and can be used for quantum metrology in noisy environments. We also propose a scalable experimental realization of these states using existing ion-trap setups.

Entangled optical vortex links

Optical vortices are lines of phase singularity which percolate through all optical fields. We report the entanglement of linked optical vortex loops in the light produced by spontaneous parametric down-conversion. As measured by using a Bell inequality, this entanglement between topological features extends over macroscopic and finite volumes. The entanglement of photons in complex three-dimensional topological states suggests the possibility of entanglement of similar features in other quantum systems describable by complex scalar functions, such as superconductors, superfluids, and Bose-Einstein condensates.

Sisyphus effects in a microwave-excited flux-qubit resonator system

Sisyphus amplification, familiar from quantum optics, has recently been reported as a mechanism to explain the enhanced quality factor of a classical resonant (tank) circuit coupled to a superconducting flux qubit. Here we present data from a coupled system, comprising a quantum mechanical rf SQUID (flux qubit) reactively monitored by an ultrahigh quality factor noise driven rf resonator and excited by microwaves. The system exhibits enhancement of the tank-circuit resonance, bringing it significantly closer (within 1%) to the lasing limit, than previously reported results.

Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits

We propose a method to achieve coherent coupling between nitrogen-vacancy (NV) centers in diamond and superconducting (SC) flux qubits. The resulting coupling can be used to create a coherent interaction between the spin states of distant NV centers mediated by the flux qubit. Furthermore, the magnetic coupling can be used to achieve a coherent transfer of quantum information between the flux qubit and an ensemble of NV centers. This enables a long-term memory for a SC quantum processor and possibly an interface between SC qubits and light.

Beyond spontaneously broken symmetry in Bose-Einstein condensates

Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus cannot explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where particles from two (possibly macroscopic) condensate sources are used for conjugate measurements of the relative phase and populations. Off-diagonal phase effects are characterized by a "quantum angle" and observed via "population oscillations," signaling quantum interference of macroscopically distinct states.