Quantum Entanglement and Correlations in Superconducting Flux Qubits

We report on the quantum correlations dissipative dynamics followed by coupled superconducting flux qubits. The coupling between the superconducting quantum register and the reservoir is described by two different mechanisms: collective and independent decoherence. By means of the Bloch?CRedfield formalism, we solve the quantum master equation and show that coupling under collective quantum noise is more robust to decoherence. This result is demonstrated for different flux qubit initial preparations, taking into account the influence due to external fields and temperature. Furthermore, we compute the entanglement and the quantum discord dissipative dynamics as controlled by external parameters. We show that the discord is more robust against decoherence effects. This fact could be harnessed in the realization of quantum computing tasks that do not need to invoke entanglement in their implementation.     

Recent Progress in Quantum Simulation Using Superconducting Circuits

Quantum systems are notoriously difficult to simulate with classical means. Recently, the idea of using another quantum system—which is experimentally more controllable—as a simulator for the original problem has gained significant momentum. Amongst the experimental platforms studied as quantum simulators, superconducting qubits are one of the most promising, due to relative straightforward scalability, easy design, and integration with standard electronics. Here I review the recent state-of-the art in the field and the prospects for simulating systems ranging from relativistic quantum fields to quantum many-body systems.     

The Quantum Phase Slip Phenomenon in Superconducting Nanowires with High-Impedance Environment

Quantum phase slip (QPS) is the particular manifestation of quantum fluctuations of the order parameter of a current-biased quasi-1D superconductor. The QPS event(s) can be considered a dynamic equivalent of tunneling through conventional Josephson junction containing static in space and time weak link(s). At low temperatures T<<T _c, the QPS effect leads to finite resistivity of narrow superconducting channels and suppresses persistent currents in tiny nanorings. Here, we demonstrate that the quantum tunneling of phase may result in Coulomb blockade: superconducting nanowire, imbedded in high-Ohmic environment, below a certain bias voltage behaves as an insulator.     

Quantum Monte Carlo Study of Entanglement in Quantum Spin Systems

We perform an extensive quantum Monte Carlo investigation of entanglement properties in quantum spin systems close to or at a quantum critical point. Making use of the Stochastic Series Expansion method, we can systematically estimate the bipartite entanglement of the ground-state wavefunction in a large class of anisotropic spin models on unfrustrated lattices and in a uniform magnetic field. The behavior of the entanglement estimators as a function of the field shows remarkable universal features independent of the lattice dimensionality, marking both the occurrence of a field-induced quantum phase transition and of an exactly factorized state.PACS numbers: 03.67.Mn, 75.10.Jm, 73.43.Nq, 05.30.-d     

Intrinsic Quantum Dissipation in Superconducting Weak Links

We evaluate the frequency spectrum for an intrinsic quantum dissipative environment for the Josephson phase φ formed by subgap Andreev bound states in superconducting weak links. We also analyze the problem of macroscopic quantum tunneling (MQT) of φ in highly transparent weak links and identify several MQT regimes. Within the exponential accuracy, we derive the expression for the supercurrent quantum decay rate both at low temperatures and in the vicinity of the quantum-to-classical crossover.     

Dynamical Phase Slipping in Superconducting Nanowires

In the present work a study of resist state dynamics of superconducting nanowires on the basis of simulation of the one-dimensional time-dependent Ginzburg-Landau equation is carried out. The parameter u characterizing the purity of a superconducting substance was introduced in this equation. It was found out that an area of the current density, in which a dynamical phase slip process is observed, exists at u > 1. This process depends on the length of the nanowires and is not defined by thermodynamic fluctuations of conductivity and order parameter in contrast to thermal activated phase slips and quantum phase slip mechanisms. Also their arising does not depend on heterogeneity of nanowire substances.     

Tunable Resonators for Quantum Circuits

We have designed, fabricated and measured high-Q λ/2 coplanar waveguide microwave resonators whose resonance frequency is made tunable with magnetic field by inserting a DC-SQUID array (including 1 or 7 SQUIDs) inside. Their tunability range is 30% of the zero field frequency. Their quality factor reaches up to 3×10⁴. We present a model based on thermal fluctuations that accounts for the dependence of the quality factor with magnetic field.      

Control System of Superconducting Quantum Computers

Journal of Superconductivity and Novel Magnetism - The past two decades have witnessed the rapid development of quantum computers. Superconducting circuits are one of the most attractive platforms,...     

Materials Physics and Quantum Coherence in Superconducting Qubits

Nonidealities of real superconductors in the form of residual rf losses and conductance below the superconducting energy gap in tunneling Josephson junctions are discussed as possible sources of decoherence in Josehphson junction flux qubits. The purpose of the paper is pedagogical and aimed at taking a first step in a unified view of the quantum behavior of superconducting qubits and the realities of the materials out of which they are constructed. The need for a dialog between the quantum physicist and the materials physicist is stressed. Residual rf losses and localized states in junction barriers are identified as important subjects for this dialog.     

From Flux Quantization to Superconducting Quantum Bits

One of the important predictions of the early phenomenological theories of superconductivity such as the London and Ginzburg–Landau (GL) theory is the quantization of magnetic flux in multiply connected superconductors, which is one of the first demonstrations of a quantum effect on a macroscopic scale. In this paper, which is devoted to Vitalij Lazarevich Ginzburg on the occasion of his 90th birthday, we analyze a superconducting cylinder acting as a flux box as well as a superconducting disk acting as a Cooper pair box in the framework of GL theory. We extend this analysis to leaky flux and Cooper pair boxes which are obtained by introducing weak links allowing for the entry and exit of flux quanta and Cooper pairs from the respective boxes at finite rates. Flux and Cooper pair slippage processes by coherent quantum tunneling result in effective two-level quantum systems forming the basis for flux and charge quantum bits presently considered for the solid-state implementation of quantum information processing. We show that the corresponding Hamiltonians describing the leaky flux and Cooper pair box can be transformed into each other by a canonical transformation. PACS numbers: 74.20.De, 74.25.Bt, 74.25.Ha, 74.50.+r     

介观电路中量子逻辑门的研究

在介观电路的研究中,提出了用超晶格量子阱如何实现基本量子门及量子开关,同时展示了在超晶格量子阱中量子信息位的具体转化过程.对垒阱中电子波动行为及隧穿情况做了详细的理论分析,并给出如何避免隧穿效应的具体条件.     

Andreev Spectroscopy for Superconducting Phase Qubits

We propose a new method to measure the coherence time ofsuperconducting phase qubits based on the analysis of themagnetic-field dependent dc nonlinear Andreev current across ahigh-resistance tunnel contact between the qubit and a dirtymetal wire and derive a quantitative relation between thesubgap I–V characteristic and the internal correlationfunction of the qubit.     

Quantum Phase in Nanoscopic Superconductors

Using the pseudospin representation and the SU(2) phase operators we introduce a complex parameter to characterize both infinite and finite superconducting systems. While in the bulk limit the parameter becomes identical to the conventional order parameter, in the nanoscopic limit its modulus reduces to the number parity effect parameter and its phase takes discrete values. We evaluate the Josephson coupling energy and show that in bulk superconductor it reproduces the conventional expression and in the nanoscopic limit it leads to quantized Josephson effect. Finally, we study the phase flow or dual Josephson effect in a superconductor with fixed number of electrons.     

Macroscopic Quantum Phenomena in High Critical Temperature Superconducting Josephson Junctions

YBa₂Cu₃O_7?δ grain boundary bi-epitaxial Josepshon junctions (JJs) allow a very clear demonstration of Josephson current variation with the misorientation angle, consistent with the d-wave symmetry of the superconducting order parameter in cuprate, high temperature superconductors. Our bi-epitaxial junctions show a strong suppression of the first harmonic, I ₁ sin ø, of the current phase relation when tunneling from a lobe into a node of the superconducting gap function. In these configurations, the contribution of the second harmonic, I ₂ sin 2ø, becomes of the same magnitude as the first one, giving rise to a characteristic two-well Josephson potential as a function of phase ø instead of the usual single well. This characteristic intrinsic property has suggested proposals of a new class of qu-bit named “quiet” because of the existence a spontaneously degenerate fundamental state without the need of applying an external field. Our experiments probe the macroscopic quantum properties in a d-wave Josephson junction by measuring macroscopic quantum tunneling and energy level quantization. The switching current out of the zero voltage state is measured as a function of temperature down to 20 mK. The temperature variation of the width of an ensemble of switching events goes over from one, which is characteristic of a thermal activation of phase fluctuations to a temperature independent width which is a token of quantum tunneling of the phase. The transition regime is affected by the two-well potential in a 45^° misorientation junction as the second harmonic term gives rise to additional thermal transitions. The difference between quantized energy levels in the harmonic potential was determined by microwave spectroscopy. From the broadening of energy levels, it was possible to extract a Q-value of about 40 for the phase oscillations. The relatively high Q indicates quantum coherence over a sizeable time in d-wave junctions and gives hopes for a realization of a “quiet” high-T _c qu-bit. The contributions of V. L. Ginzburg to several different fields of physics are impressive and long standing. In superconductivity the Ginzburg–Landau theory, for instance, still represents a very powerful approach to model a huge number of different physical systems. High Temperature Superconductors (HTS) have strongly influenced research of the last 20 years and their d-wave order parameter symmetry represents one of the most intriguing features from both the fundamental point of view and some types of innovative long-term applications.     

Nanostructures,Entanglement and the Physics of Quantum Control

Abstract

Nanostructures might be viewed as solid-state approximations to SU(N) networks, the nodes of which would, in simplest form, be analogous to elementary spins. Owing to interactions with an external light field and coupling between the local nodes these networks allow for single- and multiple-node coherence (entanglement), despite damping. By means of stochastic simulations we demonstrate how such a ‘quantum machinery’ embedded in a qualified environment would look like in terms of measurement protocols. These protocols give evidence for the underlying complex behaviour of the network, a complexity which is based on the non-local information contained in the entanglement and which would not be present in the ‘classical limit’ of using local information only.     

Carbon Nanotube Quantum Capacitance for Nonlinear Terahertz Circuits

In this paper, analog circuit applications of a nonlinear carbon nanotube (CNT) quantum capacitance such as frequency doublers and mixers are proposed. We present a balanced circuit implementation and derive the transconductance conversion gain for the nonlinear CNT quantum capacitor circuit. The balanced topology results in robust circuit performance that is insensitive to extrinsic capacitances and parasitic resistances, and is immune to the resistance of metallic nanotubes that may be in the channel. The ballistic quantum capacitance is useful up to several terahertzs (THzs), making it suitable for low-noise THz sources. Additionally, the fundamental bandwidth and performance limitations imposed by the quantum conductance and inductance are discussed.     

Dynamical Quantum Phase Transitions

A sweep through a quantum phase transition by means of a time-dependent external parameter (e.g., pressure) entails non-equilibrium phenomena associated with a break-down of adiabaticity: At the critical point, the energy gap vanishes and the response time diverges (in the thermodynamic limit). Consequently, the external time-dependence inevitably drives the system out of equilibrium, i.e., away from the ground state, if we assume zero temperature initially. In this way, the initial quantum fluctuations can be drastically amplified and may become observable—especially for symmetry-breaking (restoring) transitions. By means of several examples, possible effects of these amplified quantum fluctuations are studied and universal features (such as freezing) are discussed.     

Superfluid, Superconducting, and Magnetic Ordering in Mesoscopic Quantum Dots

The nature of superfluid, superconducting, and magnetic ordering is elucidated for mesoscopic systems in which the single-particle level spacing is much larger than both the temperature and the critical temperature of ordering. Ordering is defined as a spontaneous breaking of symmetry, the gauge invariance and time reversal being by definition symmetries broken in superfluidity (superconductivity) and magnetism contexts, respectively. Superfluidity and superconductivity are realized in thermodynamic equilibrium states with a nonintegral average number of particles and are accompanied by the spontaneous breaking of time homogeneity. In Fermi systems, two types of superfluidity and superconductivity are possible which are characterized by the presence of pair or single-particle condensates. The latter is remarkable in that spontaneous breaking of fundamental symmetries such as spatial 2 rotation and double time reversal takes place. Possible experiments on metallic nanoparticles and ultracold atomic gases in magnetic traps are discussed.     

Novel Phase Behavior in Quantum Rotors

A system of quantum linear rotors in a crystal field is found to display a novel type of phase diagram. At a certain value of the crystal field a discontinuity point appears at the orientational phase transition line. As the crystal field increases this point splits into two critical points with a single-phase-state discontinuity (hole) between them. This remarkable feature is common both for a system where all angular momentum states are allowed and for one where the angular momentum is restricted to have even values despite the fact that general aspects of the transformations induced by the crystal field differ considerably for the two systems.