Quantum phase diagram of granular superconducting quantum dots array

We study the quantum phase diagram of granular superconducting quantum dots (GSQD) array. We implement the physics of granularity by considering site dependent Josephson couplings, on-site charging energies and the intersite interactions. We predict dimer density wave and staggered phases at the insulating state for higher order commensurability. Several parts of the quantum phase diagram of GSQD are in contrast with the clean superconducting quantum dots array. We also obtain the superconducting phase of GSQD. We develop the theory for weak tunneling conductance and the Coulomb energy is smaller than the superconducting gap.     

Quantum phase transitions and vortex dynamics in superconducting networks

Josephson-junction arrays are ideal model systems to study a variety of phenomena such as phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on the quantum dynamical properties of low-capacitance Josephson-junction arrays. The two characteristic energy scales in these systems are the Josephson energy, associated with the tunneling of Cooper pairs between neighboring islands, and the charging energy, which is the energy needed to add an extra electron charge to a neutral island. The phenomena described in this review stem from the competition between single-electron effects with the Josephson effect. They give rise to (quantum) superconductor–insulator phase transitions that occur when the ratio between the coupling constants is varied or when the external fields are varied. We describe the dependence of the various control parameters on the phase diagram and the transport properties close to the quantum critical points. On the superconducting side of the transition, vortices are the topological excitations. In low-capacitance junction arrays these vortices behave as massive particles that exhibit quantum behavior. We review the various quantum–vortex experiments and theoretical treatments of their quantum dynamics.     

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.     

Quantum phase transition in one-dimensional arrays of resistively shunted small Josephson junctions

We have observed a superconductor-insulator transition in one-dimensional (1D) arrays of small Josephson junctions by changing both the resistance R(S) of normal metal resistors shunting each junction and the ratio of the Josephson coupling energy E(J) to the charging energy E(C). The phase boundary lies at R(S) approximately R(Q) (R(Q) identical with h/4e(2)=6.45 kOmega) when E(J)/E(C) is smaller than about unity. We discuss the obtained phase diagram in terms of theoretical models of the dissipation-driven quantum phase transition, with particular attention to differences from 2D arrays.     

Renormalization and quantum effects in a two-dimensional planar model

We examine the influence of the charging energy on the vortex unbinding transition in two-dimensional arrays of Josephson junctions. The fluctuations of the phase about the time-dependent vortex solutions are treated within the self-consistent harmonic approximation. A new relation between the renormalized vortex unbinding temperature T_c and the charging energy U is derived. We predict a continuous drop of T_c at a critical value of U well below the spurious first order transition of the rigidity constant. The results are interpreted as a quantum assisted dissociation of vortex pairs.     

Variable electrostatic transformer: controllable coupling of two charge qubits

We propose and investigate a novel method for the controlled coupling of two Josephson charge qubits by means of a variable electrostatic transformer. The value of the coupling capacitance is given by the discretized curvature of the lowest energy band of a Josephson junction, which can be positive, negative, or zero. We calculate the charging diagram of the two-qubit system that reflects the transition from positive to negative through vanishing coupling. We also discuss how to implement a phase gate making use of the controllable coupling.     

Phase escape of current-biased Josephson junctions

Switching current distributions of an Nb/Al--AlO_x/Nb Josephson junction are measured in a temperature range from 25~mK to 800~mK. We analyse the phase escape properties by using the theory of Larkin and Ovchinnikov (LO) which takes discrete energy levels into account. Our results show that the phase escape can be well described by the LO approach for temperatures near and below the crossover from thermal activation to macroscopic quantum tunneling. These results are helpful for further study of macroscopic quantum phenomena in Josephson junctions where discrete energy levels need to be considered.     

Phase Sensitivity of Atomic Josephson Junctions with a Bosonic Species Confined by a Double-Well Potential

We investigate the reciprocal of the mean quantum Fisher information per particle (RMQFIP) and phase sensitivity of atomic Josephson junctions with a bosonic species confined by a double-well potential. Here we are focus on the Rabi oscillation energy’s influence on RMQFIP and phase sensitivity. The better quantum entanglement and phase sensitivity may be achieved by decreasing the Rabi oscillation energy.     

Quantum dynamics of superconducting point contacts: chiral anomaly,Landau–Zener transitions,and all that

Quantum effects in the dynamics of the Josephson phase difference in Josephson junctions with large electron transparency D are studied in the adiabatic regime, when the characteristic charging energyE_C of the junction is much smaller than the superconducting energy gap Δ. In isolated junctions, quantum phase fluctuations are large and manifest themselves as Coulomb blockade of Cooper pair tunneling. The amplitude of the Coulomb blockade oscillations is calculated for single-mode junctions with arbitrary D. In particular, it is shown that the chiral anomaly completely suppresses Coulomb blockade in ballistic junctions with D =  1, and the suppression process at D →  1 can be described as the Landau–Zener transition in imaginary time. In the regime when quantum phase fluctuations are small, they lead to quantum decay of supercurrent states due to macroscopic quantum tunneling of phase through the Josephson potential barrier. The decay rate is found in the nearly-ballistic junctions.     

Coulomb effects in a ballistic one-channel S-S-S device

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E _C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q _x =CV _g . Zh. éksp. Teor. Fiz. 114, 640–653 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor     

Coexisting Condensates of Weakly Interacting Bose Gas in a Harmonic Trap

We study particles in a vortex state driven to a core state with lower energy and zero angular momentumby the trap potential asymmetries. We find that at T = 0 when the role of the thermal gas can be ignored, there will becoexisting condensates. We also calculate the fluctuation of the number difference and argue that in certain range of theparameters the state of the whole system is the macroscopic quantum self-trapping in the Josephson tunnelling regime.     

REDUCED QUANTUM FLUCTUATION IN MESOSCOPIC JOSEPHSON JUNCTION WITH SCHR?DINGER-CAT STATE FIELD

We consider the system of a mesoscopic Josephson junction interacting with a quantized radiation field and investigate the fluctuation properties of the junction variables with time evolution. Our results show that, due to the quantum entanglement between the field and junction, the mesoscopic Josephson junction subsystem can exhibit squeezing behavior.     

Coexisting Condensates of Weakly Interacting Bose Gas in a Harmonic Trap

We study particles in a vortex state driven to a core state with lower energy and zero angular momentum by the trap potential asymmetries. We find that at T=0 when the role of the thermal gas can be ignored, there will be coexisting condensates. We also calculate the fluctuation of the number difference and argue that in certa/n range of the parameters the state of the whole system is the macroscopic quantum serf-trapping in the Josephson tunnelling regime.     

Electrically tunable macroscopic quantum tunneling in a graphene-based Josephson junction

Stochastic switching-current distribution in a graphene-based Josephson junction exhibits a crossover from the classical to quantum regime, revealing the macroscopic quantum tunneling of a Josephson phase particle at low temperatures. Microwave spectroscopy measurements indicate a multiphoton absorption process occurring via discrete energy levels in washboard potential well. The crossover temperature for macroscopic quantum tunneling and the quantized level spacing are controlled with the gate voltage, implying its potential application to gate-tunable superconducting quantum bits.     

Josephson effect between superconducting nanograins with discrete energy levels

We investigate the Josephson effect between two coupled superconductors, coupled by the tunneling of pairs of electrons, in the regime that their energy level spacing is comparable to the bulk superconducting gap, but neglecting any charging effects. In this regime, BCS theory is not valid, and the notion of a superconducting order parameter with a well-defined phase is inapplicable. Using the density matrix renormalization group, we calculate the ground state of the two coupled superconductors and extract the Josephson energy. The Josephson energy is found to display a reentrant behavior (decrease followed by increase) as a function of increasing level spacing. For weak Josephson coupling, a tight-binding approximation is introduced, which illustrates the physical mechanism underlying this reentrance in a transparent way. The DMRG method is also applied to two strongly coupled superconductors and allows a detailed examination of the limits of validity of the tight-binding model.Received: 8 September 2003, Published online: 28 May 2004PACS: 74.20.-z Theories and models of superconducting state - 74.78.-w Superconducting films and low-dimensional structures - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

Josephson current in carbon nanotubes with spin-orbit interaction

We demonstrate that curvature-induced spin-orbit coupling induces a 0-π transition in the Josephson current through a carbon nanotube quantum dot coupled to superconducting leads. In the noninteracting regime, the transition can be tuned by applying a parallel magnetic field near the critical field where orbital states become degenerate. Moreover, the interplay between charging and spin-orbit effects in the Coulomb blockade and cotunneling regimes leads to a rich phase diagram with well-defined (analytical) boundaries in parameter space. Finally, the 0 phase always prevails in the Kondo regime. Our calculations are relevant in view of recent experimental advances in transport through ultraclean carbon nanotubes.     

Quantum coherence in a superfluid Josephson junction

We report a new kind of experiment in which we take an array of nanoscale apertures that form a superfluid (4)He Josephson junction and apply quantum phase gradients directly along the array. We observe collective coherent behaviors from aperture elements, leading to quantum interference. Connections to superconducting and Bose-Einstein condensate Josephson junctions as well as phase coherence among the superfluid aperture array are discussed.     

Effect of charging energy on transition temperature of granular superconductors

The effect of the zero-point fluctuations of the phase on the transition temperature T_c of a granular superconductor is calculated using a model which takes into account the short-range part of the charging energy. A self-consistent mean field theory predicts a critical value of the ratio of the Josephson coupling constant to the charging energy and the existence of two values of T_c, indicating the possibility of reentrance into normal state at the lower one.