Quantization by Parts, Maximal Symmetric Operators, and Quantum Circuits

In the context of a generalized quantum theorywhich admits maximal symmetric operators as observables,we discuss a quantization scheme which cansystematically deal with what may be called quantumcircuits. The scheme, known as the method of quantizationby parts, has recently been applied to obtain a newderivation of the Josephson equation for thesupercurrent through a Josephson junction in asuperconducting circuit. This paper presents an application ofthis scheme to several circuit configurations, namely,from one branch to many-branch circuits. We also proposean experimental test on whether the condensate is always in a pure state, using a three-branchY-shape circuit.     

Josephson current carried by Andreev levels in superconducting quantum point contacts

The dc Josephson effect in a superconducting quantum point contact, where supercurrent flows through a small number of channels, is reviewed. The central role of Andreev levels is emphasized which carry the whole supercurrent in short symmetric Josephson junctions including tunnel junctions. A simple intuitive view of the dc Josephson effect in a quantum point contact is given in terms of multiple Andreev reflections. The quantization of the critical current in superconducting quantum point contacts is briefly discussed.     

External electric field control in the charge qubits including three Josephson junctions

Based on the standard canonical quantization principle, this paper gives the quantization scheme for the charge qubits mesoscopic circuit including three Josephson junctions coupled capacitively. By virtue of the Heisenberg equation, the time evolution of the phase difference operators across the polar plates and the number operators of the Cooper-pairs on the island are investigated and the modification of the Josephson equation is discussed. The time evolution of the phase difference operators is analysed when the Josephson junctions are irradiated by the external electrical field, which is referred to as also the obtainable controlling parameter.     

Dependence of the maximal superconducting current on the resonance frequency in a shunted Josephson junction

We have analyzed the phase dynamics and current–voltage characteristics of a Josephson junction shunted by an LC circuit. When the Josephson frequency ω _J becomes equal to the natural frequency ω_rc of the formed resonance circuit, the I–V curve acquires additional branches. We have studied the features of the rc branch and the superconducting circuit for different values of the resonance frequency. It is shown that the maximal superconducting current through the Josephson junction on the rc-branch depends on the resonance frequency and is determined by the closeness of the end point of the rc branch to the critical current. We have determined the dependence of the maximal superconducting current on the resonance frequency for different values of the dissipation parameters. The limiting value of the maximal superconducting current is independent (to within 1%) of the parameters of the system.     

Field operators and their spectral properties in finite-dimensional quantum field theory

In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states wasV=C ^r. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables(L ²(R^r,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We shall show that the isomorphism between the exponential ofV andL ²(R^r,dx) can be understood as the decomposition by generalized eigenvectors of field operators (Fourier transform).     

Algebraic quantization,good operators and fractional quantum numbers

The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the failure of the Ehrenfest theorem is clarified in terms of the already defined notion ofgood (andbad) operators. The analysis of constrained Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for quantum operators without classical analogue and for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring anomalous operators, non-equivalent quantization and the latter, fractional quantum numbers. These provide the rationale behind flux quantization in superconducting rings and Fractional Quantum Hall Effect, respectively.Work partially supported by the DGICYT.     

Effective gauge potentials induced by superconducting quantum circuits

We theoretically propose a scheme to induce non-Abelian and Abelian gauge potentials by the same superconducting circuit device. The level spacings of Cooper-pair box can be designed to resonantly match or largely detune from the mode frequencies of the one-dimensional transmission line resonators. We show the appearances of the effective gauge potentials via field quadrature operators. This scheme could help investigating the fundamental characteristics of the gauge theories with Josephson circuits.     

Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature

For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q=en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.     

中国超导电子学研究及应用进展

超导体的发现距今已有近110年了,高温超导体的发现也已经有30多年了.超导材料的电子学应用在最近一二十年取得了突破性进展.高温超导微波器件显示了比传统微波器件更优越的性能,已经在移动通信、雷达和一些特殊通信系统中取得了规模化应用.超导量子干涉器件以其磁场和电流测量的超高灵敏度,成为地质勘探、磁共振成像和生物磁成像等领域不可替代的手段.包括超导隧道结混频器、超导热电子混频器、超导转变沿探测器及超导单光子探测器等在内的超导传感器/探测器可以探测全波段的电磁波及各种宇宙辐射,具有接近量子极限的超高灵敏度,在地球物理、天体物理、量子信息技术、材料科学及生物医学等众多前沿领域发挥越来越重要的作用.超导参量放大器已经成为实现超导量子计算的关键器件.超导集成电路技术已被列入国际器件与系统技术路线图,成为后摩尔时代微电子领域的前沿阵地之一.在计量科学中,超导约瑟夫森效应及约瑟夫森结阵器件被广泛应用于量子电压基准和国际单位制基本单位的重新定义中.在当前的量子信息技术热潮中,超导电子学扮演重要角色,同时量子热潮也大力推动了超导电子学的发展.本文主要对近几年我国超导电子学研究和应用的现状与进展进行概括总结.     

BFV quantization on hermitian symmetric spaces

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.     

Superconducting Josephson structures with high linearity of transformation of magnetic signal into voltage

Possible approaches to the creation of Josephson superconducting circuits with a high linearity of transformation of a magnetic signal into voltage and a wide dynamic range have been described. Realization of such circuit by the creation of a special spatial inhomogeneity in chains of Josephson junctions and connection of these chains into a differential circuit has been considered. A new method for linearizing the transfer function of a single two-junction superconducting quantum interference device, which is an elementary cell of the chain, by connecting to it an additional loop playing the role of a nonlinear transformer of the magnetic flux has been described. For both approaches, the basic analytical expressions describing the synthesized circuits are presented. The data on numerical calculation and experimental measurements of samples produced on the basis of niobium technology with the critical current density of Josephson junctions of 4.5 kA/cm² are reported. The approaches developed in the work can serve as a basis for the creation of highly efficient gigahertz superconducting amplifiers for cellular and satellite communications and can be applied for improving the characteristics of SQUID-based devices.     

Effects of a concentric superconducting nanocylinder insertion on the electrodynamic response of a two-junction quantum interferometer

The dynamical equations of a circular superconducting quantum interferometer containing two equal conventional overdamped Josephson junctions on its two symmetric arms and a concentric nanocylinder, which entraps a quantized finite value of magnetic flux, are derived. It is shown that, for given values of the quantum interferometer and nanocylinder self-inductance and of the mutual induction coefficient between these concentric superconducting loops, the conventional quantum interference device behaves like a π-SQUID.     

More about Operators Generated by Partial Isometries

It has been suggested by several authors [1, 2] that quantum mechanical canonical transformations may be generalized by admitting partially isometric operators instead of unitary transformations used so far [3, 4]. It is known that it is possible to transform a Heisenberg couple into a corresponding one in a different Hilbert space. We shall show that the operators Q = VqV⁺ and P = VpV⁺ obtained in this way — which are unitarily equivalent to EqE and EpE, respectively, in the initial domain M of V onto which E projects — though symmetric in general will not be selfadjoint, and also present an example of this. Although it does not seem to be possible to settle the question of the existence of self-adjoint extensions definitely in the general case, the example of operators generated from the Schrödinger couple q and p shows the existence of such extensions having the spectrum of angle and z-component of angular momentum. Transducing the argument further we shall show that by choosing a different subspace N ? M ?? H it is well possible to generate the action and phase operator of the quantum mechanical harmonic oscillator with the correct spectrum.     

Macroscopic quantum phenomena in superfluids and superconductors

In this paper I will discuss the common macroscopic quantum phenomena in the three superfluid systems known in condensed matter, the superconducting state of a metal, the superfluid phase of liquid⁴He, and the superfluid phases of liquid³He. The discussed phenomena will be persistent currents and their decay, critical velocities and critical magnetic fields, quantization of magnetic flux and of circulation, the two-dimensional flux and vortex lattices, and eventually the Josephson effects.Invited paper at the International Conference on Macroscopic Quantum Phenomena, Smolenice Castle, Czechoslovakia, September 18–22, 1989.     

Distributed quantum computation with superconducting qubit via LC circuit using dressed states

A scheme is proposed where two superconducting qubits driven by a classical field interacting separately with two distant LC circuits connected by another LC circuit through mutual inductance,are used for implementing quantum gates.By using dressed states,quantum state transfer and quantum entangling gate can be implemented.With the help of the time-dependent electromagnetic field,any two dressed qubits can be selectively coupled to the data bus (the last LC circuit),then quantum state can be transferred from one dressed qubit to another and multi-mode entangled state can also be formed.As a result,the promising perspectives for quantum information processing of mesoscopic superconducting qubits are obtained and the distributed and scalable quantum computation can be implemented in this scheme.     

Efficient Symmetric Five-Party Quantum State Sharing of an Arbitrary <Emphasis Type="Italic">m</Emphasis>-Qubit State

We present an efficient symmetric scheme for five-party quantum state sharing of an arbitrary m-qubit state with 2m three-particle entangled states. The implementations of this scheme only need to exploit the CNOT gate operations and the single-particle measurements, instead of the three-particle GHZ-state measurements, which makes it more convenient in a practical application than some previous schemes. In addition, its total efficiency can approach the maximal value in theory.     

Classical topology and quantum states

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its C ^K - and C ^--structures) can be reconstructed using Gel’fand-Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed.     

超导量子干涉器件

超导现象是一种宏观量子现象.磁通量子化和约瑟夫森效应是两个最能体现这种宏观量子特性的物理现象.超导量子干涉器件(superconducting quantum interference device,SQUID)是利用这两个特性而形成的超导器件.SQUID器件在磁信号灵敏探测方面具有广泛的应用.本文简要介绍低温超导和高温超导SQUID器件的相关背景和发展现状以及应用领域.