An atomtronics transistor for quantum gates

We present a mechanism for quantum gates where the qubits are encoded in the population distribution of two-component ultracold atoms trapped in a species-selective triple-well potential. The gate operation is a specific application of a different design for an atomtronics transistor where inter-species interaction is used to control transport, and can be realized with either individual atoms or aggregates like Bose–Einstein condensates (BEC). We demonstrate the operational principle with a static external potential, and show feasible implementation with a smooth dynamical potential.     

Phase space representation of quantum dynamics

We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around one of the classical limits. We explicitly analyze expansions around three such limits: (i) corpuscular or Newtonian limit in the coordinate-momentum representation, (ii) wave or Gross-Pitaevskii limit for interacting bosons in the coherent state representation, and (iii) Bloch limit for the spin systems. We discuss both the semiclassical (truncated Wigner) approximation and further quantum corrections appearing in the form of either stochastic quantum jumps along the classical trajectories or the nonlinear response to such jumps. We also discuss how quantum jumps naturally emerge in the analysis of non-equal time correlation functions. This representation of quantum dynamics is closely related to the phase space methods based on the Wigner-Weyl quantization and to the Keldysh technique. We show how such concepts as the Wigner function, Weyl symbol, Moyal product, Bopp operators, and others automatically emerge from the Feynmann's path integral representation of the evolution in the Heisenberg representation. We illustrate the applicability of this expansion with various examples mostly in the context of cold atom systems including sine-Gordon model, one- and two-dimensional Bose-Hubbard model, Dicke model and others.     

Deriving a differential equation for the spin-spin correlation in Ising systems

Summary The equipartition theorem and the high-temperature expansion are used to derive a differential equation for the spin-spin correlation in Ising systems. Some applications of this equation including improved upper bound on the three-dimensional transition temperature and correlation length are discussed. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

束流物理学的量子方法初探

 量子束流物理学是近年来发展起来的处理束流传输的全新方法，它是经典束流物理学的有益补充。介绍了量子束流物理学的热波模型和基于狄拉克方程的相对论电子束磁透镜量子理论，并与经典束流物理学方法进行了比较。     

Efimov physics in cold atoms

Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and the scattering length. In this review, we summarize the universal results that are currently known. We also summarize the experimental information that is currently available with an emphasis on 3-atom loss processes.     

Scattering models for ultracold atoms

We present a review of scattering models that can be used to describe the low-energy behavior of identical bosonic atoms. In the simplest models, the only degrees of freedom are atoms in the same spin state. More elaborate models have other degrees of freedom, such as atoms in other spin states or diatomic molecules. The parameters of the scattering models are specified by giving the S-wave phase shifts for scattering of atoms in the spin state of primary interest. The models are formulated as local quantum field theories and the renormalization of their coupling constants is determined. Some of the parameters can be constrained by renormalizability or by the absence of negative-norm states. The Green’s functions that describe the evolution of two-atom states are determined analytically. They are used to determine the T-matrix elements for atom-atom scattering and the binding energies of diatomic molecules. The scattering models all exhibit universal behavior as the scattering length in a specific spin state becomes large.     

Quantum Stochastic Walk models for quantum state discrimination

Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We consider the problem of quantum state discrimination on such a system, and we solve it by optimizing the network topology weights. Finally, we test it on different quantum network topologies and compare it with optimal theoretical bounds.     

Performance comparison between classical and quantum control for a simple quantum system

Brańczyk et al. pointed out that the quantum control scheme is superior to the classical control scheme for a simple quantum system using simulation [A.M. Brańczyk, P.E.M.F. Mendonca, A. Gilchrist, A.C. Doherty, S.D. Barlett, Quantum control theory of a single qubit, Physical Review A 75 (2007) 012329 or arXiv e-print quant-ph/0608037]. Here we rigorously prove the result. Furthermore we will show that any quantum operation does not universally “correct” the dephasing noise.     

Low temperature expansion for continuous-spin Ising models

We consider general ferromagnetic spin systems with finite range interactions and an even single-spin distribution of compact support on IR. It is shown under mild assumptions on the single-spin distribution that a low temperature expansion, in powers ofT, for the free energy and the correlation functions is asymptotic. We also prove exponential clustering in the pure phases and analyticity of the free energy and of the correlation functions in the reciprocal temperature for Re large.Supported in part by N.S.F. Grant No. Phy. 78-15920 and MCS 78-01885On leave from: Départment de Physique Théorique, Université de Louvin, BelgiumSupported in part by the Swiss National Foundation for Scientific Research     

Macroscopic instructions vs microscopic operations in quantum circuits

In many experiments on microscopic quantum systems, it is implicitly assumed that when a macroscopic procedure or “instruction” is repeated many times – perhaps in different contexts – each application results in the same microscopic quantum operation. But in practice, the microscopic effect of a single macroscopic instruction can easily depend on its context. If undetected, this can lead to unexpected behavior and unreliable results. Here, we design and analyze several tests to detect context-dependence. They are based on invariants of matrix products, and while they can be as data intensive as quantum process tomography, they do not require tomographic reconstruction, and are insensitive to imperfect knowledge about the experiments. We also construct a measure of how unitary (reversible) an operation is, and show how to estimate the volume of physical states accessible by a quantum operation.     

Phase controllable dynamical localization of a quantum particle in a driven optical lattice

The Dunlap–Kenkre (DK) result states that dynamical localization of a driven quantum particle in a periodic lattice happens when the ratio of the field magnitude to the field frequency of the diagonal drive is a root of the ordinary Bessel function of order 0. This has been experimentally verified. A generalization of the DK result is presented here. The hitherto considered DK model contains only the diagonal forcing. In the present extended version of the DK model we consider both off-diagonal and diagonal driving fields with different frequencies and a definite relative phase between them. We analytically show that new dynamical localizations conditions exist where an important role is played by the relative phase. In appropriate limits our results reduce to DK result.     

Critical fluctuations for quantum mean-field models

We propose a Ginzburg-Landau-type approximation for the local Gibbs states for quantum mean-field models that leads to the exact thermodynamics. Using this approach, we compute the spin fluctuations for some spin-1/2 models. At the critical temperature we find explicitly the distribution function showing abnormal fluctuations.On leave from the University of Torun, Poland.     

稀薄量子系统中的接触量和普适关系

对接触量和普适关系的发现是超冷原子物理中的一个重大理论突破。自檀时钠于2005年首次指出接触量这个概念以来,对普适关系的研究已经成为冷原子物理中的一个重要课题,并对其他相关的领域产生了重大的影响。文章介绍了什么是接触量和普适关系,以及普适关系的来源,并讨论在这个研究方向上最新的一些进展,包括高分波散射的接触量和接触量谱。     

Two-dimensional lattice gauge theories with superconducting quantum circuits

A quantum simulator of U(1)$U\left(1\right)$ 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.     

An axiomatic measure of one-way quantum information

I introduce an algorithm to detect one-way quantum information between two interacting quantum systems, i.e. the direction and orientation of the information transfer in arbitrary quantum dynamics. I then build an information-theoretic quantifier of one-way information which satisfies a set of desirable axioms. In particular, it correctly evaluates whether correlation implies one-way quantum information, and when the latter is transferred between uncorrelated systems. In the classical scenario, the quantity measures information transfer between random variables. I also generalize the method to identify and rank concurrent sources of quantum information flow in many-body dynamics, enabling to reconstruct causal patterns in complex networks.     

Quantum ratchet driven by broadband perturbation

Motion of an atomic ensemble trapped into a deep optical lattice is considered. We propose a novel approach to construct an atomic ratchet by superimposing two additional lattices whose amplitudes are small and subjected to broadband modulation. The broadband modulation is modeled by means of harmonic noise. Directed atomic transport occurs with the properly chosen phase shift between the signals modulating the amplitudes of the additional lattices. It is shown that efficiency of the ratchet depends non-monotonously on the parameter determining the spectral width of modulating signals.     

Resonant scheme for realizing quantum phase gates for two separate atoms via coupled cavities

We propose a scheme for realizing conditional quantum phase gates for two atoms that are distributed in two coupled cavities. Due to the resonant interaction in temporal evolution of the entire system, the gate operation time is greatly reduced as compared with that of the nonresonant schemes. We study the influence of imperfections in the interaction and the effect of decoherence and find the gate to be robust. We discuss the issue related to the practical implementation and show that the gate is accessible within the current cavity QED technology.     

Implementing phase-covariant cloning in circuit quantum electrodynamics

An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.