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Showing papers on "Quantum published in 1997"


Journal ArticleDOI
TL;DR: In this paper, a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network was proposed, which employs special laser pulses that excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wave packet that will enter a cavity at receiving node and be absorbed by an atom there with unit probability.
Abstract: We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network. The transmission protocol employs special laser pulses that excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wave packet that will enter a cavity at the receiving node and be absorbed by an atom there with unit probability. Implementation of our scheme would enable reliable transfer or sharing of entanglement among spatially distant atoms.

1,992 citations


Journal ArticleDOI
TL;DR: In this paper, a scaling analysis of Josephson-junction arrays and quantum Hall-effect systems is presented, where the authors derive scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite size scaling.
Abstract: A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite-temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of such systems, which takes the form of the classical statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations. Using these ideas, a scaling analysis of experiments on Josephson-junction arrays and quantum-Hall-effect systems is presented.

971 citations


Journal ArticleDOI
TL;DR: In this paper, the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions, were considered.
Abstract: We consider the quantum dynamics of a neutral atom Bose-Einstein condensate in a double-well potential, including many-body hard-sphere interactions. Using a mean-field factorization we show that the coherent oscillations due to tunneling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence.

864 citations


Journal ArticleDOI
TL;DR: In this paper, the authors give an explicit way to experimentally determine the evolution operators which completely describe the dynamics of a quantum-mechanical black box: an arbitrary open quantum system.
Abstract: We give an explicit way to experimentally determine the evolution operators which completely describe the dynamics of a quantum-mechanical black box: an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible and illustrate the general theory by considering specifically one-and two-quantum-bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication and computation systems.

834 citations


Book
04 Dec 1997
TL;DR: 1. Foundations 2. Coherent interactions 3. Operators and states 4. Quantum statistics of fields 5. Dissipative processes 6. Dressed states.
Abstract: 1. Foundations 2. Coherent interactions 3. Operators and states 4. Quantum statistics of fields 5. Dissipative processes 6. Dressed states Appendices Selected bibliography Index 1. Foundations 2. Coherent interactions 3. Operators and states 4. Quantum statistics of fields 5. Dissipative processes 6. Dressed states Appendices Selected bibliography Index

732 citations


Journal ArticleDOI
TL;DR: In this paper, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy.
Abstract: The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.

571 citations


Journal ArticleDOI
TL;DR: In this article, a semiclassical approach is presented that allows us to extend the usual Van Vleck-Gutzwiller formulation to the description of nonadiabatic quantum dynamics on coupled potential energy surfaces.
Abstract: A semiclassical approach is presented that allows us to extend the usual Van Vleck--Gutzwiller formulation to the description of nonadiabatic quantum dynamics on coupled potential-energy surfaces. Based on Schwinger's theory of angular momentum, the formulation employs an exact mapping of the discrete quantum variables onto continuous degrees of freedom. The resulting dynamical problem is evaluated through a semiclassical initial-value representation of the time-dependent propagator. As a first application we have performed semiclassical simulations for a spin-boson model, which reproduce the exact quantum-mechanical results quite accurately.

521 citations


Journal ArticleDOI
TL;DR: In this paper, an exact trace formula for the quantum spectrum is developed and used to investigate the origin of the connection between random matrix theory and the underlying chaotic classical dynamics, which is at the forefront of the research in quantum chaos and related fields.
Abstract: We quantize graphs (networks) which consist of a finite number of bonds and nodes. We show that their spectral statistics is well reproduced by random matrix theory. We also define a classical phase space for the graph, where the dynamics is mixing and the periodic orbits (loops on the graph) proliferate exponentially. An exact trace formula for the quantum spectrum is developed and used to investigate the origin of the connection between random matrix theory and the underlying chaotic classical dynamics. Being an exact theory, and due to its relative simplicity, it offers new insights into this problem which is at the forefront of the research in quantum chaos and related fields.

434 citations


Journal ArticleDOI
TL;DR: In this paper, a low-capacitance Josephson junction array in the parameter range where single charges can be controlled is suggested as possible physical realizations of the elements which have been considered in the context of quantum computers.
Abstract: Low-capacitance Josephson junction arrays in the parameter range where single charges can be controlled are suggested as possible physical realizations of the elements which have been considered in the context of quantum computers. We discuss single and multiple quantum-bit systems. The systems are controlled by applied gate voltages, which also allow the necessary manipulation of the quantum states. We estimate that the phase-coherence time is sufficiently long for experimental demonstration of the principles of quantum computation.

431 citations


Journal ArticleDOI
30 Jan 1997-Nature
TL;DR: In this article, the phase evolution within a resonance of a quantum dot can be explained by a model that ignores the interactions between the electrons within the dot, and the phase behaviour is identical for all resonances, and there is a sharp jump of the phase between successive resonance peaks.
Abstract: The transport properties of electronic devices are usually characterized on the basis of conductance measurements. Such measurements are adequate for devices in which transport occurs incoherently, but for very small devices—such as quantum dots1,2—the wave nature of the electrons plays an important role3. Because the phase of an electron's wavefunction changes as it passes through such a device, phase measurements are required to characterize the transport properties fully. Here we report the results of a double-slit interference experiment which permits the measurement of the phase-shift of an electron traversing a quantum dot. This is accomplished by inserting the quantum dot into one arm of an interferometer, thereby introducing a measurable phase shift between the arms. We find that the phase evolution within a resonance of the quantum dot can be accounted for qualitatively by a model that ignores the interactions between the electrons within the dot. Although these electrons must interact strongly, such interactions apparently have no observable effect on the phase. On the other hand, we also find that the phase behaviour is identical for all resonances, and that there is a sharp jump of the phase between successive resonance peaks. Adequate explanation of these features may require a model that includes interactions between electrons.

424 citations


Journal ArticleDOI
TL;DR: In this paper, the authors argue that any reference to quantum yields or quantum efficiencies in a heterogeneous medium is ill-advised unless the actual number of photons absorbed by the light harvester (the photocatalyst) has been determined.
Abstract: Quantum yield and quantum efficiency (QY) as used in heterogeneous photocatalysis (solid/liquid or solid/gas systems) have too often been used incorrectly to mean the ratio of the rate of a given event to the rate of incident photons impinging on the (external) rector walls, typically for broadband radiation. There is little accord on how to express process efficiency. At times QY is defined, often ill-defined, and more frequently workers fail to describe how it was assessed. This has led to much confusion in the literature, not only because of the different meaning of QY from that in homogeneous photochemistry, but also because this method of describing photon efficiency precludes a comparison of results from different laboratories because of the variations in light sources, reactor geometries, and overall experimental conditions. It cannot be overemphasized that the reported QY is an apparent quantum yield, indeed a lower limit of the true quantum yield. This position paper addresses this issue, and argues that any reference to quantum yields or quantum efficiencies in a heterogeneous medium is ill-advised unless the actual number of photons absorbed by the light harvester (the photocatalyst) has been determined. The extent of light scattering in a solid/liquid heterogeneous medium is significant. A practical and simple alternative for comparing process efficiencies was recently suggested by defining a relative photonic efficiency ζr. A quantum yield can subsequently be determined from ζr, as φ = ζφphenol, where φphenol is the quantum yield for the photocatalyzed oxidative disappearance of phenol (a standard secondary actinometer) using Degussa P-25 TiO2 as the standard catalyst material.

Posted Content
TL;DR: In this paper, the authors propose quantum versions of finite-state and push-down automata, and regular and context-free grammars, and find analogs of classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form.
Abstract: To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finite-state and push-down automata, and regular and context-free grammars. We find analogs of several classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form. We also show that there are quantum context-free languages that are not context-free.

Journal ArticleDOI
TL;DR: In this article, a scheme for reliable transfer of quantum information between two atoms via an optical fiber in the presence of decoherence is proposed, which is based on performing an adiabatic passage through two cavities which remain in their respective vacuum states during the whole operation.
Abstract: A scheme is proposed which allows for reliable transfer of quantum information between two atoms via an optical fibre in the presence of decoherence. The scheme is based on performing an adiabatic passage through two cavities which remain in their respective vacuum states during the whole operation. The scheme may be useful for networking several ion-trap quantum computers, thereby increasing the number of quantum bits involved in a computation.

Journal ArticleDOI
TL;DR: In this paper, the quantum erasure channel and related channels with and without the assistance of a two-way classical side channel were derived and compared to the depolarizing channel, for which only upper and lower bounds on the capacities are known.
Abstract: The quantum analog of the classical erasure channel provides a simple example of a channel whose asymptotic capacity for faithful transmission of intact quantum states, with and without the assistance of a two-way classical side channel, can be computed exactly. We derive the quantum and classical capacities for the quantum erasure channel and related channels, and compare them to the depolarizing channel, for which only upper and lower bounds on the capacities are known.

Journal ArticleDOI
11 Dec 1997-Nature
TL;DR: In this paper, the authors report the control of interference in optical absorption by quantum mechanical tunnelling, which can provide a way to make semiconductor lasers operate without population inversion.
Abstract: The sign of the interference (constructive or destructive) between quantum-mechanical paths depends on the phase difference between the paths. In the Fano effect1 two optical paths from the ground state of a system — one direct and one mediated by a resonance — to a state in an energy continuum interfere to produce an asymmetric absorption spectrum that falls to zero near the absorption maximum. Zero absorption occurs as the wavelength is scanned across the resonance, at a photon energy corresponding to a 180 ° phase difference between the paths. Similar interference effects occur when two absorption paths are mediated by two different states, and they provide the basis for lasers that operate without a population inversion2,3,4,5,6,7. Here we report the control, by quantum mechanical tunnelling, of interference in optical absorption. The two intermediate states are resonances that arise from the mixing of the states in two adjacent semiconductors quantum wells, which are broadened by tunnelling into the same energy continuum through an ultra-thin potential-energy barrier. Inverting the direction of tunnelling by reversing the position of the barrier with respect to the two quantum wells changes the interference from destructive to constructive, as predicted theoretically. This effect might provide a way to make semiconductor lasers without population inversion8.

Journal ArticleDOI
TL;DR: In this paper, the authors combine the surface hopping idea with the mean-field approximation for classical paths to model complex quantum-classical processes, and the method is shown to outperform the methods based on an adiabatic force.
Abstract: Molecular dynamics simulations of many degree of freedom systems are often comprised of classical evolutions on quantum adiabatic energy surfaces with intermittent instantaneous hops from one surface to another. However, since quantum transitions are inherently nonadiabatic processes, the adiabatic approximation underlying the classical equations of motion does not hold in the regions where quantum transitions take place, and the restriction to classical trajectories for adiabatic quantum states is an approximation. Alternatives which employ classical paths that account more fully for nonadiabaticity can be computationally expensive and algorithmically complicated. Here, we propose a new method, which combines the surface hopping idea with the mean-field approximation for classical paths. Applied to three test systems, the method is shown to outperform the methods based on an adiabatic force without significant extra effort. This makes it an appealing alternative for modeling complex quantum–classical processes.

Journal ArticleDOI
TL;DR: In this article, a fast and robust iterative method for obtaining selfconsistent solutions to the coupled system of Schrodinger's and Poisson's equations is presented, where a simple expression describing the dependence of the quantum electron density on the electrostatic potential is derived.
Abstract: A fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrodinger’s and Poisson’s equations is presented. Using quantum mechanical perturbation theory, a simple expression describing the dependence of the quantum electron density on the electrostatic potential is derived. This expression is then used to implement an iteration scheme, based on a predictor-corrector type approach, for the solution of the coupled system of differential equations. We find that this iteration approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the approach by presenting an example for the calculation of the two-dimensional bound electron states within the cross section of a GaAs-AlGaAs based quantum wire. For this example, the convergence is six times faster by applying our predictor-corrector approach compared to a corresponding underrelaxation algorithm.

Journal ArticleDOI
TL;DR: In this paper, the impact of quantum decoherence and zero point motion on non-adiabatic transition rates in condensed matter systems is studied in relation to nonadabatic molecular dynamics (MD) techniques.
Abstract: The impact of quantum decoherence and zero point motion on non-adiabatic transition rates in condensed matter systems is studied in relation to non-adiabatic (NA) molecular dynamics (MD) techniques. Both effects, and decoherence in particular, strongly influence the transition rate, while neither is accounted for by straightforward quantum-classical approaches. Quantum corrections to the quantum-classical results are rigorously introduced based on Kubo’s generating function formulation of Fermi’s Golden rule and the frozen Gaussian approximation for the nuclear wave functions. The development provides a one-to-one correspondence between the decoherence function and the Franck–Condon factor. The decoherence function defined in this paper corrects an error in our previous work [J. Chem. Phys. 104, 5942 (1996)]. The relationship between the short time approach and the real time NA MD is investigated and a specific prescription for incorporating quantum decoherence into NA simulations is given. The proposed s...

Journal ArticleDOI
TL;DR: In this article, a survey and analysis of recent work on topological phases with polarization of light is presented, which has revealed several counterintuitive features of such phase shifts such as 2 nπ anholonomies, nonlinear and discontinuous behaviour originating from high singularities, peculiar spectral dependence, etc.

Journal ArticleDOI
TL;DR: In this article, it was shown that a Schrodinger cat state can be generated in a resonator with an oscillating wall, and the effects due to the environmental couplings with this nonlinear system were considered by developing an operator perturbation procedure to solve the master equation for the field mode density operator.
Abstract: It is shown that because of the radiation pressure a Schr\"odinger cat state can be generated in a resonator with an oscillating wall. The optomechanical control of quantum macroscopic coherence and its detection is taken into account by introducing new cat states. The effects due to the environmental couplings with this nonlinear system are considered by developing an operator perturbation procedure to solve the master equation for the field mode density operator.

Journal ArticleDOI
05 Dec 1997-Science
TL;DR: The formation of bonding and antibonding states between two such "artificial atoms" was studied as a function of quantum dot separation by microscopic photoluminescence (PL) spectroscopy.
Abstract: Atomically precise quantum dots of mesoscopic size have been fabricated in the gallium arsenide-aluminum gallium arsenide material system by cleaved edge overgrowth, with a high degree of control over shape, composition, and position. The formation of bonding and antibonding states between two such "artificial atoms" was studied as a function of quantum dot separation by microscopic photoluminescence (PL) spectroscopy. The coupling strength within these "artificial molecules" is characterized by a systematic dependence of the separation of the bonding and antibonding levels, and of the PL linewidth, on the "interatomic" distance. This model system opens new insights into the physics of coupled quantum objects.

Journal ArticleDOI
TL;DR: The time-dependent quantum mechanical approach has emerged as a powerful and a practical computational tool for studying a variety of gas-phase chemical problems in recent years as mentioned in this paper, with special emphasis on methodology and application to reactive scattering, photo-excitation processes and gas-surface interaction.

Journal ArticleDOI
01 Jan 1997
TL;DR: In this paper, the eigenvalue spectrum of Dirichlet Laplacians is studied for open regions R c Rn which are tubes outside of a bounded region (quantum waveguides).
Abstract: We study the eigenvalue spectrum of Dirichlet Laplacians which model quantum waveguides associated with tubular regions outside of a bounded domain. Intuitively, our principal new result in two dimensions asserts that any domain R obtained by adding an arbitrarily small "bump" to the tube a0 = R x ( 0 , l ) (i.e., 2 no, R C W2 open and connected, R = Ro outside a bounded region) produces a t least one positive eigenvalue below the essential spectrum [7r2, m) of the Dirichlet Laplacian -A:. For /R\Ro/ sufficiently small ( 1 . / abbreviating Lebesgue measure), we prove uniqueness of the ground state En of -A: and derive the "weak coupling" result En = 7r2 + 0(/R\C20/3) using a Birman-Schwinger-type T ~ / Q \ R O / ~ analysis. As a corollary of these results we obtain the following surprising fact: Starting from the tube flo with Dirichlet boundary conditions at aRo, replace the Dirichlet condition by a Neumann boundary condition on an arbitrarily small segment (a, b) x (1). a < b, of aRo. If H(a , b) denotes the resulting Laplace operator in L ' (R~) , then H(a , b) has a discrete eigenvalue in [7r2/4,7r2) no matter how small lb a1 > 0 is. Our goal in this paper is to study the bound state spectra of the Dirichlet Laplacian -A: for open regions R c Rn which are tubes outside of a bounded region (quantum waveguides). (Following the traditional notation in quantum physics, we denote the Laplacian by -A as opposed to A in the following.) In particular, let RocR2 be defined by Ro=R x (0 , l ) . Consider open connected sets R such that: (i) For some R > 0, R n{x E R2 I 1x1 > R) =Ron{x E R2 I 1x1 > R). (ii) R, cR, R, #a. Because of condition (i), (1) aess(-~:) = fless(-Ag,) = [.ir2, 00). Then one of our main goals will be to prove Received by the editors November 13, 1995. 1991 Mathematics Subject Classification. Primary 81Q10, 35P15; Secondary 47A10, 35510.

Journal ArticleDOI
TL;DR: The transfer matrix density-matrix renormalization-group method for one-dimensional quantum lattice systems has been developed by considering the symmetry property of the transfer matrix and introducing the asymmetric reduced density matrix as mentioned in this paper.
Abstract: The transfer-matrix density-matrix renormalization-group method for one-dimensional quantum lattice systems has been developed by considering the symmetry property of the transfer matrix and introducing the asymmetric reduced density matrix. We have evaluated a number of thermodynamic quantities of the anisotropic spin-1/2 Heisenberg model using this method and found that the results agree very accurately with the exact ones. The relative errors for the spin susceptibility are less than ${10}^{\ensuremath{-}3}$ down to $T=0.01J$ with 80 states kept.

Journal ArticleDOI
12 Sep 1997-Science
TL;DR: In this chapter, Shor's proposed algorithm for finding prime factors in polynomial instead of exponential time is proposed and described.
Abstract: Quantum computing—the manipulation of a quantum mechanical system to do information processing—has attracted considerable recent attention, largely triggered by Shor's proposed algorithm for finding prime factors in polynomial instead of exponential time ([1][1]). The importance of this problem

Journal ArticleDOI
TL;DR: In this paper, centroid molecular dynamics and path integral molecular dynamics have been applied to study and modify an empirical flexible model for water, the simple point charge/flexible (SPC/F) model.
Abstract: Path integral molecular dynamics and centroid molecular dynamics have been applied to study and modify an empirical flexible model for water, the simple point charge/flexible (SPC/F) model. The quantum structural, thermodynamic and dynamical properties have been calculated and compared to their classical counterparts, as well as to experiment. The path integral molecular dynamics simulations demonstrate that the quantum liquid is less structured and exhibits less hydrogen bonding than its classical analog. Quantization also leads to a lower dielectric constant, relative to the corresponding classical value. Centroid molecular dynamics has been used to calculate single molecule time correlation functions, the Debye dielectric relaxation correlation function, and the power spectrum for the quantum model. These time correlation functions decay more rapidly than the classical ones, indicating that nuclear rotational tunneling occurs in the liquid. The power spectrum of the quantized liquid also exhibits red s...

Journal ArticleDOI
TL;DR: This work demonstrates alternative codes that correct just amplitude damping errors that allow, for example, a $t=1$, $k=1$ code using effectively $n=4.6$.
Abstract: Traditional quantum error correction involves the redundant encoding of $k$ quantum bits using $n$ quantum bits to allow the detection and correction of any $t$ bit error. The smallest general $t=1$ code requires $n=5$ for $k=1$. However, the dominant error process in a physical system is often well known, thus inviting the following question: Given a specific error model, can more efficient codes be devised? We demonstrate alternative codes that correct just amplitude damping errors that allow, for example, a $t=1$, $k=1$ code using effectively $n=4.6$. Our scheme is based on using bosonic states of photons in a finite number of optical modes. We present necessary and sufficient conditions for the codes and describe construction algorithms, physical implementation, and performance bounds.

Book ChapterDOI
TL;DR: In this paper, a quantum algorithm was proposed to find collisions in arbitrary r-to-one functions with O((N/r)^(1/3)) expected evaluations of the function.
Abstract: In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the best possible classical algorithm, even allowing probabilism. We also give a similar algorithm for finding claws in pairs of functions. Furthermore, we exhibit a space-time tradeoff for our technique. Our approach uses Grover's quantum searching algorithm in a novel way.

Journal ArticleDOI
TL;DR: An efficient algorithm and quantum network effecting $\cal SYM$--projection and the stabilizing effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction are discussed.
Abstract: We propose a method for the stabilization of quantum computations (including quantum state storage). The method is based on the operation of projection into $\cal SYM$, the symmetric subspace of the full state space of $R$ redundant copies of the computer. We describe an efficient algorithm and quantum network effecting $\cal SYM$--projection and discuss the stabilizing effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.

Journal ArticleDOI
TL;DR: In this article, the classical limit of the quantum hydrodynamic equations was analyzed as the Planck constant tends to zero in the classical limits of the system, where the equations have the form of an Euler system with a constant pressure and a dispersive regularisation term, and the main tool of the analysis is the exploitation of a kinetic equation.
Abstract: We analyse the classical limit of the quantum hydrodynamic equations as the Planck constant tends to zero The equations have the form of an Euler system with a constant pressure and a dispersive regularisation term, which (formally) tends to zero in the classical limit The main tool of the analysis is the exploitation of a kinetic equation, which lies behind the quantum hydrodynamic system The presented analysis can also be interpreted as an alternative approach to the geometrical optics (WKB)-analysis of the Schrequation