Showing papers on "Quantum published in 2000"

A Quantum Dot Single-Photon Turnstile Device

Abstract: Quantum communication relies on the availability of light pulses with strong quantum correlations among photons. An example of such an optical source is a single-photon pulse with a vanishing probability for detecting two or more photons. Using pulsed laser excitation of a single quantum dot, a single-photon turnstile device that generates a train of single-photon pulses was demonstrated. For a spectrally isolated quantum dot, nearly 100% of the excitation pulses lead to emission of a single photon, yielding an ideal single-photon source.

Dark-State Polaritons in Electromagnetically Induced Transparency

Abstract: We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in electromagnetically induced transparency. The properties of dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.

Experimental entanglement of four particles

Abstract: Quantum mechanics allows for many-particle wavefunctions that cannot be factorized into a product of single-particle wavefunctions, even when the constituent particles are entirely distinct. Such 'entangled' states explicitly demonstrate the non-local character of quantum theory, having potential applications in high-precision spectroscopy, quantum communication, cryptography and computation. In general, the more particles that can be entangled, the more clearly nonclassical effects are exhibited--and the more useful the states are for quantum applications. Here we implement a recently proposed entanglement technique to generate entangled states of two and four trapped ions. Coupling between the ions is provided through their collective motional degrees of freedom, but actual motional excitation is minimized. Entanglement is achieved using a single laser pulse, and the method can in principle be applied to any number of ions.

Quantum mirages formed by coherent projection of electronic structure

Abstract: Image projection relies on classical wave mechanics and the use of natural or engineered structures such as lenses or resonant cavities. Well-known examples include the bending of light to create mirages in the atmosphere, and the focusing of sound by whispering galleries. However, the observation of analogous phenomena in condensed matter systems is a more recent development, facilitated by advances in nanofabrication. Here we report the projection of the electronic structure surrounding a magnetic Co atom to a remote location on the surface of a Cu crystal; electron partial waves scattered from the real Co atom are coherently refocused to form a spectral image or 'quantum mirage'. The focusing device is an elliptical quantum corral, assembled on the Cu surface. The corral acts as a quantum mechanical resonator, while the two-dimensional Cu surface-state electrons form the projection medium. When placed on the surface, Co atoms display a distinctive spectroscopic signature, known as the many-particle Kondo resonance, which arises from their magnetic moment. By positioning a Co atom at one focus of the ellipse, we detect a strong Kondo signature not only at the atom, but also at the empty focus. This behaviour contrasts with the usual spatially-decreasing response of an electron gas to a localized perturbation.

Theory of quantum error correction for general noise

Abstract: A measure of quality of an error-correcting code is the maximum number of errors that it is able to correct. We show that a suitable notion of "number of errors" e makes sense for any quantum or classical system in the presence of arbitrary interactions. Thus, e-error-correcting codes protect information without requiring the usual assumptions of independence. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes.

Decoherence of quantum superpositions through coupling to engineered reservoirs

Abstract: The theory of quantum mechanics applies to closed systems. In such ideal situations, a single atom can, for example, exist simultaneously in a superposition of two different spatial locations. In contrast, real systems always interact with their environment, with the consequence that macroscopic quantum superpositions (as illustrated by the 'Schrodinger's cat' thought-experiment) are not observed. Moreover, macroscopic superpositions decay so quickly that even the dynamics of decoherence cannot be observed. However, mesoscopic systems offer the possibility of observing the decoherence of such quantum superpositions. Here we present measurements of the decoherence of superposed motional states of a single trapped atom. Decoherence is induced by coupling the atom to engineered reservoirs, in which the coupling and state of the environment are controllable. We perform three experiments, finding that the decoherence rate scales with the square of a quantity describing the amplitude of the superposition state.

Feasible Entanglement Purification for Quantum Communication

Abstract: The distribution of entangled states between distant locations will be essential for the future large scale realization of quantum communication schemes such as quantum cryptography and quantum teleportation. Because of the unavoidable noise in the quantum communication channel, the entanglement between two particles is more and more degraded the further they propagate. Entanglement purification is thus essential to distill highly entangled states from less entangled ones. Existing general purification protocols are based on the quantum controlled-NOT (CNOT) or similar quantum logic operations, which are very difficult to implement experimentally. Present realizations of CNOT gates are much too imperfect to be useful for long-distance quantum communication. Here we present a feasible scheme for the entanglement purification of general mixed entangled states, which does not require any CNOT operations, but only simple linear optical elements. Since the perfection of such elements is very high, the local operations necessary for purification can be performed with the required precision. Our procedure is within the reach of current technology and should significantly simplify the implementation of long-distance quantum communication.

Acceleration of quantum decay processes by frequent observations

Abstract: In theory, the decay of any unstable quantum state can be inhibited by sufficiently frequent measurements--the quantum Zeno effect. Although this prediction has been tested only for transitions between two coupled, essentially stable states, the quantum Zeno effect is thought to be a general feature of quantum mechanics, applicable to radioactive or radiative decay processes. This generality arises from the assumption that, in principle, successive observations can be made at time intervals too short for the system to change appreciably. Here we show not only that the quantum Zeno effect is fundamentally unattainable in radiative or radioactive decay (because the required measurement rates would cause the system to disintegrate), but also that these processes may be accelerated by frequent measurements. We find that the modification of the decay process is determined by the energy spread incurred by the measurements (as a result of the time-energy uncertainty relation), and the distribution of states to which the decaying state is coupled. Whereas the inhibitory quantum Zeno effect may be feasible in a limited class of systems, the opposite effect--accelerated decay--appears to be much more ubiquitous.

Quantum state discrimination

Abstract: There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a quantum system is prepared in a member of a known, finite set of states, and the aim is to guess which one with the minimum probability of error. Error free discrimination is also sometimes possible, if we allow for the possibility of obtaining inconclusive results. If no prior information about the state is provided, then it is impractical to try to determine it exactly, and it must be estimated instead. In addition to reviewing these various strategies, I describe connections between state discrimination, the manipulation of quantum entanglement and quantum cloning. Recent experimental work is also discussed.

Singular Perturbations of Differential Operators

Abstract: Singular perturbations of Schrodinger type operators are of interest in mathematics, e.g. to study spectral phenomena, and in applications of mathematics in various sciences, e.g. in physics, chemistry, biology, and in technology. They also often lead to models in quantum theory which are solvable in the sense that the spectral characteristics (eigenvalues, eigenfunctions, and scattering matrix) can be computed. Such models then allow us to grasp the essential features of interesting and complicated phenomena and serve as an orientation in handling more realistic situations. In the last ten years two books have appeared on solvable models in quantum theory built using special singular perturbations of Schrodinger operators. The book by S. Albeverio, F. Gesztesy, R. Hoegh-Krohn and H. Holden "Solvable Models in Quantum Mechanics" describes the models in rigorous mathematical terms. It gives a detailed analysis of perturbations of the Laplacian in R^d, d=1,2,3, by potentials with support on a discrete finite or infinite set of point sources (chosen in a deterministic, respectively, stochastic manner). Physically these operators describe the motion of a quantum mechanical particle moving under the action of a potential supported, e.g., by the points of a crystal lattice or a random solid. Such systems and models are also described in physical terms in the book by Yu.N.Demkov and V.N.Ostrovsky "Zero-range Potentials in Atomic Physics", which also contains a description of applications in other areas such as in optics and electromagnetism. Let us also remark that a translation of the book by S.Albeverio, F.Gesztesy, R.Hoegh-Krohn and H.Holden in Russian has been published with additional comments and literature. Since the appearance of these books several important new developments have taken place. It is the main aim of the present book to present some of these new developments in a unified formalism which also puts some of the basic results of the preceding books into a new light. The new developments concern in particular a systematic study of finite rank perturbations of (self--adjoint) operators (in particular differential operators), of generalized (singular) perturbations, of the corresponding scattering theory as well as infinite rank perturbations and multiple particles (many--body) problems in quantum theory. We also present the theory of point interaction Hamiltonians, as a particular case of a general theory of singular perturbations of differential operators. This theory has received steadily increasing attention over the years also for its many applications in physics (solid state physics, nuclear physics), electromagnetism (antennas), and technology (metallurgy, nanophysics). We hope this monograph can serve as a basis for orientation in a rapidly developing area of analysis, mathematical physics and their applications.

Hidden symmetries in the energy levels of excitonic 'artificial atoms'

Abstract: Quantum dots1,2,3,4,5,6,7 or ‘artificial atoms’ are of fundamental and technological interest—for example, quantum dots8,9 may form the basis of new generations of lasers The emission in quantum-dot lasers originates from the recombination of excitonic complexes, so it is important to understand the dot's internal electronic structure (and of fundamental interest to compare this to real atomic structure) Here we investigate artificial electronic structure by injecting optically a controlled number of electrons and holes into an isolated single quantum dot The charge carriers form complexes that are artificial analogues of hydrogen, helium, lithium, beryllium, boron and carbon excitonic atoms We observe that electrons and holes occupy the confined electronic shells in characteristic numbers according to the Pauli exclusion principle In each degenerate shell, collective condensation of the electrons and holes into coherent many-exciton ground states takes place; this phenomenon results from hidden symmetries (the analogue of Hund's rules for real atoms) in the energy function that describes the multi-particle system Breaking of the hidden symmetries leads to unusual quantum interferences in emission involving excited states

Multistream model for quantum plasmas

Abstract: The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schr\"odinger-Poisson system. We consider a multistream model representing a statistical mixture of N pure states, each described by a wave function. The one-stream and two-stream cases are investigated. We derive the dispersion relation for the two-stream instability and show that a new, purely quantum, branch appears. Numerical simulations of the complete Schr\"odinger-Poisson system confirm the linear analysis, and provide further results in the strongly nonlinear regime. The stationary states of the Schr\"odinger-Poisson system are also investigated. These can be viewed as the quantum mechanical counterpart of the classical Bernstein-Greene-Kruskal modes, and are described by a set of coupled nonlinear differential equations for the electrostatic potential and the stream amplitudes.

Detection of geometric phases in superconducting nanocircuits

Abstract: When a quantum-mechanical system undergoes an adiabatic cyclic evolution, it acquires a geometrical phase factor1 in addition to the dynamical one; this effect has been demonstrated in a variety of microscopic systems2 Advances in nanotechnology should enable the laws of quantum dynamics to be tested at the macroscopic level3, by providing controllable artificial two-level systems (for example, in quantum dots4 and superconducting devices5,6) Here we propose an experimental method to detect geometric phases in a superconducting device The setup is a Josephson junction nanocircuit consisting of a superconducting electron box We discuss how interferometry based on geometrical phases may be realized, and show how the effect may be applied to the design of gates for quantum computation

Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice

Abstract: In combination with Laughlin's treatment of the quantized Hall conductivity, the Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number on a periodic lattice in arbitrary dimensions. Regardless of dimensionality, interaction strength, and particle statistics (Bose or Fermi), a finite excitation gap is possible only when the particle number per unit cell of the ground state is an integer.

Locally compact quantum groups in the von Neumann algebraic setting

Abstract: In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a C*-algebraic quantum group. Further we prove several results about locally compact quantum groups which are important for applications, but were not yet settled in our paper "Locally compact quantum groups". We prove a serious strengthening of the left invariance of the Haar weight, and we give several formulas connecting the locally compact quantum group with its dual. Loosely speaking we show how the antipode of the locally compact quantum group determines the modular group and modular conjugation of the dual locally compact quantum group.

Local spin resonance and spin-peierls-like phase transition in a geometrically frustrated antiferromagnet

Abstract: Inelastic magnetic neutron scattering reveals a localized spin resonance at 4.5 meV in the ordered phase of the geometrically frustrated cubic antiferromagnet ${\mathrm{ZnCr}}_{2}{\mathrm{O}}_{4}$. The resonance develops abruptly from quantum critical fluctuations upon cooling through a first order transition to a co-planar antiferromagnet at ${T}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}12.5(5)\mathrm{K}$. We argue that this transition is a three dimensional analog of the spin-Peierls transition.

The theory of two-electron atoms: between ground state and complete fragmentation

Abstract: Since the first attempts to calculate the helium ground state in the early days of Bohr-Sommerfeld quantization, two-electron atoms have posed a series of unexpected challenges to theoretical physics. Despite the seemingly simple problem of three charged particles with known interactions, it took more than half a century after quantum mechanics was established to describe the spectra of two-electron atoms satisfactorily. The evolution of the understanding of correlated two-electron dynamics and its importance for doubly excited resonance states is presented here, with an emphasis on the concepts introduced. The authors begin by reviewing the historical development and summarizing the progress in measuring the spectra of two-electron atoms and in calculating them by solving the corresponding Schr\"odinger equation numerically. They devote the second part of the review to approximate quantum methods, in particular adiabatic and group-theoretical approaches. These methods explain and predict the striking regularities of two-electron resonance spectra, including propensity rules for decay and dipole transitions of resonant states. This progress was made possible through the identification of approximate dynamical symmetries leading to corresponding collective quantum numbers for correlated electron-pair dynamics. The quantum numbers are very different from the independent particle classification, suitable for low-lying states in atomic systems. The third section of the review describes modern semiclassical concepts and their application to two-electron atoms. Simple interpretations of the approximate quantum numbers and propensity rules can be given in terms of a few key periodic orbits of the classical three-body problem. This includes the puzzling existence of Rydberg series for electron-pair motion. Qualitative and quantitative semiclassical estimates for doubly excited states are obtained for both regular and chaotic classical two-electron dynamics using modern semiclassical techniques. These techniques set the stage for a theoretical investigation of the regime of extreme excitation towards the three-body breakup threshold. Together with periodic orbit spectroscopy, they supply new tools for the analysis of complex experimental spectra.

An algorithmic benchmark for quantum information processing

Abstract: Quantum information processing offers potentially great advantages over classical information processing, both for efficient algorithms1,2 and for secure communication3,4. Therefore, it is important to establish that scalable control of a large number of quantum bits (qubits) can be achieved in practice. There are a rapidly growing number of proposed device technologies5,6,7,8,9,10,11 for quantum information processing. Of these technologies, those exploiting nuclear magnetic resonance (NMR) have been the first to demonstrate non-trivial quantum algorithms with small numbers of qubits12,13,14,15,16. To compare different physical realizations of quantum information processors, it is necessary to establish benchmark experiments that are independent of the underlying physical system, and that demonstrate reliable and coherent control of a reasonable number of qubits. Here we report an experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits. Moreover, our experimental procedure can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems. The benchmark and the techniques can be adapted for use with other proposed quantum devices.

Quantum memory for light

Abstract: We propose an efficient method for mapping and storage of a quantum state of propagating light in atoms. The quantum state of the light pulse is stored in two sublevels of the ground state of a macroscopic atomic ensemble by activating a synchronized Raman coupling between the light and atoms. We discuss applications of the proposal in quantum information processing and in atomic clocks operating beyond quantum limits of accuracy. The possibility of transferring the atomic state back on light via teleportation is also discussed.

Water Clusters: Towards an Understanding Based on First Principles of Their Static and Dynamic Properties

Abstract: If a single molecule were to be selected as the most important chemical entity for life, most people would agree that this is water. Moreover, water has been used to find a common definition for the Fahrenheit, Celsius, and Kelvin scales through its melting, boiling, and triple points. It is clear that these points are bulk properties and that a single H2O molecule has neither a melting nor a boiling point. Therefore, water offers a paradigmatic case for studying the transition from quantum reality to classical physics: How many water molecules are necessary for the bulk properties to appear? Water clusters, discrete or polymeric (ice), can be seen as one of the simplest models connecting molecular to supramolecular chemistry. Consider, for instance, one of the possible water hexamers, I, and cyclohexane (II), both undergoing boat ‐ chair equilibria (Scheme 1). The study by

Quantum solvation and molecular rotations in superfluid helium clusters

Abstract: Spectroscopic experiments on molecules embedded in free clusters of liquid helium reveal a number of unusual features deriving from the unique quantum behavior of this nanoscale matrix environment. The apparent free rotation of small molecules in bosonic 4He clusters is one of the experimentally most well documented of these features. In this Focus article, we set this phenomenon in the context of experimental and theoretical advances in this field over the last ten years, and describe the microscopic insight which it has provided into the nature and dynamic consequences of quantum solvation in a superfluid. We provide a comprehensive theoretical analysis which is based on a unification of conclusions drawn from diffusion and path integral Monte Carlo calculations. These microscopic quantum calculations elucidate the origin of the empirical free rotor spectrum, and its relation to the boson character and superfluid nature of the quantum nanosolvent. The free rotor behavior of the molecular rotation is pre...

Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations

Abstract: Entanglement of two parts of a quantum system is a non-local property unaffected by local manipulations of these parts. It is described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of non-local properties. The set contains 18 real polynomials of the entries of the density matrix. We prove that one of two mixed states can be transformed into the other by single-bit operations if and only if these states have equal values of all 18 invariants. Corresponding local operations can be found efficiently. Without any of these 18 invariants the set is incomplete. Similarly, non-local, entangling properties of two-qubit unitary gates are invariant under single-bit operations. We present a complete set of 3 real polynomial invariants of unitary gates. Our results are useful for optimization of quantum computations since they provide an effective tool to verify if and how a given two-qubit operation can be performed using exactly one elementary two-qubit gate, implemented by a basic physical manipulation (and arbitrarily many single-bit gates).

On the Einstein-Podolsky-Rosen Paradox

Abstract: Central to the EPR paradox is a ‘thought experiment’ in which two spins are initially coupled to a state with S = 0 and are then separated to a large distance, at which they can be separately observed. Quantum mechanics apparently predicts that the two spins remain forever coupled, but this conflicts with Einstein’s principle of ‘locality’ or ‘separability’, according to which spatially well separated systems must be independent, no matter how strongly they have interacted in the past. It is now widely held that Einstein was wrong and that ‘non-locality’ follows inevitably from quantum mechanics i.e. that even distant systems are never truly separable. Here the question of separability is re-examined, within the framework of orthodox quantum mechanics but with a more realistic mathematical model than the one used in previous work, notably that by Bell. The conclusion is that there is no conflict between Einstein’s locality principle and the predictions of quantum mechanics: the discussions by Bell and others are based on an oversimplified model and on postulates that are untenable. Near the dissociation limit, states which differ only in spin coupling fall within an energy interval whose width tends to zero: representation of the system by a quantum mechanical ensemble then becomes mandatory, the coupling is broken, and the dissociation fragments become completely independent.

Full dimensional quantum calculations of the CH4+H→CH3+H2 reaction rate

Abstract: Accurate full-dimensional quantum mechanical calculations are reported for the CH4+H→CH3+H2 reaction employing the Jordan–Gilbert potential energy surface. Benchmark results for the thermal rate constant and the cumulative reaction probability are presented and compared to classical transition state theory as well as reduced dimensionality quantum scattering calculations. The importance of quantum effects in this system is highlighted.

Quantum Dynamics of Hydride Transfer in Enzyme Catalysis

Abstract: One of the strongest experimental indications of hydrogen tunneling in biology has been the elevated Swain−Schaad exponent for the secondary kinetic isotope effect in the hydride-transfer step catalyzed by liver alcohol dehydrogenase. This process has been simulated using canonical variational transition-state theory for overbarrier dynamics and optimized multidimensional paths for tunneling. Semiclassical quantum effects on the dynamics are included on a 21-atom substrate−enzyme−coenzyme primary zone embedded in the potential of a substrate−enzyme−coenzyme−solvent secondary zone. The potential energy surface is calculated by treating 54 atoms by quantum mechanical electronic structure methods and 5506 protein, coenzyme, and solvent atoms by molecular mechanical force fields. We find an elevated Swain−Schaad exponent for the secondary kinetic isotope effect and generally good agreement with other experimental observables. Quantum mechanical tunneling is calculated to account for ∼60% of the reactive flux,...

Semiclassical description of nonadiabatic quantum dynamics: Application to the S1–S2 conical intersection in pyrazine

Abstract: A recently proposed semiclassical approach to the description of nonadiabatic quantum dynamics [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997), X. Sun and W. H. Miller, J. Chem. Phys. 106, 916 (1997)] is applied to the S1–S2 conical intersection in pyrazine. This semiclassical method is based on a transformation of discrete quantum variables to continuous variables, thereby bypassing the problem of a classical treatment of discrete quantum degrees of freedom such as electronic states. Extending previous work on small systems, we investigate the applicability of the semiclassical method to larger systems with strong vibronic coupling. To this end, we present results for several pyrazine models of increasing dimensionality and complexity. In particular, we discuss the quality and performance of the semiclassical approach when the number of nuclear degrees of freedom is increased. Comparison with quantum-mechanical calculations and experimental results shows that the semiclassical method is able to describe the ultrafast dynamics in this system.

Quantum artificial neural network architectures and components

Abstract: It is shown by classical simulation and experimentation that quantum artificial neural networks (QUANNs) are more efficient and in some cases more powerful than classical artificial neural networks (CLANNs) for a variety of experimental tasks. This effect is particularly noticeable with larger and more complex domains. The gain in efficiency is achieved with no generalisation loss in most cases. QUANNs are also more powerful than CLANNs, again for some of the tasks examined, in terms of what the network can learn. What is more, it appears that not all components of a QUANN architecture need to to be quantum for these advantages to surface. It is demonstrated that a fully quantum neural network has no advantage over a partly quantum network and may in fact produce worse results. Overall, this work provides a first insight into the expected behaviour of individual components of QUANNs, if and when quantum hardware is ever built, and raises questions about the interface between quantum and classical components of future QUANNs.