Showing papers on "Quantum published in 1998"

Coherent quantum control of two-photon transitions by a femtosecond laser pulse

Abstract: Coherent quantum control1,2,3 has attracted interest as a means to influence the outcome of a quantum-mechanical interaction. In principle, the quantum system can be steered towards a desired state by its interaction with light. For example, in photoinduced transitions between atomic energy levels, quantum interference effects can lead to enhancement or cancellation of the total transition probability. The interference depends on the spectral phase distribution of the incident beam; as this phase distribution can be tuned, the outcome of the interaction can in principle be controlled. Here we demonstrate that a femtosecond laser pulse can be tailored, using ultrashort pulse-shaping4,5,6,7 techniques, to control two-photon transitions in caesium. By varying the spectral phases of the pulse components, we observe the predicted cancellation of the transitions due to destructive quantum interference; the power spectrum and energy of these ‘dark pulses’ are unchanged. We also show that the pulse shape can be modified extensively without affecting the two-photon transition probability.

Multiparticle generalization of entanglement swapping

Abstract: We generalize the procedure of entanglement swapping to obtain a scheme for manipulating entanglement in multiparticle systems. We describe how this scheme allows to establish multiparticle entanglement between particles belonging to distant users in a communication network through a prior distribution of singlets followed by only local measurements. We show that this scheme can be regarded as a method of generating entangled states of many particles and compare it with existing schemes using simple quantum computational networks. We highlight the practical advantages of using a series of entanglement swappings during the distribution of entangled particles between two parties. Applications of multiparticle entangled states in cryptographic conferencing and in reading messages from more than one source through a single measurement are also described.

The Heisenberg Representation of Quantum Computers

Abstract: Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of describing them on classical computers - also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.

Quantum-Mechanical Position Operator in Extended Systems

Abstract: The position operator (defined within the Schr\"odinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wave function, as usual in condensed matter physics. I show how to define the position expectation value by means of a simple many-body operator acting on the wave function of the extended system. The relationships of the present findings to the Berry-phase theory of polarization are discussed.

Quantized Thermal Conductance of Dielectric Quantum Wires

Abstract: Using the Landauer formulation of transport theory, we predict that dielectric quantum wires should exhibit quantized thermal conductance at low temperatures in a ballistic phonon regime. The quantum of thermal conductance is universal, independent of the characteristics of the material, and equal to ${\ensuremath{\pi}}^{2}{k}_{B}^{2}T/3h$ where ${k}_{B}$ is the Boltzmann constant, $h$ is Planck's constant, and $T$ is the temperature. Quantized thermal conductance should be experimentally observable in suspended nanostructures adiabatically coupled to reservoirs, devices that can be realized at the present time.

Josephson-Junction Qubits with Controlled Couplings

Abstract: Low-capacitance Josephson junctions, where Cooper pairs tunnel coherently while Coulomb blockade effects allow the control of the total charge, provide physical realizations of quantum bits (qubits), with logical states differing by one Cooper-pair charge on an island. The single- and two-bit operations required for quantum computation can be performed by applying a sequence of gate voltages. A basic design, described earlier [cond-mat/9706016], is sufficient to demonstrate the principles, but requires a high precision time control, and residual two-bit interactions introduce errors. Here we suggest a new nano-electronic design, close to ideal, where the Josephson junctions are replaced by controllable SQUIDs. This relaxes the requirements on the time control and system parameters substantially, and the two-bit coupling can be switched exactly between zero and a non-zero value for arbitrary pairs. The phase coherence time is sufficiently long to allow a series of operations.

Quantum vs. Classical Communication and Computation

Abstract: We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism. This allows us to obtain new positive and negative results. The positive results are novel quantum communication protocols that are built from nontrivial quantum algorithms via this simulation. These protocols, combined with (old and new) classical lower bounds, are shown to provide the first asymptotic separation results between the quantum and classical (probabilistic) two-party communication complexity models. In particular, we obtain a quadratic separation for the bounded-error model, and an exponential separation for the zero-error model. The negative results transform known quantum communication lower bounds to computational lower bounds in the black-box model. In particular, we show that the quadratic speed-up achieved by Grover for the OR function is impossible for the PARITY function or the MAJORITY function in the bounded-error model, nor is it possible for the OR function itself in the exact case. This dichotomy naturally suggests a study of bounded-depth predicates (i.e. those in the polynomial hierarchy) between OR and MAJORITY. We present black-box algorithms that achieve near quadratic speed up for all such predicates.

Quantum Transport and Dissipation

Abstract: Theory of Coherent Transport. Quantization of Transport. Single-Electron Tunneling. Dissipative Quantum Systems. Driven Quantum Systems. Chaos, Coherence, and Dissipation. Indexes.

Origin of quantum-mechanical complementarity probed by a ‘which-way’ experiment in an atom interferometer

Abstract: The principle of complementarity refers to the ability of quantum-mechanical entities to behave as particles or waves under different experimental conditions. For example, in the famous double-slit experiment, a single electron can apparently pass through both apertures simultaneously, forming an interference pattern. But if a ‘which-way’ detector is employed to determine the particle's path, the interference pattern is destroyed. This is usually explained in terms of Heisenberg's uncertainty principle, in which the acquisition of spatial information increases the uncertainty in the particle's momentum, thus destroying the interference. Here we report a which-way experiment in an atom interferometer in which the ‘back action’ of path detection on the atom's momentum is too small to explain the disappearance of the interference pattern. We attribute it instead to correlations between the which-way detector and the atomic motion, rather than to the uncertainty principle.

Structure and dynamics of few-nucleon systems

Abstract: Few-nucleon physics is a field rich with high-quality experimental data and possibilities for accurate calculations of strongly correlated quantum systems. In this article the authors discuss the traditional model of the nucleus as a system of interacting nucleons and outline many recent experimental results and theoretical developments in the field of few-nucleon physics. The authors describe nuclear structure and spectra, clustering and correlations, elastic and inelastic electromagnetic form factors, low-energy electroweak reactions, and nuclear scattering and response in the quasielastic regime. Through a review of the rich body of experimental data and a variety of theoretical developments, a coherent description of the nuclear strong- and electroweak-interaction properties emerges. In this article, the authors attempt to provide some insight into the practice and possibilities in few-nucleon physics today.

Reactions at surfaces studied by ab initio dynamics calculations

Abstract: Due to the development of efficient algorithms and the improvement of computer power it is now possible to map out potential energy surfaces (PES) of reactions at surfaces in great detail. This achievement has been accompanied by an increased effort in the dynamical simulation of processes on surfaces. The paradigm for simple reactions at surfaces -- the dissociation of hydrogen on metal surfaces -- can now be treated fully quantum dynamically in the molecular degrees of freedom from first principles, i.e., without invoking any adjustable parameters. This relatively new field of ab initio dynamics simulations of reactions at surfaces will be reviewed. Mainly the dissociation of hydrogen on clean and adsorbate covered metal surfaces and on semiconductor surfaces will be discussed. In addition, the ab initio molecular dynamics treatment of reactions of hydrogen atoms with hydrogen-passivated semiconductor surfaces and recent achievements in the ab initio description of laser-induced desorption and further developments will be addressed.

What is quantum mechanics trying to tell us

Abstract: I explore whether it is possible to make sense of the quantum mechanical description of physical reality by taking the proper subject of physics to be correlation and only correlation, and by separating the problem of understanding the nature of quantum mechanics from the hard problem of understanding the nature of objective probability in individual systems, and the even harder problem of understanding the nature of conscious awareness. The resulting perspective on quantum mechanics is supported by some elementary but insufficiently emphasized theorems. Whether or not it is adequate as a new Weltanschauung, this point of view toward quantum mechanics provides a different perspective from which to teach the subject or explain its peculiar character to people in other fields.

Spiers Memorial Lecture Quantum and semiclassical theory of chemical reaction rates

Abstract: Transition state theory (TST) has provided the qualitative picture of chemical reaction rates for over sixty years Recent theoretical developments, however, have made it possible to calculate rate constants fully quantum mechanically and efficiently, at least for small molecular systems; vestiges of TST can be seen both in the resulting flux correlation functions and in the algorithmic structure of the methodology itself One approach for dealing with more complex molecular systems is the semiclassical (SC) initial value representation (IVR), which is essentially a way of generalizing classical molecular dynamics simulations to include quantum interference; electronic degrees of freedom in an electronically non-adiabatic process can also be included on a dynamically equivalent basis Application of the SC-IVR to models of unimolecular isomerization and of electronically non-adiabatic transitions, both coupled to an infinite bath of harmonic oscillators, gives excellent agreement with (essentially exact) quantum path integral calculations for these systems over the entire range of coupling strength

D-particle bound states and generalized instantons

Abstract: We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of $\mathcal{N}=1$, $D=4,6,10$ super-Yang-Mills theories with gauge group SU(N). The results are: ${1\over{N^{2}}}$ for $D=4,6$, $\sum_{d | N} {1\over{d^{2}}}$ for D=10. We also discuss the D=3 case.

Quantum Computation

Abstract: In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool This review is about to tell the story of theoretical quantum computation I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation The review begins with background on theoretical computer science, Turing machines and Boolean circuits In light of these models, I define quantum computers, and discuss the issue of universal quantum gates Quantum algorithms, including Shor's factorization algorithm and Grover's algorithm for searching databases, are explained I will devote much attention to understanding what the origins of the quantum computational power are, and what the limits of this power are Finally, I describe the recent theoretical results which show that quantum computers maintain their complexity power even in the presence of noise, inaccuracies and finite precision I tried to put all results in their context, asking what the implications to other issues in computer science and physics are In the end of this review I make these connections explicit, discussing the possible implications of quantum computation on fundamental physical questions, such as the transition from quantum to classical physics

Symmetrizing Evolutions

Abstract: We introduce quantum procedures for making $\cal G$-invariant the dynamics of an arbitrary quantum system S, where $\cal G$ is a finite group acting on the space state of S Several applications of this idea are discussed In particular when S is a N-qubit quantum computer interacting with its environment and $\cal G$ the symmetric group of qubit permutations, the resulting effective dynamics admits noiseless subspaces Moreover it is shown that the recently introduced iterated-pulses schemes for reducing decoherence in quantum computers fit in this general framework The noise-inducing component of the Hamiltonian is filtered out by the symmetrization procedure just due to its transformation properties

Coding Theorems for Quantum Channels

Abstract: The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present paper gives a self contained treatment of the subject, following as much in parallel as possible with classical information theory and, on the other side, stressing profound differences of the quantum case. An emphasis is made on recent results, such as general quantum coding theorems including cases of infinite (possibly continuous) alphabets and constrained inputs, reliability function for pure state channels and quantum Gaussian channel. Several still unsolved problems are briefly outlined.

Quantum Associative Memory

Abstract: This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts. The unique characteristics of quantum theory may also be used to create a quantum associative memory with a capacity exponential in the number of neurons. This paper combines two quantum computational algorithms to produce such a quantum associative memory. The result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the Hopfield network. The paper covers necessary high-level quantum mechanical and quantum computational ideas and introduces a quantum associative memory. Theoretical analysis proves the utility of the memory, and it is noted that a small version should be physically realizable in the near future.

Quantization of Lie bialgebras, V

Abstract: This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting examples of such algebras. In particular, we construct a quantum vertex operator algebra from a rational, trigonometric, or elliptic R-matrix, which is a quantum deformation of the affine vertex operator algebra. The simplest vertex operator in this algebra is the quantum current of Reshetikhin and Semenov-Tian-Shansky.

Quantum interference in electron collision

Abstract: The indistinguishability of identical quantum particles can lead to quantum interferences that profoundly affect their scattering1,2 If two particles collide and scatter, the process that results in the detection of the first particle in one direction and the second particle in another direction interferes quantum mechanically with the physically indistinguishable process where the roles of the particles are reversed For bosons such as photons, a constructive interference between probability amplitudes can enhance the probability, relative to classical expectations, that both are detected in the same direction — this is known as ‘bunching’ But for fermions such as electrons, a destructive interference should suppress this probability (‘anti-bunching’); this interference is the origin of the Pauli exclusion principle, which states that two electrons can never occupy the same state Although two-particle interferences have been shown for colliding photons3,4, no similar demonstration for electrons exists2,5,6 Here we report the realization of this destructive quantum interference in the collision of electrons at a beam splitter In our experiments, the quantum interference responsible for the Pauli exclusion principle is manifest as the suppression in electron current noise after collision

Quantum Delta-Kicked Rotor: Experimental Observation of Decoherence

Abstract: We report on the experimental observation of environment induced decoherence in the quantum delta-kicked rotor. Ultracold cesium atoms are subjected to a pulsed standing wave of near resonant light. Spontaneous scattering of photons destroys dynamical localization thereby giving rise to a quantum diffusion, which approaches the classical diffusion with an increasing degree of decoherence. This tendency is enhanced by a stronger stochasticity in the underlying classical system. A comparison with theoretical predictions is presented.

Separability and entanglement of composite quantum systems

Abstract: We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of entanglement.

A topos perspective on the Kochen-Specker theorem: I. Quantum States as Generalized Valuations

Abstract: The Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalized valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalized valuation.

“Direct” and “Correct” Calculation of Canonical and Microcanonical Rate Constants for Chemical Reactions

Abstract: Theoretical approaches for calculating rate constants of chemical reactionseither the microcanonical rate for a given total energy k(E) or the canonical rate for a given temperature k(T)are described that are both “direct”, i.e., bypass the necessity of having to solve the complete state-to-state quantum reactive scattering problem, yet also “correct”, i.e., in principle exact (given a potential energy surface, assuming nonrelativistic quantum mechanics, etc.) Applications to a variety of reactions are presented to illustrate the methodology for various dynamical situations, e.g., transition-state-theory-like dynamics where the system moves directly through the interaction (transition-state) region and reactions that form long-lived collision complexes. It is also shown how this rigorous quantum theory can be combined with the Lindemann mechanism for describing the effects of collisions with a bath gas, so as to be able to treat recombination reactions and other effects of pressure. Finally, several ways ...

Quantum Dynamical Manifestation of Chaotic Behavior in the Process of Entanglement

Abstract: Manifestation of chaotic behavior is found in an intrinsically quantum property. The entanglement process, quantitatively expressed in terms of the reduced density linear entropy, is studied for the $N$-atom Jaynes-Cummings model. For a given energy, initial conditions are prepared as minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. We find for short times a faster increase in decoherence for the chaotic initial conditions as compared to regular ones, which have oscillatory increase.

Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers

Abstract: Two unidirectionally coupled external cavity semiconductor lasers showing chaotic intensity fluctuations are studied by numerically solving the Lang-Kobayashi model equations [IEEE J. Quantum Electron. QE-16, 347 (1980)]. The systems are shown to synchronize when operating in the regime of low-frequency fluctuations, which is characterized by a very high-dimensional $(dg150)$ attractor. The influence of parameter differences between the two lasers on the synchronization quality is investigated.

A new quantum transition state theory

Abstract: An old challenge in rate theory is the formulation of a quantum thermodynamic theory of rates which gives accurate estimates but does not demand any real time propagation. In this paper we attempt to answer the challenge by extending an idea suggested by Voth, Chandler and Miller [J. Phys. Chem. 93, 7009 (1989)]. A new quantum expression for the rate is derived by replacing the exact time dependent dynamics with the analytically known dynamics of a parabolic barrier and utilizing the symmetrized thermal flux operator. The new rate expression is exact for a parabolic barrier, and leads by derivation rather than by ansatz to a phase space integration of a Wigner thermal flux distribution function. The semiclassical limit is similar but not identical to Miller’s semiclassical transition state theory. Numerical computations on the symmetric and asymmetric one dimensional Eckart barrier give results which are equal to or greater than the exact ones, as expected from a transition state theory. In contrast to other approaches, the present theory is a leading term in an expansion which may be used to systematically improve the results and assess their validity.