Volume 56, Issue 2-3
February 2001, pages 137-456
pp 137-137 February 2001
pp 139-152 February 2001 Foundations Of Quantum Theory
After recalling proofs of the Bell inequality based on the assumptions of separability and of noncontextuality, the most general noncontextual contrapositive conditional probabilities consistent with the Aspect experiment are constructed. In general these probabilities are not all positive.
pp 153-159 February 2001 Foundations Of Quantum Theory
We describe the realisation of a new test of Bell inequalities using a new scheme obtained by the superposition of type I parametric down conversion produced in two different non-linear crystals pumped by the same laser, but with different polarisations. This experiment is the first test of Bell inequalities using a non-maximally entangled state and thus represents an important step in the direction of eliminating the detection loophole.
pp 161-167 February 2001 Foundations Of Quantum Theory
We examine a local realist bound in the case of a one-atom micromaser. It is shown that such a bound is violated using a simplified treatment of the micromaser. We consider the effect of dissipation in a proposed experiment with the real micromaser. It is seen that the magnitude of violation of a Bell-type inequality depends significantly on the cavity parameters.
pp 169-178 February 2001 Foundations Of Quantum Theory
Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.
pp 179-187 February 2001 Foundations Of Quantum Theory
Tripartite entangled states of systems 1, 2 and 3 involving nonorthogonal states are used to reveal two hitherto unexplored quantum effects. The first shows that kinematic entanglement between the states of 1 and 2 can affect the result of dynamical interaction between 2 and 3, though 1 and 2 may be spatially separated so that they no longer interact. The second shows that if a residual interaction persists between 1 and 2 while 2 interacts with 3 to form an entangled state, the measurement of observables of 1 can be used to determine whether 2 has interacted with 3. This effect occurs even when the measurement on 1 is made long after the residual interaction between 1 and 2 has ceased to act. Such effects resulting from interplay between unitary dynamics and kinematic entanglement have interesting implications. In particular, we discuss the significance as regards what we call the dynamic version of Einstem locality.
pp 189-197 February 2001 Foundations Of Quantum Theory
Recently it has been demonstrated that Bell inequalities for spin 1/2 particles must be modified if unsharp spin observables are considered, and furthermore, the modified Bell inequalities may not be violated by quantum mechanics if the observables are sufficiently unsharp. In case of massive particles there may be more imperfection than seems to appear in the photon EPR experiments. So the experiment proposed by Fry, Walther and Li can place experimental limits on the unsharpness of spin variables. It sheds new light on the much debated issues like non-local correlations in quantum mechanics.
pp 199-209 February 2001 Foundations Of Quantum Theory
Bell’s theorem requires the assumption that hidden variables are independent of future measurement settings. This independence assumption rests on surprisingly shaky ground. In particular, it is puzzlingly time-asymmetric. The paper begins with a summary of the case for considering hidden variable models which, in abandoning this independence assumption, allow a degree of ‘backward causation’. The remainder of the paper clarifies the physical significance of such models, in relation to the issue as to whether quantum mechanics provides a complete description of physical reality.
pp 211-215 February 2001 Foundations Of Quantum Theory
An experiment is suggested that is capable of distinguishing between the de Broglie-Bohm theory and standard quantum mechanics.
pp 217-221 February 2001 Foundations Of Quantum Theory
Extensions of standard quantum mechanics with joint probability distributions for position coordinates and momenta have been proposed in the literature. Time is assumed to be one-dimensional in these studies. In view of recent interest in two-dimensional time, the construction is extended to this situation and found to satisfy the necessary consistency conditions.
pp 223-237 February 2001 Foundations Of Quantum Theory
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its CK - and C--structures) can be reconstructed using Gel’fand-Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed.
pp 239-243 February 2001 Foundations Of Quantum Theory
Here we review our work on measurement of the Casimir force between a large aluminum coated a sphere and flat plate using an atomic force microscope. The average statistical precision is 1% of the force measured at the closest separation. We have also shown nontrival boundary dependence of the Casimir force.
pp 245-265 February 2001 Quantum Optics, Coherent States And Geometic Phases
The main properties of standard quantum mechanical coherent states and the two generalizations of Klauder and of Perelomov are reviewed. For a system of generalized coherent states in the latter sense, necessary and sufficient conditions for existence of a diagonal coherent stable representation for all Hilbert-Schmidt operators are obtained. The main ingredients are Clebsch-Gordan theory and induced representation theory.
pp 267-280 February 2001 Quantum Optics, Coherent States And Geometic Phases
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
pp 281-285 February 2001 Quantum Optics, Coherent States And Geometic Phases
We report near-noiseless (noise figure of 0.4 dB, which is an improvement over the theoretical limit of 1.2 dB for a conventional laser amplifier with the same gain of 1.7 dB) optical amplification of laser light in a phase-sensitive fibre amplifier.
pp 287-303 February 2001 Quantum Optics, Coherent States And Geometic Phases
We present an overview of polarized neutron experiments observing SU(2) phases. The first experimental separation of geometric and dynamical phases, the explicit verification of Pauli anticommutation and the first observation of interference amplitudes and phases in noncyclic evolutions are described. These experiments elucidate the physics of phases and phase jumps propounded by the Pancharatnam connection.
pp 305-319 February 2001 Quantum Optics, Coherent States And Geometic Phases
A general gauge-invariant formalism for parallel transport, geodesics and geometric phase based on the pure state density operator is propounded. A single-query quantum search algorithm is proposed.
pp 321-331 February 2001 Quantum Optics, Coherent States And Geometic Phases
The analysis of the Aharanov-Bohm phase and other similar physical effects in this paper is motivated by the philosophy that all physical changes, including phase changes, should originate in one of the local physical interactions even if they are described elegantly and concisely as topological or geometric changes. The topological or geometric nature comes about either due to an additional physical principle or due to certain special spatial or temporal property of the fields from the source. Similar remarks apply to rotation or precession of polarization and spin vectors. As a primary example I describe the Aharanov-Bohm phase as arising from the Coulomb interaction of a charge in the electrostatic potential created by other charges. The topological nature comes about because the interaction energy has zero gradient throughout space, except in a compact region enclosed by the quantum paths. This analysis brings out the unifying aspects of the scalar and the vector A-B effects, and the Aharanov-Casher phase. Then I discuss two other related problems with descriptions in the geometrical and the interaction pictures; I discuss how quantum complementarity is realized without the Heisenberg back action on momentum in certain atom interferometry experiments. In the second example, I show that the Thomas precession of the spin results from the local torque in the accelero-magnetic field, a field predicted in analogy with the gravitomagnetic field. I end the discussion with some remarks on the classical nature of fringe shifts in Aharanov-Bohm like phenomena in electromagnetism and gravitation.
pp 333-348 February 2001 Quantum Information Processing
The quantum search algorithm is a technique for searching N possibilities in only O(√N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrödinger’s equation. This paper also provides a self contained introduction to quantum computing algorithms from a new perspective.
pp 349-355 February 2001 Quantum Information Processing
Entanglement, one of the most important features of quantum mechanics, is at the core of the famous Einstein-Bohr philosophical debate  and is the principal resource for quantum information processing . We report on new experimental investigations of the properties of entangled photon pairs with emphasis on the tension between quantum mechanics and relativity [3,4]. Entangled photons are sent via an optical fiber network to two villages near Geneva, separated by more than 10 km where they are analyzed by interferometers . The photon pair source is set as precisely as possible in the center so that the two photons arrive at the detectors within a time interval of less than 5 ps (corresponding to a path length difference of less than 1 mm). This sets a lower bound on the ‘speed of quantum information’ to 107 times the speed of light. Next, one detector is set in motion  so that both detectors, each in its own inertial reference frame, are first to do the measurement! The data always reproduces the quantum correlations.
pp 357-365 February 2001 Quantum Information Processing
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement this algorithm classically.
pp 367-381 February 2001 Quantum Information Processing
Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural (and first ever!) explanation of why living organisms have 4 nucleotide bases and 20 amino acids. It is amazing that these numbers arise as solutions to an optimisation problem. Components of the DNA structure which implement Grover’s algorithm are identified, and a physical scenario is presented for the execution of the quantum algorithm. It is proposed that enzymes play a crucial role in maintaining quantum coherence of the process. Experimental tests that can verify this scenario are pointed out.
pp 383-391 February 2001 Quantum Information Processing
We present a rare example of a decay mechanism playing a constructive role in quantum information processing. We show how the state of an atom trapped in a cavity can be teleported to a second atom trapped in a distant cavity by the joint detection of photon leakage from the cavities. The scheme, which is probabilistic, requires only a single three level atom in a cavity. We also show how this scheme can be modified to a teleportation with insurance.
pp 393-401 February 2001 Quantum Information Processing
We propose a method called ‘coherence swapping’ which enables us to create superposition of a particle in two distinct paths, which is fed with initially incoherent, independent radiation. This phenomenon is also present for the charged particles, and can be used to swap the effect of flux line due to the Aharonov-Bohm effect. We propose an optical version of experimental set-up to test the coherence swapping. The phenomenon, which is simpler than entanglement swapping or teleportation, raises some fundamental questions about the true nature of wave-particle duality, and also opens up the possibility of studying the quantum erasure from a new angle.
pp 403-409 February 2001 Quantum Information Processing
It is shown that the no-signaling constraint generates the symmetric as well as the asymmetric 1 → 2 optimal universal quantum cloning machine of single qubits
pp 411-424 February 2001 Mesoscopic Systems
We study spin tunnelling in molecular magnets as an instance of a mesoscopic phenomenon, with special emphasis on the molecule Fe8. We show that the tunnel splitting between various pairs of Zeeman levels in this molecule oscillates as a function of applied magnetic field, vanishing completely at special points in the space of magnetic fields, known as diabolical points. This phenomena is explained in terms of two approaches, one based on spin-coherent-state path integrals, and the other on a generalization of the phase integral (or WKB) method to difference equations. Explicit formulas for the diabolical points are obtained for a model Hamiltonian.
pp 425-437 February 2001 Mesoscopic Systems
Universal statistical aspects of wave scattering by a variety of physical systems ranging from atomic nuclei to mesoscopic systems and microwave cavities are described. A statistical model for the scattering matrix is employed to address the problem of quantum chaotic scattering. The model, introduced in the past in the context of nuclear physics, discusses the problem in terms of a prompt and an equilibrated component: it incorporates the average value of the scattering matrix to account for the prompt processes and satisfies the requirements of flux conservation, causality and ergodicity. The main application of the model is the analysis of electronic transport through ballistic mesoscopic cavities: it describes well the results from the numerical solutions of the Schrödinger equation for two-dimensional cavities.
pp 439-452 February 2001 Mesoscopic Systems
Mesoscopic systems have provided an opportunity to study quantum effects beyond the atomic realm. In these systems quantum coherence prevails over the entire sample. We discuss several novel effects related to persistent currents in open systems which do not have analogues in closed systems. Some phenomena arising simultaneously due to two non-classical effects namely, Aharonov-Bohm effect and quantum tunneling are presented. Simple analysis of sharp phase jumps observed in double-slit Aharonov-Bohm experiments is given. Some consequences of parity violation are elaborated. Finally, we briefly describe the dephasing of Aharonov-Bohm oscillations in Aharonov-Bohm ring geometry due to spin-flip scattering in one of the arms. Several experimental manifestations of these phenomena and their applications are given.
pp 453-456 February 2001
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