Showing papers on "Quantum state published in 1995"

Hilbert space representation of the minimal length uncertainty relation.

Abstract: The existence of a minimal observable length has long been suggested in quantum gravity as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation. DAMTP/94-105, hep-th/9412167, and Phys.Rev.D52:1108 (1995)

Linking topological quantum field theory and nonperturbative quantum gravity

Abstract: Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the pullback of the curvature to the boundary is self‐dual (with a cosmological constant). A Hilbert space which describes all the information accessible by measuring the metric and connection induced in the boundary is constructed and is found to be the direct sum of the state spaces of all SU(2) Chern–Simon theories defined by all choices of punctures and representations on the spatial boundary S. The integer level k of Chern–Simons theory is found to be given by k=6π/G2Λ+α, where Λ is the cosmological constant and α is a CP breaking phase. Using these results, expectation values of observables which are functions of fields on the boundary may be evaluated in closed form. Given these results, it is natural to make the conjecture that the quantum states of the system are completely determined by measurements mad...

Quantum-state tomography and discrete Wigner function.

Abstract: A tomographical scheme is proposed to infer the quantum states of finite--dimensional systems from experiments. For this a new discrete Wigner formalism is developed.

Experimental determination of the quantum-mechanical state of a molecular vibrational mode using fluorescence tomography.

Abstract: We present a spectroscopic method for the complete characterization of the quantum state of the vibrational mode of a molecule in terms of a phase-space quasiprobability distribution. The distribution for a molecular vibrational mode excited by a short optical pulse is reconstructed from measurements of its time-dependent spectrum of fluorescence.

Veiled Reality: An Analysis Of Present- Day Quantum Mechanical Concepts

Abstract: Philosophy and Physics Matter Waves, Superposition, Linearity The Rules of Quantum Mechanics Comments Complements The Density Matrix Formalism Proper and Improper Mixtures Quantum States and the Nonseparability Problem The EPR Problem and Nonseparability On Measurement Variations on a Bohrian Theme Quantum Mechanics as a Universal Theory, Classical Appearances in a Quantum World Ontological Approaches (Hidden Variables and All That) Open Realism Veiled, Independent Reality, Empirical Reality Lessons and Hints from Quantum Physics.

Spin blockades in linear and nonlinear transport through quantum dots.

Abstract: The transport properties of a quantum dot that is weakly coupled to leads are investigated by using the exact quantum states of a finite number of interacting electrons. It is shown that, in addition to the Coulomb blockade, spin selection rules strongly influence the low temperature transport and lead to experimentally observable effects. Transition probabilities between states that correspond to successive electron numbers vanish if the total spins differ by $|\ensuremath{\Delta}S|g\frac{1}{2}$. In nonlinear transport, this can lead to negative differential conductances. The linear conductance peaks are suppressed if transitions between successive ground states are forbidden.

Quantum group symmetry and q-tensor algebras

Abstract: Origins of quantum groups representations of unitary quantum groups tensor operators in quantum groups the dual algebra and the factor group rotation functions for SUq(2) quantum groups at roots of unity algebraic induction of quantum group representations special topics.

Geometric aspects of noncyclic quantum evolutions.

Abstract: The geometric phase is defined for any arbitrary quantum evolution using a ``reference section'' of the bundle covering the curve in the projective Hilbert space. A canonical one-form is defined whose line integral gives the desired geometric phase. It is manifestly gauge, phase, and reparametrization invariant for all quantum evolutions. A simple proof of the vanishing nature of the geometric phase along the geodesic is given. Also, an elementary proof of the nonadditive nature of the geometric phase is given. In the limit of cyclic evolution of a pure quantum state, this phase reduces to the Aharonov and Anandan phase, precisely. It is observed that in addition to the geometric phase, other geometric structures exist, such as the ``length'' and ``distance'' during any arbitrary quantum evolution. The relations among all of these geometric quantities are pointed out. Finally, two simple examples are studied to illustrate the ideas introduced in this paper.

Quantum-state mapping between multilevel atoms and cavity light fields

Abstract: A scheme for the preparation of Fock states and general superposition states of the electromagnetic field in a cavity is studied in detail. The scheme uses adiabatic passage in a strongly coupled atom-cavity system to "map" atomic ground-state Zeeman coherence onto the cavity-mode field. We model photon-counting and homodyne measurements of the field exiting the cavity and demonstrate the possibility of generating and detecting highly nonclassical states of the field parameter values close to currently realizable experimental values. The adiabatic passage process is also reversible, enabling cavity-mode fields to be mapped onto atomic ground-state Zeeman coherence. Application of this property to the measurement of cavity fields is discussed, with particular consideration given to a possible scheme for quantum measurements of the intracavity photon number.

The Classical and Quantum 6j-symbols.

Abstract: * Representations of U(sl(2)) * Quantum sl(2) * The Quantum Trace and Color Representations * The Turaev-Viro Invariant

Reconstruction of the quantum mechanical state of a trapped ion.

Abstract: It is shown that the full information on the quantum state of the vibrational center-of-mass motion of a trapped ion can be transferred to its electronic dynamics by appropriately irradiating a long-living (e.g., quadrupole) electronic transition by laser light. This allows us to determine the quantum mechanical state of the ion with high quantum efficiency by probing a strong (dipole) transition for the appearance of resonance fluorescence.

Quantum state diffusion, density matrix diagonalization, and decoherent histories: A model.

Abstract: We analyse the quantum evolution of a particle moving in a potential in interaction with an environment of harmonic oscillators in a thermal state, using the quantum state diffusion (QSD) picture of Gisin and Percival. The QSD picture exploits a mathematical connection between the usual Markovian master equation for the evolution of the density operator and a class of stochastic non-linear Schrodinger equations (Ito equations) for a pure state |ψi , and appears to supply a good description of individual systems and processes. We find approximate stationary solutions to the Ito equation (exact, for the case of quadratic potentials). The solutions are Gaussians, localized around a point in phase space undergoing classical Brownian motion. We show, for quadratic potentials, that every initial state approaches these stationary solutions in the long time limit. We recover the density operator corresponding to these solutions, and thus show, for this particular model, that the QSD picture effectively supplies a prescription for approximately diagonalizing the density operator in a basis of phase space localized states. We show that the rate of localization is related to the decoherence time, and also to the timescale on which thermal and quantum fluctuations become comparable. We use these results to exemplify the general connection between the QSD picture and the decoherent histories approach to quantum mechanics, discussed previously by Diosi, Gisin, Halliwell and Percival.

Quantum Backreaction on "Classical" Variables.

Abstract: A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become entangled with the quantum variables with the result that the value of the quasiclassical variables depends on the quantum state. This provides a formalism to compute the backreaction of any quantum system on a quasiclassical one. In particular, it leads to a natural candidate for a theory of gravity coupled to quantized matter in which the gravitational field is not quantized.

Quantum Filtering of Markov Signals with White Quantum Noise

Abstract: Time-continuous non-anticipating processes of nondemolition measurements in quantum systems are described. In particular, the notion of physically realisable quantum filter is introduced and the problem of its optimisation to obtain the best a posteriori quantum state is considered. The fact that the optimal filtering of a quantum Markovian Gaussian signal with the Gaussian white quantum noise can be described by a coherent Markovian linear filter corresponding to quantum Gaussian state diffusion is proved. As an example, the problem of optimal measurement of complex amplitude for a quantum Markovian oscillator, loaded on a quantum wave communication line, is considered.

Experimental measurements of state resolved, rotationally inelastic energy transfer

Abstract: A great deal of experimental effort has been put toward measurements of integral and differential, state-to-state cross-sections for rotationally inelastic energy transfer. Throughout the years measurements in thermal gas cells, and in crossed molecular beams, have been performed at increasingly impressive levels of quantum state detail. Because the term ‘rotational energy transfer’ can include collisional interchange among nuclear rotational states, magnetic sublevels, electron spin and orbital quantum levels, and vibrational angular momentum states, and can also include rotation-translation/vibration energy transfer, the field is an expansive one. In this review an array of experimental studies is encapsulated, including discussion of quantum-state propensities, their known or speculative physical origins, and the success or failure of simple energy transfer models. Discussion of progress toward the development of accurate, intermolecular potential energy surfaces, and the results of classical ...

Decoherent histories and quantum state diffusion.

Abstract: We demonstrate a close connection between the decoherent histories approach to quantum mechanics and the quantum state diffusion picture, for open quantum systems described by a master equation of Lindblad form. The (physically unique) set of variables that localize in the quantum state diffusion picture also define an approximately decoherent set of histories in the decoherent histories approach. The degree of localization is related to the degree of decoherence, and the probabilities for histories prescribed by each approach are essentially the same.

Quantum-state engineering via discrete coherent-state superpositions

Abstract: A representation of a Fock state \ensuremath{\Vert}n〉 is given by a superposition of n+1 coherent states. These discrete coherent-state superpositions provide experimental possibilities for generating an arbitrary quantum state of a single-mode electromagnetic field.

Compensation of losses in photodetection and in quantum-state measurements.

Abstract: We show how losses in photodetection and in quantum-state measurements can be numerically compensated after the measurements have been performed. When the overall efficiency exceeds 1/2, our recipe works for all quantum states. For smaller efficiencies, however, the convergence of the compensation procedure depends on the quantum state under investigation.

Catastrophic particle production under periodic perturbation

Abstract: We develop a formalism to investigate the behavior of quantum field and quantum ground state when the field is coupled to perturbation that periodically oscillates. Working in the Schroedinger picture of quantum field theory, we confirm that the phenomenon of parametric resonance in the classical theory implies an instability of quantum vacuum, and correspondingly it gives rise to catastrophic particle production if the oscillation lasts indefinitely; the produced number of particles exponentially increases without bound as time proceeds. The density matrix describing the limiting stage of the quantum state is determined by a small set of parameters. Moreover, the energy spectrum and the intensity of produced particles are worked out in greatest detail in the limit of weak coupling or small amplitude perturbation. In the case of strong coupling or large amplitude perturbation the leading adiabatic formula is derived. Application to cosmological fate of weakly interacting spinless fields (WISF) such as the invisible axion, the Polonyi, and the modular fields is discussed. Although very little effect is expected on the invisible axion, the Polonyi type field has a chance that it catastrophically decays at an early epoch without much production of entropy, provided that an intrinsic coupling is large enough.

Quantum state endoscopy: Measurement of the quantum state in a cavity.

Abstract: We propose a measurement scheme to determine the complete state of a single mode of the quantized electromagnetic field in a cavity.

Semiclassicality and Decoherence of Cosmological Perturbations

Abstract: Transition to the semiclassical behaviour and the decoherence process for inhomogeneous perturbations generated from the vacuum state during an inflationary stage in the early Universe are considered both in the Heisenberg and the Schrodinger representations to show explicitly that both approaches lead to the same prediction: the equivalence of these quantum perturbations to classical perturbations having stochastic Gaussian amplitudes and belonging to the quasi-isotropic mode. This equivalence and the decoherence are achieved once the exponentially small (in terms of the squeezing parameter $r_k$) decaying mode is neglected. In the quasi-classical limit $|r_k|\to \infty$, the perturbation mode functions can be made real by a time-independent phase rotation, this is shown to be equivalent to a fixed relation between squeezing angle and phase for all modes in the squeezed-state formalism. Though the present state of the gravitational wave background is not a squeezed quantum state in the rigid sense and the squeezing parameters loose their direct meaning due to interaction with the environment and other processes, the standard predictions for the rms values of the perturbations generated during inflation are not affected by these mechanisms (at least, for scales of interest in cosmological applications). This stochastic background still occupies a small part of phase space.

Optimal Quantum Measurements for Two Pure and Mixed States

Abstract: An explicit formula is obtained for the entropy defect and the (maximum) information for an ensemble of two pure quantum states; an optimal basis is found, that is, an optimal measurement procedure which enables one to obtain the maximum information. Some results are also presented for the case of two mixed states, described by second-order density matrices (for example, spin polarization matrices). It is shown that in the case of two states the optimal measurement is a direct von Neumann measurement performed in the subspace of the two states.

Quantum coherence and closed timelike curves

Abstract: Various calculations of the S matrix have shown that it seems to be nonunitary for interacting fields when there are closed timelike curves. It is argued that this is because there is loss of quantum coherence caused by the fact that part of the quantum state circulates on the closed timelike curves and is not measured at infinity. A prescription is given for calculating the superscattering matrix $ on spacetimes whose parameters can be analytically continued to obtain a Euclidean metric. It is illustrated by a discussion of a spacetime in which two disks in flat space are indentified. If the disks have an imaginary time separation, this corresponds to a heat bath. An external field interacting with the heat bath will lose quantum coherence. One can then analytically continue to an almost real separation of the disks. This will give closed timelike curves but one will still get loss of quantum coherence. A comparison is made with the work of authors who find a nonunitary S matrix. It is shown that this is because the $ does not factor into an S matrix and its adjoint when the spacetime does not have the property of asymptotic completeness.

Sampling entropies and operational phase-space measurement. II. Detection of quantum coherences

Abstract: We use the operational phase-space distributions and sampling entropies developed in the preceding paper [V. Bu\ifmmode \check{z}\else \v{z}\fi{}ek, C. H. Keitel, and P. L. Knight, Phys. Rev. A 51, 2575 (1995)] to discuss the nature of quantum interference between components of superpositions of states. We show how the Wehrl entropy, a special case of the sampling entropy, is a useful discriminator between different kinds of superpositions and of statistical mixtures, and is determined essentially by the coherent-state content. Apart from interference terms, this content is given by the quantum uncertainty of a single coherent state and the classical contribution to the number of coherent states necessary to tile the dominant phase-space ``patch'' representing the quantum state of interest. We illustrate these ideas using nonclassical superpositions of coherent states, where interference modifies the phase-space distributions, and show how these features are sensitive to dissipation.

Quantum space-time fluctuations and primary state diffusion

Abstract: Nondifferentiable fluctuations in space-time on a Planck scale introduce stochastic terms into the equations for quantum states, resulting in a proposed new foundation for an existing alternative quantum theory, primary state diffusion (PSD). Planck-scale stochastic space-time structure results in quantum fluctuations, whilst larger-scale curvature is responsible for gravitational forces. The gravitational field and the quantum fluctuation field are the same, differing only in scale. The quantum mechanics of small systems, classical mechanics of large systems and the physics of quantum experiments are all derived dynamically, without any prior division into classical and quantum domains, and without any measurement hypothesis. Unlike the earlier derivation of PSD, the new derivation, based on a stochastic space-time differential geometry, has essentially no free parameters. However many features of this structure remain to be determined. The theory is falsifiable in the laboratory, and critical matter interferometry experiments to distinguish it from ordinary quantum mechanics may be feasible within the next decade.

Search for small violations of the symmetrization postulate in an excited state of helium.

Abstract: We have searched for the existence of the permutation symmetric 1{ital s}2{ital s}{sup 1}{ital S} state of helium in an atomic beam. Such a state directly violates the symmetrization postulate (SP) of quantum mechanics and implies a breakdown of the Pauli exclusion principle. Our data constrain recent SP-violating models at the 5 ppm level. This is the first experiment to look systematically for an SP-violating state with no multiple occupancy of a quantum state.