Showing papers on "Quantum state published in 1993"

A Potentially Realizable Quantum Computer

Abstract: Arrays of weakly coupled quantum systems might compute if subjected to a sequence of electromagnetic pulses of well-defined frequency and length. Such pulsed arrays are true quantum computers: Bits can be placed in superpositionsof 0 and 1, logical operations take place coherently, and dissipation is required only for error correction. Operated with frequent error correction, such a system functions as a parallel digital computer. Operated in a quantum-mechanically coherent manner, such a device functions as a generalpurpose quantum-mechanical micromanipulator, capable of both creating any desired quantum state of the array and transforming that state in any desired way.

Quantum group gauge theory on quantum spaces

Abstract: We construct quantum group-valued canonical connections on quantum homogeneous spaces, including aq-deformed Dirac monopole on the quantum sphere of Podles with quantum differential structure coming from the 3D calculus of Woronowicz onSU q (2). The construction is presented within the setting of a general theory of quantum principal bundles with quantum group (Hopf algebra) fibre, associated quantum vector bundles and connection one-forms. Both the base space (spacetime) and the total space are non-commutative algebras (quantum spaces).

Teleporting an unknown quantum state via dual classical and EPR channels

Abstract: An unknown quantum state ji can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical EPR correlations. To do so the sender, \Alice," and the receiver, \Bob," must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state ji which Alice destroyed.

Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence.

Abstract: A scheme for the preparation of general coherent superpositions of photon-number states is proposed. By strongly coupling an atom to a cavity field, atomic ground-state Zeeman coherence can be transferred by (coherent) adiabatic passage to the cavity mode and a general field state can be generated without atomic projection noise.

Breakdown of predictability in gravitational collapse

Abstract: The principle of equivalence, which says that gravity couples to the energy-momentum tensor of matter, and the quantum-mechanical requirement that energy should be positive imply that gravity is always attractive. This leads to singularities in any reasonable theory of gravitation. A singularity is a place where the classical concepts of space and time break down as do all the known laws of physics because they are all formulated on a classical space-time background. In this paper it is claimed that this breakdown is not merely a result of our ignorance of the correct theory but that it represents a fundamental limitation to our ability to predict the future, a limitation that is analogous but additional to the limitation imposed by the normal quantum-mechanical uncertainty principle. The new limitation arises because general relativity allows the causal structure of space-time to be very different from that of Minkowski space. The interaction region can be bounded not only by an initial surface on which data are given and a final surface on which measurements are made but also a "hidden surface" about which the observer has only limited information such as the mass, angular momentum, and charge. Concerning this hidden surface one has a "principle of ignorance": The surface emits with equal probability all configurations of particles compatible with the observers limited knowledge. It is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes: The black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity. Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state. This means there is no $S$ matrix for the process of black-hole formation and evaporation. Instead one has to introduce a new operator, called the superscattering operator, which maps density matrices describing the initial situation to density matrices describing the final situation.

How fast can a quantum state change with time

Abstract: Lower and upper bounds are derived for the decay and transitions of quantum states, evolving under a time-dependent Hamiltonian, in terms of the energy uncertainty of the initial and final state. The bounds are simultaneously a rigorous version of Fermi's golden rule and of the time-energy uncertainty relation. They are sharp, refer to short times, and are compared with recent long-time results for time-independent Hamiltonians. Illustrations for tunneling systems, laser-driven processes, and neutron interferometry in time-dependent magnetic fields are given.

The quantum state diffusion picture of physical processes

Abstract: In earlier papers the authors introduced a quantum state diffusion model for the evolution of an individual open quantum system and proved localization theorems based on this model. This paper shows in more detail how the diffusion leads to localization in position and phase space, and to symmetry breaking for chiral molecules. The theory of radioactive decay of absorbers and detectors is described in the state diffusion picture. The Mott and Gurney theory of latent image formation in photography is presented in its state diffusion version. It is an example of quantum detection without significant amplification.

Optical Control of Molecular Dynamics -- Liouville-Space Theory

Abstract: We lay some theoretical foundations to deal with the experimental realities faced in controlling molecular dynamics with tailored light fields: the nonideality of the light, the mixed rather than pure quantum-state nature of matter, and environmental and solvent effects. The optimal control of molecular dynamics using light fields is formulated in terms of the density matrix in Liouville space, generalizing existing wave-function-based formulations. This formulation allows the inclusion of mixed states, so that thermal and other nonpure quantum states of matter can be treated, as well as reduced descriptions useful in studying dense gas and condensed phases. In addition, it allows for general constraints and arbitrary coherent and partially coherent radiation fields and provides a unified picture for quantum, semiclassical, and classical molecular dynamics. For weak fields, the calculation simplifies and is given in terms of a molecular response function which itself does not depend upon the field. The solution of an eigenequation then directly gives the globally optimal field and the yield with respect to the target. As a demonstration, we explicitly consider a two electronic surface displaced harmonic oscillator molecular system in a Brownian oscillator solvent at finite temperatures, including nuclear and electronic solvation effects. Numerical illustrations are presented for the quantum control of thermal samples using phase-locked and random-phase light fields in the presence of solvent.

The classical limit of a self-consistent quantum-vlasov equation in 3d

Abstract: Under natural assumptions on the initial density matrix of a mixed quantum state (Hermitian, non-negative definite, uniformly bounded trace, Hilbert-Schmidt norm and kinetic energy) we prove that accumulation points (as the scaled Planck constant tends to zero) of solutions of a corresponding slightly regularized Wigner-Poisson system are distributional solutions of the classical Vlasov-Poisson system. The result holds for the gravitational and repulsive cases. Also, for every phase-space density in (with bounded kinetic energy) we prepare a sequence of density matrices satisfying the above assumptions, such that the given density is the limit of the Wigner transforms of these density matrices.

Interference of atomic states

Abstract: This monograph is devoted to the description and interpretation of interference between quantum states of an atom, as manifested in the angular distribution and polarization of spontaneous emission and absorption The basic phenomena are first introduced and explained in terms of the simple classical dipole model A more quantitative description follows, making use of the density matrix formalism and the statistical tensor The theoretical sections are complemented by detailed accounts of experimental methods and results, such that the monograph as a whole gives a comprehensive picture of this field

Measurement of number-phase uncertainty relations of optical fields

Abstract: We have experimentally determined all of the quantities involved in the uncertainty relation for the phase and photon number of a mode of the electromagnetic field when the field mode is in a coherent state of small average photon number This is accomplished by determining the quantum state of the field using optical homodyne tomography, which uses measured distributions of electric-field quadrature amplitude to determine the Wigner function and hence the density matrix The measured state is then used to calculate the uncertainty product for the number and phase, as well as the expectation value of the commutator of the number and phase operators The experimental results agree with the quantum-mechanical predictions We also present measured phase- and photon-number distributions for these weak coherent states, as well as their measured complex wave functions

Quantum key distribution using non-orthogonal macroscopic signals

Abstract: Quantum key distribution (QKD) uses non-orthogonal quantum states to distribute random information, suitable for use as a key for encryption and authentication, between two users who share secret information initially, with the assurance, based on the uncertainty principle, that it is unknown to anyone else The present invention, which can be used with a fiberoptic channel or an unguided light beam, differs from previous QKD schemes in using macroscopic signals instead of single photons The invention solves the problem of stray light and cost by using signals which are more efficient, and less noisy than photon-counting detectors at the wavelengths where optical fibers are most transparent

Complete experimental characterization of the quantum state of a light mode via the Wigner function and the density matrix: application to quantum phase distributions of vacuum and squeezed-vacuum states

Abstract: We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg–Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.

The rate of evolution of a quantum state

Abstract: How long does it take for an isolated quantum system to evolve to an orthogonal state? In a recent note in this journal1 Vaidman complained that it is not easy to find exact limits for this problem in the literature. It is the purpose of this note to supply some historical background and report some related results. The earliest discussion of the above problem known to me is the classic but apparently little-read article by Mandelstam and Tamm of 1945. 2 In this paper, Mandelstam and Tamm prove the inequality

Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space.

Abstract: A lossless beam splitter (a dielectric interface, a passive interferometer, or a linear coupler) changes the quantum state of two incident modes by an SU(2) transformation. Apart from phase shifting, the argument of the quadrature wave function of the system undergoes a rotation. Quasiprobabilities are changed by the inverse mode transformation. The use of balanced beam splitting allows the simultaneous measurement of conjugate quadrature components via homodyning the emerging beams with two strong coherent reference fields that differ in their phases by \ensuremath{\pi}/2. The measured probability distribution is given by a generalized Q function. It depends on the state of the field entering the second beam-splitter port. For a vacuum, the Q function will be obtained. The use of unbalanced beam splitting allows the measurement of a squeezed Q function without using squeezed states. Dissipation in Gaussian reservoirs corresponds exactly to a heuristic beam-splitter model. As a mathematical tool, the Fokker-Planck equation of damping in phase-sensitive reservoirs and the corresponding quantum master equation were solved. The dissipative decay of a Schr\"odinger-cat state was studied as an example. The sensitivity of quantum coherence with respect to damping can be interpreted geometrically.

Quantum phenomena in resonators with moving walls

Abstract: New solutions for the mode functions of the electromagnetic field in ideal cavity which boundary oscillates at a resonance frequency are obtained in the long‐time limit. The rate of photons creation from initial vacuum state is shown to be time independent and proportional to the amplitude of oscillations and the resonance frequency. Temperature corrections are evaluated. The squeezing coefficients for the quantum states of the field generated are calculated, as well as the backward reaction of the field on the vibrating wall.

Determination of quantum-state-specific gas—surface energy transfer and adsorption probabilities as a function of kinetic energy

Abstract: We describe a molecular beam technique for the determination of energy transfer and adsorption probabilities as a function of kinetic energy for specific quantum states of a molecule beam tailored to have a broad spread of energies. The beam is mechanically chopped into short pulses at a large distance from the surface, so that velocity dispersion in the beam causes a spread in the arrival times at the surface. Time-of-flight distributions are then recorded using state-specific laser ionization detection at points immediately before and after the beam scatters from the surface. Comparison of these two distributions then provides information on the loss or gain of molecules in the chosen quantum state as a function of kinetic energy. The method is illustrated by application to the H2(D2)/Cu(111) system. In this case we have observed loss of incident flux due to dissociative chemisorption and gain of molecules in the first vibrationally excited state due to vibrational excitation of ground state molecules.

Cosmological perturbations of quantum-mechanical origin and anisotropy of the microwave background.

Abstract: Cosmological perturbations generated quantum mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the cosmic microwave background radiation is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by observations like those by the Cosmic Background Explorer.

Various measures of quantum phase uncertainty : a comparative study

Abstract: We compare and contrast five measures of phase uncertainty of a quantum state corresponding to a single mode of the electromagnetic field. The basis of this study are the states which minimize a particular measure for a fixed number of Fock states and normalization. We find these optimal states and study their characteristic properties. These optimal states allow us to establish an ordering of the different definitions for phase uncertainty.

Quantum State Diffusion Theory and a Quantum Jump Experiment

Abstract: We use a recent stochastical diffusion model of quantum evolution to represent the evolution of a three-level quantum system undergoing quantum jumps. This is possible because the continuous change in the quantum state in this diffusion model is so rapid that it appears to be instantaneous in comparison with the time between transitions. Experimental data from a study of the intermittent fluorescence of a single trapped 24Mg+ ion and equivalent theoretical data are shown to be strikingly similar. Statistical comparisons of the data are also made.

Squeezed states with thermal noise. II. Damping and photon counting.

Abstract: We consider a single-mode radiation field initially in a displaced squeezed thermal state. The weak interaction of such a field with a heat bath of arbitrary temperature is shown to preserve the Gaussian form of the characteristic function. Accordingly, the study of the time development of the density operator reduces to our previous description [P. Marian and T. A. Marian, preceding paper, Phys. Rev. A 47, 4474 (1993)] of the initial quantum state. As examples, photon statistics and squeezing properties of the damped field are analyzed. Based on the close relation between field dissipation and photon detection, we derive simple analytic formulas for the counting distribution and its factorial moments. Nonclassical features of a displaced squeezed thermal state, such as oscillations of the photon-number distribution, survive in the counting process, provided that the quantum efficiency of the detector is high enough.

Nonperturbative production of multiboson states and quantum bubbles.

Abstract: The amplitude of production of n on-mass-shell scalar bosons by a highly virtual field φ is considered in a λφ 4 theory with weak coupling λ and spontaneously broken symmetry. The amplitude of this process is known to have an n! growth when the produced bosons are exactly at rest. Here it is shown that for n 1/λ the process goes through «quantum bubbles,» i.e., quantized droplets of a different vacuum phase, which are nonperturbative resonant states of the field φ. The bubbles provide a form factor for the production amplitude, which rapidly decreases above the threshold. As a result the probability of the process may be heavily suppressed and may decrease with energy E as esp(− const × E a ), where the power a depends on the number of space dimensions

Elements of Statistical Mechanics

Abstract: Thermodynamics, as we have studied it so far, is referred to as Classical Thermodynamics and is built upon its empirical laws. They are called empirical because they are the results of observations through the years (Chapter 4) and their validity lies with the fact that they have never failed.

Quantum superpositions, phase distributions and quasi-probabilities

Abstract: The probability distribution for finding a quantum state of the light field with a particular phase can be described by a number of theoretical methods. One of the most frequently used in quantum optics is the Pegg–Barnett phase distribution which identifies the phase distribution as the (necessarily positive) modulus square of the overlap of the quantum state with the relevant phase state. Other phase distributions have been proposed which employ the phase-sensitivity of various quantum quasi-probabilities such as the Wigner function. In this paper we discuss the connections between these approaches and illustrate their similarities and important differences for a number of pertinent quantum states of light. For some of these states, quantum interference can generate significant regions of phase space for which the Wigner quasi-probability is negative, and as we show, this may render the quasi-probability phase distribution negative. We discuss the general significance of this phenomenon.

Why “modal” interpretations of quantum mechanics don't solve the measurement problem

Abstract: According to “modal” interpretations of quantum mechanics, an observable Q can possess a definite value even when the quantum state is not an eigenstate of Q. In this paper, I discuss some interpretive difficulties faced by modal theorists. First, expanding upon Albert and Loewer, I identify two reasons why real-life measurements are never ideal, and I discuss why these considerations bode ill for modal interpretations. Second, I show that modal interpretations provide a less satisfactory explanation of “interference” effects than is provided by pilot-wave interpretations.

Classical entropy of quantum states of light.

Abstract: Classical-like, Wehrl's entropies of various quantum states of light are calculated and investigated as functions of the average value of the photon-number operator. Qualitatively similar behavior of the Wehrl entropies, corresponding to quantum states with quite different properties, is observed. A type of damping of the Wehrl entropies for states with high coherent components is pointed out and discussed

Protective Measurement and Quantum Reality

Abstract: It is shown that from the expectation values of obervables, which can be measured for a single system using protective measurements, the linear structure, inner product, and observables in the Hilbert space can be reconstructed. A universal method of measuring the wave function of a single particle using its gravitational field is given. Protective measurement is generalized to the measurement of a degenerate state and to many particle systems. The question of whether the wave function is real is examined, and an argument of Einstein in favor of the ensemble interpretation of quantum theory is refuted.