Showing papers on "Quantum published in 1980"

On the measurement of a weak classical force coupled to a quantum mechanical oscillator. i. issues of principle

Abstract: The monitoring of a quantum-mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitude-and-phase" method (position or momentum transducer with output fed through a narrow-band amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit"). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurement—a "back-action-evading" measurement of the real part X_1 (or the imaginary part X_2) of the oscillator's complex amplitude. In principle X_1 can be measured "arbitrarily quickly and arbitrarily accurately," and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that X_1 can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position (position transducer) and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The "momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor" or "negative spring." The modulated couplings are provided by an external, classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of X_1, in which one measures position (or momentum) at half-cycle intervals. Alternatively, one can make "continuous single-transducer" measurements of X_1 by modulating appropriately the output of a single transducer (position or momentum), and then filtering the output to pick out the information about X_1 and reject information about X_2. Continuous single-transducer measurements are useful in the case of weak coupling. In this case long measurement times are required to achieve good accuracy, and continuous single-transducer measurements are almost as good as perfectly coupled two-transducer measurements. Finally, the authors develop a theory of quantum nondemolition measurement for arbitrary systems. This paper (Paper I) concentrates on issues of principle; a sequel (Paper II) will consider issues of practice.

Quantum-Mechanical Radiation-Pressure Fluctuations in an Interferometer

Abstract: The interferometers now being developed to detect gravitational vaves work by measuring small changes in the positions of free masses. There has been a controversy whether quantum-mechanical radiation-pressure fluctuations disturb this measurement. This Letter resolves the controversy: They do.

Quantum theory of optical bistability. I. Nonlinear polarisability model

Abstract: A quantum treatment of a coherently driven dispersive cavity is given based on a cubic nonlinearity in the polarisability of the internal medium. This system displays bistability and hysteresis in the semiclassical solutions. Quantum fluctuations are included via a Fokker-Planck equation in a generalised P representation. The transmitted light shows a transition from a single-peaked spectrum to a double-peaked spectrum above the threshold of the lower branch. Fluctuations in the field are reduced on the upper branch and both photon bunching and photon antibunching are predicted, for different operating points. An exact solution obtained for the steady-state generalised P function shows decidedly non-equilibrium behaviour, e.g. the lack of a Maxwell construction.

Quantum Topology: Theory of Molecular Structure and its Change

Abstract: In this paper we review and exemplify a new and rigorous approach to the problem of molecular structure and its morphogenesis: the theory of quantum topology. The basis for this approach is provided by the topology of the total charge density in a given molecular system. The essential observation is that the only local maxima of a ground state distribution occur at the positions of the nuclei. The nuclei are therefore identified as point attractors of the gradient vector field of the charge density. The associated basins partition the molecular system into atomic fragments. Each atom is a stable structural unit defined as the union of an attractor and its basin. The common boundary of two neighbouring atomic fragments, the interatomic surface, contains a particular critical point, which generates a pair of gradient paths linking the two neighbouring attractors. The union of this pair of gradient paths and their endpoints is called a bond path. The network of bond paths defines a molecular graph of the system. Having defined a unique molecular graph for any molecular geometry, the total configuration space is partitioned into a finite number of regions. Each region is associated with a particular structure defined as an equivalence class of molecular graphs. A chemical reaction in which chemical bonds are broken and/or formed is therefore a trajectory in configuration space which must cross one of the boundaries between two neighbouring structural regions. These boundaries form the catastrophe set of the system which, like a phase diagram in thermodynamics, denotes the points of “balance” between neighbouring structures. A general analysis of the structural changes in an ABC type system is given in detail together with specific examples of all possible structural elements in a molecular system. The properties of the topologically defined atoms and their temporal changes are identified within a general formulation of subspace quantum mechanics. It is shown that the quantum mechanical partitioning of a system into subsystems coincides with the topological partitioning: both are defined by the same set of “zero flux” surfaces. Consequently the total energy, or any other property, is partitioned into additive atomic contributions. We show that, in general, a definite structure can be assigned to a given molecular system. Quantum mechanically this structure is associated with an open neighbourhood of the most probable nuclear geometry. Finally we generalize the notion of molecular structure to non-isolated molecules and, in contrast to recent work by Woolley, we conclude that molecular structure exists in spite of intermolecular interactions and not as a result of them.

Replica theory of quantum spin glasses

Abstract: The Sherrington-Kirkpatrick model, generalised to quantum spins, is discussed within an exact replica formalism and reduced to a (time-dependent) single-site problem. The existence of a phase transition is established for all values of the spin S.

Properties of vibrational energy levels in the quasi periodic and stochastic regimes

Abstract: Several aspects of the quantal energy spectrum are explored for the Henon–Heiles Hamiltonian system: a striking and initially unexpected continuation of sequences of eigenvalues from the quasiperiodic to the stochastic regime, the origin of large second differences Delta2Ei of eigenvalues arising from variation of a parameter, the comparison of classical and quantal spectra, and a comparison of the "classical" and quantal number of states. In the study of the second differences we find both "crossings" and "avoided crossings" of the eigenvalues. We discuss the importance of overlapping avoided crossings as a basis for a possible theory of "quantum stochasticity".

A Brief Survey of Stochastic Electrodynamics

Abstract: Stochastic electrodynamics and random electrodynamics are the names given to a particular version of classical electrodynamics. This purely classical theory is Lorentz’s classical electron theory(1) into which one introduces random electromagnetic radiation (classical zero-point radiation) as the boundary condition giving the homogeneous solution of Maxwell’s equations. The theory contains one adjustable parameter setting the scale of the random radiation, and this parameter is chosen in terms of Planck’s constant,h = 2πℏ. Many of the researchers(2–70) working on stochastic electrodynamics hope that it will provide an accurate description of atomic physics and replace or explain quantum theory. At the very least the theory makes available new tools for calculating van der Waals forces, and it deepens our understanding of the connections between classical and quantum theories.(71)

Double quantum cross polarization. Heteronuclear excitation and detection of NMR double quantum transitions in solids

Abstract: The application of Hartmann–Hahn cross polarization for the enhancement and for the detection of NMR double quantum coherence is investigated. The matching conditions and relaxation rates are discussed. It is found, in particular, that the double quantum cross relaxation rate is four times that of single quantum cross polarization. Double quantum cross polarization is utilized for the heteronuclear excitation and detection of nitrogen‐14 double quantum transitions in solids.

Quantum Mechanical Methods for Regular Polymers

Abstract: Publisher Summary The word “polymer” embraces a large class of complex and diverse compounds among which the quantum theory at present considers only a rather restricted subset. The range of applications of this quantum theory is not at all restricted to such unusual materials. The main limitation comes obviously from the ability of the model to comprise the physics and chemistry of what is actually a “regular” polymer. For all these materials, and in the same way as for simpler molecules, quantum chemistry is now starting to provide powerful instruments for interpreting and predicting the physical and chemical properties (structure, bonding, reactivity, etc.) for which a rather detailed knowledge of the electronic structure is required. Another reason for developing quantum methods for polymers is the increasing use of refined techniques (XPS, IR, NMR, etc.) to solve fundamental polymer problems—for example,XPS (or ESCA-electron spectroscopy for chemical analysis) spectra obtained with monochromatic X-ray radiation turn out to be powerful tools with which to study the electronic structure of polymers, both by providing precise information on core level binding energies and line shapes and by allowing the recording of the distribution of the valence electronic levels that might constitute a real and unique “fingerprint” of the polymer. The main conclusion of this chapter is that quantum mechanical methods are now able to provide significant understanding and insight into the electronic properties of regular polymers.

Can we undo quantum measurements

Abstract: The Schr\"odinger equation cannot convert a pure state into a mixture (just as Newton's equations cannot display irreversibility). However, to observe phase relationships between macroscopically distinguishable states, one has to measure very peculiar operators. An example, constructed explicitly, shows that the classical analog of such an operator cannot be measured, because to do so would violate classical irreversibility. This result justifies von Neumann's measurement theory, without any hypothesis on the role of the observer.

Theory of Nonlinear Spin Relaxation

Abstract: A rigorous quantum theory is developed on the nonlinear spin relaxation process. With the use of the phase space method, the quantum mechanical equation for a density matrix is mapped onto a c -number space. A quasi-probability function is then expanded in terms of spherical harmonics. It is clarified that the nonlinear relaxation process is characterized by 2 J ( J being the magnitude of a spin) different relaxation times. For J =1, time-evolutions of the first moment, fluctuation and probability function are exactly solved. An enhancement of the fluctuation is observed in the course of time development: This is similar to the phenomenon called “anomalous fluctuation” found in certain nonequilibrium systems.

Quantum Transport Theory

Abstract: Boltzmann transport theory (BTT) is an ideal theory. It has the twin virtues of conceptual and mathematical simplicity. It also works far better than one could reasonably expect from its origin as a graft from the classical theory of dilute gases. Quantum transport theory (QTT) (Kohn and Luttinger, 1957, 1958; Kubo, 1957; Dresden, 1961; Chester, 1963; Kubo, 1966; Luttinger, 1968) enjoys no such status: it is neither conceptually nor mathematically simple; it is very hard to make it work; and it often reduces, after considerable labour, to the Boltzmann picture (Peierls, 1974; Cohen and Thirrig, 1973). But even if there were no manifestly quantum transport phenomena (and we might single out transport in quantizing magnetic fields, but equally: hopping conduction, impurity conduction, polaron transport, high-frequency transport, quasi-1 D transport, the Kondo effect, size limited transport, and of course superconductivity) (Barker, 1978, 1979), we would still require QTT as an ab initio theory to explain how the phenomenological BTT picture and its related concepts actually arise from the underlying framework of reversible quantum statistical mechanics. QTT is thus concerned with: (1) an explanatory and supportive theory for the Boltzmann picture, where that exists; (2) setting confidence limits for the application of BTT; (3) developing the necessary novel concepts and transport kinetics for genuine quantum transport phenomena (the latter may be loosely defined as those effects which depend explicitly on the quantum mechanical nature of the electron, and/or those processes for which the simple relaxive local Boltzmann description fails.

The curious problem of spinor rotation

Abstract: Can the sign change of a spinor wavefunction rotated by 360 degrees be observed? If so, does this violate any basic quantum mechanical principles? The answers are yes and no, respectively. Tests of this fundamental quantum mechanical prediction are discussed, and the close analogy between the experimental methods employed and well-known processes in classical physical optics is pointed out.

Correlations and Physical Locality

Abstract: Two principles of locality used in discussions about quantum mechanics are distinguished. The intuitive no-action-at-a distance requirement is called physical locality. There is also a mathematical requirement of a kind of factorizability which is referred to as "locality". It is argued in this paper that factorizability is not necessary for physical locality. Ways of producing models that are physically local although not factorizable which are concerned with correlations between the behavior of pairs of particles are suggested. These models can account for all the quantum mechanical single and joint probabilities.

The quasiparticle view of wave propagation

Abstract: A mixed analytical and computational method of treating the propagation of single mode-type wavepackets or beams in inhomogeneous, time-varying, linear, nonlinear, or turbulent media is described. On averaging out fast space-time variations, one views a wavetrain kinetically as a system of "quasiparticles" whose distribution in position and momentum space permits the calculation of space-time dependent wavetrain properties such as envelope amplitude, phase, etc. Individual quasiparticles, which have an energy (Hamiltonian) descriptive of the mode-type, move along "ray" paths characteristic of the medium. The overall system of quasiparticles evolves in a nonsingular (caustic free) manner dependent on initial configuration and on effects of both trapped and untrapped quasiparticles. Starting from a kinetic description of the distribution of quasiparticles, one derives a "fluid dynamic" description that is equivalent to the Whitham and other averaging procedures for analyzing wavetrain propagation; a "macroparticle" description akin to known "centroid" analyses of localized wavetrains is also derivable. The particle-wave duality implied in the above analysis is discussed both from a quantum mechanical and classical standpoint. A few examples of the use of the quasiparticle method are presented.

Exact and approximate solutions for the one-dimensional transfer of polarized radiation, and applications to X-ray pulsars

Abstract: Theoretical studies of the radiation from hot, strongly magnetized plasmas, as encountered in pulsars, require a knowledge of solutions to the transfer equations for polarized radiation. We present here an analytic solution of the radiative transfer equations for one-dimensional propagation across a homogeneous slab of finite depth, as well as for a semi-infinite atmosphere. Absorption, scattering, and mode-exchange between the two polarizations are included, the role of the last being crucial. A physical discussion of the solutions for certain limiting cases and an interpretation in terms of probabilistic (quantum escape approach) arguments corroborate these solutions, and provide a better intuitive feel for the behavior of the radiated spectra. Whereas our analytic solutions are valid for any birefringent medium (not necessarily magnetic), our numerical examples and the qualitative discussion presented refer to the particular problem of the radiation from X-ray pulsars. Large-scale qualitative and quantitative changes from the nonmagnetic spectra are found, which affect both the continuum and the spectral lines.

Semiclassical quantization of multidimensional systems

Abstract: Low order classical perturbation theory is used to obtain semiclassical eigenvalues for a system of three anharmonically coupled oscillators. The results in the low energy region studied here agree well with the ’’exact’’ quantum values. The latter had been calculated by matrix diagonalization using a large basis set.

Quantum-Mechanical Fluctuations of the Resonance-Radiation Force

Abstract: The influence on atomic motion of quantum-mechanical fluctuations of the resonance-radiation force is investigated theoretically. Fluctuations due to both induced and spontaneous absorption-emission processes give rise to diffusion of atomic momentum, here described by a Fokker-Planck equation. It is shown that quantum-mechanical fluctuations of the radiation force place a lower bound on the temperature achievable by radiation cooling, inhibit cooling in a strong standing wave, and lead to finite, often short, confinement times for atoms in radiation traps.

On the relation between classical and quantum observables

Abstract: For systems with a finite number of degrees of freedom, the relation between classical and quantum observables is analysed. In particular, a precise statement of the correspondence limit is obtained.

Quantum friction in the c‐number picture: The damped harmonic oscillator

Abstract: Considering the Lagrangian proposed by Havas, that describes the classical damped motion of a particle, new momentum and position are defined in order to write a Hamiltonian that is subsequently quantized and expressed in terms of non‐Hermitian operators. Using the c‐number formalism proposed by Lax and Yuen, we associate to the quantum Liouville equation a Fokker–Planck one in terms of c‐numbers. From the properties of this equation we obtain the mean values of the position, momentum, and energy of a brownian particle and we also verify the uncertainty principle. We observe that when the system is considered under the Markov hypothesis, the stochastic force is intimately related to the uncertainty principle and to the zero point energy.