Quantum Mechanical Superposition Research Articles

Use of the Josephson junction in fundamental quantum electronics experiments

The Josephson junction provides two strong nonlinearities, the Josephson inductance utilized in parametric amplification and the sharp resistive knee used in SIS mixing. Both of these nonlinearities can be strong compared to a characteristic quantum current or voltage scale. This opens the possibility of using Josephson junctions to carry out fundamental experiments in quantum electronics that would be difficult or impossible to carry out at optical frequencies due to the lack of a correspondingly large nonlinearity in optical media. Here we propose a number of such experiments ranging from the generation of squeezed states with Josephson-parametric amplifiers to the generation of quantum-mechanical superpositions of macroscopically distinguishable states via Josephson-transmission lines. How the properties of such states can be investigated using SIS mixers will also be described. Squeezed states may be technologically useful in sensitive and precision measurement. How such states can be used to enhance interferometer sensitivity or reduce noise in phase sensitive measurement will also be described.

Testing Superposition in Quantum Mechanics

Testing Superposition in Quantum Mechanics

Quantum mechanics in coherent algebra on phase space

Quantum mechanics is formulated on a quantum mechanical phase space. The algebra of observables and states is represented by an algebra of functions on a phase space that fulfils a certain coherence condition, expressing the quantum mechanical superposition principle. The trace operation is an integration over phase space. In the case where the canonical variables independently run from - infinity to + infinity formalism reduces to the representation of quantum mechanics by Wigner distributions. However, the notion of coherent algebra allows one to apply the formalism to spaces for which the Wigner mapping is not known. The quantum mechanics of a particle in a plane in polar coordinates is discussed as an example.

Interference in atomic fluorescence excited by molecular photodissociation.

In photodissociation of a homonuclear diatomic molecule, conservation of linear and angular momenta requires that each atomic fragment follow identical but oppositely directed trajectories with respect to the molecular center of mass. For certain values of the incident photon energy, one of the atoms will be electronically excited while the other will be in its ground state. When a detector records the undispersed fluorescence from the decay of the excited atom it cannot distinguish which trajectory the excited atom followed and hence whether the photon possesses a blue or red Doppler shift corresponding to recoil towards or away from the detector. According to the principle of superposition in quantum mechanics, the wave function of the photon must be a sum over two paths corresponding to emission from an excited atom in either of the two recoil directions. Detection of such photons gives rise to an interference between the probability amplitudes for the two paths that is manifested in the output from the photodetector as a beat frequency. Since photodissociation of an ensemble of molecules gives rise to a distribution of recoil directions relative to the electric vector of the incident radiation, a range of beat frequencies must be present inmore » the detected signal. This paper gives a calculation of expected output voltage waveforms from a photodetector viewing atomic fluorescence excited by molecular photodissociation. Expressions are given for partial Fourier transforms of the photodetector signals. The results show that the shape of the voltage waveforms depends strongly on the asymmetry parameter for recoil of the photofragments and on whether or not the magnetic sublevels of the excited atomic state are created in a coherent superposition.« less

Comments on ?On the quantum mechanical superposition of macroscopically distinguishable states?

The substance of the authors' disagreement with the views of D. Gutkowski and M. V. Valdes Franco is presented.

The second law as a selection principle: The microscopic theory of dissipative processes in quantum systems

The second law of thermodynamics, for quantum systems, is formulated, on the microscopic level. As for classical systems, such a formulation is only possible when specific conditions are satisfied (continuous spectrum, nonvanishing of the collision operator, etc.). The unitary dynamical group can then be mapped into two contractive semigroups, reaching equilibrium either for t --> +infinity or for t --> -infinity. The second law appears as a symmetry-breaking selection principle, limiting the observables and density functions to the class that tends to thermodynamic equilibrium in the future (for t --> +infinity). The physical content of the dynamical structure is now displayed in terms of the appropriate semigroup, which is realized through a nonunitary transformation. The superposition principle of quantum mechanics has to be reconsidered as irreversible processes transform pure states into mixtures and unitary transformations are limited by the requirement that entropy remains invariant. In the semigroup representation, interacting fields lead to units that behave incoherently at equilibrium. Inversely, nonequilibrium constraints introduce correlations between these units.

Ermakov systems and quantum-mechanical superposition laws

Ermakov systems are pairs of coupled, time-dependent, nonlinear dynamical equations possessing a joint constant of the motion called an Ermakov invariant. The invariant provides a link between the two equations and leads to a superposition law between solutions to the Ermakov pair. Extensive studies of Ermakov systems in classical mechanics have been carried out. Here we present a detailed study of Ermakov systems from a quantum point of view, and prove that the solution to the Schr\"odinger equation for a general Ermakov system can be reduced to the solution of a time-independent Schr\"odinger equation involving the Ermakov invariant. We thereby arrive at a quantum-mechanical superposition law analogous to the classical superposition law.

Uniform semiclassical orbital calculations of heavy ion Coulomb excitation

A new semielassical approach, which can be derived from Feynman's path integral formulation of quantum mechanics, is applied to multiple Coulomb excitation for backward scattering angles. The basic features of this method are that the dynamics of the problem is treated completely classically (that is, one solves classical equations of motion) but the quantum mechanical superposition principle is retained by evaluating a phase along the classical trajectory and adding probability amplitudes for indistinguishable processes rather than probabilities themselves. One finds even a quantitative agreement with the conventional De Boer-Winther code. The limit of sudden collision (ξ = 0) for η → ∞ (η = Sommerfeld parameter) is evaluated analytically and is in very good agreement with results published for this case.

Semiclassical S-matrix theory of vibrationally inelastic collisions between two diatomic molecules

We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom-diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H2–D2 and D2–D2 collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations. We also examine in detail the classical dynamics of the collision process and show that the molecules pass through a number of intermediate states during the encounter.

Reaction Rates and the T-Matrix

A fully covariant expression is given for the rate of an arbitrary reaction based on the theory of special relativity and the superposition principle of quantum mechanics. The expression gives all phase-space and flux factors explicitly from a unified viewpoint. A useful concept, covariant beam strength, is introduced. Application is made to decay rates, cross sections, and beam-beam collisions.

A proposition-state structure

A generalization of the superposition principle of quantum mechanics is proposed introducing the concept of maximal state of a logic.

On the Principle of Superposition in Quantum Mechanics

The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."

Approximate Quantum-Mechanical Law of Corresponding States

Abstract : Use is made of a quantum-mechanical superposition approximation to derive a law of corresponding states. (Author)