Quantum Mechanical Fluctuations Research Articles

Limits on tradeoffs between third-order optical nonlinearity, absorption loss, and pulse duration in self-induced transparency and real excitation.

Self-induced transparency in a resonant two-level system creates a 2\ensuremath{\pi}-soliton pulse, which realizes large optical nonlinearities with a small absorption loss \ensuremath{\alpha} for a short pulse duration \ensuremath{\tau}. Quantum-mechanical zero-point field fluctuations introduce an ultimate dissipation loss in such a resonant and coherent process and place fundamental limits on the ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau} value. This value is independent of the dipole moment, atomic density, and pulse duration and is uniquely determined by an optical wavelength, e.g., ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau}\ensuremath{\sim}1.2\ifmmode\times\else\texttimes\fi{}${10}^{21}$${\ensuremath{\lambda}}^{4}$ esu cm/s. The similar limit on ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau} value is obtained in a usual operation mode, when the pulse duration becomes much longer than the atomic decay constants and the real excitation of the atoms occurs instead of the virtual excitation in self-induced transparency. The implication of these limits on optical squeezed-state generation, quantum nondemolition measurement, and reversible logic is discussed.

Mass distributions in different fissioning nuclei

The theory of nuclear fission is reconsidered by introducing the charge asymmetry in the asymmetric two-centre shell model as a dynamical collective coordinate. The quantum-mechanical fluctuations which are accompanied with the collective motion are responsible for the mass distributions in fission. Numerical calculations are carried out for the mass distributions and charge dispersions for the nuclear fission of the236U and238U nuclei. Also, the cross-sections of the photofission of the236U and238U nuclei are numerically calculated as a function of the photon energy. The present obtained theoretical calculations are in good agreement with the experimental measurements.

Polarization waves and super-radiance in active media

The macroscopic electrodynamics of time-dependent coherent processes in active media is reviewed. Dicke super-radiance in the two-level model and cyclotron super-radiance in a model consisting of an electron beam in a magnetic field are investigated. Similar phenomena in other media are discussed. Particular attention is devoted to polarization waves, i.e., a type of normal wave that coexists with electromagnetic waves and in many ways determines the character of coherent effects. Super-radiance is considered as a dissipative instability of negative-energy polarization waves, which occurs in an active sample as a result of losses by emission of positive-energy electromagnetic waves into the ambient space. The method of phenomenological quantization is developed for unstable modes in active samples, and directly describes the quantum-mechanical properties of collective excitations. The procedure is used to analyze macroscopic quantum-mechanical fluctuations of super-radiance.

Effects that can stabilise multiple spin-density waves

Antiferromagnetism on the face-centred cubic lattice is frustrated. The different competing spin arrangements are degenerate in the classical limit of the Heisenberg model. The author considers quantum-mechanical spin fluctuations, using the Holstein-Primakoff transformation, as a perturbation to lift this degeneracy and find that the collinear spin arrangement is stabilised. When he considers the inclusion of paramagnetic impurities, however, he finds that non-collinear arrangements are locally preferred. He suggests this scenario as a possible explanation for the fact that manganese, when quenched in a face-centred cubic lattice, can be driven from a collinear to non-collinear spin arrangement by doping with either nickel, iron or iridium.

Laser cooling of antihydrogen

We present a short review of the essential techniques of cooling free atoms by resonant laser radiation. The different contributions to the light forces are explained and their application to the problem of damping the thermal motion of free atoms is described. Due to quantum mechanical fluctuations of the light force there exists a limit temperature for a given atomic transition. Deceleration of atomic beams by the radiation pressure demands techniques to maintain the resonance condition while the Doppler shift of the decelerated atom is rapidly changing. Radiation forces may serve to compress and deflect slow atomic beams as well as to trap cold atoms. The possible use of pulsed laser radiation is discussed.

Mass Distributions and Charge Dispersion for the Nuclear Fission

AbstractThe theory of nuclear fission is reconsidered by introducing the charge asymmetry in the asymmetric two center shell model as a dynamical collective coordinate. The quantum mechanical fluctuations, which are accompanied with the collective motion as a function of the mass asymmetry, are responsible for the mass distributions in nuclear fission. Numerical calculations are carried out for the mass distributions and charge dispersions for the nuclear fission of the 236U and 238U nuclei. The present obtained theoretical calculations are in good agreement with the experimental measurements.

Still More Squeezing of Optical Noise

Quantum optics experimenters have been pushing hard to generate greater “squeezing.” This drive was encouraged by last year's milestone demonstration at AT&T Bell Labs that the noise from an optical cavity had been measurably squeezed, that is, that the noise in one phase of the signal had been reduced below the level normally associated with quantum mechanical fluctuations in the vacuum field. Until then, that vacuum noise level had represented the fundamental quantum limit to precision in optical experiments. The Bell Labs experiment reduced the noise by 7–10% below this normal quantum limit (see PHYSICS TODAY, March 1986, page 17), and several experiments since then have achieved noise reductions of at least 20%. The most spectacular results to date have been obtained by a team at the University of Texas at Austin consisting of Ling-An Wu, Min Xiao, H. Jeffrey Kimble, John L. Hall (of the Joint Institute for Laboratory Astrophysics) and Huifa Wu, who have observed noise reductions to more than 60% below the normal level.

X-RAY ABSORPTION SPECTROSCOPY (L3 EDGES, XANES, EXAFS) ON 4f MIXED-VALENT COMPOUNDS

X-RAY ABSORPTION SPECTROSCOPY (L₃ EDGES, XANES, EXAFS) ON 4f MIXED-VALENT COMPOUNDS

Quantum theory of nonlinear mixing in multimode fields: General theory.

A general quantum theory of nonlinear mixing in multimode fields is formulated. The theory is valid for arbitrary media and thus includes various diverse cases such as those corresponding to nonlinear mixing in multilevel systems, optical fibers, etc. Thus Zeeman coherence effects are automatically included. It is applicable to both degenerate and nondegenerate mixing experiments. The theory is in terms of two distinct sets of correlation functions of the polarization operators. One set of correlations is related to the nonlinear susceptibilities. The other set has no counterpart in semiclassical theory and is related to the quantum-mechanical fluctuations of the polarization operator. The general structure of the evolution of the density matrix of the generated fields is discussed. The quantum statistics of the generated fields can be studied in terms of the Wigner distribution function which is explicitly evaluated. Higher-order squeezing characteristics of the field are discussed. Conditions under which the quantization of the semiclassical equations is adequate are examined. The application of the quantum theory to nonlinear mixing in two-photon media is also presented. The theory is also capable of accounting for the interparticle correlations.

Field-induced fluctuation correlations and the effects of van der Waals interactions on molecular polarizabilities

New expressions for the van der Waals contribution to the collision-induced, static polarizability of a molecular pair (ΔαvdW) are derived within a reaction-field theory. For molecules interacting at long range, multipole expansions are used to determine the reaction field; at shorter range, where overlap is small but nonnegligible, the derivation is based on a nonlocal polarizability density model. In both cases, we obtain ΔαvdW in terms of integrals over imaginary frequencies, each involving the product of a hyperpolarizability for one molecule and a polarizability or hyperpolarizability for the other molecule. In addition, we show that the polarizability changes induced by van der Waals interactions between two molecules stem from two distinct physical effects. First, in an applied field F, each molecule is polarized nonlinearly by the simultaneous action of the field due to the fluctuating charge distribution of its neighbor and the field F. Second, the applied field F alters the correlations between the spontaneous, quantum mechanical fluctuations in the charge density of each molecule, thus affecting its interaction with the neighboring molecule. Effects of field-induced fluctuation correlations have not been included in earlier models for the van der Waals contributions to pair polarizabilities.

Path-integral methods for treating quantal behavior in solids: Mean-field theory and the effects of fluctuations.

Recent developments in the chemical literature have shown how discretized path integrals may be used to treat the quantum-mechanical internal degrees of freedom of molecules in liquids. This paper suggests that analogous methods might also be useful for quantum-mechanical solid-state problems, such as those posed by lattice-spin systems. The idea, illustrated in this paper by a common model for tunneling in solids, the transverse Ising model, is to transform the quantal spins into classical spins with ``internal structure.'' The resulting classical system can then be treated by analytical methods. For the transverse Ising model, both the traditional mean-field theory and a new approximation (which includes a fluctuation correction) are derived in this way. The effects of thermal and quantum-mechanical fluctuations are shown to be largely identical for the example considered.

Quantum Fluctuation of Pinned Charge Density Waves vs Superconducting Fluctuation in One-Dimensional Conductors

Effect of quantum fluctuation on impurity pinning of charge density wave is studied by applying the quantum Monte Carlo method to the Fukuyama-Lee model in one dimension. Existence of metastable states near the ground state and the quantum-mechanical fluctuation between them are demonstrated. A new formulation to treat the superconducting fluctuation is presented and it is shown that the competition between charge density and superconducting fluctuations is strongly affected by the local degree of pinning.

Excess electrons in simple fluids. III. Role of solvent polarization

We have extended the RISM-polaron theory of excess solvated electrons to treat the effects of quantum mechanical charge density fluctuations in the solvent particles. Our numerical results examine a model in which the solvent is composed of hard spheres with internal Drude oscillators. By varying the fundamental Drude oscillator frequency, one may explore the role of solvent polarization as it depends upon the time scale of the dipolar motions. We describe general trends predicted by the theory for this model, and we discuss the sensitivity of our results to changes in the model characterizing the interactions between the electrons and the solvent molecules.

Stabilization of stokes pulse energies in the nonlinear regime of stimulated Raman scattering

An experimental study of quantum mechanical pulse energy fluctuations in stimulated Raman scattering from hydrogen is presented. The probability density function P( W) for Stokes pulse energy W is measured for highly transient scattering in both the linear and nonlinear gain regimes. While large pulse energy fluctuations (100%) occur in the linear gain regime, the fluctuations are reduced to about 20% in the nonlinear regime where the laser pulse is depleted significantly. The results are in excellent agreement with the theoretical predictions of Lewenstein.

Bound electron dynamics: Exact solution for a one-dimensional oscillator-string model

The dynamical problem of a harmonically bound electron with standard dipole model coupling to the electromagnetic field in a finite one-dimensional space is solved exactly in a simple manner. It is easily shown that in this model the coupling between the electron and the field is “rigid”, in the sense of and in complete analogy with a recent treatment of a purely mechanical particle on a string. As a consequence the electron's quantum mechanical momentum fluctuations exhibit a logarithmic ultraviolet divergence. In the limit of infinite spatial extension of the field, and apart from quantal noise, the electron behaves exactly as a simple linearly damped harmonic oscillator.

Fission yields at different fission-product kinetic energies for thermal-neutron-induced fission of 239Pu

At the recoil spectrometer “Lohengrin” of the Institut Laue-Langevin in Grenoble, the yields of the light fission products from the thermal-neutron-induced fission of 239Pu were measured as a function of A, Z, the kinetic energy E and the ionic charge states q. The nuclear charge and mass distributions summed over all ionic charge states were determined for different light fissionproduct kinetic energies between 93 and 112 MeV. The proton odd-even effect which was measured to be (11.6 ± 0.6)% causes considerable fine structure in the yields. The average kinetic energy of even- Z elements in the light fission-product group is 0.3 ± 0.1 MeV larger than for odd- Z elements. The neutron odd-even effect is (6.5 ± 0.7)%. The comparison with previously published data 1) for thermal-neutron-induced fission of 235U reveals a correlation between the proton odd-even effect in the yield and in the kinetic energy of the elements. The dependence of the proton odd-even effect on the fragmentation is very similar for 235U and 239Pu when it is considered as a function of the nuclear charge of the heavy fission products. The isobaric variances σ z 2. for thermal-neutron fission of 235U and 239Pu coincide at all kinetic energies if the influence of the proton odd-even effect is averaged out. This supports the hypothesis that the magnitude of σ z 2 is determined only by quantum-mechanical zero-point fluctuations. The influence of the spherical shells Z = 50 and N = 82 on the fragmentation is discussed.

Fluctuations in the phase-conjugate signal generated via degenerate four-wave mixing

The excess fluctuations of the phase-conjugate (PC) signal generated via pulsed degenerate four-wave mixing (DFWM) in sodium vapor are investigated. Various dye-laser oscillator and amplifier combinations are employed to trace the sources of these fluctuations. For DFWM driven by an externally-stabilized cw dye-laser oscillator amplified with a dye system pumped by the smoothed pulses of a Nd:YAG laser, the PC excess fluctuations are very highly correlated with the energy fluctuations of the input amplified dye-laser pulses. Thus, input-pulse selection on the basis of energy alone permits observation of the quantum-mechanical fluctuations of the PC signal.

Temperature effects in five-dimensional Kaluza-Klein theory

We examine the combined effectsof thermal and quantum-mechanical fluctuations in a Kaluza-Klein universe with a single compact spatial dimension of length L¯5. From the one-loop effective potential for L¯5 two types of instability are evident. If initially L¯5 is less than a temperature-dependent critical length, L¯5 will shrink at least down to a length comparable to the Planck length. This instability has been noted by Appelquist and Chodos in the zero-temperature limit. If, on the other hand, L¯5 starts out larger than the critical length, it will tend to increase. This result suggests that temperature effects may play an important role in Kaluza-Klein cosmological models.

Low‐temperature fluctuational motion of dislocations in crystals I. Quantum and dissipative effects

AbstractA mechanism underlying fluctuational bending of dislocation segments is considered which is based on periodical ordering in the thermal motion of atoms near the dislocation core. Basic principles of calculating the probability of dislocation unpinning from local obstacles due to the fluctuations are formulated. As found, the interaction of dislocation segments experiencing fluctuational bending with phonons and/or conduction electrons, described in the framework of the usual dissipation model, can result in a reduction of the energy of atoms near the dislocation core during the fluctuation. Consequently, the effective activation energy of the dislocation unpinning from local obstacles is increased, i.e. the mean velocity of the activated dislocation motion drops. Activated dislocation motion at low temperatures is analysed with an account of the possible quantum mechanical fluctuations which can arise in condensed structures owing to the correlation of atomic zero point vibrations. An expression is derived for the probability of low temperature fluctuational dislocation with allowance for quantum mechanical effects.

Comment on path integral for general time-dependent solvable schrödinger equation

We explicitly perform the infinitely many integrations in the path integral of an arbitrary time-dependent quantum-mechanical fluctuation problem whose Schrodinger equation is solvable.