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NASA NTRS1998

Fifth International Conference on Squeezed States and Uncertainty Relations

The Fifth International Conference on Squeezed States and Uncertainty Relations was held at Balatonfured, Hungary, on 27-31 May 1997. This series was initiated in 1991 at the College Park Campus of the University of Maryland as the Workshop on Squeezed States and Uncertainty Relations. The scientific purpose of this series was to discuss squeezed states of light, but in recent years the scope is becoming broad enough to include studies of uncertainty relations and squeeze transformations in all branches of physics including quantum optics and foundations of quantum mechanics. Quantum optics will continue playing the pivotal role in the future, but the future meetings will include all branches of physics where squeeze transformations are basic. As the meeting attracted more participants and started covering more diversified subjects, the fourth meeting was called an international conference. The Fourth International Conference on Squeezed States and Uncertainty Relations was held in 1995 was hosted by Shanxi University in Taiyuan, China. The fifth meeting of this series, which was held at Balatonfured, Hungary, was also supported by the IUPAP. In 1999, the Sixth International Conference will be hosted by the University of Naples in 1999. The meeting will take place in Ravello near Naples.

Han, D.↗
NASA NTRS1996

Fourth International Conference on Squeezed States and Uncertainty Relations

The fourth International Conference on Squeezed States and Uncertainty Relations was held at Shanxi University, Taiyuan, Shanxi, China, on June 5 - 9, 1995. This conference was jointly organized by Shanxi University, the University of Maryland (U.S.A.), and the Lebedev Physical Institute (Russia). The first meeting of this series was called the Workshop on Squeezed States and Uncertainty Relations, and was held in 1991 at College Park, Maryland. The second and third meetings in this series were hosted in 1992 by the Lebedev Institute in Moscow, and in 1993 by the University of Maryland Baltimore County, respectively. The scientific purpose of this series was initially to discuss squeezed states of light, but in recent years, the scope is becoming broad enough to include studies of uncertainty relations and squeeze transformations in all branches of physics, including, of course, quantum optics and foundations of quantum mechanics. Quantum optics will continue playing the pivotal role in the future, but the future meetings will include all branches of physics where squeeze transformations are basic transformation. This transition took place at the fourth meeting of this series held at Shanxi University in 1995. The fifth meeting in this series will be held in Budapest (Hungary) in 1997, and the principal organizer will be Jozsef Janszky of the Laboratory of Crystal Physics, P.O. Box 132, H-1052. Budapest, Hungary.

Han, D.↗
NASA NTRS1994

Multimode squeezing, biphotons and uncertainty relations in polarization quantum optics

The concept of squeezing and uncertainty relations are discussed for multimode quantum light with the consideration of polarization. Using the polarization gauge SU(2) invariance of free electromagnetic fields, we separate the polarization and biphoton degrees of freedom from other ones, and consider uncertainty relations characterizing polarization and biphoton observables. As a consequence, we obtain a new classification of states of unpolarized (and partially polarized) light within quantum optics. We also discuss briefly some interrelations of our analysis with experiments connected with solving some fundamental problems of physics.

Karassiov, V. P.↗
NASA NTRS1994

High-order squeezing of the quantum electromagnetic field and the generalized uncertainty relations in two-mode squeezed states

It is found that two-mode output quantum electromagnetic field in two-mode squeezed states exhibits higher-order squeezing to all even orders. And the generalized uncertainty relations are also presented for the first time. The concept of higher-order squeezing of the single-mode quantum electromagnetic field was first introduced and applied to several processes by Hong and Mandel in 1985. Lately Li Xizeng and Shan Ying have calculated the higher-order squeezing in the process of degenerate four-wave mixing and presented the higher-order uncertainty relations of the fields in single-mode squeezed states. In this paper we generalize the above work to the higher-order squeezing in two-mode squeezed states. The generalized uncertainty relations are also presented for the first time.

Li, Xi-Zeng↗
NASA NTRS2000

Sixth International Conference on Squeezed States and Uncertainty Relations

These proceedings contain contributions from about 200 participants to the 6th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'99) held in Naples May 24-29, 1999, and organized jointly by the University of Naples "Federico II," the University of Maryland at College Park, and the Lebedev Institute, Moscow. This was the sixth of a series of very successful meetings started in 1990 at the College Park Campus of the University of Maryland. The other meetings in the series were held in Moscow (1992), Baltimore (1993), Taiyuan P.R.C. (1995) and Balatonfuered, Hungary (1997). The present one was held at the campus Monte Sant'Angelo of the University "Federico II" of Naples. The meeting sought to provide a forum for updating and reviewing a wide range of quantum optics disciplines, including device developments and applications, and related areas of quantum measurements and quantum noise. Over the years, the ICSSUR Conference evolved from a meeting on quantum measurement sector of quantum optics, to a wide range of quantum optics themes, including multifacet aspects of generation, measurement, and applications of nonclassical light (squeezed and Schrodinger cat radiation fields, etc.), and encompassing several related areas, ranging from quantum measurement to quantum noise. ICSSUR'99 brought together about 250 people active in the field of quantum optics, with special emphasis on nonclassical light sources and related areas. The Conference was organized in 8 Sections: Squeezed states and uncertainty relations; Harmonic oscillators and squeeze transformations; Methods of quantum interference and correlations; Quantum measurements; Generation and characterisation of non-classical light; Quantum noise; Quantum communication and information; and Quantum-like systems.

Han, D.↗
NASA NTRS1996

Squeezed States, Uncertainty Relations and the Pauli Principle in Composite and Cosmological Models

The importance of not only uncertainty relations but also the Pauli exclusion principle is emphasized in discussing various 'squeezed states' existing in the universe. The contents of this paper include: (1) Introduction; (2) Nuclear Physics in the Quark-Shell Model; (3) Hadron Physics in the Standard Quark-Gluon Model; (4) Quark-Lepton-Gauge-Boson Physics in Composite Models; (5) Astrophysics and Space-Time Physics in Cosmological Models; and (6) Conclusion. Also, not only the possible breakdown of (or deviation from) uncertainty relations but also the superficial violation of the Pauli principle at short distances (or high energies) in composite (and string) models is discussed in some detail.

Terazawa, Hidezumi↗
NASA NTRS1992

The Second International Workshop on Squeezed States and Uncertainty Relations

This conference publication contains the proceedings of the Second International Workshop on Squeezed States and Uncertainty Relations held in Moscow, Russia, on 25-29 May 1992. The purpose of this workshop was to study possible applications of squeezed states of light. The Workshop brought together many active researchers in squeezed states of light and those who may find the concept of squeezed states useful in their research, particularly in understanding the uncertainty relations. It was found at this workshop that the squeezed state has a much broader implication than the two-photon coherent states in quantum optics, since the squeeze transformation is one of the most fundamental transformations in physics.

D Han↗
NASA NTRS1993

Uncertainty relations, zero point energy and the linear canonical group

The close relationship between the zero point energy, the uncertainty relations, coherent states, squeezed states, and correlated states for one mode is investigated. This group-theoretic perspective enables the parametrization and identification of their multimode generalization. In particular the generalized Schroedinger-Robertson uncertainty relations are analyzed. An elementary method of determining the canonical structure of the generalized correlated states is presented.

Sudarshan, E. C. G.↗
NASA NTRS1996

Number-Phase Uncertainty Relations for Optical Fields

The Hermitian phase formalism of Pegg and Barnett allows for direct calculations of the phase variance and, consequently, the number-phase uncertainty product. This gives us a unique opportunity, inaccessible before, to study the number-phase uncertainty relations for optical fields in a direct way within a consistent quantum formalism. A few examples of fields generated in nonlinear optical processes are studied from the point of view of their number-phase uncertainty relations.

Tanas, Ryszard↗
NASA NTRS1993

Positive phase space distributions and uncertainty relations

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Kruger, Jan↗
NASA NTRS1996

Photon Number-Phase Uncertainty Relation in the Evolution of the Field in a Kerr-Like Medium

A model of a single-mode field, initially prepared in a coherent state, coupled to a two-level atom surrounded by a nonlinear Kerr-like medium contained inside a very good quality cavity is considered. We derive the photon number-phase uncertainty relation in the evolution of the field for a weak and strong nonlinear coupling respectively, within the Hermitian phase operator formalism of Pegg and Barnett, and discuss the effects of nonlinear coupling of the Kerr-like medium on photon number-phase uncertainty relation of the field.

Fan, An-Fu↗
NASA NTRS1996

Generalization of the Time-Energy Uncertainty Relation of Anandan-Aharonov Type

A new type of time-energy uncertainty relation was proposed recently by Anandan and Aharonov. Their formula, to estimate the lower bound of time-integral of the energy-fluctuation in a quantum state is generalized to the one involving a set of quantum states. This is achieved by obtaining an explicit formula for the distance between two finitely separated points in the Grassman manifold.

Hirayama, Minoru↗
NASA NTRS1994

Two new kinds of uncertainty relations

We review a statistical-geometrical and a generalized entropic approach to the uncertainty principle. Both approaches provide a strengthening and generalization of the standard Heisenberg uncertainty relations, but in different directions.

Uffink, Jos↗
NASA NTRS1994

Correlated quadratures of resonance fluorescence and the generalized uncertainty relation

Resonance fluorescence from a two-state atom has been predicted to exhibit quadrature squeezing below the Heisenberg uncertainty limit, provided that the optical parameters (Rabi frequency, detuning, laser linewidth, etc.) are chosen carefully. When the correlation between two quadratures of the radiation field does not vanish, however, the Heisenberg limit for quantum fluctuations might be an unrealistic lower bound. A generalized uncertainty relation, due to Schroedinger, takes into account the possible correlation between the quadrature components of the radiation, and it suggests a modified definition of squeezing. We show that the coherence between the two levels of a laser-driven atom is responsible for the correlation between the quadrature components of the emitted fluorescence, and that the Schrodinger uncertainty limit increases monotonically with the coherence. On the other hand, the fluctuations in the quadrature field diminish with an increasing coherence, and can disappear completely when the coherence reaches 1/2, provided that certain phase relations hold.

Arnoldus, Henk F.↗
NASA NTRS2002

Comparison of Two Methods for Estimating the Sampling-Related Uncertainty of Satellite Rainfall Averages Based on a Large Radar Data Set

The uncertainty of rainfall estimated from averages of discrete samples collected by a satellite is assessed using a multi-year radar data set covering a large portion of the United States. The sampling-related uncertainty of rainfall estimates is evaluated for all combinations of 100 km, 200 km, and 500 km space domains, 1 day, 5 day, and 30 day rainfall accumulations, and regular sampling time intervals of 1 h, 3 h, 6 h, 8 h, and 12 h. These extensive analyses are combined to characterize the sampling uncertainty as a function of space and time domain, sampling frequency, and rainfall characteristics by means of a simple scaling law. Moreover, it is shown that both parametric and non-parametric statistical techniques of estimating the sampling uncertainty produce comparable results. Sampling uncertainty estimates, however, do depend on the choice of technique for obtaining them. They can also vary considerably from case to case, reflecting the great variability of natural rainfall, and should therefore be expressed in probabilistic terms. Rainfall calibration errors are shown to affect comparison of results obtained by studies based on data from different climate regions and/or observation platforms.

Lau, William K. M.↗
NASA NTRS1994

The Stokes line width and uncertainty relations

For a function given by contour integral the two types (conventions) of asymptotic representations are considered: the usual representation by asymptotic series in inverse powers of large parameters and the special division of contour integral in contributions of high and low saddle points. It is shown that the width of the recessive term formation zone (Stokes strip) in the second convention is determined by uncertainty relation and is much less than the zone width in the first convention. The reasons of such a difference is clarified. The results of the work are useful for understanding of formation region of the exponentially small process arising on the background of the strong one.

Nikishov, A. I.↗
NASA NTRS1987

Uncertainty relations for light waves and the concept of photons

A Lorentz-covariant localization for light waves is presented. The unitary representation for the electromagnetic four-potential is constructed for a monochromatic light wave. A model for covariant superposition is constructed for light waves with different frequencies. It is therefore possible to construct a wave function for light waves carrying a covariant probability interpretation. It is shown that the time-energy uncertainty relation (Delta-t)(Delta-omega) = about 1 for light waves is a Lorentz-invariant relation. The connection between photons and localized light waves is examined critically.

Han, D.↗