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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Two photon annihilation operators and squeezed vacuum

Inverses of the harmonic oscillator creation and annihilation operators by their actions on the number states are introduced. Three of the two photon annihilation operators, viz., a(sup +/-1)a, aa(sup +/-1), and a(sup 2), have normalizable right eigenstates with nonvanishing eigenvalues. The eigenvalue equation of these operators are discussed and their normalized eigenstates are obtained. The Fock state representation in each case separates into two sets of states, one involving only the even number states while the other involving only the odd number states. It is shown that the even set of eigenstates of the operator a(sup +/-1)a is the customary squeezed vacuum S(sigma) O greater than.

Roy, Anil K.↗
NASA NTRS1995

Coherent states for the relativistic harmonic oscillator

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

Aldaya, Victor↗
NASA NTRS1996

The Squeezing Operator and the Squeezing States of Superspace

In this paper ,the unitary squeezing operator of 'superspace' is introduced and by making this operator act on the supercoherent state, the squeezing supercoherent states are obtained, then come out the four orthonormalization eigenstates of the square of annihilation operator A of the supersymmetry harmonic oscillator, and their squeezing character is also studied.

Aiqun, Ma↗
NASA NTRS1992

Going through a quantum phase

Phase measurements on a single-mode radiation field are examined from a system-theoretic viewpoint. Quantum estimation theory is used to establish the primacy of the Susskind-Glogower (SG) phase operator; its phase eigenkets generate the probability operator measure (POM) for maximum likelihood phase estimation. A commuting observables description for the SG-POM on a signal x apparatus state space is derived. It is analogous to the signal-band x image-band formulation for optical heterodyne detection. Because heterodyning realizes the annihilation operator POM, this analogy may help realize the SG-POM. The wave function representation associated with the SG POM is then used to prove the duality between the phase measurement and the number operator measurement, from which a number-phase uncertainty principle is obtained, via Fourier theory, without recourse to linearization. Fourier theory is also employed to establish the principle of number-ket causality, leading to a Paley-Wiener condition that must be satisfied by the phase-measurement probability density function (PDF) for a single-mode field in an arbitrary quantum state. Finally, a two-mode phase measurement is shown to afford phase-conjugate quantum communication at zero error probability with finite average photon number. Application of this construct to interferometric precision measurements is briefly discussed.

Shapiro, Jeffrey H.↗
NASA NTRS1992

Coherent states and parasupersymmetric quantum mechanics

It is well known that Parafermi and Parabose statistics are natural extensions of the usual Fermi and Bose ones, enhancing trilinear (anti)commutation relations instead of bilinear ones. Due to this generalization, positive parameters appear: the so-called orders of paraquantization p (= 1, 2, 3, ...) and h sub 0 (= 1/2, 1, 3/2, ...), respectively, the first value leading in each case to the usual statistics. The superpostion of the parabosonic and parafermionic operators gives rise to parasupermultiplets for which mixed trilinear relations have already been studied leading to two (nonequivalent) sets: the relative Parabose and the relative Parafermi ones. For the specific values p = 1 = 2h sub 0, these sets reduce to the well known supersymmetry. Coherent states associated with this last model have been recently put in evidence through the annihilation operator point of view and the group theoretical approach or displacement operator context. We propose to realize the corresponding studies within the new context p = 2 = 2h sub 0, being then directly extended to any order of paraquantization.

Debergh, Nathalie↗
NASA NTRS1994

Berry phase in Heisenberg representation

We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.

Andreev, V. A.↗
NASA NTRS1992

Quadratic squeezing: An overview

The amplitude of the electric field of a mode of the electromagnetic field is not a fixed quantity: there are always quantum mechanical fluctuations. The amplitude, having both a magnitude and a phase, is a complex number and is described by the mode annihilation operator a. It is also possible to characterize the amplitude by its real and imaginary parts which correspond to the Hermitian and anti-Hermitian parts of a, X sub 1 = 1/2(a(sup +) + a) and X sub 2 = i/2(a(sup +) - a), respectively. These operators do not commute and, as a result, obey the uncertainty relation (h = 1) delta X sub 1(delta X sub 2) greater than or = 1/4. From this relation we see that the amplitude fluctuates within an 'error box' in the complex plane whose area is at least 1/4. Coherent states, among them the vacuum state, are minimum uncertainty states with delta X sub 1 = delta X sub 2 = 1/2. A squeezed state, squeezed in the X sub 1 direction, has the property that delta X sub 1 is less than 1/2. A squeezed state need not be a minimum uncertainty state, but those that are can be obtained by applying the squeeze operator.

Hillery, M.↗
NASA NTRS1993

Which Q-analogue of the squeezed oscillator?

The noise (variance squared) of a component of the electromagnetic field - considered as a quantum oscillator - in the vacuum is equal to one half, in appropriate units (taking Planck's constant and the mass and frequency of the oscillator all equal to 1). A practical definition of a squeezed state is one for which the noise is less than the vacuum value - and the amount of squeezing is determined by the appropriate ratio. Thus the usual coherent (Glauber) states are not squeezed, as they produce the same variance as the vacuum. However, it is not difficult to define states analogous to coherent states which do have this noise-reducing effect. In fact, they are coherent states in the more general group sense but with respect to groups other than the Heisenberg-Weyl Group which defines the Glauber states. The original, conventional squeezed state in quantum optics is that associated with the group SU(1,1). Just as the annihilation operator a of a single photon mode (and its hermitian conjugate a, the creation operator) generates the Heisenberg Weyl algebra, so the pair-photon operator a(sup 2) and its conjugate generates the algebra of the group SU(1,1). Another viewpoint, more productive from the calculational stance, is to note that the automorphism group of the Heisenberg-Weyl algebra is SU(1,1). Needless to say, each of these viewpoints generalizes differently to the quantum group context. Both are discussed. The following topics are addressed: conventional coherent and squeezed states; eigenstate definitions; exponential definitions; algebra (group) definitions; automorphism group definition; example: signal-to-noise ratio; q-coherent and q-squeezed states; M and P q-bosons; eigenstate definitions; exponential definitions; algebra (q-group) definitions; and automorphism q-group definition.

Solomon, Allan I.↗
NASA NTRS1995

The relativistic many body problem with an oscillator interaction

We start with the total energy E for a system of three scalar relativistic particles that, because of Einstein's relation, will have square roots of functions of the momenta. By taking powers of this relation, we finally get a fourth degree polynomial in E(exp 2), where the square roots have disappeared, and which we can convert into a type of Schroedinger equation. To be in the center of mass frame we pass to Jocobi momenta and then replace them by creation and annihilation operators. We thus get an equation in terms of the generators of a U(2) group, which, in principle, we can solve in an elementary way. Finally, we rewrite our equation in a Poincare invariant form.

Moshinsky, Marcos↗
NASA NTRS1995

Oscillator-like coherent states for the Jaynes-Cummings Model

A new way of diagonalizing the Jaynes-Cummings Hamiltonian is proposed, which allows the definition of annihilation operators and coherent states for this model. Mean values and dispersions over these states are computed and interpreted.

Berubelauziere, Y.↗
NASA NTRS1989

Absorbing boundary conditions for second-order hyperbolic equations

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Jiang, Hong↗
NASA NTRS1990

Absorbing boundary conditions for second-order hyperbolic equations

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Jiang, Hong↗
NASA NTRS1993

Quons, an interpolation between Bose and Fermi oscillators

After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics, and infinite statistics, I discuss the statistics of 'quons' (pronounced to rhyme with muons), particles whose annihilation and creation operators obey the q-deformed commutation relation (the quon algebra or q-mutator) which interpolates between fermions and bosons. I emphasize that the operator for interaction with an external source must be an effective Bose operator in all cases. To accomplish this for parabose, parafermi and quon operators, I introduce parabose, parafermi, and quon Grassmann numbers, respectively. I also discuss interactions of non-relativistic quons, quantization of quon fields with antiparticles, calculation of vacuum matrix elements of relativistic quon fields, demonstration of the TCP theorem, cluster decomposition, and Wick's theorem for relativistic quon fields, and the failure of local commutativity of observables for relativistic quon fields. I conclude with the bound on the parameter q for electrons due to the Ramberg-Snow experiment.

Greenberg, O. W.↗
NASA NTRS1993

The suppression of pulsar and gamma-ray burst annihilation lines by magnetic photon splitting

Neutron stars, relativistic and compact by nature, show great potential for the copious creation of electron-positron pairs in the magnetospheres; these rapidly cool, thermalize, and then annihilate. It is therefore expected that many neutron sources might display evidence of pair annihilation lines in the 400-500 keV range. It is shown that magnetic photon splitting, which operates effectively at these energies and in the enormous neutron star magnetic fields, can destroy an annihilation feature by absorbing line photons and reprocessing them to lower energies. In so doing, photon splitting creates a soft gamma-ray bump and a broad quasi-power-law contribution to the X-ray continuum, which is too flat to conflict with the observed X-ray paucity in gamma-ray bursts. The destruction of the line occurs in neutron stars with surface fields of 5 x 10 exp 12 G or maybe even less, depending on the size of the emission region.

Baring, Matthew G.↗
NASA NTRS1987

The gamma-ray spectrometer experiment on the solar maximum mission satellite

The major activities summarized include: Gamma-Ray Spectrometer (GRS) instrument response and flight operation; solar flare studies; cosmic gamma-ray studies; summary of computer operations; search for flare-precursor protons; diffuse galactic annihilation radiation; cosmic ray bursts; atmospheric gamma ray spectrum; gamma ray line emission from supernovae and novae; improved angular resolutions using Earth occultation; and production processing of NASA IPD data. In addition, an updated list of published papers and invited papers or contributed papers presented at scientific meetings is provided.

Chupp, E. L.↗
NASA NTRS1994

Coherent states on the m-sheeted complex plane as m-photon states

Coherent states on the m-sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied. They are eigenstates of the operators a(sub m)(+), a(sub m) which create and annihilate clusters of m-particles. Applications of this formalism in the study of Hamiltonians that describe m-particle clustering are also considered.

Vourdas, Apostolos↗
NASA NTRS2003

A Scintillation Counter System Design To Detect Antiproton Annihilation using the High Performance Antiproton Trap(HiPAT)

The High Performance Antiproton Trap (HiPAT), a system designed to hold up to l0(exp 12) charge particles with a storage half-life of approximately 18 days, is a tool to support basic antimatter research. NASA's interest stems from the energy density represented by the annihilation of matter with antimatter, 10(exp 2)MJ/g. The HiPAT is configured with a Penning-Malmberg style electromagnetic confinement region with field strengths up to 4 Tesla, and 20kV. To date a series of normal matter experiments, using positive and negative ions, have been performed evaluating the designs performance prior to operations with antiprotons. The primary methods of detecting and monitoring stored normal matter ions and antiprotons within the trap includes a destructive extraction technique that makes use of a micro channel plate (MCP) device and a non-destractive radio frequency scheme tuned to key particle frequencies. However, an independent means of detecting stored antiprotons is possible by making use of the actual annihilation products as a unique indicator. The immediate yield of the annihilation event includes photons and pie mesons, emanating spherically from the point of annihilation. To "count" these events, a hardware system of scintillators, discriminators, coincident meters and multi channel scalars (MCS) have been configured to surround much of the HiPAT. Signal coincidence with voting logic is an essential part of this system, necessary to weed out the single cosmic ray events from the multi-particle annihilation shower. This system can be operated in a variety of modes accommodating various conditions. The first is a low-speed sampling interval that monitors the background loss or "evaporation" rate of antiprotons held in the trap during long storage periods; provides an independent method of validating particle lifetimes. The second is a high-speed sample rate accumulating information on a microseconds time-scale; useful when trapped antiparticles are extracted against a target, providing an indication of quantity. This paper details the layout of this system, setup of the hardware components around HiPAT, and applicable checkouts using normal matter radioactive sources.

Martin, James J.↗