16492315
Empirical State Determination of Entangled Two-Level Systems and Its Relation to Information Theory
Theoretical methods for empirical state determination of entangled two-level systems are analyzed in relation to information theory. We show that hidden variable theories would lead to a Shannon index of correlation between the entangled subsystems which is larger than that predicted by quantum mechanics. Canonical representations which have maximal correlations are treated by the use of Schmidt and Hilbert-Schmidt decomposition of the entangled states, including especially the Bohm singlet state and the GHZ entangled states. We show that quantum mechanics does not violate locality, but does violate realism.
27052128
Parity-dependent squeezing of light
A parity-dependent squeezing operator is introduced which imposes different SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator Hilbert space. This operator is used to define parity-dependent squeezed states which exhibit highly non-classical properties such as strong antibunching, quadrature squeezing, strong oscillations in the photon-number distribution, etc. In contrast to the usual squeezed states whose Q and Wigner functions are simply Gaussians, the parity-dependent squeezed states have much more complicated Q and Wigner functions that exhibit an interesting interference in phase space. The generation of these states by parity-dependent quadratic Hamiltonians is also discussed.
119995096
Coherent and thermal coherent state
The characterization of coherent states as the quantum states that split into two uncorrelated beams is considered. The characterization leads to the study of coherent states at finite temperature—thermal coherent states (TCS’s). These TCS’s are defined within the formalism of thermo field dynamics (TFD). TFD allows a generalization of the uncertainty relation that accounts for both thermal and quantum fluctuations. The TCS is shown to be a minimal state for the generalized uncertainty relation.
40587572
Inverted spectroscopy and interferometry for quantum-state reconstruction of systems with SU(2) symmetry
We consider how the conventional spectroscopic and interferometric schemes can be rearranged to serve for reconstructing quantum states of physical systems possessing SU(2) symmetry. The discussed systems include a collection of two-level atoms, a two-mode quantized radiation field with a fixed total number of photons, and a single laser-cooled ion in a two-dimensional harmonic trap with a fixed total number of vibrational quanta. In the proposed rearrangement, the standard spectroscopic and interferometric experiments are inverted. Usually one measures an unknown frequency or phase shift using a system prepared in a known quantum state. Our aim is just the inverse, i.e., to use a well-calibrated apparatus with known transformation parameters to measure unknown quantum states.
16820646
Analytic representations based on SU(1,1) coherent states and their applications
We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disc based on the SU(1,1) Perelomov coherent states and the Barut - Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A `weak' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index k is smaller than . Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.
15829252
Factorization of analytic representations in the unit disc and number-phase statistics of a quantum harmonic oscillator
The inner - outer part factorization of analytic representations in the unit disc is used for an effective characterization of the number-phase statistical properties of a quantum harmonic oscillator. It is shown that the factorization is intimately connected with the number-phase Weyl semigroup and its properties. In the Barut - Girardello analytic representation the factorization is implemented as a convolution. Several examples are given which demonstrate the physical significance of the factorization and its role for quantum statistics. In particular, we study the effect of phase-space interference on the factorization properties of a superposition state.
118973535
Some Recent Advances in Neutrino Physics
One answer to questions concerning the subject matter of elementary particle physics and its position within the physical sciences is that particle physics is the study of creation. To justify this idea, at least in part, consider the “big bang” model of creation of the universe. In that model the primeval fireball involved very high temperatures, estimated to be greater than 1011 degrees Kelvin (°K), which is to be compared with the interior temperature of the sun at about 107 degrees Kelvin. We believe the sun to be a nuclear furnace, generating its energy by individual nuclear interactions in the million electron volt (MeV) energy range. In the “big bang” the energies involved in the individual particle interactions would have been more than 104 times larger than in the sun, and thus in the tens of giga-electron volts (GeV). This is precisely the energy region of present-day high energy or elementary particle physics laboratory experiments. In this sense, then, laboratory experiments that study, even indirectly, lepton-lepton scattering or quark-quark interactions are revisiting creation.
123016244
Observation of new particle production by high energy neutrinos and antineutrinos
123621331
APPROACH TO THE NUCLEAR MANY-BODY PROBLEM BY VARIATIONALLY DETERMINED TRANSFORMATION. II.
We present a generalization of the Hartree-Fock (HF) method incorporating two-body correlations. The correlations are introduced by means of a unitary operator ${e}^{\mathrm{iF}}$, where $F$ is a Hermitian one- and two-body operator to be determined by the variational principle. Assuming that the matrix elements of $F$ are small so that powers of $F$ higher than the second may be neglected, a set of linear equations determining $F$ is obtained. The relation between our method and methods used to treat singular interactions is discussed. The method is applied to two recently suggested models and is compared with the HF method, second-order perturbation theory, and with the random-phase approximation. It is found that our method yields very good results within the range of validity of our approximations, which seems to call forth applications to more realistic problems. Possible applications to the study of collective phenomena in nuclei are indicated.
122959606
New Features of Neutrino Physics as Observed in Fermilab Exp. 1A
With the advent of large counter experiments and high energy accelerators many new phenomena have appeared in neutrino physics. Apart from the discovery of weak neutral currents [1] the most striking development has been the observation of v and v interactions with two muons in the final state [2a] (dimuon events) and more recently of v interactions with a muon and a positron in the final state [3]. Of equal importance has been the observation of departure from the scaling predictions observed in high energy v weak charged current reactions [4].
116105210
Observation of prompt muons from nucleon--nucleon interactions