Teaching Innovations in An Introductory Physics Course for Non-Science Majors

I have made several innovations to Physics 114: Physics of Sound, a course for Communication Disorders and General Education students at the University of Massachusetts. These changes include the use of a network of wireless communication devices called a Personal Response System, on-line tutorials and classnotes, a collaborative discussion section, exam corrections, microthemes, extra-credit papers, group extra-credit projects, and the use of student teaching assistants

Quantum Statistics: Is there an effective fermion repulsion or boson attraction?

Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins of such exchange force ideas, the validity for them, and the areas where they are highly misleading. We propose that future explanations of quantum statistics should avoid the idea of a effective force completely and replace it with more appropriate physical insights, some of which are suggested here.Comment: 26 pages, 3 figures. Submitted to American Journal of Physic

Quantum properties of a single beam splitter

When a single beam-splitter receives two beams of bosons described by Fock states (Bose-Einstein condensates at very low temperatures), interesting generalizations of the two-photon Hong-Ou-Mandel effect take place for larger number of particles. The distributions of particles at two detectors behind the beam splitter can be understood as resulting from the combination of two effects, the spontaneous phase appearing during quantum measurement, and the quantum angle. The latter introduces quantum "population oscillations", which can be seen as a generalized Hong-Ou-Mandel effect, although they do not always correspond to even-odd oscillations.Comment: 14 pages, 11 figure

Angular momentum conservation in measurements on spin Bose-Einstein condensates

We discuss a thought experiment where two operators, Alice and Bob, perform transverse spin measurements on a quantum system; this system is initially in a double Fock spin state, which extends over a large distance in space so that the two operators are far away from each other. Standard quantum mechanics predicts that, when Alice makes a few measurements, a large transverse component of the spin angular momentum may appear in Bob's laboratory. A paradox then arises since local angular momentum conservation seems to be violated. It has been suggested that this angular momentum may be provided by the interaction with the measurement apparatuses. We show that this solution of the paradox is not appropriate, so that another explanation must be sought. The general question is the retroaction of a quantum system onto a measurement apparatus. For instance, when the measured system is entangled with another quantum system, can its reaction on a measurement apparatus be completely changed? Is angular momentum conserved only on average over several measurements, but not during one realization of the experiment?Comment: 11 pages, 3 figure

Validity of the Hohenberg Theorem for a Generalized Bose-Einstein Condensation in Two Dimensions

Several authors have considered the possibility of a generalized Bose-Einstein condensation (BEC) in which a band of low states is occupied so that the total occupation number is macroscopic, even if the occupation number of each state is not extensive. The Hohenberg theorem (HT) states that there is no BEC into a single state in 2D; we consider its validity for the case of a generalized condensation and find that, under certain conditions, the HT does not forbid a BEC in 2D. We discuss whether this situation actually occurs in any theoretical model system.Comment: 6 pages, Latex, JLTP class, accepted by Jour. Low Temp. Phys., Quantum Fluids and Solids Conference QFS200

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.Comment: 6 pages, 1 figur

Beyond spontaneously broken symmetry in Bose-Einstein condensates

Spontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus not explain Bell inequality violations. We describe another situation that is beyond a SSB treatment: an experiment where particles from two (possibly macroscopic) condensate sources are used for conjugate measurements of the relative phase and populations. Off-diagonal phase effects are characterized by a "quantum angle" and observed via "population oscillations", signaling quantum interference of macroscopically distinct states (QIMDS).Comment: 10 pages 4 figure

Shot noise of interference between independent atomic systems

We study shot (counting) noise of the amplitude of interference between independent atomic systems. In particular, for the two interfering systems the variance of the fringe amplitude decreases as the inverse power of the number of particles per system with the coefficient being a non-universal number. This number depends on the details of the initial state of each system so that the shot noise measurements can be used to distinguish between such states. We explicitly evaluate this coefficient for the two cases of the interference between bosons in number states and in broken symmetry states. We generalize our analysis to the interference of multiple independent atomic systems. We show that the variance of the interference contrast vanishes as the inverse power of the number of the interfering systems. This result, implying high signal to noise ratio in the interference experiments, holds both for bosons and for fermions.Comment: 5 pages, 1 figure, final version, added a simple quantum-mechanical argument why two independent condensates with fixed number of particles in each must interfere in a generic experimental setu