Mullin, William
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Professor Emeritus, Department of Physics, College of Natural Sciences
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Mullin
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William
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Physics
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Publication Open Access Bose-Einstein condensation in a harmonic potential(1997) Mullin, WJWe examine several features of Bose-Einstein condensation (BEC) in an external harmonic potential well. In the thermodynamic limit, there is a phase transition to a spatial Bose-Einstein condensed state for dimensionD≥2. The thermodynamic limit requires maintaining constant average density by weakening the potential while increasing the particle numberN to infinity, while of course in real experiments the potential is fixed andN stays finite. For such finite ideal harmonic systems we show that a BEC still occurs, although without a true phase transition, below a certain “pseudo-critical” temperature, even forD=1. We study the momentum-space condensate fraction and find that it vanishes as 1/sqrt(N) in any number of dimensions in the thermodynamic limit. InD≤2 the lack of a momentum condensation is in accord with the Hohenberg theorem, but must be reconciled with the existence of a spatial BEC inD=2. For finite systems we derive theN-dependence of the spatial and momentum condensate fractions and the transition temperatures, features that may be experimentally testable. We show that theN-dependence of the 2D ideal-gas transition temperature for a finite system cannot persist in the interacting case because it violates a theorem due to Chester, Penrose, and Onsager.Publication Open Access Giant viscosity enhancement in a spin-polarized fermi liquid(2007-01) Akimoto, H; Xia, JS; Candela, D; Mullin, WJ; Adams, ED; Sullivan, NSThe viscosity is measured for a Fermi liquid, a dilute 3He-4He mixture, under extremely high magnetic field/temperature conditions (B≤14.8 T, T≥1.5 mK). The spin-splitting energy μB is substantially greater than the Fermi energy kBTF; as a consequence the polarization tends to unity and s-wave quasiparticle scattering is suppressed for T≪TF. Using a novel composite vibrating-wire viscometer an enhancement of the viscosity is observed by a factor of more than 500 over its low-field value. Good agreement is found between the measured viscosity and theoretical predictions based upon a t-matrix formalism.Publication Metadata only ANALYSIS OF CERTAIN BINARY COLLISION APPROXIMATION CLOSURES OF THE BBGKY HIERARCHY(1995) SNIDER, RF; Mullin, WJ; LALOE, FThe closure of the BBGKY hierarchy to obtain the Boltzmann equation requires, in particular, restricting particle interactions to include only isolated binary collisions. Boercker and Dufty accomplish this by approximating the three-particle reduced density operator in a particular manner that favours correlation between two of the particles, while ignoring the correlation with the third. The tradition of most other closures has more closely followed Boltzmann's original thinking to completely neglect any reference to three-particle effects while assuming a generalized form of molecular chaos for the pair density operator. The two closures are compared in two ways: (a) by finding iterated series solutions of the BBGKY hierarchy and of the Boltzmann equation; (b) by computing an exact correction to the quantum Boltzmann equation. A consequence of the comparison of the iterated series shows that an important, but little emphasized, difference between the BBGKY and Boltzmann hierarchies is the effective instantaneousness of binary collisions in the latter. The form for the correction found is shown to vanish for either closure provided the instantaneousness of the binary collisions is imposed. It is shown moreover that the correction is closely related to the three-body collision integral arising in the standard theory of the density corrections to the Boltzmann equation. We also comment on the related work of Klimontovich, who introduces an approximation analogous to that of Boercker and Dufty.Publication Metadata only LONGITUDINAL RELAXATION-TIME FOR DILUTE QUANTUM GASES(1990) Mullin, WJ; LALOE, F; RICHARDS, MGWe calculate the longitudinal relaxation timeT 1 for a polarized spin-1/2 Fermi gas, in zero magnetic field, for conditions of temperatureT and densityn such that Boltzmann statistics are valid. Our results show generally thatT 1 is independent of polarization of the gas. At highT, where the thermal wavelength lambda is small compared to the scattering lengtha, T 1 is proportionalT 1/2, while at lowT, such that lambda is greater thana, T 1 is proportional toT –1/2.T 1 thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. Physical arguments show that the existence of the minimum does not depend on the presence of an attractive part of the potential. As an example of the expected temperature dependence we calculateT 1 numerically, via the distorted-wave Born approximation, for the case of a gas interacting via a hard core. We also computeT 1 for a spin-1/2 Bose gas, which also shows a minimum.Publication Open Access Interferometry with independent Bose-Einstein condensates: parity as an EPR/Bell quantum variable(2009-01) Laloe, F; Mullin, WJWhen independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement, with two possible results ±1. With two interferometers and two BEC’s, the parity (product of all results obtained at each interferometer) has all the features of an Einstein-Podolsky-Rosen quantity, with perfect correlations predicted by quantum mechanics when the settings (phase shifts of the interferometers) are the same. When they are different, significant violations of Bell inequalities are obtained. These violations do not tend to zero when the number N of particles increases, and can therefore be obtained with arbitrarily large systems, but a condition is that all particles should be detected. We discuss the general experimental requirements for observing such effects, the necessary detection of all particles in correlation, the role of the pixels of the CCD detectors, and that of the alignments of the interferometers in terms of matching of the wave fronts of the sources in the detection regions. Another scheme involving three interferometers and three BEC’s is discussed; it leads to Greenberger-Horne-Zeilinger (GHZ) sign contradictions, as in the usual GHZ case with three particles, but for an arbitrarily large number of them. Finally, generalizations of the Hardy impossibilities to an arbitrarily large number of particles are introduced. BEC’s provide a large versality for observing violations of local realism in a variety of experimental arrangements.Publication Open Access Evolution of additional (hidden) quantum variables in the interference of Bose-Einstein condensates(2006-01) Mullin, WJ; Krotkov, R; Laloe, FAdditional variables (also often called “hidden variables”) are sometimes added to standard quantum mechanics in order to remove its indeterminism or “incompleteness” and to make the measurement process look more classical. Here we discuss a case in which an additional variable arises almost spontaneously from the quantum formalism: the emergence of a relative phase between two highly populated Fock-state Bose-Einstein condensates. The model simulated here involves the interference of two Bose condensates, one with all up spins and the other with down spins, along a z axis. With the clouds overlapping, we consider the results of measuring spins in a transverse plane (the general direction is studied in an appendix). The determination of the previously “hidden” phase becomes progressively more definite as additional measurements are made. We also provide an analysis of a recent and closely related experiment.Publication Metadata only EXACT TRANSPORT-PROPERTIES OF DEGENERATE, WEAKLY INTERACTING, AND SPIN-POLARIZED FERMIONS(1983) Mullin, WJ; MIYAKE, KExact results for the transport coefficients of a highly degenerate spin-polarized Fermi system are presented. The case of weakly interacting particles, such as dilute3He in4He or D darr, is treated. The results are compared to the variational treatment and corrections as large as 8% are found. Detailed behavior of the polarization of an ideal Fermi gas as a function of temperature and magnetic field is discussed as a model for dilute3He in4He. Limits of applicability of the formulas are given. We find that at appropriate fields and temperatures, the two spin species may be considered to be a mixture of a degenerate and a classical gas.Publication Metadata only Path-integral Monte Carlo and the squeezed trapped Bose-Einstein gas(2006-01) Fernandez, JP; Mullin, WJBose-Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two-dimensional (2D). We confirm the plausibility of this result by performing path-integral Monte Carlo (PIMC) simulations of trapped Bose gases of increasing anisotropy and comparing them to the predictions of finite-temperature many-body theory. PIMC simulations provide an essentially exact description of these systems; they yield the density profile directly and provide two different estimates for the condensate fraction. For the ideal gas, we find that the PIMC column density of the squeezed gas corresponds quite accurately to that of the exact analytic solution and, moreover, is well mimicked by the density of a 2D gas at the same temperature; the two estimates for the condensate fraction bracket the exact result. For the interacting case, we find 2D Hartree-Fock solutions whose density profiles coincide quite well with the PIMC column densities and whose predictions for the condensate fraction are again bracketed by the PIMC estimates.Publication Metadata only SOLUTION OF THE KINETIC-EQUATION FOR POLARIZED FERMI SYSTEMS AT ALL TEMPERATURES(1987) JEON, JW; Mullin, WJWe have solved the kinetic equation for a dilute, polarized Fermi system for a range of temperatures from the degenerate limit to the Boltzmann case. The solution is possible because we have been able to reduce the collision integral to two-fold form. We calculate the spin diffusion constant and find the expected results for the degenerate and Boltzmann limits, improved results for the high polarization regime in which one spin species is degenerate and one Boltzmann, and values for all intermediate temperatures as well. Because of a relation between the collision time and the “spin rotation quality parameter”, µ, we give results for that quantity valid for all temperatures. A similar analysis should allow the computation of other transport coefficients.Publication Open Access Beyond Spontaneously Broken Symmetry in Bose-Einstein Condensates(2010-01) Mullin, WJ; Laloe, FSpontaneous symmetry breaking (SSB) for Bose-Einstein condensates cannot treat phase off-diagonal effects, and thus cannot 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.