arXiv subjects

W. J. Mullin

Publications and source records attributed to W. J. Mullin.

At least 19 recordsLinked to original sources

arXiv2015

Interference Effects in Potential-Wells

We propose using an array of potential wells as an interferometer, in which the beam splitters are provided by tunneling during an appropriate time through the barrier between wells. This arrangement allows demonstration of generalized Hong-Ou-Mandel effects with multiple particles traversing one or several beam splitters. Other interferometer effects can occur, including a violation of the Bell-Clauser-Horne-Shimony-Holt form of the Bell inequality. With interactions, one sees various effects including so-called fermionization, collective tunneling, and self-trapping.

quant-ph↗

arXiv2014

$^3$He impurities and mass transport through solid $^4$He: a universal temperature dependence and flux extinction

The flux, $F$, carried by solid $^4$He in the range $25.6 - 26.3$ bar rises with falling temperature and at a temperature $T_d$ the flux decreases toward zero. We study $F$ as a function of $^3$He impurity concentration, $χ$. At temperatures above $T_d$ the flux has an unexpected universal temperature dependence and the flux terminates in a narrow window near a characteristic temperature $T_h \approx$ 610 mK, which is independent of $χ$. We find that $T_d$ is an increasing function of increasing $χ$. We document that the extinction of the flux at $T_d$ is prompt and precipitous, with the transition complete within a few mK. Comparison of our ($T_d, χ$) results with a calculated phase separation line suggests that the extinction of the flux is related to phase separation.

cond-mat.other↗

arXiv2013

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?

quant-ph↗

arXiv2012

Amplitude control of quantum interference

Usually, the oscillations of interference effects are controlled by relative phases. We show that varying the amplitudes of quantum waves, for instance by changing the reflectivity of beam splitters, can also lead to quantum oscillations and even to Bell violations of local realism. We first study theoretically a generalization of the Hong-Ou-Mandel experiment to arbitrary source numbers and beam splitter transmittivity. We then consider a Bell type experiment with two independent sources, and find strong violations of local realism for arbitrarily large source number $N$; for small $N$, one operator measures essentially the relative phase of the sources and the other their intensities. Since, experimentally, one can measure the parity of the number of atoms in an optical lattice more easily than the number itself, we assume that the detectors measure parity.

quant-ph↗

arXiv2011

NOON-state formation from Fock-state Bose-Einstein condensates

NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and $b$ are single particle states) have been used for predicting violations of local realism (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state Bose-Einstein condensates as sources in a modified Mach-Zehnder interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is a subset of the total number of particles in the two condensates. The modification of the interferometer involves making {}"side" measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter if the phase states are orthogonal. When they are not orthogonal, a {}"feedforward" correction circuit is shown to convert them into proper form so a NOON results. We apply the NOON to the measurement of phase. Here the NOON experiment is equivalent to one in which a large molecule passes through two slits. The NOON components can be recombined in a final beam splitter to show interference.

quant-ph↗

arXiv2010

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.

quant-ph↗

arXiv2010

Classical phases and quantum angles in the description of interfering Bose-Einstein condensates

The interference of two Bose-Einstein condensates, initially in Fock states, can be described in terms of their relative phase, treated as a random unknown variable. This phase can be understood, either as emerging from the measurements, or preexisting to them; in the latter case, the originating states could be phase states with unknown phases, so that an average over all their possible values is taken. Both points of view lead to a description of probabilities of results of experiments in terms of a phase angle, which plays the role of a classical variable. Nevertheless, in some situations, this description is not sufficient: another variable, which we call the "quantum angle", emerges from the theory. This article studies various manifestations of the quantum angle. We first introduce the quantum angle by expressing two Fock states crossing a beam splitter in terms of phase states, and relate the quantum angle to off-diagonal matrix elements in the phase representation. Then we consider an experiment with two beam splitters, where two experimenters make dichotomic measurements with two interferometers and detectors that are far apart; the results lead to violations of the Bell-Clauser-Horne-Shimony-Holt inequality (valid for local-realistic theories, including classical descriptions of the phase). Finally, we discuss an experiment where particles from each of two sources are either deviated via a beam splitter to a side collector or proceed to the point of interference. For a given interference result, we find "population oscillations" in the distributions of the deviated particles, which are entirely controlled by the quantum angle. Various versions of population oscillation experiments are discussed, with two or three independent condensates.

quant-ph↗

arXiv2009

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).

quant-ph↗

arXiv2008

Quantum-limited mass flow of liquid $^{3}$He

We consider theoretically the possibility of observing unusual quantum fluid behavior in liquid $^{3}$He and solutions of $^{3}$He in $^{4}$He systems confined to nano-channels. In the case of pure ballistic flow at very low temperature conductance will be quantized in units of $2m^{2}/h$. We show that these steps should be sensitive to increases in temperature. We also use of a random scattering matrix simulation to study flow with diffusive wall scattering. Universal conductance fluctuations analogous to those seen in electron systems should then be observable. Finally we consider the possibility of the cross-over to a one-dimensional system at sufficiently low temperature where the system could form a Luttinger liquid.

cond-mat.mes-hall↗

arXiv2007

Giant viscosity enhancement in a spin-polarized Fermi liquid

The viscosity is measured for a Fermi liquid, a dilute $^3$He-$^4$He mixture, under extremely high magnetic field/temperature conditions ($B \leq 14.8$ T, $T \geq 1.5$ mK). The spin splitting energy $μB$ is substantially greater than the Fermi energy $k_B T_F$; as a consequence the polarization tends to unity and s-wave quasiparticle scattering is suppressed for $T \ll T_F$. 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.

cond-mat.other↗

arXiv2006

The evolution of additional (hidden) quantum variables in the interference of Bose-Einstein condensates

Additional variables (also often called ``hidden variables'') are sometimes added to standard quantum mechanics in order to remove its indeterminism or ``incompletness,'' 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 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.

cond-mat.other↗

arXiv2006

Spin Diffusion in Trapped Gases: Anisotropy in Dipole and Quadrupole Modes

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows unusual diffusion anisotropy in both dipole and quadrupole modes. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.

cond-mat.other↗

arXiv2006

The origin of phase in the interference of Bose-Einstein condensates

We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a so-called condensate wave functions having a definite phase. We investigate the origin of this phase and the theoretical basis of treating interference. It is possible to construct a phase state, for which the particle number is uncertain, but phase is known. However, how one would prepare such a state before an experiment is not obvious. We show that a phase can also arise from experiments using condensates in Fock states, that is, having known particle numbers. Analysis of measurements in such states also gives us a prescription for preparing phase states. The connection of this procedure to questions of ``spontaneously broken gauge symmetry'' and to ``hidden variables'' is mentioned.

cond-mat.other↗

arXiv2005

Landau Damping of Spin Waves in Trapped Boltzmann Gases

A semiclassical method is used to study Landau damping of transverse pseudo-spin waves in harmonically trapped ultracold gases in the collisionless Boltzmann limit. In this approach, the time evolution of a spin is calculated numerically as it travels in a classical orbit through a spatially dependent mean field. This method reproduces the Landau damping results for spin-waves in unbounded systems obtained with a dielectric formalism. In trapped systems, the simulations indicate that Landau damping occurs for a given spin-wave mode because of resonant phase space trajectories in which spins are "kicked out" of the mode (in spin space). A perturbative analysis of the resonant and nearly resonant trajectories gives the Landau damping rate, which is calculated for the dipole and quadrupole modes as a function of the interaction strength. The results are compared to a numerical solution of the kinetic equation by Nikuni et al.

cond-mat.stat-mech↗

arXiv2004

Anisotropic Spin Diffusion in Trapped Boltzmann Gases

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.

cond-mat.stat-mech↗

arXiv2003

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.

physics.ed-ph↗

arXiv2002

Bose-Einstein Condensation, Fluctuations, and Recurrence Relations in Statistical Mechanics

We calculate certain features of Bose-Einstein condensation in the ideal gas by using recurrence relations for the partition function. The grand canonical ensemble gives inaccurate results for certain properties of the condensate that are accurately provided by the canonical ensemble. Calculations in the latter can be made tractable for finite systems by means of the recurrence relations. The ideal one-dimensional harmonic Bose gas provides a particularly simple and pedagogically useful model for which detailed results are easily derived. An analysis of the Bose system via permutation cycles yields insight into the physical meaning of the recurrence relations.

cond-mat.stat-mech↗

arXiv2002

New Evidence for Zero-Temperature Relaxation in a Spin-Polarized Fermi Liquid

Spin-echo experiments are reported for 3He-4He solutions under extremely high B/T conditions, B=14.75 T and T >= 1.73 mK. The 3He concentration x_3 was adjusted close to the value x_c = 3.8% at which the spin rotation parameter muM_0 vanishes. In this way the transverse and longitudinal spin diffusion coefficients D_perp, D_parallel were measured while keeping |muM_0| < 1. It is found that the temperature dependence of D_perp deviates strongly from 1/T^2, with anisotropy temperature T_a = 4.26 +/- 0.18 mK. This value is close to the theoretical prediction for dilute solutions, and suggests that spin current relaxation remains finite as the temperature tends to zero.

cond-mat↗