Macroscopic quantum waves in boson systems ii

Yatendra Singh Jain

Macro-orbital representation of a particle (detailed account given in cond-mat/0603784) has been used to develop the microscopic theory of a system of interacting bosons. It concludes that: (i) below certain temperature (say, $T_λ$), particles assume a state of (q, -q) bound pairs, (ii) the $λ-$transition is a consequence of inter-particle quantum correlations clubbed with zero-point repulsion and inter-particle attraction and represents an onset of the order-disorder of particles in their $ϕ-$space followed simultaneously by their BEC as (q, -q) bound pairs in a state of q = $q_o = π/d$ and K = 0, (iii) particles at $T \le T_λ$ acquire collective binding which locks them at = 0, = $λ/2$ and $Δϕ= 2nπ$ (with n = 1, 2, 3, ...), (iv) the entire system assumes mechanical strain in inter-particle bonds and behaves like a single macroscopic molecule, (v) there exists an energy gap between the superfluid and normal fluid phases of the system, (vi) the $λ-$transition represents the twin phenomena of broken gauge symmetry and phase coherence, (vii) the system does not have p = 0 condensate, (viii) a new kind of quantum quasi-particle "omon" (a phononlike wave of the oscillations of the momentum coordinates of particles) exists in superfluid phase, etc. It explains the properties of He-II, including the origin of quantized vortices, critical velocities, logarithmic singularity of specific heat, etc. at quantitative level and provides microscopic foundation to two fluid theory, $Ψ-$theory, idea of macroscopic wave function, etc. The framework of the theory can unify the physics of interacting bosons and fermions.

Eugene P. Gross

Tyler J. Volkoff

In this dissertation, I analyze certain problems in the following areas: 1) quantum dynamical phenomena in macroscopic systems of interacting, degenerate bosons (Parts II, III, and V), and 2) measures of macroscopicity for a large class of two-branch superposition states in separable Hilbert space (Part IV). Part I serves as an introduction to important concepts recurring in the later Parts. In Part II, a microscopic derivation of the effective action for the relative phase of driven, aperture-coupled reservoirs of weakly-interacting condensed bosons from a (3 + 1)D microscopic model with local U(1) gauge symmetry is presented. The effective theory is applied to the transition from linear to sinusoidal current vs. phase behavior observed in recent experiments on liquid 4He driven through nanoaperture arrays. Part III discusses path-integral Monte Carlo (PIMC) numerical simulations of quantum hydrodynamic properties of reservoirs of He II communicating through simple nanoaperture arrays. In addition to calculating the local superfluid density in these systems, new estimators for hydrodynamic observables and novel methods for extracting the length scale characterizing the decay of superfluidity at the system boundary from PIMC data are introduced with the aim of exploring the mechanism of superfluid weak-link formation in nanoscale containers.Part IV consists of an analysis of macroscopicity measures for a large class of Schrodinger cat states of N-mode photonic systems. For cat states of this class, it is shown that a well-known measure of superposition size based on the optimal distinguishability of the branches and another based on metrological usefulness of the superposition relative to its branches agree (i.e., designate the same superpositions as macroscopic) when the inner product of the branches of the superposition is sufficiently small. For certain superpositions in this class, a technique is presented for deriving a state-specific textit{metrological macroscopicity algebra} of observables. The dynamics of superposition size measures is also considered, leading to the notion of "distinguishability time,'' a generalization of the orthogonalization times of Mandelstam-Tamm and Margolus-Levitin. In Part V, an investigation of the nonequilibrium dynamics of a quantum dot-Josephson junction-quantum dot nanodevice is presented. The nonequilibrium action of the system is calculated by making use of the Keldysh formalism and a potential use of the device for transferring macroscopic superposition states between a spin-system and an s-wave superconductor is discussed.

P. Silvestrini

V. S. Shchesnovich

Christoph Schenke, Anna Minguzzi, F. W. J. Hekking

We consider a strongly interacting quasi-one-dimensional Bose gas on a tight ring trap subjected to a localized barrier potential. We explore the possibility of forming a macroscopic superposition of a rotating and a nonrotating state under nonequilibrium conditions, achieved by a sudden quench of the barrier velocity. Using an exact solution for the dynamical evolution in the impenetrable-boson (Tonks-Girardeau) limit, we find an expression for the many-body wave function corresponding to a superposition state. The superposition is formed when the barrier velocity is tuned close to multiples of an integer or half-integer number of Coriolis flux quanta. As a consequence of the strong interactions, we find that (i) the state of the system can be mapped onto a macroscopic superposition of two Fermi spheres rather than two macroscopically occupied single-particle states as in a weakly interacting gas, and (ii) the barrier velocity should be larger than the sound velocity to better discriminate the two components of the superposition.