arXiv subjects

K. Thompson

Publications and source records attributed to K. Thompson.

9 recordsLinked to original sources

arXiv2026

Odd-frequency pair correlations in the trapped fermionic Tonks-Girardeau gas

The fermionic Tonks-Girardeau gas is an exactly solvable model realizing a conventional macroscopic condensate of p-wave Cooper pairs. Here we demonstrate that, when confined by a trapping potential, it also hosts unconventional odd-frequency pairing, i.e., pair correlations with s-wave symmetry that are only present with a finite time delay t between fermions forming a pair. Quantitative results for fixed particle number are obtained using a generalization of Yang's theory of off-diagonal long-range order to define a t-dependent order parameter that is antisymmetric under combined t inversion and exchange of fermion-pair indices. Odd-frequency pairing in the fermionic Tonks-Girardeau gas is found to be a mesoscopic effect, localized at the system's boundary and therefore nonextensive thermodynamically. Our results show that this elusive hidden order is accessible in systems having fixed particle number, suggesting new avenues towards its experimental realization and further detailed study.

cond-mat.quant-gas↗

arXiv2024

Odd-frequency superfluidity from a particle-number-conserving perspective

We investigate odd-in-time - or odd-frequency - pairing of fermions in equilibrium systems within the particle-number-conserving framework of Penrose, Onsager and Yang, where superfluid order is defined by macroscopic eigenvalues of reduced density matrices. We show that odd-frequency pair correlations are synonymous with even fermion-exchange symmetry in a time-dependent correlation function that generalises the two-body reduced density matrix. Macroscopic even-under-fermion-exchange pairing is found to emerge from conventional Penrose-Onsager-Yang condensation in two-body or higher-order reduced density matrices through the symmetry-mixing properties of the Hamiltonian. We identify and characterise a transformer matrix responsible for producing macroscopic even fermion-exchange correlations that coexist with a conventional Cooper-pair condensate, while a generator matrix is shown to be responsible for creating macroscopic even fermion-exchange correlations from hidden orders such as a multi-particle condensate. The transformer scenario is illustrated using the spin-balanced s-wave superfluid with Zeeman splitting as an example. The generator scenario is demonstrated by the composite-boson condensate arising for itinerant electrons coupled to magnetic excitations. Structural analysis of the transformer and generator matrices is shown to provide general conditions for odd-frequency pairing order to arise in a given system. Our formalism facilitates a fully general derivation of the Meissner effect for odd-frequency superconductors that holds also beyond the regime of validity for mean-field theory.

cond-mat.supr-con↗

arXiv2021

Coexistence of topological and nontopological Fermi-superfluid phases

The two-dimensional spin-imbalanced Fermi gas subject to s-wave pairing and spin-orbit coupling is considered a promising platform for realizing a topological chiral-p-wave superfluid. In the BCS limit of s-wave pairing, i.e., when Cooper pairs are only weakly bound, the system enters the topological phase via a second-order transition driven by increasing the Zeeman spin-splitting energy. Stronger attractive two-particle interactions cause the system to undergo the BCS-BEC crossover, in the course of which the topological transition becomes first-order. As a result, topological and nontopological superfluids coexist in spatially separated domains in an extended region of phase space spanned by the strength of s-wave interactions and the Zeeman energy. Here we investigate this phase-coexistence region theoretically using a zero-temperature mean-field approach. Exact numerical results are presented to illustrate basic physical characteristics of the coexisting phases and to validate an approximate analytical description derived for weak spin-orbit coupling. Besides extending our current understanding of spin-imbalanced superfluid Fermi systems, the present approach also provides a platform for future studies of unconventional Majorana excitations that, according to topology, should be present at the internal interface between coexisting topological and nontopological superfluid parts of the system.

cond-mat.quant-gas↗

arXiv2019

Chiral twodimensional p-wave superfluid from s-wave pairing in the BEC regime

Twodimensional spin-orbit-coupled Fermi gases subject to s-wave pairing can be driven into a topological phase by increasing the Zeeman spin splitting beyond a critical value. In the topological phase, the system exhibits the hallmarks of chiral p-wave superfluidity, including exotic Majorana excitations. Previous theoretical studies of this realization of a twodimensional topological Fermi superfluid have focused on the BCS regime where the s-wave Cooper pairs are only weakly bound and, hence, the induced chiral p-wave order parameter has a small magnitude. Motivated by the goal to identify potential new ways for the experimental realization of robust topological superfluids in ultra-cold atom gases, we study the BCS-to-BEC crossover driven by increasing the Cooper-pair binding energy for this system. In particular, we obtain phase diagrams in the parameter space of two-particle bound-state energy and Zeeman spin-splitting energy. Ordinary characteristics of the BCS-to-BEC crossover, in particular the shrinking and eventual disappearance of the Fermi surface, are observed in the nontopological phase. In contrast, the topological phase retains all features of chiral p-wave superfluidity, including a well-defined underlying Fermi surface, even for large s-wave pair-binding energies. Compared to the BCS limit, the topological superfluid in the BEC regime turns out to be better realizable even for only moderate magnitude of spin-orbit coupling because the chiral p-wave order parameter is generally larger and remnants of s-wave pairing are suppressed. We identify optimal parameter ranges that can aid further experimental investigations and elucidate the underlying physical reason for the persistence of the chiral p-wave superfluid.

cond-mat.quant-gas↗

arXiv2015

BICEP2/Keck Array IV: Optical Characterization and Performance of the BICEP2 and Keck Array Experiments

BICEP2 and the Keck Array are polarization-sensitive microwave telescopes that observe the cosmic microwave background (CMB) from the South Pole at degree angular scales in search of a signature of inflation imprinted as B-mode polarization in the CMB. BICEP2 was deployed in late 2009, observed for three years until the end of 2012 at 150 GHz with 512 antenna-coupled transition edge sensor bolometers, and has reported a detection of B-mode polarization on degree angular scales. The Keck Array was first deployed in late 2010 and will observe through 2016 with five receivers at several frequencies (95, 150, and 220 GHz). BICEP2 and the Keck Array share a common optical design and employ the field-proven BICEP1 strategy of using small-aperture, cold, on-axis refractive optics, providing excellent control of systematics while maintaining a large field of view. This design allows for full characterization of far-field optical performance using microwave sources on the ground. Here we describe the optical design of both instruments and report a full characterization of the optical performance and beams of BICEP2 and the Keck Array at 150 GHz.

astro-ph.IM↗

arXiv2012

BICEP2 and Keck Array operational overview and status of observations

The BICEP2 and Keck Array experiments are designed to measure the polarization of the cosmic microwave background (CMB) on angular scales of 2-4 degrees (l=50-100). This is the region in which the B-mode signal, a signature prediction of cosmic inflation, is expected to peak. BICEP2 was deployed to the South Pole at the end of 2009 and is in the middle of its third year of observing with 500 polarization-sensitive detectors at 150 GHz. The Keck Array was deployed to the South Pole at the end of 2010, initially with three receivers--each similar to BICEP2. An additional two receivers have been added during the 2011-12 summer. We give an overview of the two experiments, report on substantial gains in the sensitivity of the two experiments after post-deployment optimization, and show preliminary maps of CMB polarization from BICEP2.

astro-ph.IM↗

arXiv2006

A Poset Hierarchy

This article extends a paper of Abraham and Bonnet which generalised the famous Hausdorff characterisation of the class of scattered linear orders. Abraham and Bonnet gave a poset hierarchy that characterised the class of scattered posets which do not have infinite antichains (abbreviated FAC for finite antichain condition). An antichain here is taken in the sense of incomparability. We define a larger poset hierarchy than that of Abraham and Bonnet, to include a broader class of ``scattered'' posets that we call $κ$-scattered. These posets cannot embed any order such that for every two subsets of size $ < κ$, one being strictly less than the other, there is an element in between. If a linear order has this property and has size $κ$ we call this set $\qkappa$. Such a set only exists when $κ^{<κ}=κ$. Partial orders with the property that for every $a<b$ the set $\{x: a<x<b\}$ has size $\geq κ$ are called weakly $κ$-dense, and partial orders that do not have a weakly $κ$-dense subset are called strongly $κ$-scattered. We prove that our hierarchy includes all strongly $κ$-scattered FAC posets, and that the hierarchy is included in the class of all FAC $κ$-scattered posets. In addition, we prove that our hierarchy is in fact the closure of the class of all $κ$-well-founded linear orders under inversions, lexicographic sums and FAC weakenings. For $κ=\aleph_0$ our hierarchy agrees with the one from the Abraham-Bonnet theorem.

math.LO↗

arXiv2004

Scientific optimization of a ground-based CMB polarization experiment

We investigate the science goals achievable with the upcoming generation of ground-based Cosmic Microwave Background polarization experiments and calculate the optimal sky coverage for such an experiment including the effects of foregrounds. We find that with current technology an E-mode measurement will be sample-limited, while a B-mode measurement will be detector-noise-limited. We conclude that a 300 sq deg survey is an optimal compromise for a two-year experiment to measure both E and B-modes, and that ground-based polarization experiments can make an important contribution to B-mode surveys. Focusing on one particular experiment, QUaD, a proposed bolometric polarimeter operating from the South Pole, we find that a ground-based experiment can make a high significance measurement of the acoustic peaks in the E-mode spectrum, and will be able to detect the gravitational lensing signal in the B-mode spectrum. Such an experiment could also directly detect the gravitational wave component of the B-mode spectrum if the amplitude of the signal is close to current upper limits. We also investigate how a ground-based experiment can improve constraints on the cosmological parameters. We estimate that by combining two years of QUaD data with the four-year WMAP data, an optimized ground-based polarization experiment can improve constraints on cosmological parameters by a factor of two. If the foreground contamination can be reduced, the measurement of the tensor-to-scalar ratio can be improved by up to a factor of six over that obtainable from WMAP alone.

astro-ph↗

arXiv2001

The Next Linear Collider Extraction Line Design

The two main functions of the NLC extraction line include: 1) transmission of the outgoing disrupted beam and secondary particles to the dump with minimal losses; and 2) beam diagnostics and control. In this report, we describe the extraction line optics, present the results of tracking studies, and discuss the extraction line instrumentation.

physics.acc-ph↗