S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case

A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S-matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c /T_F is approximately 0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3 approximately 1.3 where n is the density and lambda the thermal wavelength, which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure

Effect of Doublon-Holon Binding on Mott transition---Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models

To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length $\xi_{\rm dh}$ and the minimum D-D exclusion length $\xi_{\rm dd}$. Generally, a Mott transition occurs when $\xi_{\rm dh}$ becomes comparable to $\xi_{\rm dd}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other ($\xi_{\rm dh}>\xi_{\rm dd}$); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.Comment: 16 pages, 22 figures, submitted to J. Phys. Soc. Jp

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure

Building a Quantum Engineering Undergraduate Program

Contribution: A roadmap is provided for building a quantum engineering education program to satisfy U.S. national and international workforce needs. Background: The rapidly growing quantum information science and engineering (QISE) industry will require both quantum-aware and quantum-proficient engineers at the bachelor\u27s level. Research Question: What is the best way to provide a flexible framework that can be tailored for the full academic ecosystem? Methodology: A workshop of 480 QISE researchers from across academia, government, industry, and national laboratories was convened to draw on best practices; representative authors developed this roadmap. Findings: 1) For quantum-aware engineers, design of a first quantum engineering course, accessible to all STEM students, is described; 2) for the education and training of quantum-proficient engineers, both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors are detailed, requiring only three to four newly developed courses complementing existing STEM classes; 3) a conceptual QISE course for implementation at any postsecondary institution, including community colleges and military schools, is delineated; 4) QISE presents extraordinary opportunities to work toward rectifying issues of inclusivity and equity that continue to be pervasive within engineering. A plan to do so is presented, as well as how quantum engineering education offers an excellent set of education research opportunities; and 5) a hands-on training plan on quantum hardware is outlined, a key component of any quantum engineering program, with a variety of technologies, including optics, atoms and ions, cryogenic and solid-state technologies, nanofabrication, and control and readout electronics

Building a Quantum Engineering Undergraduate Program

The rapidly growing quantum information science and engineering (QISE) industry will require both quantum-aware and quantum-proficient engineers at the bachelor's level. We provide a roadmap for building a quantum engineering education program to satisfy this need. For quantum-aware engineers, we describe how to design a first quantum engineering course accessible to all STEM students. For the education and training of quantum-proficient engineers, we detail both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors. We propose that such programs typically require only three or four newly developed courses that complement existing engineering and science classes available on most larger campuses. We describe a conceptual quantum information science course for implementation at any post-secondary institution, including community colleges and military schools. QISE presents extraordinary opportunities to work towards rectifying issues of inclusivity and equity that continue to be pervasive within engineering. We present a plan to do so and describe how quantum engineering education presents an excellent set of education research opportunities. Finally, we outline a hands-on training plan on quantum hardware, a key component of any quantum engineering program, with a variety of technologies including optics, atoms and ions, cryogenic and solid-state technologies, nanofabrication, and control and readout electronics. Our recommendations provide a flexible framework that can be tailored for academic institutions ranging from teaching and undergraduate-focused two- and four-year colleges to research-intensive universities.Comment: 25 pages, 2 figure

Gauge Theories with Ultracold Atoms

We discuss and review in this chapter the developing field of research of quantum simulation of gauge theories with ultracold atoms.Comment: Contribution for the proceedings of the Advanced School and Workshop on "Strongly Coupled Field Theories for Condensed Matter and Quantum Information Theory" held in Natal from 2-21/8 of 2015. Published in "Springer Proceedings in Physics" (ISBN 978-3-030-35473-2), with material from the PhD Thesis of Jo\~ao C. Pinto Barros, available at https://iris.sissa.it/handle/20.500.11767/57731#.XcQtPk6YWh