499 research outputs found
Professor Chen Ping Yang's early significant contributions to mathematical physics
In the 60's Professor Chen Ping Yang with Professor Chen Ning Yang published
several seminal papers on the study of Bethe's hypothesis for various problems
of physics. The works on the lattice gas model, critical behaviour in
liquid-gas transition, the one-dimensional (1D) Heisenberg spin chain, and the
thermodynamics of 1D delta-function interacting bosons are significantly
important and influential in the fields of mathematical physics and statistical
mechanics. In particular, the work on the 1D Heisenberg spin chain led to
subsequent developments in many problems using Bethe's hypothesis. The method
which Yang and Yang proposed to treat the thermodynamics of the 1D system of
bosons with a delta-function interaction leads to significant applications in a
wide range of problems in quantum statistical mechanics. The Yang and Yang
thermodynamics has found beautiful experimental verifications in recent years.Comment: 5 pages + 3 figure
Exact Entanglement dynamics in Three Interacting Qubits
Motivated by recent experimental study on coherent dynamics transfer in three
interacting atoms or electron spins \cite{Barredo:2015,Rosenfeld:2018}, here we
study entanglement entropy transfer in three interacting qubits. We
analytically calculate time evolutions of wave function, density matrix and
entanglement of the system. We find that initially entangled two qubits may
alternatively transfer their entanglement entropy to other two qubit pairs. So
that dynamical evolution of three interacting qubits may produce a genuine
three-partite entangled state through entanglement entropy transfers. In
particular, different pairwise interactions of the three qubits endow symmetric
and asymmetric evolutions of the entanglement transfer, characterized by the
quantum mutual information and concurence. Finally, we discuss an experimental
proposal of three Rydberg atoms for testing the entanglement dynamics transfer
of this kind.Comment: 6 pages + 5 figure
The spin-s homogeneous central spin model: exact spectrum and dynamics
We consider the problem of a central spin with arbitrary spin s that
interacts pairwise and uniformly with a bath of N spins with s=1/2. We present
two approaches for determining the exact spectrum of this model, one based on
properties of SU(2), and the other based on integrability. We also analyze the
exact time evolution of a spin coherent state, and compute the time evolution
of various quantities of physical interest, including the entanglement entropy,
spin polarization and Loschmidt echo.Comment: 19 page
Transition from Tonks-Girardeau gas to super-Tonks-Girardeau gas as an exact many-body dynamics problem
We investigate transition of a one-dimensional interacting Bose gas from a
strongly repulsive regime to a strongly attractive regime, where a stable
highly excited state known as the super Tonks-Girardeau gas was experimentally
realized very recently. By solving exact dynamics of the integrable
Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a
very stable dynamic state. Furthermore we calculate the breathing mode of the
super Tonks-Girardeau gas which is found to be in good agreement with
experimental observation. Our results show that the highly excited super
Tonks-Girardeau gas phase can be well understood from the fundamental theory of
the solvable Bose gas.Comment: 4 pages, 4 figures, version to appear in Phys. Rev. A as a Rapid
Communicatio
Exact quantum dynamics of XXZ central spin problems
We obtain analytically close forms of benchmark quantum dynamics of the
collapse and revival (CR), reduced density matrix, Von Neumann entropy, and
fidelity for the XXZ central spin problem. These quantities characterize the
quantum decoherence and entanglement of the system with few to many bath spins,
and for a short to infinitely long time evolution. For the homogeneous central
spin problem, the effective magnetic field , coupling constant and
longitudinal interaction significantly influence the time scales of
the quantum dynamics of the central spin and the bath, providing a tunable
resource for quantum metrology. Under the resonance condition , the
location of the -th revival peak in time reaches a simple relation for a large . For , and a
small polarization in the initial spin coherent state, our analytical result
for the CR recovers the known expression found in the Jaynes-Cummings model,
thus building up an exact dynamical connection between the central spin
problems and the light-matter interacting systems in quantum nonlinear optics.
In addition, the CR dynamics is robust to a moderate inhomogeneity of the
coupling amplitudes, while disappearing at strong inhomogeneity.Comment: added new result on inhomogeneous central spin problem and added new
references and supplementary material, 6 pages + 15 pages; 4 figures + 14
figure
Realization of effective super Tonks-Girardeau gases via strongly attractive one-dimensional Fermi gases
A significant feature of the one-dimensional super Tonks-Girardeau gas is its
metastable gas-like state with a stronger Fermi-like pressure than for free
fermions which prevents a collapse of atoms. This naturally suggests a way to
search for such strongly correlated behaviour in systems of interacting
fermions in one dimension. We thus show that the strongly attractive Fermi gas
without polarization can be effectively described by a super Tonks-Girardeau
gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A
natural description of such super Tonks-Girardeau gases is provided by Haldane
generalized exclusion statistics. In particular, we find that they are
equivalent to ideal particles obeying more exclusive statistics than
Fermi-Dirac statistics.Comment: 4 pages, 2 figure
Universal Properties of Fermi Gases in One-dimension
In this Rapid Communication, we investigate the universal properties of a
spin-polarized two-component Fermi gas in one dimension (1D) using Bethe
ansatz. We discuss the quantum phases and phase transitions by obtaining exact
results for the equation of state, the contact, the magnetic susceptibility and
the contact susceptibility, giving a precise understanding of the 1D analogue
of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in
three dimension (3D) and the associated universal magnetic properties. In
particular, we obtain the exact form of the magnetic susceptibility at low temperatures, where is the
energy gap and is the temperature. Moreover, we establish exact upper and
lower bounds for the relation between polarization and the contact for
both repulsive and attractive Fermi gases. Our findings emphasize the role of
the pair fluctuations in strongly interacting 1D fermion systems that can shed
light on higher dimensions.Comment: 4 figures, the main pape
- …