16,982 research outputs found
Berry phases of quantum trajectories in semiconductors under strong terahertz fields
Quantum evolution of particles under strong fields can be essentially
captured by a small number of quantum trajectories that satisfy the stationary
phase condition in the Dirac-Feynmann path integrals. The quantum trajectories
are the key concept to understand extreme nonlinear optical phenomena, such as
high-order harmonic generation (HHG), above-threshold ionization (ATI), and
high-order terahertz sideband generation (HSG). While HHG and ATI have been
mostly studied in atoms and molecules, the HSG in semiconductors can have
interesting effects due to possible nontrivial "vacuum" states of band
materials. We find that in a semiconductor with non-vanishing Berry curvature
in its energy bands, the cyclic quantum trajectories of an electron-hole pair
under a strong terahertz field can accumulate Berry phases. Taking monolayer
MoS as a model system, we show that the Berry phases appear as the Faraday
rotation angles of the pulse emission from the material under short-pulse
excitation. This finding reveals an interesting transport effect in the extreme
nonlinear optics regime.Comment: 5 page
Quantum discord: "discord" between the whole and its constituent
Quantum discord, a measure of quantum correlation beyond entanglement, is
initially defined as the discord between two classically equivalent while
quantum discordant definitions of mutual information. In this paper, we report
some new interpretations of discord which rely on the differences between
measurement induced effects on the local measured system and the whole system.
Specifically, with proper quantitative definitions introduced in [Buscemi,
Hayashi and Horodecki, Phys. Rev. Lett. 100, 2210504 (2008)], we find that
quantum discord can be interpreted as the differences of measurement induced
disturbance or information gain on the local measured system and on the whole
system. Combined with previous similar results based on measurement induced
entanglement and decoherence, our results provide a unified view on quantum
discord.Comment: title changed, abstract rewritten. Rank-1 POVM measurements are
needed for our result
Imaginary geometric phases of quantum trajectories
A quantum object can accumulate a geometric phase when it is driven along a
trajectory in a parameterized state space with non-trivial gauge structures.
Inherent to quantum evolutions, a system can not only accumulate a quantum
phase but may also experience dephasing, or quantum diffusion. Here we show
that the diffusion of quantum trajectories can also be of geometric nature as
characterized by the imaginary part of the geometric phase. Such an imaginary
geometric phase results from the interference of geometric phase dependent
fluctuations around the quantum trajectory. As a specific example, we study the
quantum trajectories of the optically excited electron-hole pairs, driven by an
elliptically polarized terahertz field, in a material with non-zero Berry
curvature near the energy band extremes. While the real part of the geometric
phase leads to the Faraday rotation of the linearly polarized light that
excites the electron-hole pair, the imaginary part manifests itself as the
polarization ellipticity of the terahertz sidebands. This discovery of
geometric quantum diffusion extends the concept of geometric phases.Comment: 5 pages with 3 figure
Nonlinear optical response induced by non-Abelian Berry curvature in time-reversal-invariant insulators
We propose a general framework of nonlinear optics induced by non-Abelian
Berry curvature in time-reversal-invariant (TRI) insulators. We find that the
third-order response of a TRI insulator under optical and terahertz light
fields is directly related to the integration of the non-Abelian Berry
curvature over the Brillouin zone. We apply the result to insulators with
rotational symmetry near the band edge. Under resonant excitations, the optical
susceptibility is proportional to the flux of the Berry curvature through the
iso-energy surface, which is equal to the Chern number of the surface times
. For the III-V compound semiconductors, microscopic calculations based
on the six-band model give a third-order susceptibility with the Chern number
of the iso-energy surface equal to three
Non-monogamy of quantum discord and upper bounds for quantum correlation
We consider a monogamy inequality of quantum discord in a pure tripartite
state and show that it is equivalent to an inequality between quantum mutual
information and entanglement of formation of two parties. Since this inequality
does not hold for arbitrary bipartite states, quantum discord can generally be
both monogamous and polygamous. We also carry out numerical calculations for
some special states. The upper bounds of quantum discord and classical
correlation are also discussed and we give physical analysis on the invalidness
of a previous conjectured upper bound of quantum correlation. Our results
provide new insights for further understanding of distributions of quantum
correlations.Comment: Title changed, abstract and introduction revised, references adde
New approach for solving master equation of open atomic system
We describe a new approach called Ket-Bra Entangled State (KBES) Method which
enables one convert master equations into Schr\"odinger-like equation. In
sharply contrast to the super-operator method, the KBES method is applicable
for any master equation of finite-level system in theory, and the calculation
can be completed by computer. With this method, we obtain the exact dynamic
evolution of a radioactivity damped 2-level atom in time-dependent external
field, and a 3-level atom coupled with bath; Moreover, the master equation of
N-qubits Heisenberg chain each qubit coupled with a reservoir is also resolved
in Sec.III; Besides, the paper briefly discuss the physical implications of the
solution.Comment: 7 pages, 5figure
Dynamic Entanglement Evolution of Two-qubit XYZ Spin Chain in Markovian Environment
We propose a new approach called Ket-Bra Entangled State (KBES) Method for
converting master equation into Schr\"{o}dinger-like equation. With this
method, we investigate decoherence process and entanglement dynamics induced by
a -qubit spin chain that each qubit coupled with reservoir. The spin chain
is an anisotropy Heisenberg model in the external magnetic field , the
corresponding master equation is solved concisely by KBES method; Furthermore,
the effects of anisotropy, temperature, external field and initial state on
concurrence dynamics is analyzed in detail for the case that initial state is
Extended Wenger-Like(EWL) state. Finally we research the coherence and
concurrence of the final state (namely the density operator for time tend to
infinite
Giant Faraday rotation induced by Berry phase in bilayer graphene under strong terahertz fields
High-order terahertz (THz) sideband generation (HSG) in semiconductors is a
phenomenon with physics similar to high-order harmonic generation but in a much
lower frequency regime. It was found that the electron-hole pairs excited by a
weak optical laser can accumulate Berry phases along a cyclic path under the
driving of a strong THz field. The Berry phases appear as the Faraday rotation
angles of the emission signal under short-pulse excitation in monolayer
MoS. In this paper, the theory of Berry phase in THz extreme nonlinear
optics is applied to biased bilayer graphene with Bernal stacking, which has
similar Bloch band features and optical properties to the monolayer MoS,
such as time-reversal related valleys and valley contrasting optical selection
rules. The bilayer graphene has much larger Berry curvature than monolayer
MoS, which leads to a giant Faraday rotation of the optical emission
( 1 rad for a THz field with frequency 1 THz and strength 8 kV/cm). This
provides opportunities to use bilayer graphene and low-power THz lasers for
ultrafast electro-optical devices.Comment: 6 pages, 3 figure
Tuning-Free Heterogeneity Pursuit in Massive Networks
Heterogeneity is often natural in many contemporary applications involving
massive data. While posing new challenges to effective learning, it can play a
crucial role in powering meaningful scientific discoveries through the
understanding of important differences among subpopulations of interest. In
this paper, we exploit multiple networks with Gaussian graphs to encode the
connectivity patterns of a large number of features on the subpopulations. To
uncover the heterogeneity of these structures across subpopulations, we suggest
a new framework of tuning-free heterogeneity pursuit (THP) via large-scale
inference, where the number of networks is allowed to diverge. In particular,
two new tests, the chi-based test and the linear functional-based test, are
introduced and their asymptotic null distributions are established. Under mild
regularity conditions, we establish that both tests are optimal in achieving
the testable region boundary and the sample size requirement for the latter
test is minimal. Both theoretical guarantees and the tuning-free feature stem
from efficient multiple-network estimation by our newly suggested approach of
heterogeneous group square-root Lasso (HGSL) for high-dimensional
multi-response regression with heterogeneous noises. To solve this convex
program, we further introduce a tuning-free algorithm that is scalable and
enjoys provable convergence to the global optimum. Both computational and
theoretical advantages of our procedure are elucidated through simulation and
real data examples.Comment: 29 pages for the main text including 1 figure and 7 tables, 28 pages
for the Supplementary Materia
Series expansion in fractional calculus and fractional differential equations
Fractional calculus is the calculus of differentiation and integration of
non-integer orders. In a recently paper (Annals of Physics 323 (2008)
2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted.
Based on this theorem, in this paper we introduce fractional series expansion
method to fractional calculus. We define a kind of fractional Taylor series of
an infinitely fractionally-differentiable function. Further, based on our
definition we generalize hypergeometric functions and derive corresponding
differential equations. For finitely fractionally-differentiable functions, we
observe that the non-infinitely fractionally-differentiability is due to more
than one fractional indices. We expand functions with two fractional indices
and display how this kind of series expansion can help to solve fractional
differential equations.Comment: 15 pages, no figur
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