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- Exceptional point - Wikipedia
- Exceptional points in optics and photonics | Science - AAAS
- Exceptional points and non-Hermitian photonics at the nanoscale
- Enhanced sensitivity at higher-order exceptional points
- Exceptional dynamics at exceptional points | Light: Science
- The physics of exceptional points - arXiv.org
- Exceptional–point–enhanced phase sensing | Science Advances
- [1210.7536] The physics of exceptional points - arXiv.org
- Classification of Exceptional Points and Non-Hermitian …
- A Whole Surface of Exceptional Points - Physics
Exceptional point GudangMovies21 Rebahinxxi LK21
In quantum physics, exceptional points are singularities in the parameter space where two or more eigenstates (eigenvalues and eigenvectors) coalesce. These points appear in dissipative systems, which make the Hamiltonian describing the system non-Hermitian.
Photonics
The losses in photonic systems, are a feature used to study non-Hermitian physics. Adding non-Hermiticity (such as dichroism) to photonic systems which present Dirac points transforms these degeneracy points into pairs of exceptional points. This has been demonstrated experimentally in numerous photonic systems such as microcavities and photonic crystals. The first demonstration of exceptional points was made by Woldemar Voigt in 1902 for optical modes in crystals.
Fidelity and fidelity susceptibility
In condensed matter and many-body physics, fidelity is often used to detect quantum phase transitions in parameter space. The definition of fidelity is the inner product of the ground state wave functions of two adjacent points in parameter space,
F
=
|
⟨
ψ
0
(
λ
)
|
ψ
0
(
λ
+
ϵ
)
⟩
|
2
{\displaystyle F=|\langle \psi _{0}(\lambda )|\psi _{0}(\lambda +\epsilon )\rangle |^{2}}
, where
ϵ
{\displaystyle \epsilon }
is a small quantity. After series expansion,
F
=
1
−
χ
F
ϵ
2
+
O
(
ϵ
3
)
{\displaystyle F=1-\chi _{F}\epsilon ^{2}+{\mathcal {O}}(\epsilon ^{3})}
, the first-order correction term of fidelity is zero, and the coefficient of the second-order correction term is called the fidelity susceptibility. The fidelity susceptibility diverges toward positive infinity as the parameters approach the quantum phase transition point.
lim
λ
→
λ
Q
C
P
R
e
χ
F
=
∞
{\displaystyle \lim _{\lambda \to \lambda _{\mathrm {QCP} }}\mathbb {Re} \chi _{F}=\infty }
For the exceptional points of non-Hermitian quantum systems, after appropriately generalizing the definition of fidelity,
F
=
⟨
ψ
0
L
(
λ
)
|
ψ
0
R
(
λ
+
ϵ
)
⟩
⟨
ψ
0
L
(
λ
+
ϵ
)
|
ψ
0
R
(
λ
)
⟩
{\displaystyle F=\langle \psi _{0}^{L}(\lambda )|\psi _{0}^{R}(\lambda +\epsilon )\rangle \langle \psi _{0}^{L}(\lambda +\epsilon )|\psi _{0}^{R}(\lambda )\rangle }
the real part of the fidelity susceptibility diverges toward negative infinity when the parameters approach the exceptional points.
lim
λ
→
λ
E
P
R
e
χ
F
=
−
∞
{\displaystyle \lim _{\lambda \to \lambda _{\mathrm {EP} }}\mathbb {Re} \chi _{F}=-\infty }
For non-Hermitian quantum systems with PT symmetry, fidelity can be used to analyze whether exceptional points are of higher-order. Many numerical methods such as the Lanczos algorithm, Density Matrix Renormalization Group (DMRG), and other tensor network algorithms are relatively easy to calculate only for the ground state, but have many difficulties in computing the excited states. Because fidelity only requires the ground state calculations, this approach allows most numerical methods to analyze non-Hermitian systems without excited states, and find the exceptional point, as well as to determine whether it is a higher-order exceptional point.
See also
Dirac cones
Non-Hermitian quantum mechanics
References
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exceptional point
Daftar Isi
Exceptional point - Wikipedia
In quantum physics, exceptional points [1] are singularities in the parameter space where two or more eigenstates (eigenvalues and eigenvectors) coalesce. These points appear in dissipative systems, which make the Hamiltonian describing the system non-Hermitian.
Exceptional points in optics and photonics | Science - AAAS
Jan 4, 2019 · Exceptional points are branch point singularities in the parameter space of a system at which two or more eigenvalues, and their corresponding eigenvectors, coalesce and become degenerate.
Exceptional points and non-Hermitian photonics at the nanoscale
Jun 29, 2023 · Exceptional points (EPs) arising in non-Hermitian systems have led to a variety of intriguing wave phenomena, and have been attracting increased interest in various physical platforms.
Enhanced sensitivity at higher-order exceptional points
Aug 10, 2017 · Non-Hermitian degeneracies, also known as exceptional points, have recently emerged as a new way to engineer the response of open physical systems, that is, those that interact with the...
Exceptional dynamics at exceptional points | Light: Science
Jan 8, 2024 · Exceptional points (EPs), singularities of non-Hermitian systems, often exhibit exotic behaviors by engineering the balance between the system gain and loss. Now, EPs have been demonstrated...
The physics of exceptional points - arXiv.org
Exceptional points occur generically in eigenvalue problems that depend on a parameter. By variation of such parameter (usually into the complex plane) one can generically find points where eigenvalues coincide.
Exceptional–point–enhanced phase sensing | Science Advances
Apr 5, 2024 · Exceptional points (EPs), identified in non-Hermitian systems, offer great potential for advanced sensors, given their marked response to perturbations. However, strict physical requirements for operating a sensor at EPs limit broader applications.
[1210.7536] The physics of exceptional points - arXiv.org
Oct 25, 2012 · A short resume is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems.
Classification of Exceptional Points and Non-Hermitian …
Aug 9, 2019 · Here we present the complete classification of generic topologically stable exceptional points according to two types of complex-energy gaps and fundamental symmetries of charge conjugation, parity, and time reversal.
A Whole Surface of Exceptional Points - Physics
Dec 4, 2019 · Researchers fabricated a cavity device with a large number of “exceptional points,” which are modes that exhibit exotic phenomena, such as extreme sensitivity to external parameters. Figure 1: An exceptional point is where several modes (depicted as blue and red) coalesce into a single mode.