Dynamical Evolution of an Effective Two-Level System with ${\mathscr{P}}{\mathscr{T}}$ Symmetry

Du, Lei; Xu, Zhihao; Yin, Cong; Guo, Liping

doi:10.1088/0256-307x/35/5/050301

Cited by 5 publications

(7 citation statements)

References 46 publications

(53 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…More specifically, for sσ > r 2 sin 2 φ, the system in unbroken phase has pure real eigenvalues, and the EUR undergoes an periodic oscillatory behavior with T = π/ω. This result is similar to what we have observed in the Hermitian case, since the non-Hermitian system with real eigenvalues is equivalent to Hermitian system by a similarity transformation [38,39]. While for sσ < r 2 sin 2 φ in broken phase regime, the system with complex spectra turns up, the oscillation of EUR breaks down.…”

Section: Entropic Uncertainty Relation In Non-hermitian Systemssupporting

confidence: 87%

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

Guo¹,

Wang²

2021

Preprint

View full text Add to dashboard Cite

Non-Hermitian systems with exceptional points lead to many intriguing phenomena due to the coalescence of both eigenvalues and corresponding eigenvectors, in comparison to Hermitian systems where only eigenvalues degenerate. In this paper, we have investigated entropic uncertainty relation (EUR) in a non-Hermitian system and revealed a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitary dynamics determined by a Hermitian Hamiltonian, the behaviors of EUR can be well defined in two different ways depending on whether the system is located in unbroken or broken phase regimes. In unbroken phase regime, EUR undergoes an oscillatory behavior while in broken phase regime where the oscillation of EUR breaks down. The exceptional points mark the oscillatory and non-oscillatory behaviors of the EUR. In the dynamical limit, we have identified the witness of critical behavior of non-Hermitian systems in terms of the EUR. Our results reveal that the EUR witness can exactly detect the critical points of non-Hermitian systems beyond (anti-) PT-symmetric systems. Our results may have potential applications to witness and detect phase transition in non-Hermitian systems.

show abstract

Section: Entropic Uncertainty Relation In Non-hermitian Systemssupporting

confidence: 87%

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

Guo¹,

Wang²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…More specifically, for sσ > r 2 sin 2 φ, the system in unbroken phase has pure real eigenvalues, and the EUR undergoes an periodic oscillatory behavior with T = π/ω. This result is not surprised because of the fact that the non-Hermitian system with real eigenvalues is equivalent to Hermitian system by a similarity transformation [39,40]. While for sσ < r 2 sin 2 φ in broken phase regime, the system with complex spectra turns up, the oscillation of EUR breaks down.…”

Section: Entropic Uncertainty Relation In Non-hermitian Systemsmentioning

confidence: 93%

Witnessing criticality in non-Hermitian systems via entopic uncertainty relation

Guo

Wang

2022

New J. Phys.

View full text Add to dashboard Cite

Non-Hermitian systems with exceptional points lead to many intriguing phenomena due to the coalescence of both eigenvalues and corresponding eigenvectors, in comparison to Hermitian systems where only eigenvalues degenerate. In this paper, we propose an alternative proposal based on the entropy uncertainty relation (EUR) to detect the exceptional points and identify different phases of the non-Hermitian systems. We first investigate the EUR in a non-Hermitian system and then reveal a general connection between the EUR and the exceptional points of non-Hermitian system. Compared to the unitary Hermitian dynamics, the behaviors of EUR in the non-Hermitian system are well defined in two different ways depending on whether the system is located in unbroken or broken phase regimes. In unbroken phase regime where EUR undergoes an oscillatory behavior, while in broken phase regime where the oscillation of EUR breaks down. In the dynamical limit, we identify the critical phenomena of non-Hermitian systems in terms of the EUR. It is found that the EUR can exactly detect the critical points of non-Hermitian systems beyond PT-(anti-PT) symmetric systems. Finally, we comment on the possible experimental situation.

show abstract

“…Specifically, consider a three level Λ type atom with the hyperfine levels represented by |ψ 1 , |ψ 2 and |ψ 3 , such that |ψ 1 and |ψ 3 are coupled by an radio-frequency field and at the same time are connected to |ψ 2 by two optical fields, see figure 1. The dynamics of this system can be reduced to an effective two level system by adiabatically eliminating excited state |ψ 2 , under large detuning condition [18,45].…”

Section: Pt Symmetric Time Evolutionmentioning

confidence: 99%

PT symmetric evolution, coherence and violation of Leggett–Garg inequalities

Naikoo¹,

Kumari²,

Banerjee³

et al. 2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We report an unusual buildup of the quantum coherence in a qubit subjected to non-Hermitian evolution generated by a parity-time () symmetric Hamiltonian, which is reinterpreted as a Hermitian system in a higher dimensional space using Naimark dilation. The coherence is found to be maximum about the exceptional points (EPs), i.e. the points of coalescence of the eigenvalues as well as the eigenvectors. The nontrivial physics about EPs has been observed in various systems, particularly in photonic systems. As a consequence of enhancement in coherence, the various formulations of Leggett–Garg inequality tests show maximal violation about the EPs.

show abstract

Dynamical Evolution of an Effective Two-Level System with ${\mathscr{P}}{\mathscr{T}}$ Symmetry

Cited by 5 publications

References 46 publications

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

Witnessing criticality in non-Hermitian systems via entopic uncertainty relation

PT symmetric evolution, coherence and violation of Leggett–Garg inequalities

Contact Info

Product

Resources

About