Time-dependent 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>
-symmetric quantum mechanics in generic non-Hermitian systems

Zhang, Da-Jian; Wang, Qinghai; Gong, Jiangbin

doi:10.1103/physreva.100.062121

Cited by 37 publications

(30 citation statements)

References 78 publications

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“…Several proposals have been given to simulate PT-symmetric systems [ 12 , 14 , 18 , 19 , 28 , 69 ], P -pseudo-Hermitian systems, [ 18 , 55 , 57 ], and anti-PT-symmetric systems [ 20 , 21 ] based on different theories. However, quantum simulation designed for anti- P -pseudo-Hermitian systems is absent.…”

Section: Introductionmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

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Section: Introductionmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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“…Not only the exact point of symmetry breaking leads to remarkable physics, but also the systems found in the vicinity of EPs can exhibit features as potentially enhanced sensitivity 35 , 36 . The latest studies are commonly associating real-valued spectra with the respective symmetry requirements and EPs with symmetry breaking 3 , 4 , 37 – 42 .…”

Section: Introductionmentioning

confidence: 99%

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $${\mathscr{PT}}$$ symmetry

Lange

Chimczak

Kowalewska-Kudłaszyk

et al. 2020

Sci Rep

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We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time ($${{\mathscr{PT}}}$$ PT ) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time ($${\mathscr{RT}}$$ RT ) symmetry. We observe that $${\mathscr{RT}}$$ RT -symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing $${\mathscr{RT}}$$ RT -symmetric Hamiltonians. We believe that our results on the $${\mathscr{RT}}$$ RT -symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the $${{\mathscr{PT}}}$$ PT -symmetric systems.

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“…Usually, the (invertible) Hermitian operator η in the above equation is called the metric operator [6,11]. In particular, when η is time independent, (4) reduces to…”

Section: The Concepts Of Metric Operator and Dilationmentioning

confidence: 99%

“…To simulate the broken PT -symmetric systems, researchers usually consider the time dependent case, namely (4). In this case, there are also interesting results [11,12]. In this paper, we only consider the time independent case and the metric operators always refer to the operators satisfying (5).…”

Section: The Concepts Of Metric Operator and Dilationmentioning

confidence: 99%

“…This explains why we consider the condition that the metric operator is positive in the unbroken PT -symmetric phase. Equation (11) shows that when 1 is small, E d (θ) is also small. It means that when the metric operator is closer to the broken PT -symmetry, an unbroken PT -symmetric system is more difficult to be effectively realized.…”

Section: Another Way To Measure the Difference Between Metric Operatorsmentioning

confidence: 99%

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To Quantify the Difference of η-Inner Products in $\mathcal {P}\mathcal {T}$-Symmetric Theory

Huang

Zhang

2021

Int J Theor Phys

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In this paper, we consider a typical continuous two dimensional PT -symmetric Hamiltonian and propose two different approaches to quantitatively show the difference between the η-inner products. Despite the continuity of Hamiltonian, the η-inner product is not continuous in some sense. It is shown that the difference between the η-inner products of broken and unbroken PT -symmetry is lower bounded. Moreover, such a property can lead to some uncertainty relation.

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Time-dependent PT -symmetric quantum mechanics in generic non-Hermitian systems

Cited by 37 publications

References 78 publications

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $${\mathscr{PT}}$$ symmetry

To Quantify the Difference of η-Inner Products in $\mathcal {P}\mathcal {T}$-Symmetric Theory

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