Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories

Minganti, Fabrizio; Miranowicz, Adam; Chhajlany, Ravindra W.; Arkhipov, Ievgen I.; Nori, Franco

doi:10.1103/physreva.101.062112

Cited by 91 publications

(74 citation statements)

References 74 publications

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“…Such points in the parameter space are known as EPs. Since some of eigenvectors are parallel in EP, Hermitian Hamiltonians cannot exhibit any EP 9,57 . The Hamiltonian (1) is non-Hermitian, so in Fig.…”

Section: Resultsmentioning

confidence: 99%

“…One can easily check using 37 , 38 that because of the last two terms of , which describe loss in the mode A and gain in the mode B . The gain-loss terms are, however, crucial for the existence of EPs, because non-Hermiticity is necessary for the emergence of EPs 9 , 57 . Moreover, modelling losses is unavoidable as they are present in all real systems.…”

Section: Resultsmentioning

confidence: 99%

“…Remarkably, spectral singularities can be found also in non-Hermitian systems that are not -symmetric 9 , 57 . Therefore now the question arises: can a given bosonic non- -symmetric systems display any singularity and how to engineer such systems?…”

Section: Resultsmentioning

confidence: 99%

“…However, EPs can be studied in systems without any relation to the symmetry 1 , 2 . Recently, the concept of EPs have been generalised to describe fully quantum systems including quantum jumps 7 – 9 . Possible applications of EPs for quantum sensing have been attracting much interest (see 10 and references therein).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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show abstract

“…The description of dissipation based on the use ofĤ e f f in the Schrödinger equation suffers from the fact that the state vector |ψ (t ) undergoes a nonunitary evolution and neglects quantum jumps. As such a description can be regarded as a semiclassical limit of the Markovian dynamics of the open quantum system and can naturally appear in postselection of quantum trajectories [67,68], increasing attention is currently devoted to unveiling NHSE beyond the semiclassical limit [24,56,61,62]. A unitary dynamics is restored by considering a stochastic Schrödinger equation, where stochastic terms are added to the deterministic evolution of |ψ (t ) so as to preserve the norm [69].…”

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confidence: 99%

Unraveling the non-Hermitian skin effect in dissipative systems

Longhi

2020

Phys. Rev. B

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The non-Hermitian skin effect, i.e., eigenstate condensation at the edges in lattices with open boundaries, is an exotic manifestation of non-Hermitian systems. In Bloch theory, an effective non-Hermitian Hamiltonian is generally used to describe dissipation, which, however, is not norm preserving and neglects quantum jumps.Here it is shown that in a self-consistent description of the dissipative dynamics in a one-band lattice, based on the stochastic Schrödinger equation or Lindblad master equation with a collective jump operator, the skin effect and its dynamical features are washed out. Nevertheless, both short-and long-time relaxation dynamics provide a hidden signature of the skin effect found in the semiclassical limit. In particular, relaxation toward a maximally mixed state with the largest von Neumann entropy in a lattice with open boundaries is a manifestation of the semiclassical skin effect.

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Transition Characteristics of Non‐Hermitian Skin Effects in a Zigzag Lattice Without Chiral Symmetry

Wang

Chen

et al. 2023

Advanced Physics Research

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Non‐Hermitian systems recently have attracted tremendous attention due to their plentiful unique and fascinating properties, among which is the localization of an otherwise extensive bulk eigen‐state at the boundary when the open boundary condition (OBC) is imposed, an interesting phenomenon now referred to as non‐Hermitian skin effect (NHSE). Here, a non‐Hermitian Zigzag lattice model with/without chiral symmetry is investigated with respect to different nearest‐neighbor and long‐range hopping amplitudes and study the transition signature of NHSE by extracting information from the complex eigen‐energy spectra of the system under the periodic boundary condition (PBC), which is verified by the directional inverse participation ratio under OBC. Such an approach provides great simplicity in judging transitions of NHSE especially in lattices without chiral symmetry, where the obtained transition signatures are further confirmed by calculating the topological winding number of the energy under PBC. This work reveals a fundamental way to explore transitions of NHSE, and has a potential in helping understand more other complicated topological physics unique to non‐Hermitian systems.

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Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories

Cited by 91 publications

References 74 publications

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

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

Unraveling the non-Hermitian skin effect in dissipative systems

Transition Characteristics of Non‐Hermitian Skin Effects in a Zigzag Lattice Without Chiral Symmetry

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