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

We analyse two quantum systems with hidden parity-time ($${\mathscr {P}\mathscr {T}}$$ P T ) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce a damping frame (DF), in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden $${\mathscr {P}\mathscr {T}}$$ P T symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system.

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“…2 with the results presented in 44 . The real part of the eigenvalues in 44 diverge, whereas these seen in Fig. 2 are finite and continuous.…”

Section: Resultssupporting

confidence: 64%

“…It is worth comparing the results presented in Fig. 2 with the results presented in 44 . The real part of the eigenvalues in 44 diverge, whereas these seen in Fig.…”

Section: Resultsmentioning

confidence: 83%

The effect of thermal photons on exceptional points in coupled resonators

Chimczak

Kowalewska-Kudłaszyk

Lange

et al. 2023

Sci Rep

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“…rotationtime symmetric. It has been demonstrated in Ref [53] that RT symmetry is a superset i.e. a more general notion compared to PT , such that a wide class of hamiltonians may be identified that have properties similar to that of PT -symmetric systems, despite not being explicitly PT -symmetric (PT symmetry is only a special class of RT symmetry).…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, some authors have used the PT -symmetric nature of non-hermitian hamiltonians to produce efficient algorithms to compute their spectra with arbitrarily high precision [49,50]. RT -symmetric bosonic and fermionic systems have been studied in various capacities ranging from exactly solvable models, to quantum batteries, detection of exceptional points through dynamics and unbroken phase through quantum-information-related techniques in [51][52][53][54][55][56]. Some authors have focused on solvable fermionic spin chains, for example in Refs.…”

Section: Introductionmentioning

confidence: 99%

Spectral crossover in non-hermitian spin chains: comparison with random matrix theory

Sarkar¹,

Sen²,

Kumar³

2023

Preprint

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We systematically study the short range spectral fluctuation properties of three non-hermitian spin chain hamiltonians using complex spacing ratios. In particular we focus on the non-hermitian version of the standard one-dimensional anisotropic XY model having intrinsic rotation-time-reversal (RT ) symmetry that has been explored analytically by Zhang and Song in [Phys.Rev.A 87, 012114 (2013)]. The corresponding hermitian counterpart is also exactly solvable and has been widely employed as a toy model in several condensed matter physics problems. We show that the presence of a random field along the x-direction together with the one along z facilitates integrability and RT -symmetry breaking leading to the emergence of quantum chaotic behaviour indicated by a spectral crossover resembling Poissonian to Ginibre unitary ensemble (GinUE) statistics of random matrix theory. Additionally, we consider two n × n dimensional phenomenological random matrix models in which, depending upon crossover parameters, the fluctuation properties measured by the complex spacing ratios show an interpolation between 1D-Poisson to GinUE and 2D-Poisson to GinUE behaviour. Here 1D and 2D Poisson correspond to real and complex uncorrelated levels, respectively.

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“…Many interesting and nontrivial effects are associated with the presence of EPs [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. One of these is enhanced system sensitivity to external perturbations in the vicinity of EPs [35][36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Generating high-order quantum exceptional points in synthetic dimensions

Arkhipov,

Minganti,

Miranowicz

et al. 2021

Preprint

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Recently, there has been intense research in proposing and developing various methods for constructing high-order exceptional points (EPs) in dissipative systems. These EPs can possess a number of intriguing properties related to, e.g., chiral transport and enhanced sensitivity. Proposals to realize high-order EPs have been based on the use of non-Hermitian Hamiltonians (NHHs) of composite systems, i.e., the operators describing the evolution of coupled post-selected systems or coupled intense light fields. In both cases, quantum jumps play no role. Here, by considering the full quantum dynamics of a quadratic Liouvillian superoperator, we introduce a simple and effective method for engineering NHHs with high-order quantum EPs, derived from evolution matrices of system operators moments. That is, by quantizing higher-order moments of system operators, e.g., of a quadratic two-mode system, the resulting evolution matrices can be interpreted as the new NHHs describing, e.g., networks of coupled resonators. Notably, such a mapping allows to correctly reproduce the results of the Liouvillian dynamics, including quantum jumps. By applying this mapping, we demonstrate that quantum EPs of any order can be engineered in dissipative systems and can, thus, be probed by the coherence and spectral functions. As an example, we consider a U (1)-symmetric quadratic Liouvillian describing an optical cavity with incoherent mode coupling, which can also possess anti-PT -symmetry. Compared to their PT -symmetric counterparts, such anti-PT -symmetric systems could be easier to scale and, thus, can serve as a promising platform for engineering quantum systems with high-order EPs.

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

Cited by 8 publications

References 69 publications

The effect of thermal photons on exceptional points in coupled resonators

The effect of thermal photons on exceptional points in coupled resonators

Spectral crossover in non-hermitian spin chains: comparison with random matrix theory

Generating high-order quantum exceptional points in synthetic dimensions

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