The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.The emergence of parity-time (PT) symmetry has greatly enriched our study of symmetry-enabled non-Hermitian physics, but the realization of quantum PT symmetry faces an intrinsic issue of unavoidable symmetry-breaking Langevin noises. Here we construct a quantum pseudo-anti-PT (pseudo-APT) symmetry in a two-mode bosonic system without involving Langevin noises. We show that the spontaneous pseudo-APT symmetry breaking leads to an exceptional point, across which there is a transition between different types of quantum squeezing dynamics; i.e., the squeezing factor increases exponentially (oscillates periodically) with time in the pseudo-APT-symmetric (broken) region. Such dramatic changes of squeezing factors and quantum dynamics near the exceptional point are utilized for ultraprecision quantum sensing. These exotic quantum phenomena and sensing applications can be experimentally observed in two physical systems: spontaneous wave mixing nonlinear optics and atomic Bose-Einstein condensates. Our Letter offers a physical platform for investigating exciting APT symmetry physics in the quantum realm, paving the way for exploring fundamental quantum non-Hermitian effects and their quantum technological applications.

arXiv:2108.12873Physical Review LettersApr 29, 202278 citations

Parity-Time Symmetry of Plasma Waves

Hong Qin

The susceptibility tensor of a homogeneous collisionless magnetized plasma possesses parity-time (PT) symmetry. For a stationary gyrotropic equilibrium, with the wave vector $\mathbf{k}$ and the equilibrium magnetic field $\mathbf{B}_0$ in the $x$ -- $z$ plane, the kinetic response satisfies $χ(ω^*,\mathbf{k})=Rχ(ω,\mathbf{k})^*R$ , where $R=\operatorname{diag}(1,-1,1)$ . We show that the susceptibility PT-symmetry is a reduced-response-space manifestation of PT symmetry of the underpinning kinetic system. We identify parity $P$ and time reversal $T$ on the electromagnetic kinetic eigenmode space and show that the Hamiltonian operator $\mathcal{H}_{\mathrm{VM}}$ of the linearized Vlasov--Maxwell system is PT-symmetric, satisfying $PT\mathcal{H}_{\mathrm{VM}}(PT)^{-1}=\mathcal{H}_{\mathrm{VM}}$ . The PT symmetry of the homogeneous magnetized Vlasov--Poisson eigenproblem is also established. Many kinetic instabilities associated with nonmonotonic distributions, rings, loss cones, and resonant energetic-particle populations are fundamentally spontaneous PT-symmetry breaking, which is achieved through and only through Krein collisions. Three examples demonstrate distinct utilities of this analysis. Definite-sign cyclotron residues protect thermal Bernstein modes from spontaneous PT-symmetry breaking. The nonmonotonic Dory--Guest--Harris distribution permits sign-indefinite residues and Krein collisions, for which we derive an analytical instability threshold and growth rate. The recently discovered mode-pole resonance instability provides a distinct realization of spontaneous PT-symmetry breaking and illustrates how PT symmetry can guide the discovery of kinetic instabilities with applications to fusion energy. These results establish PT symmetry as a structural principle of plasma waves and instabilities and open new directions for studying spectral topology in kinetic plasmas.The susceptibility tensor of a homogeneous collisionless magnetized plasma possesses parity-time (PT) symmetry. For a stationary gyrotropic equilibrium, with the wave vector $\mathbf{k}$ and the equilibrium magnetic field $\mathbf{B}_0$ in the $x$--$z$ plane, the kinetic response satisfies $χ(ω^*,\mathbf{k})=Rχ(ω,\mathbf{k})^*R$, where $R=\operatorname{diag}(1,-1,1)$. We show that the susceptibility PT-symmetry is a reduced-response-space manifestation of PT symmetry of the underpinning kinetic system. We identify parity $P$ and time reversal $T$ on the electromagnetic kinetic eigenmode space and show that the Hamiltonian operator $\mathcal{H}_{\mathrm{VM}}$ of the linearized Vlasov--Maxwell system is PT-symmetric, satisfying $PT\mathcal{H}_{\mathrm{VM}}(PT)^{-1}=\mathcal{H}_{\mathrm{VM}}$. The PT symmetry of the homogeneous magnetized Vlasov--Poisson eigenproblem is also established. Many kinetic instabilities associated with nonmonotonic distributions, rings, loss cones, and resonant energetic-particle populations are fundamentally spontaneous PT-symmetry breaking, which is achieved through and only through Krein collisions. Three examples demonstrate distinct utilities of this analysis. Definite-sign cyclotron residues protect thermal Bernstein modes from spontaneous PT-symmetry breaking. The nonmonotonic Dory--Guest--Harris distribution permits sign-indefinite residues and Krein collisions, for which we derive an analytical instability threshold and growth rate. The recently discovered mode-pole resonance instability provides a distinct realization of spontaneous PT-symmetry breaking and illustrates how PT symmetry can guide the discovery of kinetic instabilities with applications to fusion energy. These results establish PT symmetry as a structural principle of plasma waves and instabilities and open new directions for studying spectral topology in kinetic plasmas.

physics.plasm-phCross-listedarXiv:2610.03433Oct 5, 2026

Parity and Group Theory

Willi-Hans Steeb

Springer eBooksJan 1, 19980 citations

Experimental simulation of anti-parity-time symmetric Lorentz dynamics

Qiang Li, Chengjie Zhang, Ze-Di Cheng +11 more

The recent experimental progress in parity-time (PT) symmetry has attracted great interest. However, compared with PT symmetry, there are only a few reported results on its counterpart, anti-PT symmetry, which would lead to new insights and applications. Experimentally simulating and demonstrating the properties of anti-PT symmetry is of particular interest. Here, we present experimental research for simulating the dynamics of bosonic Bogoliubov quasi-particles with anti-PT symmetry based on single photons generated from a point defect in a gallium nitride film. The dynamical evolution under a non-unitary operator is a continuous complex Lorentz transformation in a complex Minkowski space. The evolved states are located on hyperbolic curves, depending on the values of the new defined inner product, which remain invariant during the evolution. Three types of state, space-like, light-like, and time-like, which are analogous to those predicted by the special relativity, are demonstrated. The results of our work could be helpful to investigate the dynamics of quasi-particles in diverse systems and promote deep understanding of non-Hermitian quantum mechanics in open systems.The recent experimental progress in parity-time (PT) symmetry has attracted great interest. However, compared with PT symmetry, there are only a few reported results on its counterpart, anti-PT symmetry, which would lead to new insights and applications. Experimentally simulating and demonstrating the properties of anti-PT symmetry is of particular interest. Here, we present experimental research for simulating the dynamics of bosonic Bogoliubov quasi-particles with anti-PT symmetry based on single photons generated from a point defect in a gallium nitride film. The dynamical evolution under a non-unitary operator is a continuous complex Lorentz transformation in a complex Minkowski space. The evolved states are located on hyperbolic curves, depending on the values of the new defined inner product, which remain invariant during the evolution. Three types of state, space-like, light-like, and time-like, which are analogous to those predicted by the special relativity, are demonstrated. The results of our work could be helpful to investigate the dynamics of quasi-particles in diverse systems and promote deep understanding of non-Hermitian quantum mechanics in open systems.

OpticaJan 11, 201947 citations

Symmetry and quantum systems

Anthony Brinton Wolbarst

Jan 1, 19776 citations

The susceptibility tensor of a homogeneous collisionless magnetized plasma possesses parity-time (PT) symmetry. For a stationary gyrotropic equilibrium, with the wave vector

\mathbf{k}

and the equilibrium magnetic field

\mathbf{B}_0

in the

x

z

plane, the kinetic response satisfies

χ(ω^*,\mathbf{k})=Rχ(ω,\mathbf{k})^*R

, where

R=\operatorname{diag}(1,-1,1)

. We show that the susceptibility PT-symmetry is a reduced-response-space manifestation of PT symmetry of the underpinning kinetic system. We identify parity

P

and time reversal

T

on the electromagnetic kinetic eigenmode space and show that the Hamiltonian operator

\mathcal{H}_{\mathrm{VM}}

of the linearized Vlasov--Maxwell system is PT-symmetric, satisfying

PT\mathcal{H}_{\mathrm{VM}}(PT)^{-1}=\mathcal{H}_{\mathrm{VM}}

. The PT symmetry of the homogeneous magnetized Vlasov--Poisson eigenproblem is also established. Many kinetic instabilities associated with nonmonotonic distributions, rings, loss cones, and resonant energetic-particle populations are fundamentally spontaneous PT-symmetry breaking, which is achieved through and only through Krein collisions. Three examples demonstrate distinct utilities of this analysis. Definite-sign cyclotron residues protect thermal Bernstein modes from spontaneous PT-symmetry breaking. The nonmonotonic Dory--Guest--Harris distribution permits sign-indefinite residues and Krein collisions, for which we derive an analytical instability threshold and growth rate. The recently discovered mode-pole resonance instability provides a distinct realization of spontaneous PT-symmetry breaking and illustrates how PT symmetry can guide the discovery of kinetic instabilities with applications to fusion energy. These results establish PT symmetry as a structural principle of plasma waves and instabilities and open new directions for studying spectral topology in kinetic plasmas.