Quantum simulation of parity\u2013time symmetry breaking with a superconducting quantum processor

Exceptional points (EPs) in photonics are associated with non-Hermitian Hamiltonians with energy gain or loss, a notable example is EPs in parity-time symmetric Hamiltonians. We show that, counterintuitively, actual energy gain or loss is not required to generate this type of non-Hermitian degeneracy, since the eigenvalue of the optical Hamiltonian is the mode's propagation constant and not the energy. This is demonstrated by a simple three-layer insulator-metal-insulator (I-M-I) plasmonic waveguide, the eigenmodes of which are known to experience degeneracy at a certain point in the parametric space suggested to be used for rainbow trapping. We identify this point to be, in fact, an EP with the coalescence of the eigenmodes, despite the system having neither parity nor time symmetry. Furthermore, we demonstrate the manifestation of a third-order EP, which is generated by merging two separate EPs in the parametric space of the I-M-I waveguide. The presented results reveal unconventional properties of the Hamiltonian of a simple plasmonic waveguide and provide an insight into the nature of EPs in non-Hermitian plasmonic systems in general, suggesting the possibility of accessing even higher-order EP regimes in simple photonic structures without the need for optical gain or loss.

Unconventional properties of non-Hermitian systems, such as the existence of exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes however remains unclear. In this work, we analyze the parametric-sensing properties of linear coupled-mode systems that are described by effective non-Hermitian Hamiltonians. Our analysis fully accounts for noise effects in both classical and quantum regimes, and also fully treats a realistic and optimal measurement protocol based on coherent driving and homodyne detection. Focusing on two-mode devices, we derive fundamental bounds on the signal power and signal-to-noise ratio for any such sensor. We use these to demonstrate that enhanced signal power requires gain, but not necessarily any proximity to an exceptional point. Further, when noise is included, we show that nonreciprocity is a powerful resource for sensing: it allows one to exceed the fundamental bounds constraining any conventional, reciprocal sensor.

Recently, non-Hermitian Hamiltonians have gained a lot of interest, especially in optics and electronics. In particular, the existence of real eigenvalues of non-Hermitian systems has opened a wide set of possibilities, especially, but not only, for sensing applications, exploiting the physics of exceptional points. In particular, the square root dependence of the eigenvalue splitting on different design parameters, exhibited by 2 × 2 non-Hermitian Hamiltonian matrices at the exceptional point, paved the way to the integration of high-performance sensors. The square root dependence of the eigenfrequencies on the design parameters is the reason for a theoretically infinite sensitivity in the proximity of the exceptional point. Recently, higher-order exceptional points have demonstrated the possibility of achieving the nth root dependence of the eigenfrequency splitting on perturbations. However, the exceptional sensitivity to external parameters is, at the same time, the major drawback of non-Hermitian configurations, leading to the high influence of noise. In this review, the basic principles of PT-symmetric and anti-PT-symmetric Hamiltonians will be shown, both in photonics and in electronics. The influence of noise on non-Hermitian configurations will be investigated and the newest solutions to overcome these problems will be illustrated. Finally, an overview of the newest outstanding results in sensing applications of non-Hermitian photonics and electronics will be provided.

This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration are taken with continuous spectrum and the following cases are examined: an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum and an exceptional point situated inside of continuous spectrum. In the present work the rigorous proofs are given for the resolutions of identity in both cases.

The paper is devoted to the memory of Dmitry Diakonov. We discuss gravity emerging in the fermionic vacuum as suggested by Diakonov 10 years ago in his paper “Towards lattice-regularized Quantum Gravity”. [1] Gravity emerges in the phase transition. The order parameter in this transition is the tetrad field e^a_mu, which appears as the bilinear composite of the fermionic fields. The similar scenario of the symmetry breaking takes place in the B-phase of superfluid ^3He, where the real part of the spin-triplet p-wave order parameter matrix A_{a i} plays the role of the emerging tetrad (triad). In Diakonov theory this symmetry breaking gives 6 Nambu-Goldstone modes; 6 gauge bosons in the spin-connection fields, which absorb 6 NG modes and become massive gauge bosons; and 6 Higgs fields. In ^3He-B, these Higgs collective modes correspond to 6 massive gravitons, while in the emerging general relativity the Higgs collective modes give rise to two massless gravitational waves.

In this paper, we provide a comprehensive review of unidirectional reflectionless light propagation in photonic devices at exceptional points (EPs). EPs, which are branch point singularities of the spectrum, associated with the coalescence of both eigenvalues and corresponding eigenstates, lead to interesting phenomena, such as level repulsion and crossing, bifurcation, chaos, and phase transitions in open quantum systems described by non‐Hermitian Hamiltonians. Recently, it was shown that judiciously designed photonic synthetic matters could mimic the complex non‐Hermitian Hamiltonians in quantum mechanics and realize unidirectional reflection at optical EPs. Unidirectional reflectionlessness is of great interest for optical invisibility. Achieving unidirectional reflectionless light propagation could also be potentially important for developing optical devices, such as optical network analyzers. Here, we discuss unidirectional reflectionlessness at EPs in both parity‐time ( PT )‐symmetric and non‐ PT ‐symmetric optical systems. We also provide an outlook on possible future directions in this field.

There is considerable interest in the dynamics of topological defects formed during a symmetry breaking phase transition in fields as diverse as condensed matter physics, particle physics and cosmology. Liquid crystals, with their many symmetry breaking phase transitions are ideal materials for such studies. Here we report on light transmission studies of the coarsening of three-dimensional defect tangles in uniaxial nematic liquid crystals subjected to a sudden pressure jump from the isotropic phase to the nematic phase. We have verified that the type 1/2 disclination line density, as a function of time, scales as t−v with v = 1.0 ± 0.1 over four decades in time. The transmitted light intensity exhibits two distinct scaling regimes depending on whether propagation without scattering or diffusive propagation with multiple scattering dominates the light reaching the detector.

We demonstrate symmetry-selective control of nonlinear photoconductivity in monolayer MoSe2, where near-resonant, linearly polarized light induces transition-specific symmetry breaking and topological phase transitions without violating time-reversal symmetry. Combining Floquet theory with first-principles modeling, we show that x-polarized light breaks both the threefold rotation C3 and the antiunitary mirror $${\mathcal{T}}{M}_{x}$$, whereas y-polarized light preserves $${\mathcal{T}}{M}_{x}$$, enabling polarization-resolved generation of interband Berry curvature dipoles. This selective symmetry breaking yields a circular photogalvanic current whose direction and magnitude are tunable via the pump frequency, offering a direct ultrafast probe of Floquet-induced band inversion. These findings establish a viable pathway for detecting light-driven topological currents in nonchiral two-dimensional semiconductors and advancing terahertz optoelectronic applications.

The precise manipulation of electronic properties through the introduction of foreign atoms—doping—remains the central paradigm of condensed matter physics and the foundational technology of the information age. From the early formulation of rigid-band semiconductor theory to the contemporary exploration of quantum materials, the physics of doping has evolved from a perturbative treatment of impurities to a complex study of thermodynamic self-regulation, symmetry breaking, and topological phase transitions.1While the twentieth century was defined by the mastery of covalent semiconductors like silicon (Si) and gallium arsenide (GaAs), where dopants act as simple hydrogenic centers, the current frontier involves

In a recent paper a toy model (hypercubic model) undergoing a first-order -symmetry-breaking phase transition (-SBPT) was introduced. The hypercubic model was inspired by the topological hypothesis, according to which a phase transition may be entailed by suitable topological changes of the equipotential surfaces (Σv’s) of configuration space. In this paper we show that at the origin of a -SBPT there is a geometric property of the Σv’s, i.e. dumbbell-shaped Σv’s suitably defined, which includes a topological change as a limiting case. This property is necessary and sufficient condition to entail a -SBPT. This new approach has been applied to three models: a modified version introduced here of the hypercubic model, a model introduced in a recent paper with a continuous -SBPT belonging to several universality classes, and finally to a physical models, i.e. the mean-field ϕ4 model and a simplified version of it.

Non-Hermitian Hamiltonians may still have real eigenvalues, provided that a combined parity-time (ƤƮ) symmetry exists. The prospect of ƤƮ symmetry has been explored in several physical systems such as photonics, acoustics, and electronics. The eigenvalues in these systems undergo a transition from real to complex at exceptional points (EPs), where the ƤƮ symmetry is broken. Here, we demonstrate the existence of EP in magnonic devices composed of two coupled magnets with different magnon losses. The eigenfrequencies and damping rates change from crossing to anti-crossing at the EP when the coupling strength increases. The magnonic dispersion includes a strong "acoustic-like" mode and a weak "optic-like" mode. Moreover, upon microwave radiation, the ƤƮ magnonic devices act as magnon resonant cavity with unique response compared to conventional magnonic systems.

We study the influence of random anisotropy type quenched disorder on the phase behavior of the system, which exhibits in undistorted case the 2nd order continuous symmetry breaking phase transition. Invoking the central limit theorem we express the free energy of the system in terms of the order parameter η and the characteristic length ξ of the gauge field ϕ. The latter exhibits the Goldstone fluctuation mode and is consequently extremely susceptible to the imposed disorder. In case of negligible distribution width ΔT of the local transition temperatures the disorder converts the 2nd order transition into a discontinuous one for W<WC, where Wrepresents the disorder strength. Above the critical disorder strength WC the transition becomes gradual. However for the finite width ΔT the transition becomes gradual for any W>0. We demonstrate that for large enough values of ΔT the system behavior is dominated by the distribution of temperatures, while the details of the random field interaction term play a secondary role. The influence of distribution of local (quasi) phase transitions is in most theoretical approaches dealing with randomly perturbed systems neglected from the outset.

<sec> We theoretically and experimentally demonstrate the anisotropic exceptional points (EPs) in the cavity magnonics system where magnons in a one millimeter-diameter yttrium iron garnet (YIG) sphere are coherently coupled with the microwave photons in a three-dimensional microwave cavity. The damping nature makes the cavity magnonics system inherently non-Hermitian. By solving the eigenvalues and eigenvectors of non-Hermitian Hamiltonian, a series of interesting and essential characteristics of the system can be obtained. Therefore, non-Hermitian physics has received more and more attention in both theory and experiment communities. Among them, exceptional points correspond to the non-Hermitian system’s degenerate states where the eigenvalues of the non-Hermitian system are identical, and the eigenvectors are parallel. The coupled cavity photon-magnon system has high tunability of coupling strength and cavity external damping rate, which is very suitable for studying EPs -related physics.</sec><sec> Exceptional points (EPs) are crucial in all kinds of non-Hermitian physical systems, which have both fundamental and applicational importance. For instance, it can be used for sensitive detection by monitoring spectrum splitting of degenerate modes when a perturbation to be sensed occurs. The EPs can be anisotropic, which means that it has a different function relation when the system approaches the EPs along different parameter paths of the system. In this paper, by carefully designing the parameter space, we observe the anisotropic exceptional point in the coupled cavity photon-magnon system. It shows the linear and square-root behavior when the EPs are approached from different directions in the parameter space. One of the parameters is the position of the YIG sphere in the cavity, which determines the coherent coupling strength between the cavity mode and the magnon mode. Another parameter is the number of the gasket between the cavity signal loading port and the cavity external surface, which determines the external damping rate of the cavity mode. Both of these parameters can be easily and accurately adjusted experimentally.</sec><sec> Our study paves the way for exploring anisotropic EPs based sensing technologies and more non-Hermitian related physics in the cavity magnonics system.</sec>

Depending on the parity of the rotational quantum number J, solid hydrogens exhibit either pressure-driven broken symmetry phase (BSP) transitions (even-J species – para-hydrogen (p-H2), and ortho-deuterium (o-D2)) or usual order-disorder phase transitions (odd-J species – o-H2 and p-D2) with the phase transition temperature increasing monotonically with pressure from the phase transition point at zero pressure. At the same time, for solid HD the BSP phase transition line displays a minimum, indicating that the disordered phase is reentrant. In this work a model of quantum linear rotors is used to study characteristic features of the P–T phase diagrams for ortho–para mixtures in solid H2 and D2. We developed a mean-field theory of even-J – odd-J mixtures of quantum linear rotors on a 3D lattice. Two limiting cases are considered: mixtures at thermodynamic equilibrium, where the conversion time is small or comparable with the thermalization time, and the opposite case, frozen mixtures, when the conversion time is large compared with other relevant times. We found that for all equilibrium linear rotor systems — the even-J – odd-J mixtures — the reentrant behavior of the phase transition lines is an entropy-driven phenomenon, as was previously found for the all-J system. Experimentally, conditions to find the reentrant BSP transition line are most favorable for H2 mixtures, whereas the frozen monotonic phase lines should be the case for D2 even-J – odd-J mixtures. These results may therefore be particularly useful for understanding the anomalous transition region of the BSP transition documented for D2 mixtures.

The recent growth in popularity of the non-Hermitian quantum Hamiltonians H(λ) with real spectra is strongly motivated by the phenomenologically innovative possibility of an access to the non-Hermitian degeneracies called exceptional points (EPs). What is actually presented in the present paper is a perturbation-theory-based demonstration of a fine-tuned nature of this access. This result is complemented by a toy-model-based analysis of the related details of quantum dynamics in the almost degenerate regime with λ≈λ(EP). In similar studies, naturally, one of the decisive obstacles is the highly nontrivial form of the underlying mathematics. Here, many of these obstacles are circumvented via several drastic simplifications of our toy models—i.a., our N by N matrices H(λ)=H(N)(λ) are assumed real, tridiagonal and PT-symmetric, and our H(N)(λ) is assumed to be split into its Hermitian and non-Hermitian components staying in interaction. This is shown to lead to several remarkable spectral features of the model. Up to N=8, their description is even shown tractable non-numerically. In particular, it is shown that under generic perturbation, the “unfolding” removal of the spontaneous breakdown of PT-symmetry proceeds via intervals of λ with complex energy spectra.