Parity Conservation Research Articles

Nonequilibrium dissociative dynamics of D2 in two-color, few-photon excitation and ionization

${\mathrm{D}}_{2}$ molecules, excited by linearly cross-polarized femtosecond extreme ultraviolet (XUV) and near-infrared (NIR) light pulses, reveal highly structured ${\mathrm{D}}^{+}$ ion fragment momenta and angular distributions that originate from two different four-step dissociative ionization pathways after four-photon absorption (one XUV $+$ three NIR). We show that, even for very low dissociation kinetic energy release $\ensuremath{\le}$ 240 meV, specific electronic excitation pathways can be identified and isolated in the final ion momentum distributions. With the aid of ab initio electronic structure and time-dependent Schr\"odinger equation calculations, angular momentum, energy, and parity conservation are used to identify the excited neutral molecular states and molecular orientations relative to the polarization vectors in these different photoexcitation and dissociation sequences of the neutral ${\mathrm{D}}_{2}$ molecule and its ${\mathrm{D}}_{2}^{+}$ cation. In one sequential photodissociation pathway, molecules aligned along either of the two light polarization vectors are excluded, while another pathway selects molecules aligned parallel to the light propagation direction. The evolution of the nuclear wave packet on the intermediate $B{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ electronic state of the neutral ${\mathrm{D}}_{2}$ molecule is also probed in real time.

Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries

We prove two Lieb-Schultz-Mattis type theorems that apply to any translationally invariant and local fermionic $d$-dimensional lattice Hamiltonian for which fermion-number conservation is broken down to the conservation of fermion parity. We show that when the internal symmetry group $G^{\,}_{f}$ is realized locally (in a repeat unit cell of the lattice) by a nontrivial projective representation, then the ground state cannot be simultaneously nondegenerate, symmetric (with respect to lattice translations and $G^{\,}_{f}$), and gapped. We also show that when the repeat unit cell hosts an odd number of Majorana degrees of freedom and the cardinality of the lattice is even, then the ground state cannot be simultaneously nondegenerate, gapped, and translation symmetric.

Quantum Parity Conservation in Planar Quantum Electrodynamics

Quantum parity conservation is verified at all orders in perturbation theory for a massless parity-even $U(1)\times U(1)$ planar quantum electrodynamics (QED$_3$) model. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) subtraction scheme, in the framework of the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method, in order to subtract the infrared divergences induced by the ultraviolet subtractions at 1- and 2-loops, however thanks to the superrenormalizability of the model the ultraviolet divergences are bounded up to 2-loops. Finally, it is proved that the BPHZL renormalization method preserves parity for the model taken into consideration, contrary to what happens to the ordinary massless parity-even $U(1)$ QED$_3$.

Symmetry Protected Invariant Scattering Properties for Incident Plane Waves of Arbitrary Polarizations

AbstractPolarization independent Mie scattering of building blocks is fundamental for constructions of optical systems with robust functionalities. Conventional studies for such polarization independence are generally restricted to special states of either linear or circular polarizations, widely neglecting elliptically‐polarized states that are generically present in realistic applications. Here, a comprehensive recipe to achieve invariant scattering properties in terms of cross sections for plane waves of arbitrary polarizations is presented, requiring only rotation symmetry and absence of optical activities. It is discovered that sole rotation symmetries can effectively decouple the two scattering channels that originate from the incident circularly polarized plane waves of opposite handedness, leading to invariance of all scattering properties for any polarizations on the same latitude circle of the Poincaré sphere. Further incorporations of extra inversion or mirror symmetries would eliminate the optical activities and thus ensure scattering property invariance for arbitrary polarizations. The all‐polarization invariance revealed is induced by the joint functions of discrete spatial symmetries, reciprocity, parity conservation and helicity preservation along the forward direction. This symmetry‐protected intrinsic invariance, independent of wavelength or material parameters, is robust against any symmetry‐preserving perturbations, which may render extra flexibilities for designing optical devices with stable functionalities.

Duality and domain wall dynamics in a twisted Kitaev chain

The Ising chain in transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, topological defects, quantum criticality, and duality. Although the quasi-1D ferromagnet CoNb$_2$O$_6$ has been put forward as the best material example of the transverse field Ising model, it exhibits significant deviations from ideality. Through a combination of THz spectroscopy and theory, we show that CoNb$_2$O$_6$ in fact is well described by a different model with strong bond dependent interactions, which we dub the {\it twisted Kitaev chain}, as these interactions share a close resemblance to a one-dimensional version of the intensely studied honeycomb Kitaev model. In this model the ferromagnetic ground state of CoNb$_2$O$_6$ arises from the compromise between two distinct alternating axes rather than a single easy axis. Due to this frustration, even at zero applied field domain-wall excitations have quantum motion that is described by the celebrated Su-Schriefer-Heeger model of polyacetylene. This leads to rich behavior as a function of field. Despite the anomalous domain wall dynamics, close to a critical transverse field the twisted Kitaev chain enters a universal regime in the Ising universality class. This is reflected by the observation that the excitation gap in CoNb$_2$O$_6$ in the ferromagnetic regime closes at a rate precisely twice that of the paramagnet. This originates in the duality between domain walls and spin-flips and the topological conservation of domain wall parity. We measure this universal ratio `2' to high accuracy -- the first direct evidence for the Kramers-Wannier duality in nature.

The lifetimes for each state of $$l=0$$ levels of the para-positronium

We developed a model for a para-positronium system by taking into account the annihilation condition which requires $$l=0$$ . A para-positronium system composed by an electron-antielectron pair is an unstable system that decays predominantly into two gamma photons via self-annihilation process. This is because of the conservation of (overall) charge conjugation parity. Our $$2+1$$ -dimensional model was based on an exact solution of a two-body Dirac–Coulomb type equation (one-time). The resulting non-perturbative spectra were found to have a form of quasi-normal modes that naturally give proper and damping oscillations of the system. As a result, with a single equation, not only the binding energies and total annihilation energy transmitted by the annihilation photons but also the lifetimes, $$\tau \left( n,\alpha \right) \propto n^{3}/\alpha ^{3}$$ , for each state of $$l=0$$ levels of the para-positronium were obtained. With this unique presentation of above-mentioned characteristic of the system, we also calculated transition frequencies and transition times between differing n level of $$l=0$$ . This also gave us an opportunity to discuss the screening effect from electronic environment of the system. For this, the effective dielectric constant of the medium that surrounds the annihilation point was adapted into the calculated non-perturbative spectra. This may provide an important tool for the positron annihilation lifetime spectroscopy studies and for development of related techniques.

Gravitational Wave Implications for the Parity Symmetry of Gravity in the High Energy Region

Abstract Einstein's general relativity, as the most successful theory of gravity, is one of the cornerstones of modern physics. However, the experimental tests for gravity in the high energy region are limited. The emerging gravitational-wave astronomy has opened an avenue for probing the fundamental properties of gravity in a strong and dynamical field, and in particular, a high energy regime. In this work, we test the parity conservation of gravity with gravitational waves. If the parity symmetry is broken, the left- and right-handed modes of gravitational waves would follow different equations of motion, dubbed as birefringence. We perform full Bayesian inference by comparing the state-of-the-art waveform with parity violation with the compact binary coalescence data released by LIGO and Virgo collaboration. We do not find any violations of general relativity, thus constrain the lower bound of the parity-violating energy scale to be 0.09 GeV through the velocity birefringence of gravitational waves. This provides the most stringent experimental test of gravitational parity symmetry to date. We also find third generation gravitational-wave detectors can enhance this bound to GeV if there is still no violation, comparable to the current energy scale in particle physics, which indicates gravitational-wave astronomy can usher in a new era of testing the ultraviolet behavior of gravity in the high energy region.

Arbitrary polarization-independent backscattering or reflection by rotationally symmetric reciprocal structures

We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further demonstrated that the same principle is also applicable for infinite periodic structures in terms of reflection, which simultaneously guarantees the transmission invariance if there are neither Ohmic losses nor extra diffraction channels. At the presence of losses, extra reflection symmetries (with reflection planes either parallel or perpendicular to the incident direction) can be incorporated to ensure simultaneously the invariance of transmission and absorption. The principles we have revealed are protected by fundamental laws of reciprocity and parity conservation, which are fully independent of the optical or geometric parameters of the photonic structures. The optical invariance obtained is intrinsically robust against perturbations that preserve reciprocity and the geometric symmetries, which could be widely employed for photonic applications that require stable backscatterings or reflections.

Toward Nonlocal Electrodynamics of Accelerated Systems

We revisit acceleration-induced nonlocal electrodynamics and the phenomenon of photon spin-rotation coupling. The kernel of the theory for the electromagnetic field tensor involves parity violation under the assumption of linearity of the field kernel in the acceleration tensor. However, we show that parity conservation can be maintained by extending the field kernel to include quadratic terms in the acceleration tensor. The field kernel must vanish in the absence of acceleration; otherwise, a general dependence of the kernel on the acceleration tensor cannot be theoretically excluded. The physical implications of the quadratic kernel are briefly discussed.

Spurious poles in the scattering of electric and magnetic charges

Theories with both electric and magnetic charges (“mutually non-local” theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one of the U(1)’s being broken. Here we show how the constraints of confinement and parity conservation on observable processes manages to cancel the spurious poles in scattering and pair production amplitudes, paving the way for systematic studies of the experimental signatures of “dark” electric-magnetic processes. Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes.

Kinematics and Selection Rules for Light-by-Light Scattering in a Strong Magnetic Field

Selection rules that follow from parity and four-momentum conservation are listed for head-on light-by-light scattering in a strong magnetic field taking into account nontrivial dispersion laws of different photon eigen-modes. The wave-length shifts occur for certain transitions between photon eigen-modes.

Majorana end states in an interacting quantum wire

We propose and investigate a simple one-dimensional model for a single-channel quantum wire hosting electrons that interact repulsively and are subject to a significant spin-orbit interaction. We show that an external Zeeman magnetic field, applied at the right angle to the Rashba spin-orbit axis, drives the wire into a correlated spin-density wave state with gapped spin and gapless charge excitations. By computing the ground-state degeneracies of the model with either (anti-)periodic or open boundary conditions, we conclude that the correlated spin-density state realizes a gapless symmetry-protected topological phase, as the ground state is unique in the ring geometry while it is two-fold degenerate in the wire with open boundaries. Microscopically the two-fold degeneracy is found to be protected by the conservation of the magnetization parity. Open boundaries induce localized zero-energy (midgap) states which are described, at the special Luther-Emery point of the model, by Majorana fermions. We find that spin densities at the open ends of the wire exhibit unusual long-ranged correlations despite the fact that all correlations in the bulk of the wire decay in a power-law or exponential fashion. Our study exposes the crucial importance of the long-ranged string operator needed to implement the correct commutation relations between spin densities at different points in the wire. Along the way we rederive the low-energy theory of Galilean-invariant electron systems in terms of current operators.

Dynamical evidence for a fifth force explanation of the ATOMKI nuclear anomalies

Recent anomalies in $^8$Be and $^4$He nuclear decays can be explained by postulating a fifth force mediated by a new boson $X$. The distributions of both transitions are consistent with the same $X$ mass, 17 MeV, providing kinematic evidence for a single new particle explanation. In this work, we examine whether the new results also provide dynamical evidence for a new particle explanation, that is, whether the observed decay rates of both anomalies can be described by a single hypothesis for the $X$ boson's interactions. We consider the observed $^8$Be and $^4$He excited nuclei, as well as a $^{12}$C excited nucleus; together these span the possible $J^P$ quantum numbers up to spin 1. For each transition, we determine whether scalar, pseudoscalar, vector, or axial vector $X$ particles can mediate the decay, and we construct the leading operators in a nuclear physics effective field theory that describes them. Assuming parity conservation, the scalar case is excluded and the pseudoscalar case is highly disfavored. Remarkably, however, the protophobic vector gauge boson, first proposed to explain only the $^8$Be anomaly, also explains the $^4$He anomaly within experimental uncertainties. We predict signal rates for other closely related nuclear measurements, which, if confirmed, will provide overwhelming evidence that a fifth force has been discovered.

Attosecond transient absorption spectroscopy without inversion symmetry

Transient absorption is a very powerful observable in attosecond experiments on atoms, molecules and solids and is frequently used in experiments employing phase-locked few-cycle infrared and XUV laser pulses derived from high harmonic generation. We show numerically and analytically that in non-centrosymmetric systems, such as many polyatomic molecules, which-way interference enabled by the lack of parity conservation leads to new spectral absorption features, which directly reveal the laser electric field. The extension of attosecond transient absorption spectroscopy (ATAS) to such targets hence becomes sensitive to global and local inversion symmetry. We anticipate that ATAS will find new applications in non-centrosymmetric systems, in which the carrier-to-envelope phase of the infrared pulse becomes a relevant parameter and in which the orientation of the sample and the electronic symmetry of the molecule can be addressed.

Convergence analysis and parity conservation of a new form of a quadratic explicit spline with applications to integral equations

In this study, a new form of a quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve integral equations.

Decoherence dynamics of Majorana qubits under braiding operations

We study the decoherence dynamics of Majorana qubit braiding operations in a topological superconducting chain (TSC) system, in which the braiding is performed by controlling the electron-chemical potentials of the TSCs and the couplings between them. By solving rigorously the Majorana qubit dynamics, we show how the Majorana qubit coherence is generated through bogoliubon correlations formed by exchanging Majorana zero modes (MZMs) between two TSCs in braiding operations. Using the exact master equation, we demonstrate how MZMs and also the bogoliubon correlations dissipate due to charge fluctuations of the controlling gates at both the zero and finite temperatures. As a result, Majorana qubit coherence and the fermion parity conservation cannot be immune from local perturbations during braiding operations.

Controlling photoionization using attosecond time-slit interferences

When small quantum systems, atoms or molecules, absorb a high-energy photon, electrons are emitted with a well-defined energy and a highly symmetric angular distribution, ruled by energy quantization and parity conservation. These rules are based on approximations and symmetries which may break down when atoms are exposed to ultrashort and intense optical pulses. This raises the question of their universality for the simplest case of the photoelectric effect. Here we investigate photoionization of helium by a sequence of attosecond pulses in the presence of a weak infrared laser field. We continuously control the energy of the photoelectrons and introduce an asymmetry in their emission direction, at variance with the idealized rules mentioned above. This control, made possible by the extreme temporal confinement of the light-matter interaction, opens a road in attosecond science, namely, the manipulation of ultrafast processes with a tailored sequence of attosecond pulses.

Scattering activities bounded by reciprocity and parity conservation

Scattering activities are generally manifest through different optical responses of scattering bodies to circularly polarized light of opposite handedness. Similar to the ubiquitous roles played by scattering theory across different branches of photonics, scattering activities can serve as a fundamental concept to clarify underlying mechanisms of various chiroptical effects, both within and beyond scattering systems. In this work we investigate scattering activities for reciprocal systems that exhibit various geometric symmetries but are intrinsically achiral. We reveal how scattering activities are generally bounded by reciprocity and parity conservation, demonstrating that though extinction activity is usually eliminated by symmetry, scattering activities in forms of distinct absorptions, scatterings or angular scattering patterns can more widely emerge. Since our analyses are solely based on fundamental laws of reciprocity and parity conservation, regardless of geometric and optical parameters of the scattering systems studied, the principles revealed are generically applicable. The intuitive and pictorial framework we have established is beyond any specific coupling models, able to reveal hidden connections between seemingly unrelated chiral manifestations, and thus more accessible for a unified understanding of various chiroptical effects.

Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models

The random matrix theory (RMT) can be used to classify both topological phases of matter and quantum chaos. We develop a systematic and transformative RMT to classify the quantum chaos in the colored Sachdev-Ye-Kitaev (SYK) model first introduced by Gross and Rosenhaus. Here we focus on the 2-colored case and 4-colored case with balanced number of Majorana fermion $N$. By identifying the maximal symmetries, the independent parity conservation sectors, the minimum (irreducible) Hilbert space, and especially the relevant anti-unitary and unitary operators, we show that the color degree of freedoms lead to novel quantum chaotic behaviours. When $N$ is odd, different symmetry operators need to be constructed to make the classifications complete. The 2-colored case only show 3-fold Wigner-Dyson way, and the 4-colored case show 10-fold generalized Wigner-Dyson way which may also have non-trivial edge exponents. We also study 2- and 4-colored hybrid SYK models which display many salient quantum chaotic features hidden in the corresponding pure SYK models. These features motivate us to develop a systematic RMT to study the energy level statistics of 2 or 4 un-correlated random matrix ensembles. The exact diagonalizations are performed to study both the bulk energy level statistics and the edge exponents and find excellent agreements with our exact maximal symmetry classifications. Our complete and systematic methods can be easily extended to study the generic imbalanced cases. They may be transferred to the classifications of colored tensor models, quantum chromodynamics with pairings across different colors, quantum black holes and interacting symmetry protected (or enriched) topological phases.

Suppressing nonadiabatic transitions during adiabatic generation of highly entangled states in bosonic Josephson junctions

We study suppression of nonadiabatic transitions during adiabatic generation of a cat-like state (a superposition of different size cat states) and a spin squeezed state in a bosonic Josephson junction. In order to minimize the adiabatic error, we use quantum adiabatic brachistochrone, which enables us to track a geometrically efficient path in parameter space under given conditions without requiring additional terms. For creation of a cat-like state, divergence of the quantum geometric tensor associated with gap closing at the critical point is avoided because of the parity conservation. The resulting schedules of parameters are smooth and monotonically decreasing curves. Use of these schedules offers reduction of time to generate both of a cat-like state and a spin squeezed state.