Imaginary Coupling Research Articles

Complexified synchrony.

The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost five decades of research, many questions remain open, in particular, for finite-size systems. Here, we generalize recent work [Thümler et al., Phys. Rev. Lett. 130, 187201 (2023)] on the finite-size Kuramoto model with its state variables analytically continued to the complex domain and also complexify its system parameters. Intriguingly, systems of two units with purely imaginary coupling do not actively synchronize even for arbitrarily large magnitudes of the coupling strengths, |K|→∞, but exhibit conservative dynamics with asynchronous rotations or librations for all |K|. For generic complex coupling, both traditional phase-locked states and asynchronous states generalize to complex locked states, fixed points off the real subspace that exist even for arbitrarily weak coupling. We analyze a new collective mode of rotations exhibiting finite, yet arbitrarily large rotation numbers. Numerical simulations for large networks indicate a novel form of discontinuous phase transition. We close by pointing to a range of exciting questions for future research.

Non-Hermitian p -wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas

We theoretically investigate non-Hermitian p-wave Fermi superfluidity in one-dimensional spin-polarized Fermi gases which is relevant to recent ultracold atomic experiments. Considering an imaginary atom-dimer coupling responsible for the three-body recombination process in the Lindblad formalism, we discuss the stability of the superfluid state against the atomic loss effect. Within the two-channel non-Hermitian BCS-Eagles-Leggett theory, the atomic loss is characterized by the product of the imaginary atom-dimer coupling and the p-wave effective range. Our results indicate that for a given imaginary atom-dimer coupling, a smaller magnitude of the effective ranges of p-wave interaction is crucial for reaching the non-Hermitian p-wave Fermi superfluid state. Moreover, our theoretical framework for many-body systems with the three-body loss, which is inevitable in ultracold atoms, would promote further progress in non-Hermitian cold-atomic physics. Published by the American Physical Society 2024

Generalized Fano resonance theory based on Fabry-Perot cavity

Fano resonance is a pervasive phenomenon observed across many systems, which has traditionally been interpreted through the coupled harmonic oscillator model. However, the traditional model is limited, especially for different line shapes. In this study, we offer a generalized model by incorporating an imaginary coupling coefficient. This approach fundamentally differs from existing theories by identifying two unique Fano line shapes in the electric field of metallic Fabry–Perot cavity. The model connects the imaginary coupling coefficient with phase distribution of the coupling mode, thus revealing the relationship between Fano line shapes and the trend of phase shifts. This provides a new way for understanding and manipulating Fano resonance. The Fano resonance generation has been validated experimentally through reflection spectra. Our investigation offers a new perspective for understanding of Fano resonance via the coupled harmonic oscillator model and paves a way for the development of dynamically tunable Fano resonance devices.

Real supersymmetric solutions of (3,2) signature five-dimensional supergravity

We classify supersymmetric solutions of D = 5 (3,2) signature supergravity with either vanishing or imaginary gauge coupling constant preserving the minimal N = 2 supersymmetry. We prove that the geometry of such solutions is characterized by a nilpotent integrable endomorphism, and obtain the necessary and sufficient conditions on the fluxes imposed by supersymmetry. We also construct examples of supersymmetric domain wall solutions for which the nilpotent integrable endomorphism is associated with a Killing–Yano two-form, as well as a new descendant ‘preon’ solution which preserves N = 6 supersymmetry. This is notable as such N = 6 descendant solutions do not exist in the standard signature D = 5 supergravity.

Asynchronous topological phase transition in trimer lattices

We propose a model of a non-reciprocal double-layer trimer photonic lattice. In this model, two types of topological phases are presented. By adjusting the imaginary coupling coefficients and intra-cell coupling coefficients in this model, two topological phases appear in different coefficient ranges. They exhibit asynchronous topological phase transitions as the coupling coefficients change. We discover that these asynchronous topological phase transitions can impact the light transmission properties of the system. When the coupling coefficients are adjusted to put the system in a topologically non-trivial state, the injected light beam tends to localize at the edge. Moreover, before and after the phase transition, the lowest energy band exhibits oscillatory and non-oscillatory behavior in the evolution of the light beam at the boundary. Asynchronous topological phase transitions can be utilized to manipulate the light transmission properties of the system, offering potential applications in optical communication and the development of photonic integrated circuits.

The Standard Model and quantum state reduction from Heim’s field theory

Abstract Core parts of the Standard Model are derived from B. Heim’s quantum field theory, whose poly-metric describes spacetime and matter in a unified formalism. Its non-linear eigenvalue equation transforms into the Einstein field equation in the macroscopic limit. The 6-dimensional Heim space can be determined as locally isomorphic to a SU(2) ⊗ SU(2) ⊗ U(1) ⊗ U(1) symmetry and thus to the SU(3), which allows to connect to the local gauge symmetries and boson fields of the Standard Model. The Fermion and Higgs field and their coupling are deduced from Heim’s basic equations, providing new insight into possible correlations of these fields. Furthermore, the derivation yields an additional imaginary coupling term which seems to account for quantum mechanical state reduction in the non-relativistic limit. The recently performed calculation of the mass spectrum of elementary particles in a new approach based on Heim’s theory (with average error to the data < 1 % ${< } 1\%$ ) appears as even more relevant, having now shown that the theory can connect to the achievements of the Standard Model.

Multicriticality in Yang-Lee edge singularity

In this paper we study the non-unitary deformations of the two-dimensional Tricritical Ising Model obtained by coupling its two spin ℤ2 odd operators to imaginary magnetic fields. Varying the strengths of these imaginary magnetic fields and adjusting correspondingly the coupling constants of the two spin ℤ2 even fields, we establish the presence of two universality classes of infrared fixed points on the critical surface. The first class corresponds to the familiar Yang-Lee edge singularity, while the second class to its tricritical version. We argue that these two universality classes are controlled by the conformal non-unitary minimal models mathcal{M} (2, 5) and mathcal{M} (2, 7) respectively, which is supported by considerations based on PT symmetry and the corresponding extension of Zamolodchikov’s c-theorem, and also verified numerically using the truncated conformal space approach. Our results are in agreement with a previous numerical study of the lattice version of the Tricritical Ising Model [1]. We also conjecture the classes of universality corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.

Imaginary coupling induced Dirac points and group velocity control in the non-reciprocal Hermitian lattice.

We propose a mechanism to achieve the group velocity control of bifurcation light via an imaginary coupling effect in the non-reciprocal lattice. The physical model is composed of two-layer photonic lattices with non-reciprocal coupling in each unit cell, which can support a real energy spectrum with a pair of Dirac points due to the hermicity. Furthermore, we show that the systems experience topological phase transition at the Dirac points, allowing the existence of topological edge states on the left or right boundaries of respective lattice layers. By adjusting the imaginary coupling and the wave number, the group velocity of the light wave can be manipulated, and bifurcation light transmission can be achieved both at the Dirac points and the condition without the group velocity dispersion. Our work might guide the design of photonic directional couplers with group velocity control functions.

Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss

Spin-orbital coupling (SOC) and parity-time symmetry both have attracted paramount research interest in condensed matter physics, cold atom physics, optics and acoustics to develop spintronics, quantum computation, precise sensors and novel functionalities. Natural SOC is an intrinsic relativistic effect. However, there is an increasing interest in synthesized SOC nowadays. Here, we show that in a -symmetric pseudo spin-1/2 system (in other words, two-state system), the momentum-dependent balanced gain and loss can synthesize a new type of SOC, which we call imaginary SOC. The imaginary SOC can substantially change the energy spectrum of the system. Firstly, we show that it can generate a pure real energy spectrum with a double-valleys structure. Therefore, it has the ability to generate supersolid stripe states. Especially, the imaginary SOC stripe state can have a high contrast of one. Moreover, the imaginary SOC can also generate a spectrum with tunable complex energy band, in which the waves are either amplifying or decaying. Thus, the imaginary SOC would also find applications in the engineering of -symmetry-based coherent wave amplifiers/absorbers. Potential experimental realizations of imaginary SOC are proposed in cold atomic gases and systems of coupled waveguides constituted of nonlocal gain and loss.

Critical Field Theories with OSp(1|2M) Symmetry

In the paper [L. Fei etal., J. High Energy Phys. 09 (2015) 076JHEPFG1029-847910.1007/JHEP09(2015)076] a cubic field theory of a scalar field σ and two anticommuting scalar fields, θ and θ[over ¯], was formulated. In 6-ε dimensions it has a weakly coupled fixed point with imaginary cubic couplings where the symmetry is enhanced to the supergroup OSp(1|2). This theory may be viewed as a "UV completion" in 2<d<6 of the nonlinear sigma model with hyperbolic target space H^{0|2} described by a pair of intrinsic anticommuting coordinates. It also describes the q→0 limit of the critical q-state Potts model, which is equivalent to the statistical mechanics of spanning forests on a graph. In this Letter we generalize these results to a class of OSp(1|2M) symmetric field theories whose upper critical dimensions are d_{c}(M)=2[(2M+1)/(2M-1)]. They contain 2M anticommuting scalar fields, θ^{i}, θ[over ¯]^{i}, and one commuting one, with interaction g(σ^{2}+2θ^{i}θ[over ¯]^{i})^{(2M+1)/2}. Ind_{c}(M)-ε dimensions, we find a weakly coupled IR fixed point at an imaginary value of g. We propose that these critical theories are the UV completions of the sigma models with fermionic hyperbolic target spaces H^{0|2M}. Of particular interest is the quintic field theory with OSp(1|4) symmetry, whose upper critical dimension is 10/3. Using this theory, we make a prediction for the critical behavior of the OSp(1|4) lattice system in three dimensions.

Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators

Exceptional point (EP) degeneracies in coupled cavities with gain and loss provide on-chip photonic devices with unconventional features and performance. However, such systems with realistic structures often miss the exact EPs even in simulation, and the mechanism of this EP disruption has yet to be thoroughly identified. Here, we extend the coupled-mode theory of one-dimensional non-Hermitian resonator arrays to study the effects of the imaginary part of the inter-cavity coupling, which is a second-order term and attributed to material amplification, absorption, and radiation. By taking an appropriate gauge for the model, we clarify that the imaginary coupling components have a symmetric form in the effective Hamiltonian and hence represent non-Hermiticity. These additional factors can lift the gain- and loss-based EP degeneracies. However, they are proportional to the sum of the imaginary permittivities for involved cavity pairs. Thus, when the amplification and absorption of adjacent cavities are balanced, their contribution to the imaginary coupling is canceled, and the EP singularity can be restored. Radiation-induced imaginary couplings measure the change in net radiation loss by the interference between cavity modes. Their impact on the EP can also be counteracted by small cavity resonance detuning even in loss-biased cases. We show and analyze eligible simulation examples based on photonic crystal nanocavities, and highlight design of an ideal EP degeneracy that is protected by generalized PT symmetry and induced by radiation.

Topological properties of the one-dimensional &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}${\cal {PT}}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;-symmetric non-Hermitian spin-orbit-coupled Su-Schrieffer-Heeger model

The topological property and the energy property of one-dimensional non-Hermitian spin-orbit-coupled Su-Schrieffer-Heeger (SSH) model are investigated theoretically, by introducing spin-dependent imaginary potentials with gain and loss effects. It is found that the imaginary potential leads the imaginary energy spectra to appera in the topologically nontrivial region of this system, and the &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}${\cal {PT}}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M5.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M5.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; phase transition to happen in the topologically trivial region. In addition, the imaginary potential energy and spin-orbit coupling work together to make the topological phase transition occur in the topologically trivial region, and the topological non-trivial region becomes wider. The energy spectrum results show that the imaginary potential energy and the spin-orbit coupling can obviously control the zero-energy states of the system, which mainly lies in the presence of four zero-energy states with four different localities and numbers. This shows the special adjustment effect of imaginary potential energy and spin-orbit coupling on the energy band structure of the system. It is believed that these results are helpful in understanding the topological phase transition behavior of &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}${\cal {PT}}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20220796_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;-symmetric non-Hermitian system.

Coupling-induced nonunitary and unitary scattering in anti- PT -symmetric non-Hermitian systems

We investigate the properties of two anti-parity-time (anti-PT )-symmetric four-site scattering centers. The anti-PT -symmetric scattering center may have imaginary couplings, real couplings, and real on-site potentials. The only difference between the two scattering centers is the coupling between two central sites of the scattering center, which plays a crucial role in determining the parity of anti-PT symmetry and significantly affects the scattering properties. For the imaginary coupling, the even-parity anti-PT -symmetric scattering center possesses nonunitary scattering and the difference between the reflection and transmission is unity; for the real coupling, the odd-parity anti-PT -symmetric scattering center possesses unitary scattering and the sum of the reflection and transmission is unity. The coupling-induced different scattering behaviors are verified in the numerical simulations. Our findings reveal that a significant difference in the dynamics can be caused by a slight difference between two similar anti-PT -symmetric non-Hermitian scattering centers.

Remarks on a melonic field theory with cubic interaction

We revisit the Amit-Roginsky (AR) model in the light of recent studies on Sachdev-Ye-Kitaev (SYK) and tensor models, with which it shares some important features. It is a model of N scalar fields transforming in an N-dimensional irreducible representation of SO(3). The most relevant (in renormalization group sense) invariant interaction is cubic in the fields and mediated by a Wigner 3jm symbol. The latter can be viewed as a particular rank-3 tensor coupling, thus highlighting the similarity to the SYK model, in which the tensor coupling is however random and of even rank. As in the SYK and tensor models, in the large-N limit the perturbative expansion is dominated by melonic diagrams. The lack of randomness, and the rapidly growing number of invariants that can be built with n fields, makes the AR model somewhat closer to tensor models. We review the results from the old work of Amit and Roginsky with the hindsight of recent developments, correcting and completing some of their statements, in particular concerning the spectrum of the operator product expansion of two fundamental fields. For 5.74 < d < 6 the fixed-point theory defines a real CFT, while for smaller d complex dimensions appear, after a merging of the lowest dimension with its shadow. We also introduce and study a long-range version of the model, for which the cubic interaction is exactly marginal at large N , and we find a real and unitary CFT for any d < 6, both for real and imaginary coupling constant, up to some critical coupling.

Nonstandard Neutrino Interactions as a Solution to the NOνA and T2K Discrepancy.

The latest data of the two long-baseline accelerator experiments NOνA and T2K, interpreted in the standard three-flavor scenario, display a discrepancy. A mismatch in the determination of the standard CP phase δ_{CP} extracted by the two experiments is evident in the normal neutrino mass ordering. While NOνA prefers values close to δ_{CP}∼0.8π, T2K identifies values of δ_{CP}∼1.4π. Such two estimates are in disagreement at more than 90%C.L. for 2degrees of freedom. We show that such a tension can be resolved if one hypothesizes the existence of complex neutral-current nonstandard interactions (NSIs) of the flavor changing type involving the e-μ or the e-τ sectors with couplings |ϵ_{eμ}|∼|ϵ_{eτ}|∼0.2. Remarkably, in the presence of such NSIs, both experiments point towards the same common value of the standard CP phase δ_{CP}∼3π/2. Our analysis also highlights an intriguing preference for maximal CP violation in the nonstandard sector with the NSI CP phases having best fit close to ϕ_{eμ}∼ϕ_{eτ}∼3π/2, hence pointing towards imaginary NSI couplings.

Probabilistic cellular automata for interacting fermionic quantum field theories

A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Classical cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics. Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model. This euclidean lattice model can be investigated by standard techniques of statistical physics as Monte Carlo simulations. Our model is an example how quantum mechanics emerges from classical statistics.

Tensor network formulation of two-dimensional gravity

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the TRG to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Liouville action for two dimensional quantum gravity.

Topological Edge Modes in Non-Hermitian Photonic Aharonov-Bohm Cages

We investigate the topological edge modes in a rhombic waveguide array with imaginary coupling, which is realized by incorporating auxiliary waveguide between the coupled waveguides. By suitably tuning both real and imaginary couplings to generate an effective π flux, a non-Hermitian analog of Aharonov-Bohm (AB) cage is formed as the band structures become flat and coalesce into third-order exceptional points (EPs). We show the array can support gapped topological edge modes, which can be explained by mapping the system Hamiltonian into the square root of an anti-parity-time (PT) -symmetric waveguide array. In contrast to the linear power increase of bulk modes, the propagation of edge modes can be conserved or exponentially amplified depending on which termination is initially excited. Our study provides a promising way to realizing robust light propagation.

Extended SSH Model in Non-Hermitian Waveguides with Alternating Real and Imaginary Couplings

We studied the topological properties of an extended Su–Schrieffer–Heeger (SSH) model composed of a binary waveguide array with alternating real and imaginary couplings. The topological invariant of the periodic structures remained quantized with chiral symmetry even though the system was non-Hermitian. The numerical results indicated that phase transition arose when the absolute values of the two couplings were equal. The system supported a topological zero mode at the boundary of nontrivial structures when chiral symmetry was preserved. By adding onsite gain and loss to break chiral symmetry, the topological modes dominated in all supermodes with maximum absolute value of imaginary energy. This study enriches research on the SSH model in non-Hermitian systems and may find applications in optical routers and switches.

Symbolic expressions for fully differential single top quark production cross section and decay width of polarized top quark in the presence of anomalous Wtb couplings

Spin correlations in the t-channel single top quark production and its subsequent decay are investigated for the case of contributions involving anomalous Wtb couplings. We obtain analytical expressions for the differential widths for the three-particle decay of a polarized t quark in its rest frame and also expressions for the differential cross sections of the full process of production and decay of the t quark ($2\to 4$) as a function of the energy of a charged lepton and two angles of orientation of the quantization axis of the t-quark spin. The expression is presented in the most general form for the case of real and imaginary vector and tensor anomalous Wtb couplings. We show that shapes of certain multidimensional kinematic distributions of final state particles are significantly different for the contributions proportional to different combinations of the anomalous couplings. The most noticeable differences appear in the shape of the surfaces of two-dimensional distributions, where one of the variables is the energy of a charged lepton and the other is one of the t-quark spin orientation angles. Observed properties are confirmed by two methods of computations either from the obtained symbolic expression for the differential cross sections of the full process of the polarized single top quark production with its subsequent decay or by means of the CompHEP program for the complete process involving the t-channel single top. In addition, using the obtained analytical expressions, we estimate the statistical accuracy of extracting values of the anomalous Wtb couplings for different levels of the expected integral luminosity at the LHC.