Beyond-mean-field analysis of the Townes soliton and its breathing mode

We spectroscopically investigate a pathway for the conversion of 23Na39K Feshbach molecules into rovibronic ground state molecules via stimulated Raman adiabatic passage. Using photoassociation spectroscopy from the diatomic scattering threshold in the a3Σ+ potential, we locate the resonantly mixed electronically excited intermediate states and which, due to their singlet–triplet admixture, serve as an ideal bridge between predominantly a3Σ+ Feshbach molecules and pure X1Σ+ ground state molecules. We investigate their hyperfine structure and present a simple model to determine the singlet–triplet coupling of these states. Using Autler–Townes spectroscopy, we locate the rovibronic ground state of the 23Na39K molecule () and the second rotationally excited state N = 2 to unambiguously identify the ground state. We also extract the effective transition dipole moment from the excited to the ground state. Our investigations result in a fully characterized scheme for the creation of ultracold bosonic 23Na39K ground state molecules.

The Standard Model Lagrangian has an approximate scale symmetry in the high-energy limit. This observation can be included in the fundamental principle of the ultimate theory of Nature as the requirement of the exact quantum scale invariance. In this setup, all low-energy particle phenomenology can be obtained as a result of the spontaneous breaking of scale symmetry leading to the presence of the extra massless scalar field -- the dilaton. We explore the scenario in which this field is capable of solving the strong CP-problem in QCD in a similar way as in QCD axion models. The dilaton, playing the role of the axion, is coupled to the QCD sector and acquires a mass term due to non-perturbative breaking of scale symmetry. We show that the dilaton can form dark matter after the low-scale inflation. As a proof of concept, we construct a model of Higgs-driven inflation consistently realising the axion-like dilaton dark matter production compatible with the CMB data.

It was known that by a duality transformation, interacting bosons at filling factorf = p/q hopping on a lattice can be mapped to interacting vortices hopping onthe dual lattice subject to a fluctuating dual ‘magnetic field’ whoseaverage strength through a dual plaquette is equal to the boson densityf = p/q. So the kinetic term of the vortices is the same as the Hofstadterproblem of electrons moving in a lattice in the presence off = p/q flux per plaquette. Motivated by this mapping, we study theHofstadter bands of vortices hopping in the presence of magnetic fluxf = p/q per plaquette on five most common bipartite and frustrated lattices namelysquare, honeycomb, triangular, dice and Kagome lattices. We count the totalnumber of bands, and determine the number of minima and their locations inthe lowest band. We also numerically calculate the bandwidths of the lowestHofstadter bands in these lattices that directly measure the mobility of the dualvortices. The less mobile the dual vortices are, the more likely are the bosonsto be in a superfluid state. We find that apart from the Kagome lattice at oddq, they all satisfy theexponential decay law W = Ae−cq even at the smallest q. At given q, thebandwidth W decreases in the order of triangle, square and honeycomb lattice. This indicates thatthe domain of the superfluid state of the original bosons increases in the orderof the corresponding direct lattices: honeycomb, square and triangular. Whenq = 2, we find that the lowest Hofstadter band is completely flat for both Kagome and dicelattices. There is a gap on the Kagome lattice, but no gap on the dice lattice. Thisindicates that the boson ground state at half filling with nearest neighbour hopping onKagome lattice is always a superfluid state. The superfluid state remains stable slightlyaway from the half filling. Our results show that the behaviours of bosons at or near halffilling on Kagome lattices are quite distinct from those in square, honeycomb andtriangular lattices studied previously.

In many well-motivated new physics models, the pseudo-Nambu-Goldstone boson (pNGB) from U(1) symmetry breaking emerges as a promising dark matter candidate. Its coupling, suppressed by the symmetry breaking scale, prevents thermal equilibrium in the early Universe for high scale symmetry breaking. Thus, pNGB dark matter is predominantly produced via non-thermal mechanisms, such as the freeze-in process through a new portal coupling. In this work, we explore a novel mechanism for the production of pNGB dark matter even with feeble Higgs portal coupling — arising from Hawking radiation or superradiance of primordial black holes. We systematically investigate the production of light and heavy pNGB dark matter, both for Schwarzschild and Kerr black holes. We also discuss its potential gravitational wave signatures from domain wall collapse, density perturbations, and Hawking radiation. If the ultraviolet (UV) model is considered, the recent 𝒪(100) PeV neutrino event KM3-230213A at KM3NeT can be naturally explained.

We present a comprehensive analysis of the Higgs boson spectra in several versions of the supersymmetric left--right model based on the gauge symmetry $SU(3)_c \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}$. A variety of symmetry breaking sectors are studied, with a focus on the constraints placed on model parameters by the lightest neutral CP even Higgs boson mass $M_h$. The breaking of $SU(2)_R$ symmetry is achieved by Higgs fields transforming either as triplets or doublets, and the electroweak symmetry breaking is triggered by either bi--doublets or doublets. The Higgs potential is analyzed with or without a gauge singlet Higgs field present. Seesaw models of Type I and Type II, inverse seesaw models, universal seesaw models and an $E_6$ inspired alternate left--right model are included in our analysis. Several of these models lead to the tree--level relation $M_h \leq \sqrt{2}\,m_W$ (rather than $M_h \leq m_Z$ that arises in the MSSM), realized when the $SU(2)_R$ symmetry breaking scale is of order TeV. With such an enhanced upper limit, it becomes possible to accommodate a Higgs boson of mass 126 GeV with relatively light stops that mix negligibly. In models with Higgs triplets, a doubly charged scalar remains light below a TeV with its mass arising entirely from radiative corrections. We carry out the complete one--loop calculation for its mass induced by the Majorana Yukawa couplings and show the consistency of the framework. We argue that these models prefer a low $SU(2)_R$ breaking scale. Other theoretical and phenomenological implications of these models are briefly discussed.

Generally "exact" quantum Monte Carlo computations for the ground state of many bosons make use of importance sampling. The importance sampling is based either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of path integral ground state (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a nonzero overlap with the ground state, which gives rise to a discrete path which is sampled via a Metropolis-like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid (4)He with PIGS by considering as initial wave function a constant, i.e., the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e., there is no importance sampling. For both phases we obtain results converging to those obtained by considering the best available variational wave function (the shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance, a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function, and the static structure factor, but also for off-diagonal ones, such as the one-body density matrix. This robustness of PIGS can be traced back to the fact that the chosen initial wave function acts only at the beginning of the path without affecting the imaginary time propagator. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature path integral Monte Carlo. On the other hand, a judicious choice of the initial wave function greatly improves the rate of convergence to the exact results.

Recent experimental progress in magnetic atoms and polar molecules has created the prospect of simulating dipolar Hubbard models with off-site interactions. When applied to real-space cylindrical optical lattices, these anisotropic dipole-dipole interactions acquire a tunable spatially-dependent component while they remain translationally-invariant in the axial direction, creating a sublattice structure in the azimuthal direction. We numerically study how the coexistence of these classes of interactions affects the ground state of hardcore dipolar bosons at half-filling in a finite-size cylindrical optical lattice with octagonal rings. When these two interaction classes cooperate, we find a solid state where the density order is determined by the azimuthal sublattice structure and builds smoothly as the interaction strength increases. For dipole polarisations where the axial interactions are sufficiently repulsive, the repulsion competes with the sublattice structure, significantly increasing entanglement and creating two distinct ordered density patterns. The spatially-varying interactions cause the emergence of these ordered states in small lattices as a function of interaction strength to be staggered according to the azimuthal sublattices.

In this work we investigate the different states of a system of spin-1 bosons in two potential wells connected by tunneling, with spin-dependent interaction. The model utilizes the well-known Bose-Hubbard Hamiltonian, adding a local interaction term that depends on the modulus of the total spin in a well, favoring a high- or low-spin state for different signs of the coupling constant. We employ the concept of fidelity to detect critical values of parameters for which the ground state undergoes significant changes. The nature of the states is investigated through evaluation of average occupation numbers in the wells and of spin correlations. A more detailed analysis is done for a two-particle system, but a discussion of the three-particle case and some results for larger numbers are also presented.

Recent experiments on ultracold dipoles in optical lattices open exciting possibilities for the quantum simulation of extended Hubbard models. When considered in one dimension, these models present at unit filling a particularly interesting ground-state physics, including a symmetry-protected topological phase known as Haldane insulator. We show that the tail of the dipolar interaction beyond nearest-neighbors, which may be tailored by means of the transversal confinement, does not only modify quantitatively the Haldane insulator regime and lead to density waves of larger periods, but results as well in unexpected insulating phases. These insulating phases may be topological or topologically trivial, and are characterized by peculiar correlations of the site occupations. These phases may be realized and observed in state-of-the-art experiments.

Condensate ground states of hardcore bosons induced by an array of impurities

The model of free charged Bosons in an external constant magnetic field inside a cylinder, one of the few locally gauge covariant systems amenable to analytic treatment, is rigorously investigated in the semiclassical approximation. The model was first studied by Schafroth and is suitable for the description of quasi-bound electron pairs localized in physical space, the so-called Schafroth pairs, which occur in certain compounds. Under the assumption of existence of a solution of the semiclassical problem for which the ground state (g.s.) expectation value of the current \( \) is of the London form, i.e., \( = -c |\phi _{0}(\vec {x})|^{2} \vec {A}(\vec {x})\), where c is a positive constant, \(\vec {A}\) the vector potential and \(\phi _{0}\) the one-particle g.s. wave function, as well as some regularity assumptions, the magnetic induction may be proved to decay exponentially from its value on the surface of the cylinder. An important role is played by a theorem on the pointwise monotonicity of the ground state wave function on the potential.

We study nonthermal production of heavy dark matter from the dynamics of the background scalar field during a first-order phase transition, predominantly from bubble collisions. In scenarios where bubble walls achieve runaway behavior and get boosted to very high energies, we find that it is possible to produce dark matter with mass several orders of magnitude above the symmetry breaking scale or the highest temperature ever reached by the thermal plasma. We also demonstrate that the existing formalism for calculating particle production from bubble dynamics in a first-order phase transition is not gauge invariant, and can lead to spurious results. While a rigorous and complete resolution of this problem is still lacking, we provide a practical prescription for the computation that avoids unphysical contributions and should provide reliable order-of-magnitude estimates of this effect. Furthermore, we point out the importance of three-body decays of the background field excitations into scalars and gauge bosons, which provide the dominant contributions at energy scales above the scale of symmetry breaking. Using our improved results, we find that scalar, fermion, and vector dark matter are all viable across a large range of mass scales, from O(10) TeV to a few orders of magnitude below the Planck scale, and the corresponding phase transitions can be probed with current and future gravitational wave experiments.

The nonperturbative dynamics of chiral and scale symmetry breaking in asymptotically free and non-asymptotically free (with an ultraviolet stable fixed point) vector-like gauge theories is investigated. In the two-loop approximation analytical expressions for the chiral and gluon condensates are obtained. The hypothesis about a soft behaviour at small distances of composite operators in non-asymptotically free gauge theories with a fixed point is put forward and substantiated. It is shown that in these theories the form of the scale anomaly depends on the type of the phase in coupling constant to which it relates. The two component conception of scale symmetry breaking in gauge theories is suggested. The mass relation for the singlet scalar fermion-antifermion bound state is obtained. The important ingredient of this approach is a large (<it>d</it> ≃2) dynamical dimension of composite chiral fields. The application of this approach to QCD and technicolour models is discussed.

This study explores the phenomenology of distortion products in nonlinear cochlear models, predicting their amplitude and phase along the basilar membrane. The existence of a backward-traveling wave at the distortion-product frequency, which has been recently questioned by experiments measuring the phase of basilar-membrane vibration, is discussed. The effect of different modeling choices is analyzed, including feed-forward asymmetry, micromechanical roughness, and breaking of scaling symmetry. The experimentally observed negative slope of basilar-membrane phase is predicted by numerical simulations of nonlinear cochlear models under a wide range of parameters and modeling choices. In active models, positive phase slopes are predicted by the quasi-linear analytical computations and by the fully nonlinear numerical simulations only if the distortion-product sources are localized apical to the observation point and if the stapes reflectivity is unrealistically small. The results of this study predict a negative phase slope whenever the source is distributed over a reasonably wide cochlear region and/or a reasonably high stapes reflectivity is assumed. Therefore, the above-mentioned experiments do not contradict "classical" models of cochlear mechanics and of distortion-product generation.

An approach is presented toward validating the assumption that the ground state of bosons with repulsive interactions at low densities is characterized by macroscopic occupation of the zero momentum level. We use a cell model which affords a simple description of the high-density region, where fluctuations in number density are small and where no single-particle level is macroscopically occupied. As the density decreases, fluctuntions increase, and we reach a critical density at which the small fluctuntion approximation becomes unstable with respect to plane wave states of zero momenturn. At this critical density, the single-particle energy gap disappears, and the dependence of excitation on momentum changes from quadratic to linear, for small values of momentum. (auth)