Effects of neighboring transitions on the mechanisms of electromagnetically induced absorption and transparency in an open degenerate multilevel system

In this study, optical Bloch equations with and without neighboring hyperfine states near the degenerate two-level system (DTLS) in the challenging case of $$^{85}$$ 85 Rb D2 transition, which involves the Doppler broadening effect, are solved. The calculated spectra agree well with the experimental results obtained based on the coupling-probe scheme with orthogonal linear polarizations of the coupling and probe fields. The mechanisms of electromagnetically induced absorption (electromagnetically induced transparency) for the open $$F_g=3 \rightarrow F_e=2$$ F g = 3 → F e = 2 and 3 transitions (open $$F_g=2 \rightarrow F_e=2$$ F g = 2 → F e = 2 and 3 transitions) are determined to be the effect of the strong closed $$F_g=3 \rightarrow F_e=4$$ F g = 3 → F e = 4 transition line (strong closed $$F_g=2 \rightarrow F_e=1$$ F g = 2 → F e = 1 transition line); this finding is based on a comparison between the calculated absorption profiles of the DTLS without neighboring states and those of all levels with neighboring states, depending on the coupling and probe power ratios. Furthermore, based on the aforementioned comparison, the crucial factors that enhance or reduce the coherence effects and lead to the transformation between electromagnetically induced absorption and electromagnetically induced transparency, are (1) the power ratios between the coupling and probe beams, (2) the openness of the excited state, and (3) effects of the neighboring states due to Doppler broadening in a real atomic system.

THE BOUNDARY VALUE PROBLEM OF FINDING A RIGHT-HAND SIDE FOR MIXED TYPE EQUATION WITH CHAPLYGIN’S TYPE OPERATOR

In this paper, we study the inverse problem for a mixed-type equation with power degeneracy on a transition line by definition of its right-hand side, depending on the spatial coordinate. The theory of identity has been proved. In the case of degree degeneracy, the uniqueness criterion for the solution of the problem is proved, and the solution itself is con- structed in the form of a sum of orthogonal series. The consistency of series in the class of solutions of the given equation is justified and the validity of the solution with respect to the boundary conditions is proved.

Flicker noise in two-dimensional electron gas

Using the method developed in a recent paper (Euro. Phys. J. B 92.8 (2019): 1-28) we consider 1/f noise in two-dimensional electron gas (2DEG). The electron coherence length of the system is considered as a basic parameter for discretizing the space, inside which the dynamics of electrons is described by quantum mechanics, while for length scales much larger than it the dynamics is semi-classical. For our model, which is based on the Thomas-Fermi-Dirac approximation, there are two control parameters: temperature T and the disorder strength (∆). Our Monte Carlo studies show that the system exhibits 1/f noise related to the electronic avalanche size, which can serve as a model for describing the experimentally observed flicker noise in 2DEG. The power spectrum of our model scales with frequency with an exponent in the interval 0.3 < αPS < 0.6. We numerically show that the electronic avalanches are scale invariant with power-law behaviors in and out of the metal-insulator transition line.

Gliding Down the QCD Transition Line, from Nf = 2 till the Onset of Conformality

We review the hot QCD transition with varying number of flavours, from two till the onset of the conformal window. We discuss the universality class for Nf=2, along the critical line for two massless light flavours, and a third flavour whose mass serves as an interpolator between Nf=2 and Nf=3. We identify a possible scaling window for the 3D O(4) universality class transition, and its crossover to a mean field behaviour. We follow the transition from Nf=3 to larger Nf, when it remains of first order, with an increasing coupling strength; we summarise its known properties, including possible cosmological applications as a model for a strong electroweak transition. The first order transition, and its accompanying second order endpoint, finally morphs into the essential singularity at the onset of the conformal window, following the singular behaviour predicted by the functional renormalisation group.

Coupled Flow-Seepage–Elastoplastic Modeling for Competition Mechanism between Lateral Instability and Tunnel Erosion of a Submarine Pipeline

The instability of a partially embedded pipeline under ocean currents involves complex fluid–pipe–soil interactions, which may induce two typical instability modes; i.e., the lateral instability of the pipe and the tunnel erosion of the underlying soil. In previous studies, such two instability modes were widely investigated, but separately. To reveal the competition mechanism between the lateral instability and the tunnel erosion, a coupled flow-seepage–elastoplastic modeling approach was proposed that could realize the synchronous simulation of the pipe hydrodynamics, the seepage flow, and elastoplastic behavior of the seabed soil beneath the pipe. The coupling algorithm was provided for flow-seepage–elastoplastic simulations. The proposed model was verified through experimental and numerical results. Based on the instability criteria for the lateral instability and tunnel erosion, the two instability modes and their corresponding critical flow velocities could be determined. The instability envelope for the flow–pipe–soil interaction was established eventually, and could be described by three parameters; i.e., the critical flow velocity (Ucr), the embedment-to-diameter ratio (e/D), and the non-dimensional submerged weight of the pipe (G). There existed a transition line on the envelope when switching from one instability mode to the other. If the flow velocity of ocean currents gets beyond the instability envelope, either tunnel erosion or lateral instability could be triggered. With increasing e/D or concurrently decreasing G, the lateral instability was more prone to being triggered than the tunnel erosion. The present analyses may provide a physical insight into the dual-mode competition mechanism for the current-induced instability of submarine pipelines.

Theoretical and Experimental Study of Optimization of Polarization Spectroscopy for the D2 Closed Transition Line of 87Rb Atoms

We experimentally and theoretically investigated the optimal condition of polarization spectroscopy for frequency stabilization on various pump beam intensities and vapor cell temperatures for the D2 closed transition line of 87Rb atoms. We compared the experimental results, such as the amplitude, width, and slope, of the polarization spectroscopy signal with the theoretical results obtained from the numerical calculation of temporal density matrix equations. Based on the results, we found the optimal parameters, such as the pump beam intensity and vapor cell temperature, for polarization spectroscopy. The theoretically expected optimal parameters were, qualitatively, in good agreement with the experimental results.

Unravelling the Mechanisms of Electromagnetically Induced Absorption and Transparency in Open Degenerate Multilevel System: Effects of Neighboring Transitions

Optical Bloch equations with and without neighboring hyperfine states near the degenerate two-level system (DTLS) in the challenging case of 85Rb D2 transition that involves the Doppler broadening effect are solved herein. The calculated spectra agree well with the experimental results obtained using the coupling-probe scheme with orthogonal linear polarizations of the coupling and probe fields. The mechanisms of electromagnetically induced absorption (electromagnetically induced transparency) for the open Fg = 3 → Fe = 2 and 3 transitions (open Fg = 2 → Fe = 2 and 3 transitions) are clearly determined to be the effect of the strong closed Fg = 3 → Fe = 4 transition line (strong closed Fg = 2 → Fe = 1 transition line) based on the comparisons of the calculated absorption profiles of a DTLS without neighboring states and those of all levels with neighboring states depending on the coupling and probe power ratios. The crucial factors established based on comparisons of the calculated absorption profiles of DTLS with and without neighboring states, which enhance or reduce coherence effects and result in transformation between electromagnetically induced absorption and electromagnetically induced transparency, are the power ratios between coupling and probe beams, openness of the excited state, and effects of the neighboring states due to the Doppler broadening in a real atomic system.

The Undrained Characteristics of Tengger Desert Sand from True Triaxial Testing

Aimed at the characteristics of aeolian sand under rapid construction conditions in desert geotechnical engineering, a series of the true triaxial undrained test were carried out on the GDS apparatus. The 3D deformation, failure, and other characteristics of the dense sand are obtained. Under the condition of same p c , the state transition point where the void water pressure changes from increasing to decreasing appears earlier and leads to enhanced dilatancy with the increase of b, which means the enhanced dilatancy of dense sand caused the increase in strength. The results of the same b shows that the void water pressure generally indicates a decrease at low confining pressure and an increase at high confining pressure, indicating that the aeolian sand shows dilatancy at low confining pressure and contraction at high confining pressure. The state transition point increases with the increase of p c , but all points tend to the same critical state line and state transition line. When b = 0, the critical state line is q = 1.57 p ′ , and the state transition line is q = 1.23 p ′ . When b = 1, the critical state line is q = 1.24 p ′ , and the state transition line is q = 1.04 p ′ . The results at same b obtained the unified critical state line and the state transition line. Therefore, the true triaxial test can obtain the unified relationship of void ratio, p c and b, which overcomes the fact that the existing test cannot consider the influence of b. The test results provide a basis data for the design, construction, and maintenance of geotechnical engineering in Tengger Desert.

Lattice regularisation and entanglement structure of the Gross-Neveu model

We construct a Hamiltonian lattice regularisation of the N-flavour Gross-Neveu model that manifestly respects the full O(2N) symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorems. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large N limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for N = 2, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of O(4), corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

Evidence for the Fulde–Ferrell–Larkin–Ovchinnikov state in bulk NbS2

We present measurements of the magnetic torque, specific heat and thermal expansion of the bulk transition metal dichalcogenide (TMD) superconductor NbS2 in high magnetic fields, with its layer structure aligned strictly parallel to the field using a piezo rotary positioner. The upper critical field of superconducting TMDs in the 2D form is known to be dramatically enhanced by a special form of Ising spin orbit coupling. This Ising superconductivity is very robust to the Pauli paramagnetic effect and can therefore exist beyond the Pauli limit for superconductivity. We find that superconductivity beyond the Pauli limit still exists in bulk single crystals of NbS2 for a precisely parallel field alignment. However, the comparison of our upper critical field transition line with numerical simulations rather points to the development of a Fulde-Ferrell-Larkin-Ovchinnikov state above the Pauli limit as a cause. This is also consistent with the observation of a magnetic field driven phase transition in the thermodynamic quantities within the superconducting state near the Pauli limit.