Photon Number-Phase Uncertainty Relation in the Evolution of the Field in a Kerr-Like Medium

A model of a single-mode field, initially prepared in a coherent state, coupled to a two-level atom surrounded by a nonlinear Kerr-like medium contained inside a very good quality cavity is considered. We derive the photon number-phase uncertainty relation in the evolution of the field for a weak and strong nonlinear coupling respectively, within the Hermitian phase operator formalism of Pegg and Barnett, and discuss the effects of nonlinear coupling of the Kerr-like medium on photon number-phase uncertainty relation of the field

Cavity-Heisenberg spin chain quantum battery

We propose a cavity-Heisenberg spin chain (CHS) quantum battery (QB) with the long-range interactions and investigate its charging process. The performance of the CHS QB is substantially improved compared to the Heisenberg spin chain (HS) QB. When the number of spins $N \gg 1$, the quantum advantage $\alpha$ of the QB's maximum charging power can be obtained, which approximately satisfies a superlinear scaling relation $P_{max} \propto N^{\alpha}$. For the CHS QB, $\alpha$ can reach and even exceed $1.5$, while the HS QB can only reach about $\alpha=0.75$. We find that the maximum stored energy of the CHS QB has a critical phenomenon. By analyzing the Wigner function, von Neumann entropy, and logarithmic negativity, we demonstrate that entanglement can be a necessary ingredient for QB to store more energy, but not sufficient

Closed-loop three-level charged quantum battery

Quantum batteries are energy storage or extract devices in a quantum system. Here, we present a closed-loop quantum battery by utilizing a closed-loop three-state quantum system in which the population dynamics depends on the three control fields and associated phases. We investigate the charging process of the closed-loop three-level quantum battery. The charging performance is greatly improved due to existence of the third field in the system to form a closed-contour interaction. Through selecting an appropriate the third control field, the maximum average power can be increased, even far beyond the most ideal maximum power value of non-closed-loop three-level quantum battery (corresponding to the most powerful charging obtainable with minimum quantum speed limit time and the maximum charging energy). We study the effect of global driving-field phase on the charging process and find the maximum extractable work (`ergotropy') and charging power vary periodically under different control field, with a period of $2\pi$. Possible experimental implementation in nitrogen-vacancy spin is discussed

The Quantum Phase-Dynamical Properties of the Squeezed Vacuum State Intensity-Couple Interacting with the Atom

The Phase-dynamical properties of the squeezed vacuum state intensity-couple interacting with the two-level atom in an ideal cavity are studied using the Hermitian phase operator formalism. Exact general expressions for the phase distribution and the associated expectation value and variance of the phase operator have been derived. we have also obtained the analytic results of the phase variance for two special cases-weakly and strongly squeezed vacuum. The results calculated numerically show that squeezing has a significant effect on the phase properties of squeezed vacuum

Redetermination of 2,4′-methyl­ene­diphenol

In the previous determination [Finn & Musti (1950 ▶). J. Soc. Chem. Ind. (London), 69, S849] of the title compound, C13H12O2, the three-dimensional coordinates and displacement parameters were not reported. This redetermination at room temperature reveals that the dihedral angle between the benzene rings is 79.73 (6)°. In the crystal, inter­molecular O—H⋯O hydrogen bonds between adjacent mol­ecules result in two-dimensional wave-like supra­molecular motifs parallel to the ab plane

Poly[[diaqua­(μ2-1,4-dioxane-κ2 O:O′)(μ2-2,3,5,6-tetra­fluoro­benzene-1,4-dicarboxyl­ato-κ2 O 1:O 4)copper(II)] 1,4-dioxane disolvate dihydrate]

In the title complex, {[Cu(C8F4O4)(C4H8O2)(H2O)2]·2C4H8O2·2H2O}n, the CuII ion is six-coordinated by two oxygen donors from two trans 2,3,5,6-tetra­fluoro-1,4-dicarboxyl­ate (BDC-F4) ligands, two O atoms from two chair 1,4-dioxane ligands and two O atoms from two terminal water mol­ecules, adopting a distorted octa­hedral coordinated geometry. Each BDC-F4 anion bridges two CuII ions in a bis-monodentate fashion, forming a [Cu(BDC-F4)]n chain. These chains are further linked by bridging 1,4-dioxane ligands, generating a two-dimensional net with approximately recta­ngular grids of 11.253 × 7.654 Å. Such adjacent parallel layers are connected by O—H⋯O hydrogen bonds between guest water mol­ecules and the uncoordinated carboxyl­ate O atoms and coordinated water mol­ecules into the final three-dimensional supra­molecular network

Spatial and temporal hydrochemical variations of the spring-fed travertine-depositing stream in the Huanglong Ravine, Sichuan, SW China

Automatic hydrochemical logging and in situ titration com­bined withlaboratory analysis were used to understand the spatial and temporal hydrochemical variations of the spring-fed, travertine-depositing stream in celebrated Huanglong Ravine, Sichuan, SW China. This is essential for protection of the Huanglong World Natural Heritage travertine land­scape. It was found that the deposition of travertine was due to very strong CO2 degassing from the water, leading to de­crease in pCO2 and specific conductivity (SpC), and increase in pH and SIc downstream from the Spring. However, regular downstream hydrochemical evolution was interrupted by di­lution withsnow-melt water and by renewed CO2 from some downstream springs. The chemistry of Huanglong Spring itself was stable at a diurnal scale thoughit was altered by the great Wenchuan earthquake of May 12 2008. However, in spring-fed pools downstream, pCO2 and SpC were lower, and pH and SIc were higher in daytime than at night, whichindicates that the deposition of travertine was faster during the daylight hours. This was due to the combined effects of higher water tempera­tures and higher aquatic algae photosynthesis. In addition, it was found that the phosphate concentration in the stream in­creased remarkably downstream in the tourist midseason, in­dicating water pollution by tourism activities. The increase of phosphate (an inhibitor of calcite precipitation) may be one of the reasons for the decrease in travertine deposition rates and accelerated propagation of discoloration by diatoms during the past decades, whichneeds to be given more comprehensive study and tackled in future for the protection of these world famous travertine deposits

1,4-Bis(2-pyridylmethyl­eneamino­meth­yl)benzene

The asymmetric unit of the centrosymmetric title compound, C20H18N4, contains one half-mol­ecule. The pyridine and benzene rings are oriented at a dihedral angle of 77.21 (7)°

Decision ambiguity is mediated by a late positive potential originating from cingulate cortex

People often make decisions in the face of ambiguous information, but it remains unclear how ambiguity is represented in the brain. We used three types of ambiguous stimuli and combined EEG and fMRI to examine the neural representation of perceptual decisions under ambiguity. We identified a late positive potential, the LPP, which differentiated levels of ambiguity, and which was specifically associated with behavioral judgments about choices that were ambiguous, rather than passive perception of ambiguous stimuli. Mediation analyses together with two further control experiments confirmed that the LPP was generated only when decisions are made (not during mere perception of ambiguous stimuli), and only when those decisions involved choices on a dimension that is ambiguous. A further control experiment showed that a stronger LPP arose in the presence of ambiguous stimuli compared to when only unambiguous stimuli were present. Source modeling suggested that the LPP originated from multiple loci in cingulate cortex, a finding we further confirmed using fMRI and fMRI-guided ERP source prediction. Taken together, our findings argue for a role of an LPP originating from cingulate cortex in encoding decisions based on task-relevant perceptual ambiguity, a process that may in turn influence confidence judgment, response conflict, and error correction