Nodeless energy gaps of single-crystalline Ba0.68K0.32Fe2As2 as seen via 75As NMR

We report $^{75}$As nuclear magnetic resonance studies on a very clean hole-doped single-crystal Ba$_{0.68}$K$_{0.32}$Fe$_{2}$As$_{2}$ ($T_{\rm {c}}=38.5$ K). The spin-lattice relaxation rate $1/T_{1}$ shows an exponential decrease below $T \simeq 0.45 T_{\rm c}$ down to $T \simeq 0.11 T_{\rm c}$, which indicates a fully opened energy gap. From the ratio $(T_{1})_{c} / (T_{1})_{a}$, where $a$ and $c$ denote the crystal directions, we find that the antiferromagnetic spin fluctuation is anisotropic in the spin space above $T_{\rm c}$. The anisotropy decreases below $T_{\rm c}$ and disappears at $T \rightarrow 0$. We argue that the anisotropy stems from spin-orbit coupling whose effect vanishes when spin-singlet electron pairs form with a nodeless gap.Comment: 10 pages, 6 figure

A study on the negative binomial distribution motivated by Chv\'atal's theorem

Let $B(n,p)$ denote a binomial random variable with parameters $n$ and $p$. Chv\'{a}tal's theorem says that for any fixed $n\geq 2$, as $m$ ranges over $\{0,\ldots,n\}$, the probability $q_m:=P(B(n,m/n)\leq m)$ is the smallest when $m$ is closest to $\frac{2n}{3}$. Motivated by this theorem, in this note we consider the infimum value of the probability $P(X\leq E[X])$, where $X$ is a negative binomial random variable. As a consequence, we give an affirmative answer to the conjecture posed in [Statistics and Probability Letters, 200 (2023) 109871].Comment: 10 page

Integrated photonic qubit quantum computing on a superconducting chip

We study a quantum computing system using microwave photons in transmission line resonators on a superconducting chip as qubits. We show that all control necessary for quantum computing can be implemented by coupling to Josephson devices on the same chip, and take advantage of their strong inherent nonlinearities to realize qubit interactions. We analyze the gate error rate to demonstrate that our scheme is realistic even for Josephson devices with limited decoherence times. A conceptually innovative solution based on existing technologies, our scheme provides an integrated and scalable approach to the next key milestone for photonic qubit quantum computing.Comment: 5 pages, 3 figure