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1. An optical atomic clock using $4D_J$ states of rubidium

   https://doi.org/10.1088/2058-9565/ad77ef  

   Duspayev, A.; Owens, C.; Dash, B.; Raithel, G. (September 2024, Quantum Science and Technology)

   Abstract We analyze an optical atomic clock using two-photon $5S_{1/2}\to 4D_J$transitions in rubidium. Four one- and two-color excitation schemes to probe the $4D_{3/2}$and $4D_{5/2}$fine-structure states are considered in detail. We compare key characteristics of Rb $4D_J$and $5D_{5/2}$two-photon clocks. The $4D_J$clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the ${10}^{-13}/\sqrt{\tau \left(s\right)}$-level, with integration timeτin seconds, and a relative accuracy of $\sim {10}^{-13}$. We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb $4D_J$-states. 

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2. Toward Astrometric Constraints on a Supermassive Black Hole Binary in the Early-type Galaxy NGC 4472

   https://doi.org/10.3847/1538-4357/ac680b  

   Wrobel, J. M.; Lazio, T. J. W. (May 2022, The Astrophysical Journal)

   Abstract The merger of two galaxies, each hosting a supermassive black hole (SMBH) of mass 10⁶M_⊙or more, could yield a bound SMBH binary. For the early-type galaxy NGC 4472, we study how astrometry with a next-generation Very Large Array could be used to monitor the reflex motion of the primary SMBH of massM_pri, as it is tugged on by the secondary SMBH of mass $M_{\sec }$. Casting the orbit of the putative SMBH binary in terms of its periodP, semimajor axisa_bin, and mass ratio $q=M_{\sec }/M_{\mathrm{pri}}\le 1$, we find the following: (1) Orbits with fiducial periods ofP= 4 yr and 40 yr could be spatially resolved and monitored. (2) For a 95% accuracy of 2μas per monitoring epoch, subparsec values ofa_bincould be accessed over a range of mass ratios notionally encompassing major $\left(q>\frac{1}{4}\right)$and minor $\left(q<\frac{1}{4}\right)$galaxy mergers. (3) If no reflex motion is detected forM_priafter 1 (10) yr of monitoring, an SMBH binary with periodP= 4 (40) yr and mass ratioq> 0.01 (0.003) could be excluded. This would suggest no present-day evidence for a past major merger like that recently simulated, where scouring by aq∼ 1 SMBH binary formed a stellar core with kinematic traits like those of NGC 4472. (4) Astrometric monitoring could independently check the upper limits onqfrom searches for continuous gravitational waves from NGC 4472. 

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3. Length and Velocity Scales in Protoplanetary Disk Turbulence

   https://doi.org/10.3847/1538-4357/ad2c89  

   Sengupta, Debanjan; Cuzzi, Jeffrey N; Umurhan, Orkan M; Lyra, Wladimir (April 2024, The Astrophysical Journal)

   Abstract In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, Ω_L, is the local Keplerian frequency Ω_K. In terms of the standard dimensionless Shakura–Sunyaevαparameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by $\sqrt{\alpha }H$and $\sqrt{\alpha }c$, in whichHandcare the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where Ω_L≥ Ω_Kand show that, under these conditions, the characteristic length and velocity scales are respectively $\sqrt{\alpha /R\prime }H$and $\sqrt{\alpha R\prime }c$, where $R\prime \equiv {\mathrm{\Omega }}_L/{\mathrm{\Omega }}_K$is twice the Rossby number. It follows that $\alpha =\tilde{\alpha }/R\prime$, where $\sqrt{\tilde{\alpha }}c$is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For $R\prime >1$, the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation. 

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4. On the simultaneous reconstruction of the nonlinearity coefficient and the sound speed in the Westervelt equation

   https://doi.org/10.1088/1361-6420/aceef2  

   Kaltenbacher, Barbara; Rundell, William (August 2023, Inverse Problems)

   Abstract This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameter $\kappa \left(x\right)$often referred to as $B/A$in the acoustics literature and the wave speed $c_0\left(x\right)$. The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. For a reformulation of the problem in terms of the squared slowness $\mathfrak{s}=1/c_0^2$and the combined coefficient $\eta =\frac{\kappa }{c_0^2}$we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples. 

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5. Low-energy magnetic states of Tb adatom on graphene

   https://doi.org/10.1088/1361-648X/ad8fe9  

   Shaikh, Monirul; Klein, Alison; Wysocki, Aleksander L (November 2024, Journal of Physics: Condensed Matter)

   Abstract Electronic structure and magnetic interactions of a Tb adatom on graphene are investigated from first principles using combination of density functional theory and multiconfigurational quantum chemistry techniques including spin–orbit coupling (SOC) . We determine that the six-fold symmetry hollow site is the preferred adsorption site and investigate electronic spectrum for different adatom oxidation states including Tb³⁺, Tb²⁺, Tb¹⁺, and Tb⁰. For all charge states, the Tb $4f^8$configuration is retained with other adatom valence electrons being distributed over $5d_{xy}$, $5d_{x2+y2}$, and $6s/5d_0$single-electron orbitals. We find strong intra-site adatom exchange coupling that ensures that the $5d6s$spins are parallel to the4fspin. For Tb³⁺, the energy levels can be described by theJ = 6 multiplet split by the graphene crystal field (CF). For other oxidation states, the interaction of4felectrons with spin and orbital degrees of freedom of $6s5d$electrons in the presence of SOC results in the low-energy spectrum composed closely lying effective multiplets that are split by the graphene CF. Stable magnetic moment is predicted for Tb³⁺and Tb²⁺adatoms due to uniaxial magnetic anisotropy and effective anisotropy barrier around 440 cm⁻¹controlled by the temperature assisted quantum tunneling of magnetization through the third excited doublet. On the other hand, in-plane magnetic anisotropy is found for Tb¹⁺and Tb⁰adatoms. Our results indicate that the occupation of the $6s5d$orbitals can dramatically affect the magnetic anisotropy and magnetic moment stability of rare earth adatoms. 

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