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1. A driven Kerr oscillator with two-fold degeneracies for qubit protection

   https://doi.org/10.1073/pnas.2311241121  

   Venkatraman, Jayameenakshi; Cortiñas, Rodrigo G; Frattini, Nicholas E; Xiao, Xu; Devoret, Michel H (June 2024, Proceedings of the National Academy of Sciences)

   We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive. We find that when the detuning Δ between the frequency of the oscillator and the second subharmonic of the drive equals an even multiple of the Kerr coefficientK, $\mathrm{\Delta }/K=2m$, the oscillator displays $m+1$exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. These degeneracies can be explained by the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime, thus creating a protected cat qubit in the ground state manifold of our oscillator. Our results illustrate the relationship between degeneracies and noise protection in a driven quantum system. 

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2. Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination

   https://doi.org/10.1038/s41535-020-00303-4  

   Sharma, Rahul; Kreisel, Andreas; Sulangi, Miguel Antonio; Böker, Jakob; Kostin, Andrey; Allan, Milan P.; Eisaki, H.; Böhmer, Anna E.; Canfield, Paul C.; Eremin, Ilya; et al (January 2021, npj Quantum Materials)

   Abstract Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$, for all momentakon the Fermi surface of every bandα. While there are a variety of techniques for determining$$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$ $\mid {\Delta }_k^{\alpha }\mid$, no general method existed to measure the signed values of$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$. Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting allk-space regions where$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$has the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$it generates to the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$determined from single-atom scattering in FeSe where s_±energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$ ${\Delta }_k^{\alpha }$of opposite sign. 

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3. Improved effective dynamics of loop-quantum-gravity black hole and Nariai limit

   https://doi.org/10.1088/1361-6382/ac44a0  

   Han, Muxin; Liu, Hongguang (January 2022, Classical and Quantum Gravity)

   Abstract We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1 + 1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical HamiltonianH_Δ. The holonomy correction inH_Δis implemented by the $\overline{\mu }$-scheme regularization with a Planckian area scale Δ (which often chosen as the minimal area gap in loop quantum gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g.R_μνρσR^μνρσ∼ 1/Δ². Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry dS₂×S²with Planckian radii $\sim \sqrt{\mathrm{\Delta }}$. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition. 

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4. Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

   https://doi.org/10.3847/1538-4357/ad34ab  

   Zank, G. P.; Zhao, L. -L.; Adhikari, L.; Telloni, D.; Baruwal, Prashant; Baruwal, Prashrit; Zhu, Xingyu; Nakanotani, M.; Pitňa, A.; Kasper, J. C.; et al (April 2024, The Astrophysical Journal)

   Abstract Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumberk) for each mode. Entropy density fluctuations have a wavenumber anisotropy ofk_∥≫k_⊥, whereas slow-mode density fluctuations havek_⊥>k_∥. Magnetic field fluctuations are primarily magnetic island modes (δBⁱ) with anO(1) smaller contribution from unidirectionally propagating Alfvén waves (δB^A+) giving a variance anisotropy of $〈{\delta B^i}^2〉/〈{\delta B^A}^2〉=4.1$. Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like $k_{\perp }^{-1.6}$in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are $k_{\parallel }^{-1.6}$and $k_{\perp }^{-1.5}$. Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due toβ_p≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes. 

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5. 3D Mirror Symmetry for Instanton Moduli Spaces

   https://doi.org/10.1007/s00220-023-04831-5  

   Koroteev, Peter; Zeitlin, Anton M. (September 2023, Communications in Mathematical Physics)

   Abstract We prove that the Hilbert scheme ofkpoints on$${\mathbb {C}}^2$$ $C^2$($$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ ${\text{Hilb}}^k\left[C^2\right]$) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the$${\mathbb {C}}^\times _\hbar $$ $C_{ħ}^{\times }$-action. First, we find a two-parameter family$$X_{k,l}$$ $X_{k,l}$of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ ${\text{Hilb}}^k\left[C^2\right]$is obtained via direct limit$$l\longrightarrow \infty $$ $l⟶\infty$and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted$$\hbar $$ $ħ$-opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-Nsheaves on$${\mathbb {P}}^2$$ $P^2$with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual. 

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