arXiv subjects

M. Larsen

Publications and source records attributed to M. Larsen.

5 recordsLinked to original sources

arXiv2020

An all-optical intrinsic atomic gradiometer with sub-20 fT/cm/$\sqrt{\rm Hz}$ sensitivity in a 22 $\mu$T earth-scale magnetic field

In this work we demonstrate a high sensitivity atomic gradiometer capable of operation in earth-field level environments. We apply a light-pulse sequence at four times the Larmor frequency to achieve gradiometer sensitivity <20 fT/cm/$\sqrt{\rm Hz}$ at the finite field strength of 22 $\mu$T. The experimental timing sequence can be tuned to the field magnitude of interest. Our one dimensional all-optical gradiometer performs a differential measurement between two regions of a single vapor cell on a 4 cm baseline. Our results pave the way for extensions to operation in higher dimensions, vector sensitivity, and more advanced gradiometers.

physics.atom-ph↗

arXiv2019

Continuous Comagnetometry using Transversely Polarized Xe Isotopes

We demonstrate a transversely polarized spin-exchange pumped noble gas comagnetometer which suppresses systematic errors from longitudinal polarization. Rb atoms as well as $^{131}$Xe and $^{129}$Xe nuclei are simultaneously polarized perpendicular to a pulsed bias field. Both Xe isotopes' nuclear magnetic resonance conditions are simultaneously satisfied by frequency modulation of the pulse repetition rate. The Rb atoms detect the Xe precession. We highlight the importance of magnetometer phase shifts when performing comagnetometry. For detection of non-magnetic spin-dependent interactions the sensing bandwidth is 1 Hz, the white-noise level is 7 $\mu$Hz /$\sqrt{\text{Hz}}$, and the bias stability is $\approx1$ $\mu$Hz.

physics.atom-ph↗

arXiv2013

A Laboratory Search for a Long-Range T-odd, P-odd Interaction from Axion-Like Particles using Dual Species Nuclear Magnetic Resonance with Polarized Xe-129 and Xe-131 Gas

We place new limits on potential T- and P- violating monopole-dipole interactions between unpolarized nucleons and neutrons using dual species magnetic resonance in polarzed Xe gas. Free-induction decay transients with relaxation times ~20 s allow high precision measurements of the NMR frequencies, whose ratios cancel magnetic fluctuations. The new limits on the product gsgp improve on previous laboratory work by 2 orders of magnitude.

physics.atom-ph↗

arXiv2008

Representation Growth of Linear Groups

Let $Γ$ be a group and $r_n(Γ)$ the number of its $n$-dimensional irreducible complex representations. We define and study the associated representation zeta function $\calz_Γ(s) = \suml^\infty_{n=1} r_n(Γ)n^{-s}$. When $Γ$ is an arithmetic group satisfying the congruence subgroup property then $\calz_Γ(s)$ has an ``Euler factorization". The "factor at infinity" is sometimes called the "Witten zeta function" counting the rational representations of an algebraic group. For these we determine precisely the abscissa of convergence. The local factor at a finite place counts the finite representations of suitable open subgroups $U$ of the associated simple group $G$ over the associated local field $K$. Here we show a surprising dichotomy: if $G(K)$ is compact (i.e. $G$ anisotropic over $K$) the abscissa of convergence goes to 0 when $\dim G$ goes to infinity, but for isotropic groups it is bounded away from 0. As a consequence, there is an unconditional positive lower bound for the abscissa for arbitrary finitely generated linear groups. We end with some observations and conjectures regarding the global abscissa.

math.GR↗

arXiv2004

Grothendieck ring of pretriangulated categories

We consider the abelian group $PT$ generated by quasi-equivalence classes of pretriangulated DG categories with relations coming from semi-orthogonal decompositions of corresponding triangulated categories. We introduce an operation of "multiplication" $\bullet$ on the collection of DG categories which makes this abelian group into a commutative ring. A few applications are considered: representability of "standard" functors between derived categories of coherent sheaves on smooth projective varieties and a construction of an interesting motivic measure.

math.AG↗