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Amir Mohammadi

Publications and source records attributed to Amir Mohammadi.

54 records · Page 3Linked to original sources
arXiv2016

Reactive two-body and three-body collisions of Ba$^+$ in an ultracold Rb gas

We analyze reactive collisions of a single Ba$^+$ ion in contact with an ultracold gas of Rb atoms at low three-body collision energies of 2.2(9) mK$\times k_{\mathrm{B}}$. Mapping out the Ba$^+$ loss rate dependence on the Rb atom density we can discern two-body reactive collisions from three-body ones and for the first time determine both rate coefficients which are $k_2=3.1(6)(6)\times 10^{-13}\textrm{cm}^{3}\textrm{s}^{-1}$ and $k_3=1.04(4)(45)\times 10^{-24}\textrm{cm}^{6}\textrm{s}^{-1}$, respectively (statistical and systematic errors in parenthesis). Thus, the measured ternary recombination dominates over binary reactions even at moderate atom densities of $n\approx 10^{12}\: \textrm{cm}^{-3}$. The results for Ba$^+$ and Rb are representative for a wide range of cold ion-atom systems and can serve as a guidance for the future development of the field of hybrid atom-ion research.

physics.atom-ph↗
arXiv2016

Energy scaling of cold atom-atom-ion three-body recombination

We study three-body recombination of Ba$^+$ + Rb + Rb in the mK regime where a single $^{138}$Ba$^{+}$ ion in a Paul trap is immersed into a cloud of ultracold $^{87}$Rb atoms. We measure the energy dependence of the three-body rate coefficient $k_3$ and compare the results to the theoretical prediction, $k_3 \propto E_{\textrm{col}}^{-3/4}$ where $E_{\textrm{col}}$ is the collision energy. We find agreement if we assume that the non-thermal ion energy distribution is determined by at least two different micro-motion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed into an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.

physics.atom-ph↗
arXiv2015

Invariant Radon measures for Unipotent flows and products of Kleinian groups

Let G=PSL(2, F) where F= R or C, and consider the space Z=(Γ_1 x Γ_2)\ (G x G) where Γ_1<G is a co-compact lattice and Γ_2<G is a finitely generated discrete Zariski dense subgroup. The work of Benoist-Quint gives a classification of all ergodic invariant Radon measures on Z for the diagonal G-action. In this paper, for a horospherical subgroup N of G, we classify all ergodic, conservative, invariant Radon measures on Z for the diagonal N-action, under the additional assumption that Γ_2 is geometrically finite.

math.DS↗
arXiv2015

Classification of joinings for Kleinian groups

We classify all locally finite joinings of a horospherical subgroup action on Γ\ G when Γis a Zariski dense geometrically finite subgroup of G=PSL_2(R) or PSL_2(C). This generalizes Ratner's 1983 joining theorem for the case when Γis a lattice in G. One of the main ingredients is equidistribution of non-closed horospherical orbits with respect to the Burger-Roblin measure which we prove in a greater generality where G is the connected component of the identity in SO(n,1) for n at least 2 and Γis any Zariski dense geometrically finite subgroup of G.

math.DS↗
arXiv2015

Isolation, equidistribution, and orbit closures for the SL(2,R) action on Moduli space

We prove results about orbit closures and equidistribution for the SL(2,R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure classification theorem of [EMi2] and a certain isolation property of closed SL(2,R) invariant manifolds developed in this paper.

math.DS↗
arXiv2014

Permanent magnetic microtraps for ultracold atoms

We propose and numerically study two permanent magnetic micro-structures for creating Ioffe-Pritchard microtraps. A bias magnetic field is used to vary the depth, trap frequencies and the minimum of each microtrap. After the Bose-Einstein condensation achievement, the bias magnetic field can be slowly removed to increase the trap barrier heights for more efficiently holding the Bose-Einstein condensates. Even without the external magnetic field, it is possible to hold ultracold atoms in the microtraps. These microtraps may also be useful for single atom experiments for quantum information processing due to their very high confinement.

cond-mat.quant-gas↗
arXiv2013

Translate of horospheres and counting problems

Let G be a semisimple Lie group without compact factors, Γbe an irreducible lattice in G. In the first part of the article we give the necessary and sufficient condition under which a sequence of translates of probability "horospherical measures" is convergent. And the limiting measure is also determined when it is convergent (see Theorems 1 and 2 for the precise statements). In the second part, two applications are presented. The first one is of geometric nature and the second one gives an alternative way to count the number of rational points on a flag variety.

math.DS↗
arXiv2013

Matrix coefficients, Counting and Primes for orbits of geometrically finite groups

Let G:=SO(n,1)^\circ and Γbe a geometrically finite Zariski dense subgroup with critical exponent delta bigger than (n-1)/2. Under a spectral gap hypothesis on L^2(Γ\ G), which is always satisfied for delta>(n-1)/2 for n=2,3 and for delta>n-2 for n>= 4, we obtain an {\it effective} archimedean counting result for a discrete orbit of Γin a homogeneous space H\G, where H is the trivial group, an affine symmetric subgroup or a horospherical subgroup. More precisely, we show that for any effectively well-rounded family {B_T} of compact subsets in H\G, there exists η>0 such that #[e]\G\cap B_T=M(B_T) +O(M(B_T)^{1-η}) for an explicit measure M on H\G, which depends on Gamma. We also apply affine sieve and describe the distribution of almost primes on orbits of Γin arithmetic settings. One of key ingredients in our approach is an effective asymptotic formula for the matrix coefficients of L^2(Γ\ G) that we prove by combining methods from spectral analysis, harmonic analysis and ergodic theory. An effective mixing for the Bowen-Margulis-Sullivan measure is also obtained as an application of our methods.

math.NT↗
arXiv2011

S-Arithmetic Khintchine-Type Theorem

In this article we prove a convergence S-arithmetic Khintchine-type theorem for product of non-degenerate v-adic manifolds, where one of them is the Archimedian place.

math.NT↗
arXiv2011

A Sawtooth Permanent Magnetic Lattice for Ultracold Atoms and BECs

We propose a new permanent magnetic lattice for creating periodic arrays of Ioffe-Pritchard permanent magnetic microtraps for holding and controlling ultracold atoms and Bose-Einstein condensates (BECs). Lattice can be designed on thin layer of magnetic films such as $Tb_6$$Gd_10$$Fe_{80}$$Co_4$. In details, we investigate single layer and two crossed layers of sawtooth magnetic patterns with thicknesses of 50 and 500nm respectively with a periodicity of 1$μ$m. Trap depth and frequencies can be changed via an applied bias field to handle tunneling rates between lattice sites. We present analytical expressions and using numerical calculations show that this lattice has non-zero potential minima to avoid majorana spin flips. One advantage of this lattice over previous ones is that it is easier to manufacture.

cond-mat.quant-gas↗
arXiv2010

A joining classification and a special case of Raghunathan's conjecture in positive characteristic (with an appendix by Kevin Wortman)

We prove the classification of joinings for maximal horospherical subgroups acting on homogeneous spaces without any restriction on the characteristic. Using the linearization technique we deduce a special case of Raghunathan's orbit closure conjecture. In the appendix quasi-isometries of higher rank lattices in semisimple algebraic groups over fields of positive characteristic are characterized.

math.DS↗
arXiv2010

The extremal symmetry of arithmetic simplicial complexes

Let $G$ be a higher-rank semisimple Lie group over a nonarchimedean local field, for example $G={\rm PGL}(n,Q_P)$. To any lattice $L$ in $G$ there is an associated simplicial complex $B_L$, given by the quotient by $L$ of the Bruhat-Tits building associated to $G$. In this paper prove that the simplicial structure $B_L$ exhibits some remarkable and extremal symmetry properties, in particular when compared to any other simplicial structure on (any cover of) $B_L$.

math.GR↗