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K. Pilch

Publications and source records attributed to K. Pilch.

16 recordsLinked to original sources
arXiv2009

Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances

We present an analytic model to calculate the atomic scattering length near a Feshbach resonance from data on the molecular binding energy. Our approach considers finite-range square-well potentials and can be applied near broad, narrow, or even overlapping Feshbach resonances. We test our model on Cs$_2$ Feshbach molecules. We measure the binding energy using magnetic-field modulation spectroscopy in a range where one broad and two narrow Feshbach resonances overlap. From the data we accurately determine the Cs atomic scattering length and the positions and widths of two particular resonances.

cond-mat.other↗
arXiv2008

Observation of interspecies Feshbach resonances in an ultracold Rb-Cs mixture

We report on the observation of interspecies Feshbach resonances in an ultracold, optically trapped mixture of Rb and Cs atoms. In a magnetic field range up to 300 G we find 23 interspecies Feshbach resonances in the lowest spin channel and 2 resonances in a higher channel of the mixture. The extraordinarily rich Feshbach spectrum suggests the importance of different partial waves in both the open and closed channels of the scattering problem along with higher-order coupling mechanisms. Our results provide, on one hand, fundamental experimental input to characterize the Rb-Cs scattering properties and, on the other hand, identify possible starting points for the association of ultracold heteronuclear RbCs molecules.

cond-mat.other↗
arXiv2006

Experimental Evidence for Efimov Quantum States

Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems.

cond-mat.other↗
arXiv2006

Evidence for Efimov quantum states in an ultracold gas of cesium atoms

Systems of three interacting particles are notorious for their complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics. However, the observation of Efimov quantum states has remained an elusive goal. Here we report the observation of an Efimov resonance in an ultracold gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied. We also detect a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems. While Feshbach resonances have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter to the world of few-body quantum phenomena.

cond-mat.other↗
arXiv2005

Holographic Duals of a Family of N=1 Fixed Points

We construct a family of warped AdS_5 compactifications of IIB supergravity that are the holographic duals of the complete set of N=1 fixed points of a Z_2 quiver gauge theory. This family interpolates between the T^{1,1} compactification with no three-form flux and the Z_2 orbifold of the Pilch-Warner geometry which contains three-form flux. This family of solutions is constructed by making the most general Ansatz allowed by the symmetries of the field theory. We use Killing spinor methods because the symmetries impose two simple projection conditions on the Killing spinors, and these greatly reduce the problem. We see that generic interpolating solution has a nontrivial dilaton in the internal five-manifold. We calculate the central charge of the gauge theories from the supergravity backgrounds and find that it is 27/32 of the parent N=2, quiver gauge theory. We believe that the projection conditions that we derived here will be useful for a much larger class of N=1 holographic RG-flows.

hep-th↗
arXiv2000

Continuous distributions of D3-branes and gauged supergravity

States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.

hep-th↗
arXiv1999

Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem

We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N=4 gauged supergravity theory holographically dual to a sector of N=2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For even-dimensional boundaries, the c-function coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.

hep-th↗
arXiv1998

New Vacua of Gauged N=8 Supergravity

We analyze a particular SU(2) invariant sector of the scalar manifold of gauged N=8 supergravity in five dimensions, and find all the critical points of the potential within this sector. The critical points give rise to Anti-de Sitter vacua, and preserve at least an SU(2) gauge symmetry. Consistent truncation implies that these solutions correspond to Anti-de Sitter compactifications of IIB supergravity, and hence to possible near-horizon geometries of 3-branes. Thus we find new conformal phases of softly broken N=4 Yang--Mills theory. One of the critical points preserves N=2 supersymmetry in the bulk and is therefore completely stable, and corresponds to an N=1 superconformal fixed point of the Yang--Mills theory. The corresponding renormalization group flow from the N=4 point has c_{IR}/c_{UV} = 27/32. We also discuss the ten-dimensional geometries corresponding to these critical points.

hep-th↗
arXiv1998

On deformed W-algebras and quantum affine algebras

We discuss some aspects of the deformed W-algebras W_{q,t}[g]. In particular, we derive an explicit formula for the Kac determinant, and discuss the center when t^2 is a primitive k-th root of unity. The relation of the structure of W_{q,t}[g] to the representation ring of the quantum affine algebra U_q(\hat g), as discovered recently by Frenkel and Reshetikhin, is further elucidated in some examples.

math.QA↗
arXiv1997

The deformed Virasoro algebra at roots of unity

We discuss some aspects of the representation theory of the deformed Virasoro algebra $\virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the center of $\virpq$ for $q$ a primitive N-th root of unity. We derive explicit expressions for the generators of the center in the limit $t=qp^{-1}\to \infty$ and elucidate the connection to the Hall-Littlewood symmetric functions. Furthermore, we argue that for $q=\sqrtN{1}$ the algebra describes `Gentile statistics' of order $N-1$, i.e., a situation in which at most $N-1$ particles can occupy the same state.

q-alg↗
arXiv1995

On the W-gravity spectrum and its G-structure

We present results for the BRST cohomology of $\cW[\bfg]$ minimal models coupled to $\cW[\bfg]$ gravity, as well as scalar fields coupled to $\cW[\bfg]$ gravity. In the latter case we explore an intricate relation to the (twisted) $\bfg$ cohomology of a product of two twisted Fock modules.

hep-th↗
arXiv1993

On the BRST structure of W_3 gravity coupled to c=2 matter

We present some explicit results on the structure of singular vectors in $c=2$ Verma modules of the $\cW_3$ algebra. Using the embedding patterns of those vectors we construct resolutions for the $c=2$ irreducible modules, and thus are able to compute some of the BRST cohomology of $\cW_3$ gravity coupled to $c=2$ matter. In particular, we determine the states in the ground ring of the theory. (To appear in the proceedings of the AMS Special Session on "Geometry and Physics", USC, Los Angeles, November 5-6, 1992)

hep-th↗
arXiv1993

Semi-infinite cohomology of W-algebras

We generalize some of the standard homological techniques to $\cW$-algebras, and compute the semi-infinite cohomology of the $\cW_3$ algebra on a variety of modules. These computations provide physical states in $\cW_3$ gravity coupled to $\cW_3$ minimal models and to two free scalar fields.

hep-th↗
arXiv1991

Ground ring for the 2D NSR string

We discuss the BSRT quantization of 2D $N=1$ supergravity coupled to superconformal matter with $\hat{c} \leq 1$ in the conformal gauge. The physical states are computed as BRST cohomology. In particular, we consider the ring structure and associated symmetry algebra for the 2D superstring ($\hat{c} = 1$).

hep-th↗
arXiv1991

Some aspects of free field resolutions in 2D CFT with application to the quantum Drinfeld-Sokolov reduction

We review some aspects of the free field approach to two-dimensional conformal field theories. Specifically, we discuss the construction of free field resolutions for the integrable highest weight modules of untwisted affine Kac-Moody algebras, and extend the construction to a certain class of admissible highest weight modules. Using these, we construct resolutions of the completely degenerate highest weight modules of W-algebras by means of the quantum Drinfeld-Sokolov reduction. As a corollary we derive character formulae for these degenerate highest weight modules.

hep-th↗