arXiv subjects

N. P. Mehta

Publications and source records attributed to N. P. Mehta.

9 recordsLinked to original sources

arXiv2025

Observation of Fano-suppression in scattering resonances of bosonic erbium atoms

The collisional properties of lanthanides exhibit remarkable complexity due to their many valence electrons, leading to an extraordinarily dense Feshbach spectrum showing signs of quantum chaos. Here we explore the situation of bosonic spin mixtures of erbium, adding the additional spin degree of freedom to the problem. We detect several inter- and intra-spin scattering resonances, exhibiting a peculiar asymmetric shape with a pronounced loss minimum. By developing a simplified multi-channel model we are able to recreate this characteristic behavior and to trace its origin to destructive interference between multiple pathways as predicted by Fano. We additionally observe a series of Fano-Feshbach resonances across multiple spin channels connected to the same molecular state, again confirmed by our theory. Our work opens the door for a detailed investigation to study multi-spin strongly-coupled scattering phenomena.

cond-mat.quant-gas↗

arXiv2015

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in the strongly and weakly interacting limits can be accurately described using wave function factorized in hyperspherical coordinates. Inspired by this result we propose an interpolation ansatz for the wave function for arbitrary repulsive zero-range interactions. By comparison to numerical calculations, we show that this interpolation scheme yields an extremely good approximation to the numerically exact solution both in terms of the energies and also in the spin-resolved densities. As an outlook, we discuss the case of mass imbalanced systems in the strongly interacting limit. Here we find spectra that demonstrate that the triply degenerate spectrum at infinite coupling strength of the equal mass case is in some sense a singular case as this degeneracy will be broken down to a doubly degenerate or non-degenerate ground state by any small mass imbalance.

cond-mat.quant-gas↗

arXiv2011

The Hyperspherical Four-Fermion Problem

The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behavior of superconductors, fermionic superfluids, and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulas that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS-BEC crossover problem Derivations and relevant formulas are also included for the calculation of challenging few-body processes such as recombination.

physics.atom-ph↗

arXiv2010

Green's Functions and the Adiabatic Hyperspherical Method

We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in $d$-dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of three-particles with s-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semi-analytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom-loss due to three-body recombination for a three-component fermi-gas of $^{6}$Li atoms is presented.

physics.atom-ph↗

arXiv2009

A general theoretical description of N-body recombination

A formula for the cross section and event rate constant describing recombination of N particles are derived in terms of general S-matrix elements. Our result immediately yields the generalized Wigner threshold scaling for the recombination of N bosons. A semi-analytic formula encapsulates the overall scaling with energy and scattering length, as well as resonant modifications by the presence of borromean N-body states near the threshold collision energy in the entrance channel. We then apply our model to the case of four-boson recombination into an Efimov trimer and a free atom.

physics.atom-ph↗

arXiv2008

Dimer-dimer collisions at finite energies in two-component Fermi gases

We introduce a major theoretical generalization of existing techniques for handling the three-body problem that accurately describes the interactions among four fermionic atoms. Application to a two-component Fermi gas accurately determines dimer-dimer scattering parameters at finite energies and can give deeper insight into the corresponding many-body phenomena. To account for finite temperature effects, we calculate the energy-dependent complex dimer-dimer scattering length, which includes contributions from elastic and inelastic collisions. Our results indicate that strong finite-energy effects and dimer dissociation are crucial for understanding the physics in the strongly interacting regime for typical experimental conditions. While our results for dimer-dimer relaxation are consistent with experiment, they confirm only partially a previously published theoretical result.

physics.atom-ph↗

arXiv2008

Efimov states embedded in the three-body continuum

We consider a multichannel generalization of the Fermi pseudopotential to model low-energy atom-atom interactions near a magnetically tunable Feshbach resonance, and calculate the adiabatic hyperspherical potential curves for a system of three such interacting atoms. In particular, our model suggests the existence of a series of quasi-bound Efimov states attached to excited three-body thresholds, far above open channel collision energies. We discuss the conditions under which such states may be supported, and identify which interaction parameters limit the lifetime of these states. We speculate that it may be possible to observe these states using spectroscopic methods, perhaps allowing for the measurement of multiple Efimov resonances for the first time.

cond-mat.other↗

arXiv2007

Three-Body Recombination in One Dimension

We study the three-body problem in one dimension for both zero and finite range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all combinations of the parity and exchange symmetries. For bosons, we provide a numerical demonstration of several universal features that appear in the three-body system, and discuss how certain universal features in three dimensions are different in one dimension. We show that the probability for inelastic processes vanishes as the range of the pair-wise interaction is taken to zero and demonstrate numerically that the recombination threshold law manifests itself for large scattering length.

quant-ph↗

arXiv2003

Low-energy operators in effective theories

Modern effective-theory techniques are applied to the nuclear many-body problem. A novel approach is proposed for the renormalization of operators in a manner consistent with the construction of the effective potential. To test this approach, a one-dimensional, yet realistic, nucleon-nucleon potential is introduced. An effective potential is then constructed by tuning its parameters to reproduce the exact effective-range expansion and a variety of bare operators are renormalized in a fashion compatible with this construction. Predictions for the expectation values of these effective operators in the ground state reproduce the results of the exact theory with remarkable accuracy (at the 0.5% level). This represents a marked improvement over a widely practiced approach that uses effective interactions but retains bare operators. Further, it is shown that this improvement is more impressive as the operator becomes more sensitive to the short-range structure of the potential. We illustrate the main ideas of this work using the elastic form factor of the deuteron as an example.

nucl-th↗