相关论文: Quantum-Mechanical Supersymmetry in Traps
For isotropic confining Ioffe-Pritchard or TOP potentials, a valence fermion trapped with a closed core of other fermions can be described by an analytical effective one-particle model with a physical eigenspectrum. Related constructions…
In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore…
The dynamics of two traps with ultracold atoms and connected by Josephson type coupling, is shown to exhibit a transition from dispersive dynamics to localized coherent oscillations. This transition is controlled by coupling strength and…
We examine a one-dimensional two-component fermionic system in a trap, assuming that all particles have the same mass and interact through a strong repulsive zero-range force. First we show how a simple system of three strongly interacting…
This paper begins with some background information and a summary of results in atomic supersymmetry. The connection between the supersymmetric Coulomb and oscillator problems in arbitrary dimensions is outlined. Next, I treat the issue of…
Pairing gaps for fermionic atoms in harmonic oscillator traps are calculated for a wide range of interaction strengths and particle number, and compared to pairing in nuclei. Especially systems, where the pairing gap exceeds the level…
A novel approach is proposed to analyze a rather vast counter-rotating Hamiltonian interaction in the context of cavity quantum electrodynamics. The method relies upon the supersymmetric mapping of the corresponding rotating interaction and…
We describe a model for s-wave collisions between ground state atoms in optical lattices, considering especially the limits of quasi-one and two dimensional axisymmetric harmonic confinement. When the atomic interactions are modelled by an…
The hamiltonian describing a single fermion in a Penning trap is shown to be supersymmetric in certain cases. The supersymmetries of interest occur when the ratio of the cyclotron frequency to the axial frequency is 3/2 and the particle has…
A new strategy for trapping quantum particles is presented, which behaves like an effective harmonic oscillator potential trap wherever is desired. The approach is based on harmonic contraction and expansion of the system around a fixed…
We investigate controlled collisions between trapped but separated ultracold atoms. The interaction between atoms is treated self-consistently using an energy-dependent delta-function pseudopotential model, whose validity we establish. At a…
We consider a dilute two-component atomic fermion gas with unequal populations in a harmonic trap potential using the mean field theory and the local density approximation. We show that the system is phase separated into concentric shells…
We provide an analytically tractable toy model of an infinitely heavy impurity interacting with the spin-polarized gas of bath fermions via a contact potential in 1D and placed in a harmonic trap. The solution to this problem requires…
We consider the system of two interacting atoms confined in axially symmetric harmonic trap. Within the pseudopotential approximation, we solve the Schroedinger equation exactly, discussing the limits of quasi-one and quasi-two-dimensional…
We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small…
We establish a new geometric wave function that combined with a variational principle efficiently describes a system of bosons interacting in a one-dimensional trap. By means of a a combination of the exact wave function solution for…
We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the…
We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail.…
Supersymmetric quantum mechanics is constructed in a new non-Hermitian representation. Firstly, the map between the partner operators $H^{(\pm)}$ is chosen antilinear. Secondly, both these components of a super-Hamiltonian ${\cal H}$ are…
We use a BCS-type variational wavefunction to study attractively-interacting quasi one-dimensional (1D) fermionic atomic gases, motivated by cold-atom experiments that access the 1D regime using an anisotropic harmonic trapping potential…