Rydberg Blockade,Van Der Waals Interaction Strength Between Alkali Rydberg Atoms

Atoms excited to Rydberg states experience enhanced coupling to the environment.The capability of controlling interactions among individual atoms in a system are essential for developing advanced techniques for studying quantum information process.The extravagant characteristics of the Rydberg atoms meet the technological challenges to control and isolate the individual channels interactions in ultra-cold gases.If the interaction potential is high enough in a pair of atoms,only one electron will be excited through the highest state(Rydberg state)at a time for the same laser.In this work,the interaction potential of two atoms under s,p and d states are calculated in the regime where van der Waals effects dominate.The van der Waals force strength among two Rydberg atoms is calculated here in detail by using the tools of quantum information process for Rydberg blockade.The alkali metals(CS and K)in the n quantum number states were used to calculate the interaction potential.We use some possible channels of the angular momentum including the states of s,p and d for determining the interaction strength.The obtained results were then generalized for all angular momentum channels which mostly have small interactions and therefor are poor candidate for blockade experiments.A specific emphasis was put on the angular dependence of the inter-atomic interaction.These calculations required some specific characteristics like the involved interaction channel energy separation,radial matrix elements and van der Waals interaction coefficients.The interaction potential in the atoms of Cs and K dipole matrix elements was calculated first and then relevant energy levels were determined by using the quantum defects theory.The radial wave function was calculated numerically with the integration of radial Schrodinger equation.Also the coefficients of van der Waals interactions for various channels was calculated.