We have developed a low temperature ultrahigh resolution system for polarization dependent angle-resolved photoemission spectroscopy (ARPES) using a vacuum ultraviolet (vuv) laser (hnu=6.994 eV) as a photon source. With the aim of addressing low energy physics, we show the system performance with angle-integrated PES at the highest energy resolution of 360 mueV and the lowest temperature of 2.9 K. We describe the importance of a multiple-thermal-shield design for achieving the low temperature, which allows a clear measurement of the superconducting gap of tantalum metal with a T(c)=4.5 K. The unique specifications and quality of the laser source (narrow linewidth of 260 mueV, high photon flux), combined with a half-wave plate, facilitates ultrahigh energy and momentum resolution polarization dependent ARPES. We demonstrate the use of s- and p-polarized laser-ARPESs in studying the superconducting gap on bilayer-split bands of a high T(c) cuprate. The unique features of the quasi-continuous-wave vuv laser and low temperature enables ultrahigh-energy and -momentum resolution studies of the spectral function of a solid with large escape depth. We hope the present work helps in defining polarization dependent laser excited angle-resolved photoemission spectroscopy as a frontier tool for the study of electronic structure and properties of materials at the sub-meV energy scale.