The branching fractions from the excited state 6P[/2 of singly charged barium ion has been measured with a precision 0.03% in an ion trap experiment. This measurement along with the known value of the upper state lifetime allowed the determination of the dipole matrix elements for the transitions P-S and P-D to below the 1% level. Therefore, it is now possible to compare the many-body calculations of these matrix elements at a level which is of significance to any parity-nonconservation experiment on barium ion. Moreover, these dipole matrix elements are the most significant contributors to the parity-violating matrix element between the S-D transition, contributing up to 90% to the total. Our results on the dipole matrix elements are 3.305 ± 0.014 a.u. and 3.042 ± 0.016 a.u. for the S-P and P-D transitions, respectively. Trapping and laser cooling of ions provide a perturbationfree environment to measure atomic state lifetime [1], light shift [2], branching ratio [3], and other fundamental properties of atoms with high precision [4], This leads to the use of trapped and laser cooled ions for quantum state manipulation [5,6], atomic clocks [7] and to study fundamental interac tions [8], The study of fundamental interactions via atomic properties include measurements of the Lamb shift [9], the parity-nonconservation (PNC) in atomic system [10], the conserved vector current hypothesis [ 11 ], the electron-electric dipole moment (e-EDM) [12], etc. As most of the original experiments have been carried out with atomic beams, they suffered from large systematic uncertainties due to limited control over the environment. These systematics are largely absent for stored atomic systems, and in addition, they provide long observation time. Therefore, in recent years, trapped and laser cooled ions have emerged as potential candidates to per form high precision experiments of fundamental importance like atomic parity violation [13,14] and e-EDM [8], Barium ion is particularly suitable for the investigation of PNC as was pointed out by Fortson [13] because of its large nuclear charge and ease of laser cooling and trapping.The best atomic PNC measurement performed so far is that of cesium with a precision of 0.3% [10]. However, the nuclear anapole moment obtained from this measurement shows a discrepancy with other nuclear data strongly suggesting the need to measure atomic PNC in other species in order to verify or to go beyond the standard model of particle physics. In this context, a number of experimental groups are pursuing an ion-trap-based atomic PNC experiment which has been proposed to be capable of limiting systematic uncertainty to below the 1% level. In addition to the experiment, one also needs the theoretical value of the parity-violating dipole matrix element with a similar precision. In principle, different variants ol the coupled cluster theory [15][16][17][18] are capable of providing such precision, provided the many-body wave functions are accurately known. Precision measurement of atomic properties of the lo...