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In recently, we have proposed a scheme to sensitive quantum measurement using ultracold atoms [1]. Most attractive properties of the system, its measurement sensitivity limit is very high due to the quantum nature of the ultracold atoms. Here, we propose a temperature sensitivity measurement of the order of Pico-Kelvin and an another sensitive measurement of purity gas of bosons in phase-space. The impurity in the gases changes the effective mass of the system; this combined mass is the reduced mass. This mass difference will result in relative phase difference which we measured in Wigner phase-space. In this scheme we showed a measurement when mass difference is 2.4 % of actual mass. [ABSTRACT FROM AUTHOR]

Bose-Einstein condensate has become a highly tunable physical system, which is proven to mimic a number of interesting physical phenomena in condensed matter physics. We study the dynamics of a two-dimensional Bose Einstein condensate (BEC) in the presence of a flat harmonic confinement and time-dependent sharp potential peak. Condensate density can be meticulously controlled with time by tuning the physically relevant parameters: frequency of the harmonic trap, width of the peaks, frequency of their oscillations, initial density etc. By engineering various trap profile, we solve the system, numerically, and explore the resulting spatial interference patters. [ABSTRACT FROM AUTHOR]