can we perform an experiment which can show wave and particle nature at the same time? I think the answer is no. If that is the case, is that not what heisenberg uncertainty principle saying then.? or heisenberg uncertainty principle has some other meaning. Looks like uncertainty principle is direct consequence of dual nature but a limitation that you cant observe both the nature in a single experiment
Here is the result of the double-slit experiment, performed with a very low-intensity source of electrons (source: https://en.wikipedia.org/wiki/File:Elektronenbeugung_Doppelspalt_gerendert.png):
This result clearly shows both the wave and particle nature of the electron. The particle nature is apparent because we see from the image that individual electrons have a well-defined position when they interact with the detector (that is because the detector measures the position, collapsing the wavefunction). The wave nature is apparent because there is a diffraction pattern in the density of electrons.
The whole concept of wave-particle duality is a very outdated one. The reality is that everything is fundamentally wavelike. However, sometimes the waves can take the form of a 'wave packet' in a what's known as a coherent state. These coherent states behave as if they were a classical particle, but really it's just a complex interaction between a superposition of waves that looks like it's behaving classically.
Heisenberg's uncertainty principle refers to simultaneous measurements of different physical properties (as has been pointed out here, experiments may very well show particle and wave behaviour of the same entity), and is a consequence of quantum logic: non-commuting observables are incompatible physical properties, meaning they cannot exist in conjunction, so they cannot be measured simultaneously.