Spontaneous symmetry breaking is a fundamental concept in many areas of physics. The (space) crystals, superconductors and ferromagnets are respective examples of continuous space translation, gauge and rotational invariance breaking. Despite its popularity, the idea of breaking the discrete time-translation symmetry (DTTS) has received attention only very recently and manifested in the form of the discrete time crystals (DTCs) [1–4]. It was shown that isolated periodically driven ultracold atoms [2] are able to spontaneously self–reorganise their motion leading to DTTS breaking. Here I focus on these kinds of systems bouncing resonantly on an oscillating atom mirror with the interaction between atoms greater than a critical value. Such a driven cloud of ultracold atoms moves with a period s-times longer than that of the mirror (s:1 resonance condition of motion is fulfilled) due to DTTS breaking, and the so-called s-tupling discrete time crystals is formed. In this talk I will intuitively introduce the concept of discrete time-translation symmetry breaking and DTCs based on the comparison with space crystals. Later in the talk I will summarize investigations of quantum many-body fluctuations of DTCs within the Bogoliubov theory and demonstrate that DTCs are resistant to quantum many-body effects. [1] F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012)[2] K. Sacha, Phys. Rev. A 91, 033617 (2015)[3] V. Khemani et al., Phys. Rev. Lett. 116, 250401 (2016)[4] D. Else et al., Phys. Rev. Lett 117, 090402 (2016)
