This study reports the experimental observation of higher-order and fractional discrete time crystals (DTCs) in Floquet-driven Rydberg atomic gases. The research demonstrates that these exotic phases of matter, where discrete time translation symmetry is broken into higher-order and non-integer categories, can be observed in a quantum many-body system. The experiments involve using periodic radio-frequency (RF) pulses to drive the system out of equilibrium, leading to complex subharmonic responses. The system's response is found to be periodic with an integral multiple of the driving period, with n ≥ 2, and includes both integer and fractional DTCs. The study shows that the system can transition between adjacent integer DTCs, during which fractional DTCs are investigated. The results align with theoretical predictions and highlight the rich dynamics that can emerge from driven and dissipative systems, offering new insights into non-equilibrium physics. The research team observed multiple n-DTCs with integer values of n = 2, 3, and 4, as well as fractional n-DTCs with n values beyond integers. The system's response transitions between adjacent integer DTCs, and the fractional DTCs are studied. The findings expand the understanding of non-equilibrium dynamics and provide a platform for exploring more complex temporal symmetries. The experiments involved a quantum many-body system of interacting cesium atoms with Rydberg states, driven by an RF field. The system's response was analyzed using Fourier spectroscopy, revealing subharmonic peaks that indicate the presence of DTCs. The results show that the system can exhibit Z_n symmetry (n ≥ 2) protected by Floquet driving. The study also observed the phase transition between distinct DTCs, including the transition from 2-DTC to 3-DTC. The phase transition was characterized by a nonzero order parameter, indicating symmetry breaking. The results show that the system can exhibit fractional DTCs, where the oscillations occur at fractional time intervals. These fractional DTCs are robust against perturbations and are protected by a combination of many-body interactions and Floquet driving. The experiments also revealed the melting effect, where higher-order DTCs become less stable under certain conditions. The findings demonstrate the potential of Floquet-driven Rydberg atomic systems for studying complex temporal symmetries and non-equilibrium dynamics. The results provide a deeper understanding of DTCs and their properties, offering new avenues for exploration in quantum many-body systems. The study highlights the importance of driven and dissipative systems in the emergence of exotic phases of matter and their potential applications in quantum information science and technology.This study reports the experimental observation of higher-order and fractional discrete time crystals (DTCs) in Floquet-driven Rydberg atomic gases. The research demonstrates that these exotic phases of matter, where discrete time translation symmetry is broken into higher-order and non-integer categories, can be observed in a quantum many-body system. The experiments involve using periodic radio-frequency (RF) pulses to drive the system out of equilibrium, leading to complex subharmonic responses. The system's response is found to be periodic with an integral multiple of the driving period, with n ≥ 2, and includes both integer and fractional DTCs. The study shows that the system can transition between adjacent integer DTCs, during which fractional DTCs are investigated. The results align with theoretical predictions and highlight the rich dynamics that can emerge from driven and dissipative systems, offering new insights into non-equilibrium physics. The research team observed multiple n-DTCs with integer values of n = 2, 3, and 4, as well as fractional n-DTCs with n values beyond integers. The system's response transitions between adjacent integer DTCs, and the fractional DTCs are studied. The findings expand the understanding of non-equilibrium dynamics and provide a platform for exploring more complex temporal symmetries. The experiments involved a quantum many-body system of interacting cesium atoms with Rydberg states, driven by an RF field. The system's response was analyzed using Fourier spectroscopy, revealing subharmonic peaks that indicate the presence of DTCs. The results show that the system can exhibit Z_n symmetry (n ≥ 2) protected by Floquet driving. The study also observed the phase transition between distinct DTCs, including the transition from 2-DTC to 3-DTC. The phase transition was characterized by a nonzero order parameter, indicating symmetry breaking. The results show that the system can exhibit fractional DTCs, where the oscillations occur at fractional time intervals. These fractional DTCs are robust against perturbations and are protected by a combination of many-body interactions and Floquet driving. The experiments also revealed the melting effect, where higher-order DTCs become less stable under certain conditions. The findings demonstrate the potential of Floquet-driven Rydberg atomic systems for studying complex temporal symmetries and non-equilibrium dynamics. The results provide a deeper understanding of DTCs and their properties, offering new avenues for exploration in quantum many-body systems. The study highlights the importance of driven and dissipative systems in the emergence of exotic phases of matter and their potential applications in quantum information science and technology.