According to our current understanding of physics, there is no well-established minimum possible length of time similar to the Planck length. The Planck length arises from combining fundamental constants such as the speed of light, the gravitational constant, and Planck's constant, in a way that provides a natural scale for the fabric of spacetime. It represents a length scale below which our current theories of physics break down, and it is often associated with the scale at which quantum gravitational effects become important.
However, when it comes to time, the concept of a minimum possible duration is not as clear. Time in modern physics is treated as a continuous parameter rather than being quantized like particles or energy. The most successful theories in physics, such as general relativity and quantum mechanics, do not inherently impose a minimum time interval.
That being said, some approaches to quantum gravity, such as loop quantum gravity and certain formulations of string theory, suggest the possibility of discrete or quantized structures at the fundamental level, including the notion of discrete or "quantum" time. These ideas propose that spacetime itself may have a discrete structure at extremely small scales. However, these theories are still highly speculative and the existence of a minimum time interval is not yet confirmed by experimental evidence.
It's important to note that our understanding of fundamental physics is still incomplete, especially when it comes to unifying quantum mechanics and gravity. As future research and discoveries unfold, we may gain a deeper understanding of the nature of time and whether it has a fundamental granularity.