Mathematics

Professor Deepak Dhar
IISER Pune

There is a well-known result in quantum mechanics which has been called quantum Zeno effect: a watched quantum pot never boils!
In particular, if you prepare a quantum system in a particular state, and check after every small time interval $Delta t$ if it has decayed to an orthogonal state due to some perturbation, the probability that it has not decayed up to some large time T can be made as close to1 as we please by making $Delta t$ small enough.

I will describe the problem of state-preservation in a quantum system using inverting pulses, with variable time interval, which is a more effective way to suppress quantum transitions. This strategy is potentially very powerful and the probability of state not remaining the same can be made very small. Analysis of the strategy involves solving coupled polynomial equations in many variables. To be precise, we get (2^n -1) specific polynomial equations in n variables, of degree up to n. Amazingly, it turns out that these equations are consistent for all n and they do have a solution. However, the reason for this miracle is quite obscure yet. Finding a nice proof of this result remains a challenge.