Frequency estimation by frequency jumps

The frequency of a quantum harmonic oscillator cannot be precisely determined through static measurement strategies on a prepared state. Therefore, dynamical procedures must be employed, involving measurements taken after the system has evolved and encoded the frequency information. This paper explores the precision achievable in a protocol where a known detuning suddenly shifts the oscillator's frequency, which then reverts to its original value after a specific time interval. Our results demonstrate that the squeezing induced by this frequency jump can effectively enhance the encoding of frequency information, significantly improving the quantum signal-to-noise ratio (QSNR) compared to standard free evolution at the same resource (energy and time) cost. The QSNR exhibits minimal dependence on the actual frequency and increases with both the magnitude of the detuning and the overall duration of the protocol. Furthermore, incorporating multiple frequency jumps into the protocol could further enhance precision, particularly for lower frequency values.