We study the effects of an intermittent harmonic potential of strength $mu = mu_0 u$ -- that switches on and off stochastically at a constant rate $gamma$, on an overdamped Brownian particle with damping coefficient $ u$. This can be thought of as a realistic model for realisation of stochastic resetting. We show that this dynamics admits a stationary solution in all parameter regimes and compute the full time dependent variance for the position distribution and find the characteristic relaxation time. We find the exact non-equilibrium stationary state distributions in the limits -- (i) $gammallmu_0 $ which shows a non-trivial distribution, in addition as $mu_0toinfty$, we get back the result for resetting with refractory period; (ii) $gammaggmu_0$ where the particle relaxes to a Boltzmann distribution of an Ornstein-Uhlenbeck process with half the strength of the original potential and (iii) intermediate $gamma=2nmu_0$ for $n=1, 2$. The mean first passage time (MFPT) to find a target exhibits an optimisation with the switching rate, however unlike instantaneous resetting the MFPT does not diverge but reaches a stationary value at large rates. MFPT also shows similar behavior with respect to the potential strength. Our results can be verified in experiments on colloids using optical tweezers.
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