A colloidal suspension of active Brownian particles (ABPs) driven by controllable forces into directed or persistent motions can serve as a model for understanding the biological systems. Experiments and numerical simulations are established to investigate the motions of an ABP, a single, induced-charge electrophoretic (ICEP) metallic Janus particle, confined in a quadratic potential well. On the one hand, 1-D position histograms of the trapped active particle, behaving differently from that of a Boltzmann distribution, reveal a splitting from a single peak of the ABP positional distribution to a bimodal distribution. Decoupling the thermal and non-thermal contributions from the overall histogram is non-trivial. However, the two contributions can be examined by convoluting numerically generated thermal and non-thermal contributions into a full histogram. On the other hand, temporal fluctuations analyzed by the power spectral density (PSD), reveal two unique frequencies characterizing the stiffness of the trap and the rotational diffusion of the particle, respectively. Connections between the spatial and temporal fluctuations are obtained by the separate analysis of the temporal and spatial fluctuations of an ABP trapped in a quadratic potential well. This study reveals how thermal and nonthermal fluctuations play against each other in a confined environment.
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