We investigate the transition probability rate of a Unruh-DeWitt (UD) detector interacting with massless scalar field for a finite duration of proper time, $T$, of the detector. For a UD detector moving at a uniform acceleration, $a$, we explicitly show that the finite-time transition probability rate can be written as a sum of purely thermal terms, and nonthermal transient terms. While the thermal terms are independent of time, $T$, the nonthermal transient terms depend on $(\mathrm{\Delta }ET)$, $(aT)$, and $(\mathrm{\Delta }E/a)$, where $\mathrm{\Delta }E$ is the energy gap of the detector. Particularly, the nonthermal terms are oscillatory with respect to the variable $(\mathrm{\Delta }ET)$, so that they may be averaged out to be insignificant in the limit $\mathrm{\Delta }ET\gg 1$, irrespective of the values of $(aT)$ and $(\mathrm{\Delta }E/a)$. To quantify the contribution of nonthermal transient terms to the transition probability rate of a uniformly accelerating detector, we introduce a parameter, ${ϵ}_{\mathrm{nt}}$, called the nonthermal parameter. The smaller the nonthermal parameter is, the smaller the contribution due to nonthermal transient terms is, when compared with the purely thermal terms. Demanding the contribution of nonthermal terms in the finite-time transition probability rate to be negligibly small, i.e., ${ϵ}_{\mathrm{nt}}=\delta \ll 1$, we calculate the thermalization time—the time required for the detector to interact with the scalar field to arrive at the required nonthermality, ${ϵ}_{\mathrm{nt}}=\delta$, so that the nonthermal terms to be negligibly small, and the detector to be (almost) thermalized with the Unruh bath in its comoving frame. Specifically, for small accelerations, $a\ll \mathrm{\Delta }E$, we find the thermalization time, ${\tau }_{\mathrm{th}}$, to be ${\tau }_{\mathrm{th}}\sim (\mathrm{\Delta }E{)}^{-1}\times {\mathrm{e}}^{2\pi |\mathrm{\Delta }E|/a}/\delta$, and for large accelerations, $a\gg \mathrm{\Delta }E$, we find the thermalization time to be ${\tau }_{\mathrm{th}}\sim (\mathrm{\Delta }E{)}^{-1}/\delta$. We comment on the possibilities of bringing down the exponentially large thermalization time at small accelerations, $a\ll \mathrm{\Delta }E$.

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• Quantum fields in curved spacetime
• Unruh effect