PACS 78.47.+p, 78.67.Hc Temperature dependence of the homogeneous linewidth of CuBr quantum dots in glass and NaBr matrices and CdSe quantum dots in glass matrix has been investigated using heterodyne-detected accumulated photon echo. We can reproduce the observed nonlinear temperature dependence considering two characteristic mechanisms: the small energy excitation in two-level system and the two-phonon Raman process of confined acoustic phonons. The interaction with the two-level system is dominant below 15 K and 10 K for CuBr and CdSe quantum dots, respectively. Above these temperatures the interaction with confined phonons is dominant. These results are similar to those of a previous study of CuCl quantum dots in glass, showing the universal influence of confined phonons and surrounding matrices on the lowtemperature dephasing process of very small semiconductor quantum dots.1 Introduction Semiconductor quantum dots (QDs) are promising candidates for all optical implementation of quantum information processing because of their sharp discrete spectra and very long dephasing time [1,2]. Dephasing time ranging from tens of picoseconds to a nanosecond of I -VII, II-VI and III-V semiconductor QDs are reported recently [3 -7]. From the fundamental physical point of view, it is most important to fully understand the mechanism which restricts the optical coherence time. So far, temperature dependence of homogeneous linewidth has been widely investigated to clarify the dephasing mechanism of QDs, however, serious difference was present in understanding them. Linear temperature broadening or activation type nonlinear temperature broadening was contradictorily reported in the selfassembled quantum dots [3,4]. On the other hand, two-phonon Raman process of confined acoustic phonons was reported in CuCl QDs in the weak confinement regime [5,6]. In Ref.[5], smaller energy excitation process in the two-level system (TLS), which is related to surrounding matrix of QDs, was proposed besides. Two-acoustic-phonon process alone was also reported in CdSe QDs embedded in polymer [7]. The possible difference between these results seems to arise from the different condition whether phonon confinement occurs or not. To clarify the role of confined phonon and surrounding matrix, which should affect the homogeneous linewidth for very small quantum dots, systematic investigation is needed using different kinds of QDs whose acoustic phonons are confined. In this work, we studied CuBr QDs in NaBr and glass matrices in the weak or intermediate confinement regime as well as CdSe QDs in glass matrix in the strong confinement regime at very low temperatures.