  We propose that n-type semiconductor quantum dots with the Rashba and
Dresselhaus spin orbit interactions may be used for single electron
manipulation through adiabatic transformations between degenerate states. All
the energy levels are discrete in quantum dots and possess a double degeneracy
due to time reversal symmetryin the presence of the Rashba and/or Dresselhaus
spin orbit coupling terms. We find that the presence of double degeneracy does
not necessarily give rise to a finite non-Abelian (matrix) Berry phase. We show
that a distorted two-dimensional harmonic potential may give rise to
non-Abelian Berry phases. The presence of the non-Abelian Berry phase may be
tested experimentally by measuring the optical dipole transitions.
