Abstract

Wave function control and engineering has reached an advanced level in atomic and molecular physics. Examples include the creation of a localized wave packet in a Rydberg atom [1] as well as a full characterization of a wave function by its amplitude and phase[2]. Recent developments in studies of quantum dot excitons in semiconductors have shown similarities with atoms including features such as very narrow linewidths, homogeneous broadening [3] and excited states. In this work we apply wave function control techniques and demonstrate the first step towards wave function engineering in this single quantum system. Fig. a) shows the discrete energy manifold of the quantum dot. The excited eigenstate E₁ is split into two states due to symmetry breaking in the dot leading to X and Y polarized states with a splitting of 60 μeV, see inset. Excitation of the X state with a pair of phase locked laser pulses gives rise to the photoluminescence (PL) detected quantum interferogram[4] as a function of the optical delay between the pulses in Fig. b). The PL, proportional to the absolute square of the excited state E₁ wave function, not only demonstrates coherent control of the population, but the decay of the envelope as a function of time delay measures the dephasing time. The measured value of T₂ ~ 40 ps is in excellent agreement with the linewidth of 17 μeV. This type of wave function interferometry, which in this case is a wave function autocorrelation measurement, represents a way to control the excitation amplitudes via quantum interference between two quantum mechanical path ways. In Fig. c) we show the result of exciting a coherent superposition of the X and Y states, see inset. The envelope of the wave function autocorrelation is now modulated with the first maximum at zero delay and with an oscillation periode of T_osc ~ 69 ps in agreement with the splitting between the two eigenstates. This demonstrates a measurement of the time evolution of the non-stationary wavefunction. In the last example in Fig d) the polarization of the second pulse is rotated 90 degrees with respect to the first pulse, see inset The second wave function is now 180 degrees shifted relative to the first wave function. A measurement of the cross-correlation function shows this phase shift in the interferogram. The oscillation is now a minimum at zero delay and a maximum at T_osc/2. The interference at zero delay in Fig. d) is not complete because the X-Y oscillator strengths are different. With these applications of wave function engineering techniques to semiconductor quantum dots we have brought coherent control to the ultimate quantum limit of a single exciton per control box Fig. a) The PL from the quantum dot exciton ground state E„ and corresponding PL excitation spectrum. The inset shows the splitting between the linearly polarized eigenstates of the excited stale E, b) The coherent control experiment exciting the X state measures tire dephasing lime 1. Compared to the laser pulse autocorrelation the quantum interference is evident, c) Exciting both the X and the Y slate in phase, see inset, the envelope of the decay is now modulated corresponding to the X-Y splitting, d) Exciting X and Y with the polarization of the second pulse rotated 90 degrees shows a modulation of the envelope that is 180 degrees out of phase with the measurement in Fig c)

© 1998 IEEE