Manifestation of fundamental quantum complementarities in time-domain interference experiments with quantum dots: A theoretical analysis

A theoretical analysis is presented showing that fundamental complementarity between the particlelike properties of an exciton confined in a semiconductor quantum dot and the ability of the same system to show interference may be studied in a time domain interference experiment, similar to those currently performed. The feasibility of such an experiment, including required pulse parameters and the dephasing effect of the environment, is studied.

Figure 1

(a) The diagram of energy levels and transitions in the system, assuming that the excitons are confined in neighboring dots with different transition energies. The pulses inducing transitions on the system S have broad spectrum so that both transitions are possible. The pulse acting on the QP system is spectrally selective and tuned to the biexcitonic transition, so that the single-exciton transition is energetically forbidden in this subsystem. (b) The sequence of pulses used in the experiment. (c) Quantum-logic diagram (Ref. 27) of the performed operations. Here $R_{\alpha }=\cos (\alpha ∕2)\mathbb{I}-i\sin (\alpha ∕2){\sigma }_x$. The $R_{\beta }$ rotation on the QP subsystem (dashed box) is applied for optimal measurement of the extracted information in the extended scheme.

Figure 2

Solid line, visibility of interference fringes as a function of the QP pulse area (determining the certainty with which the presence of the exciton is detected). Dashed line, the squares of visibility and distinguishability add to 1. The plotted values are obtained from a simulation of system dynamics, for pulse parameters as discussed in the text, without dephasing.

Figure 3

Upper, the exciton occupation fringe visibility as a function of the a priori amount of extracted knowledge on the exciton occupation for $T_1=T_2∕2=100\mathrm{ps}$ and additional pure dephasing rates as shown (in ${\mathrm{ps}}^{-1}$). Lower, the distinguishability-visibility relation under conditions as above. Left-hand panels show the results for a long QP pulse, and right-hand panels show the results for a short double pulse.