Radiative Corrections and Quantum Gates in Molecular Systems

We propose a method for quantum information processing using molecules coupled to an external laser field. This utilizes molecular interactions, control of the external field, and an effective energy shift of the doubly excited state of two coupled molecules. Such a level shift has been seen in the two-photon resonance experiments recently reported by Hettich et al. Here we show that this can be explained in terms of the QED Lamb shift. We quantify the performance of the proposed quantum logic gates in the presence of dissipative mechanisms. The unitary transformations required for performing one- and two-qubit operations can be implemented with present day molecular technology. The proposed techniques can also be applied to coupled quantum dot and biomolecular systems.

Figure 1

Eigenstate coefficients ${\alpha }_{ij}$ of the coupled system in the absence and presence of laser pumping as a function of ${\Delta }_{-}$ and detuning ${\Delta }_{+}/2$. The weights of the basis states of the four-level system have been plotted for $V_{12}=950\mathrm{M}\mathrm{H}\mathrm{z}$ [graphs (a) and (c)] and for $V_{12}=10\mathrm{M}\mathrm{H}\mathrm{z}$ [(b) and (d)]. ${\Delta }_{-}=2320\mathrm{M}\mathrm{H}\mathrm{z}$ in graphs (c) and (d). Notice the difference in eigenstates behavior for ${\Delta }_{-}\sim V_{12}$ and ${\Delta }_{-}/V_{12}\gg 1$ [3].

Figure 2

Steady-state density matrix elements as a function of the laser detuning parameter ${\Delta }_{+}/2$. The occupation probabilities give the structure of the resonance fluorescence spectrum, as is shown in (a) for different excitation intensities ${\ell }_i$ and in (b) for different effective shifts ${\Delta }_{ϵ}$; ${\ell }_i\equiv \Omega$, ${\Gamma }_i=50\mathrm{M}\mathrm{H}\mathrm{z}$, ${\Gamma }_{12}=9\mathrm{M}\mathrm{H}\mathrm{z}$, ${\Delta }_{-}/2=1160\mathrm{M}\mathrm{H}\mathrm{z}$, and $V_{12}=950\mathrm{M}\mathrm{H}\mathrm{z}$.

Figure 3

(a) cnot gate operation: a ${\pi }_{{\Omega }_{12}}$ pulse is applied in order to generate the conditional logic $|e_1{g}_2⟩\mapsto |e_1{e}_2⟩$. The corresponding populations are shown as a function of time in the absence and presence of dissipative channels. ${\Delta }_{+}/2=-1319\mathrm{M}\mathrm{H}\mathrm{z}$, ${\Delta }_{-}=-2320\mathrm{M}\mathrm{H}\mathrm{z}$, ${\ell }_i\equiv \Omega =200\mathrm{M}\mathrm{H}\mathrm{z}$, ${\Delta }_{ϵ}=160\mathrm{M}\mathrm{H}\mathrm{z}$, and $V_{12}=50\mathrm{M}\mathrm{H}\mathrm{z}$. (b) Fidelity (see text) in the generation of the MES $\frac{1}{\sqrt{2}}(|g_1{g}_2⟩+|e_1{e}_2⟩)$. The bar signals the end of the applied ${\pi }_{{\Omega }_{12}}$ pulse and indicates a measure of the actual entangled state achieved in the absence and presence of dissipation. Input parameters are as before, except for $\Omega =50\mathrm{M}\mathrm{H}\mathrm{z}$. Decay rates are given in ${10}^6{\mathrm{s}}^{-1}$ units.