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arXiv:2006.14531 · Physical Review Research

On-demand generation of higher-order Fock states in quantum-dot–cavity systems

M. Cosacchi, J. Wiercinski, T. Seidelmann, Moritz Cygorek, A. Vagov, D. E. Reiter, V. M. Axt

Published Sep 24, 2020• 29 citations
arXivHTMLPDF

Abstract

The on-demand preparation of higher-order Fock states is of fundamental importance in quantum information sciences.We propose and compare different protocols to generate higher-order Fock states in solid state quantum-dot-cavity systems.The protocols make use of a series of laser pulses to excite the quantum dot exciton and off-resonant pulses to control the detuning between dot and cavity.Our theoretical studies include dot and cavity loss processes as well as the pure-dephasing type coupling to longitudinal acoustic phonons in a numerically complete fashion.By going beyond the two-level approximation for quantum dots, we study the impact of a finite exchange splitting, the impact of a higher energetic exciton state, and an excitation with linearly polarized laser pulses leading to detrimental occupations of the biexciton state.We predict that under realistic conditions, a protocol which keeps the cavity at resonance with the quantum dot until the desired target state is reached is able to deliver fidelities to the Fock state |5 well above 40%.

DOI
10.1103/physrevresearch.2.033489

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The effect of phonons on a nonlinear optical response of a quantum dot-cavity system in quantum strong coupling regime can be accounted for by a fully analytical treatment, provided that the exciton-phonon dynamics is much faster than the exciton-cavity dynamics. Modern experiments involving semiconductor quantum dots embedded in optical microcavities typically meet this criterion. We find that, for a relatively small exciton-cavity coupling, the effect of phonons is concentrated mainly in the polaron shift of the exciton frequency and reduction of exciton-cavity coupling by the Huang-Rhys factor. We have generalized this result to an arbitrary optical nonlinearity and demonstrated a good agreement with the exact solution in a wide range of temperatures. This generalization provides access to higher rungs of the Jaynes-Cummings ladder, where exact numerical approaches are impractical or even impossible. At larger coupling strengths and low temperatures, our approximation is also in good agreement with the exact solution, which makes it a very useful tool for addressing the phonon contribution to the coherent dynamics of a nonlinear optical system. We demonstrate our results for third-order optical polarization with varying observation time and delay time between excitation pulses in the form of two-dimensional spectra. These spectra provide useful information about the coherent coupling between the exciton and the cavity modes. The presented analytical approach is also compared with another useful approximation, having the form of a matrix product, which is a special case of the asymptotically exact solution in the limit of a short phonon memory time.
We demonstrate the simultaneous dressing of both vacuum-to-exciton and exciton-to-biexciton transitions of a single semiconductor quantum dot in a high-Q micropillar cavity, using photoluminescence spectroscopy. Resonant two-photon excitation of the biexciton is achieved by spectrally tuning the quantum dot emission with respect to the cavity mode. The cavity couples to both transitions and amplifies the Rabi frequency of the likewise resonant continuous wave laser, driving the transitions. We observe strong-field splitting of the emission lines, which depend on the driving Rabi field amplitude and the cavity-laser detuning. A dressed state theory of a driven 4-level atom correctly predicts the distinct spectral transitions observed in the emission spectrum, and a detailed description of the emission spectra is further provided through a polaron master equation approach which accounts for cavity coupling and acoustic phonon interactions of the semiconductor medium.
We investigate theoretically the temporal behavior of a quantum dot under off-resonant optical excitation targeted at fast acoustic phonon-assisted state preparation. We demonstrate that in a preparation process driven by short laser pulses, three processes can be identified: a dressing of the states during the switch-on of the laser pulse, a subsequent phonon-induced relaxation, and an undressing at the end of the pulse. By analyzing excitation scenarios with different pulse shapes we highlight the decisive impact of an adiabatic undressing on the final state in short-pulse protocols. Furthermore, we show that in exciton-biexciton systems the laser characteristics such as the pulse detuning and the pulse length as well as the biexciton binding energy can be used to select the targeted quantum dot state.
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