Microcavity controlled coupling of excitonic qubits

Abstract

Controlled non-local energy and coherence transfer enables light harvesting in photosynthesis and non-local logical operations in quantum computing. This process is intuitively pictured by a pair of mechanical oscillators, coupled by a spring, allowing for a reversible exchange of excitation. On a microscopic level, the most relevant mechanism of coherent coupling of distant quantum bits--like trapped ions, superconducting qubits or excitons confined in semiconductor quantum dots--is coupling via the electromagnetic field. Here we demonstrate the controlled coherent coupling of spatially separated quantum dots via the photon mode of a solid state microresonator using the strong exciton-photon coupling regime. This is enabled by two-dimensional spectroscopy of the sample's coherent response, a sensitive probe of the coherent coupling. The results are quantitatively understood in a rigorous description of the cavity-mediated coupling of the quantum dot excitons. This mechanism can be used, for instance in photonic crystal cavity networks, to enable a long-range, non-local coherent coupling.

Figure 1. Characterization of the investigated quantum dot - micropillar system.

(a) Sketch of the micropillar structure including the light coupling from the top facet. (b) Temperature-dependent photoluminescence spectral intensity under non-resonant excitation on a linear grey scale black (0) to white (maximum). The bare resonance energies of excitons and the cavity mode (white dotted lines and dashed line, respectively), and the coupled polariton energies (solid lines) obtained from a Lorentzian lineshape fit and modelling (see Supplementary Note 2) are overlayed to the data. The corresponding average detuning δ (see equation 1) is shown on the upper axis scale. (c) Coupled resonance linewidths (measured: symbols, modelling: lines). Colours and linestyles as in b.

Figure 2. Level scheme and relevant transitions.

The level scheme of the Tavis-Cummings ladder of the three exciton-one cavity system, and transitions relevant for the coherent FWM response, for δ=−29 μeV. (a) Coherence created by the pulse arriving first (E₁ for , E₂ for ). (b) Transitions emitting FWM after the arrival of the second pulse.

Figure 3. Coherent dynamics measured in four-wave mixing.

Delay time dependence of the coherent response for T=19 K (top) and T=13.5 K (bottom). Spectrally resolved FWM power , measured (a,f) and predicted (b,g), on a logarithmic colour scale over four orders of magnitude. Time-resolved FWM power , measured (c,h) and predicted (d,i) over three orders. (e,j) Time-integrated FWM power , measured (black circles) and predicted (red line), and measured (blue triangles). The noise of is given as open circles.

Figure 4. Cavity-mediated coherent coupling revealed by two-dimensional FWM.

Two-dimensional FWM at T=19 K with  meV. measured and phase corrected (a) and predicted with (b) and without (c) phase correction. The amplitude is given as height, while the phase is given as hue of the surface colour, as indicated. The white line shows the diagonal on the surface. (d–f) As (a–c), but showing the post-selected . Different representations of the data are shown in Supplementary Figs S10 and S11.