Cavity-Mediated Coherent Coupling between Distant Quantum Dots

Giorgio Nicolí, Michael Sven Ferguson, Clemens Rössler, Alexander Wolfertz, Gianni Blatter, Thomas Ihn, Klaus Ensslin, Christian Reichl, Werner Wegscheider, and Oded Zilberberg

Phys. Rev. Lett. 120, 236801 – Published 7 June 2018

Abstract

Scalable architectures for quantum information technologies require one to selectively couple long-distance qubits while suppressing environmental noise and cross talk. In semiconductor materials, the coherent coupling of a single spin on a quantum dot to a cavity hosting fermionic modes offers a new solution to this technological challenge. Here, we demonstrate coherent coupling between two spatially separated quantum dots using an electronic cavity design that takes advantage of whispering-gallery modes in a two-dimensional electron gas. The cavity-mediated, long-distance coupling effectively minimizes undesirable direct cross talk between the dots and defines a scalable architecture for all-electronic semiconductor-based quantum information processing.

Received 22 December 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.236801

Physics Subject Headings (PhySH)

Coulomb blockade Local density of states Quantum transport

Quantum dots Two-dimensional electron gas

Exact diagonalization Transport techniques

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Giorgio Nicolí¹, Michael Sven Ferguson², Clemens Rössler³, Alexander Wolfertz¹, Gianni Blatter², Thomas Ihn¹, Klaus Ensslin¹, Christian Reichl¹, Werner Wegscheider¹, and Oded Zilberberg²

¹Solid State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
²Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
³Infineon Technologies Austria, Siemensstraße 2, 9500 Villach, Austria

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Vol. 120, Iss. 23 — 8 June 2018

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Images

Figure 1
(a) Scanning electron micrograph of the device; bright features are metallic top gates. Negative voltages can be applied to all the gates, with labels indicating those explicitly discussed in the text. The (yellow) circles mark the two quantum dots. A numerically calculated local density of states map (using kwant [32]) of a whispering-gallery cavity mode close to the Fermi energy, $ϵ_{F} = 7.85 meV$ is shown as an overlay. The three boxes ( $S$ ), ( $D$ ), and ( $R$ ) label Ohmic contacts to the two-dimensional electron gas. The contact to reservoir ( $R$ ) is grounded at all times, while the other two are connected to dc voltage sources. The sign of the measured currents $I_{S}$ , $I_{D}$ , and $I_{R}$ is positive when electrons flow in the direction of the arrows. (b) Schematic energy diagram of the full dot-cavity-dot system including the confined energy levels of the two dots (black solid lines), the continuous electronic dispersion in the leads (gray boxes), and the cavity modes (black dashed lines). Full black arrows indicate coherent tunneling within the dot-cavity-dot hybrid, dotted arrows are tunneling events into either of the dots from the source or drain leads, and the wiggly green arrows represent electron relaxation to the chemical potential in the reservoir. In addition to these couplings, the different parameters of the system are the charging energies $U_{1} ≃ U_{2} ≃ 1 meV$ of dots 1 and 2, respectively, the chemical potentials $μ_{α}$ of the source, reservoir and drain ( $α = S$ , $R$ , $D$ ), and the cavity level spacing $δ_{cav}$ . (c) Transport spectroscopy of the dot-cavity system (experiment I). Vertical lines correspond to transport through resonances of the left dot, while the diagonal lines are identified as cavity modes. Avoided crossings between these two sets of features are evidence of dot-cavity hybridization [23, 24, 25]. The sketch on the right indicates the gates used for this experiment. As indicated by (A), the splitting of cavity features due to its charging energy $U_{cav}$ cannot be resolved because of the broadening of the cavity resonances. The offset indicated by (B) defines an upper bound on the dot-cavity electrostatic interaction $U_{dot-cav}$ .
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Figure 2
(a)–(c) Spectroscopy of the dot-cavity-dot system exhibiting long-distance coupling between the two dots [experiment II; a small bias is simultaneously applied with respect to the reservoir ( $R$ ) to the source ( $S$ ) and drain ( $D$ ) leads; the three measured currents are indicated and color coded in Fig. 1]. The (gray) boxes in (a) and (c) indicate dot-cavity-dot coupling-related features, corresponding to transport category (iii) (see discussion in the text), i.e., avoided crossings between vertical and horizontal resonances. The charging energy of the two dots $U_{i}$ ( $i = 1$ , 2) is highlighted in (b). The (blue) points correspond to the peak position of the Coulomb resonances. Several avoided crossings appear, one of them indicated by the (white) arrows, which provides the effective tunnel coupling $t_{eff} \sim 480 μ eV$ . The (green) dashed circle in the bottom-left corner belongs to transport category (i) where the two resonances associated with the left and right dot are decoupled [with the individual resonances visible in (a) and (c), respectively]. This crossing constrains the interdot charging energy to be negligibly small (C). The dashed diagonal lines refer to a transport signature of type (ii). (d),(e) Transport measurements of the same system as in experiment II, but with asymmetric tunnel barriers (experiment III). Weaker (d) and stronger (e) coupling regimes of the dot-cavity-dot hybrid are probed [symbols refer to the same quantities as in (b)]. The upper-left insets sketch which gates are active for each measurement.
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Figure 3
Transport through a hybrid system consisting of a twice extended electronic cavity that couples next-nearest-neighbor quantum dots (experiment IV). The bottom-right inset schematically shows the gates’ configuration for the experiment [33]. Similar to experiment II, we find horizontal and vertical type (i) resonances due to separate transport through the energy levels of the two dots. Avoided crossings of type (iii), appear at the intersection between specific resonances; see the magnified upper-left inset (black arrows). These are a clear signature for coherent dot-cavity-dot coupling [33]. The (blue) dashed lines are guides to the eye.
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