Long-distance coherent coupling in a quantum dot array

Journal name:
Nature Nanotechnology
Year published:
Published online


Controlling long-distance quantum correlations is central to quantum computation and simulation. In quantum dot arrays, experiments so far rely on nearest-neighbour couplings only, and inducing long-distance correlations requires sequential local operations. Here, we show that two distant sites can be tunnel-coupled directly. The coupling is mediated by virtual occupation of an intermediate site, with a strength that is controlled via the energy detuning of this site. It permits a single charge to oscillate coherently between the outer sites of a triple dot array without passing through the middle, as demonstrated through the observation of Landau–Zener–Stückelberg interference. The long-distance coupling significantly improves the prospects of fault-tolerant quantum computation using quantum dot arrays, and opens up new avenues for performing quantum simulations in nanoscale devices.

At a glance


  1. Linear array of three quantum dots and real-time tunnelling measurements.
    Figure 1: Linear array of three quantum dots and real-time tunnelling measurements.

    a, SEM image of a sample identical to the one used for the measurements. Dotted circles indicate quantum dots, squares indicate Fermi reservoirs in the 2DEG, which are contacted through ohmic contacts. Both the current through (white arrow) and the reflectance of the SQD are monitored and used to determine the occupancies of the triple quantum dot. b, Numerical derivative (along the VLP axis) of current through the SQD as a function of the voltages on gates LP and RP, mapping out a charge stability diagram of the triple dot in the few-electron regime. The (0,0,0)–(0,1,0) charging transition appears fragmented because of low tunnelling rates from the reservoirs to the centre dot. c, Real-time traces of the sensing dot reflectometry signal, taken at points L, R and C as indicated in b. We use a 50 kHz low-pass filter (Avens Signal Equipment AP220) to filter the reflectometry signal to obtain sufficient signal-to-noise.

  2. Co-tunnelling between outer dots.
    Figure 2: Co-tunnelling between outer dots.

    a,b, Schematic representations of the co-tunnelling process in terms of the relevant electrochemical potentials in the linear dot array. The two panels illustrate the two possible pathways for co-tunnelling between and , as explained in the main text.

  3. Real-time tunnelling.
    Figure 3: Real-time tunnelling.

    a, Real-time traces of the SQD reflectometry signal, taken at zero detuning between the outer dot levels, for three values of VMP corresponding to three values of δ1 and δ2. b, Plot of the measured co-tunnelling rate Γ versus detuning δ1. The non-monotonous dependence is a clear indication that the transfer proceeds via co-tunnelling. This is corroborated by the fact that the measured data points can be fitted well with the predicted expression for Γ (red curve). To make the fit, we rewrite equation (1) as , where a, b, c and d are positive constants. For the detuning axis, gate voltages are converted to energies using microwave-induced sidebands as an energy reference (Supplementary Section S6). The error bars on the obtained values for Γ include errors associated with the threshold analysis of the real-time traces (low-frequency noise modulates the baseline signal, so the precise value of the threshold slightly affects the statistics) and sampling errors due to the finite number of transfer events per trace29 (we sample over 100 ms traces). Note that the use of a low-pass filter results in an overall underestimation of Γ.

  4. Microwave-driven transitions.
    Figure 4: Microwave-driven transitions.

    a, Schematic view of PAT processes between different pairs of dots. Charges can be transferred from one dot to another when the detuning between the corresponding electrochemical potentials matches the photon energy. The left and middle panels correspond to PAT, and the right panel corresponds to PACT. Note that similar resonances to the ones shown exist for negative detunings. b, Charge stability diagram in the same configuration as in Fig. 1b, but now with microwave excitation (15 GHz) applied via a bias-tee to gate LP. The microwaves were chopped at the reference frequency of a lock-in amplifier and combined with a small-amplitude modulation of the same reference frequency. The colourscale data are the numerical derivative (along the VLP axis) of the SQD signal acquired via the lock-in amplifier. Multiple sidebands develop where PAT or PACT occurs.

  5. LZS interference.
    Figure 5: LZS interference.

    a, Schematic energy level diagram as a function of detuning between and , displaying an avoided crossing due to co-tunnel coupling. Red arrows represent the response of the system to microwaves modulating the detuning. Multiple passings of the avoided crossing result in quantum interference of the two paths. b, Numerical derivative (along the detuning axis) of the lock-in signal of ISQD (as in Fig. 4b) as a function of detuning and microwave power. LZS interference fringes are clearly visible along both axes.


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Author information


  1. Kavli Institute of Nanoscience, TU Delft, 2600 GA Delft, The Netherlands

    • F. R. Braakman,
    • P. Barthelemy &
    • L. M. K. Vandersypen
  2. Solid State Physics Laboratory, ETH Zürich, 8093 Zürich, Switzerland

    • C. Reichl &
    • W. Wegscheider


F.R.B. performed the experiment. C.R. and W.W. grew the heterostructure. F.R.B. fabricated the sample. F.R.B. and P.B. carried out the data analysis. F.R.B., P.B and L.M.K.V. contributed to interpretation of the data and commented on the manuscript. F.R.B. and L.M.K.V. wrote the manuscript.

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