Landau-Zener interferometry of valley-orbit states in Si/SiGe double quantum dots

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Landau-Zener interferometry of valley-orbit states in Si/SiGe double quantum dots

X. Mi, S. Kohler, and J. R. Petta

Phys. Rev. B 98, 161404(R) – Published 12 October 2018

Abstract

Electrons confined in Si quantum dots possess orbital, spin, and valley degrees of freedom (DOF). We perform Landau-Zener-Stückelberg-Majorana (LZSM) interferometry on a Si double quantum dot that is strongly coupled to a microwave cavity to probe the valley DOF. The resulting LZSM interference pattern is asymmetric as a function of level detuning and persists for drive periods that are much longer than typical charge decoherence times. By correlating the LZSM interference pattern with charge-noise measurements, we show that valley-orbit hybridization provides some protection from the deleterious effects of charge noise. Our work opens the possibility of harnessing the valley DOF to engineer charge-noise-insensitive qubits in Si.

Received 17 May 2018
Revised 3 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.161404

Physics Subject Headings (PhySH)

Landau-Zener effect Quantum interference effects Valleytronics

Double quantum dots Quantum dots Superconducting devices

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

X. Mi^1,*, S. Kohler², and J. R. Petta^1,†

¹Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Instituto de Ciencia de Materiales de Madrid, CSIC, E-28049 Madrid, Spain

^*Present address: Google Inc., Santa Barbara, California 93117, USA.
^†petta@princeton.edu

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Vol. 98, Iss. 16 — 15 October 2018

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Images

Figure 1
(a) Optical image of the superconducting cavity. (b) Tilted-angle false-color scanning electron microscope image of the DQD. (c) Experiment schematic: The DQD is probed by a cavity photon with energy $h f$ and interferometry is performed by periodically driving the detuning parameter $ε (t)$ . (d) Cavity transmission amplitude $A / A_{0}$ as a function of $V_{P1}$ and $V_{P2}$ near the $(1, 0) \leftrightarrow (0, 1)$ interdot transition. (e) Left panel: $A / A_{0}$ as a function of $ε$ and $f$ . Right panel: $A / A_{0}$ as a function of $f$ at $ε = 0$ . The lever-arm conversion between gate voltage and energy is $α = Δ ε / Δ V_{P1} = 72 μ eV / mV$ [26].
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Figure 2
(a) LZSM interference pattern obtained by measuring $A / A_{0}$ as a function of $ε_{0}$ and $e V_{ac}$ . Inset: Theoretical predictions plotted using the same color scale and axes range as the experimental data. (b) DQD energy-level diagram calculated with $E_{L} = 37.5 μ eV$ , $E_{R} = 38.3 μ eV$ , $t = 25.4 μ eV$ , and $t^{'} = 11.8 μ eV$ . The gray dashed lines show the energy levels with $t = t^{'} = 0$ . (c) Transition frequency between the two lowest-energy states $E_{VO} / h$ as a function of $ε$ . The cavity frequency $f_{c}$ is denoted with a black dashed line. The qubit-cavity detuning $E_{VO} / h - f_{c} ≫ g_{VO} / 2 π$ and has a minimum of 55 MHz at $ε = 0$ . The red curve represents the detuning trajectory when $e V_{ac} \approx E_{L,R}$ , which is confined to the parabolic parts of $E_{VO} (ε) / h$ (shaded in red). The green curve represents the detuning trajectory when $e V_{ac} ≫ E_{L,R}$ , where the detuning trajectory samples flat parts of $E_{VO} (ε) / h$ as well (shaded in green). For comparison, the gray dashed line shows the transition frequency of a two-level charge qubit $E_{CQ} / h = \sqrt{ε^{2} + 4 t_{c}^{2}} / h$ with $t_{c} = 16.2 μ eV$ .
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Figure 3
(a) Histograms showing the out-of-phase component of the cavity output field $Q$ sampled at a frequency of 250 kHz over 1 s at $ε = - 8 μ eV$ (cyan) and $ε = - 60 μ eV$ (red). Black lines are fits to Gaussian functions. The inset shows $Q (ε)$ and the colored dots represent the locations where the histograms are taken. $e V_{ac} = 0$ for these measurements. (b) Power spectral density of the noise in $ε$ , $S_{ε} (f)$ , with a fit to $S_{ε} (f) \approx S_{0} {[(1 Hz) / f]}^{β}$ . $S_{ε} (f)$ is too small to be resolved beyond $f = 1$ kHz using this method.
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Figure 4
(a) $A / A_{0}$ as a function of $ε_{0}$ and $e V_{ac}$ , with $f_{g} = 100$ MHz. (b) Theoretically predicted LZSM interference patterns obtained from a four-level valley-orbit model (left) and a standard two-level charge qubit model (right). The color scale is the same as in (a). (c) $A / A_{0}$ as a function of $e V_{ac}$ , taken along the dashed lines in (a) and (b). The experimental data and calculation based on valley-orbit states are plotted along the bottom $x$ axis, whereas the calculation based on a charge qubit is plotted along the top $x$ axis.
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