Probing Two Driven Double Quantum Dots Strongly Coupled to a Cavity

Si-Si Gu, Sigmund Kohler, Yong-Qiang Xu, Rui Wu, Shun-Li Jiang, Shu-Kun Ye, Ting Lin, Bao-Chuan Wang, Hai-Ou Li, Gang Cao, and Guo-Ping Guo

Phys. Rev. Lett. 130, 233602 – Published 9 June 2023

Abstract

We experimentally and theoretically study a driven hybrid circuit quantum electrodynamics (cQED) system beyond the dispersive coupling regime. Treating the cavity as part of the driven system, we develop a theory applicable to such strongly coupled and to multiqubit systems. The fringes measured for a single driven double quantum dot (DQD)-cavity setting and the enlarged splittings of the hybrid Floquet states in the presence of a second DQD are well reproduced with our model. This opens a path to study Floquet states of multiqubit systems with arbitrarily strong coupling and reveals a new perspective for understanding strongly driven hybrid systems.

Received 20 December 2022
Accepted 3 May 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.233602

Physics Subject Headings (PhySH)

Landau-Zener effect Quantum circuits Quantum interference effects Semiconductor quantum optics

Double quantum dots

Cavity resonators

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Si-Si Gu^1,2, Sigmund Kohler ^3,*, Yong-Qiang Xu^1,2, Rui Wu^1,2, Shun-Li Jiang^1,2, Shu-Kun Ye^1,2, Ting Lin^1,2, Bao-Chuan Wang^1,2, Hai-Ou Li^1,2,4, Gang Cao^1,2,4,†, and Guo-Ping Guo^1,2,4,5,‡

¹CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
²CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
³Instituto de Ciencia de Materiales de Madrid, CSIC, E-28049 Madrid, Spain
⁴Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
⁵Origin Quantum Computing Company Limited, Hefei, Anhui 230088, China

^*sigmund.kohler@csic.es
^†gcao@ustc.edu.cn
^‡gpguo@ustc.edu.cn

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Vol. 130, Iss. 23 — 9 June 2023

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Images

Figure 1
(a) Optical micrograph of the device that is cooled to a temperature of $\sim 20 mK$ . Inset: false-color scanning electron micrograph of ${DQD}_{j}$ which can be tuned by the gate electrodes ${BL}_{j}$ , ${PL}_{j}$ , ${MU}_{j}$ , ${PR}_{j}$ , ${BR}_{j}$ , and ${MD}_{j}$ . The plunger gate ${PL}_{j}$ (red) is connected to the cavity. (b),(c) Charge stability diagrams of ${DQD}_{1}$ and ${DQD}_{2}$ , respectively, as a function of gate voltages measured by the cavity transmission amplitude $| S_{21} |$ , where $(n_{1}, n_{2})$ and $(m_{1}, m_{2})$ denote DQD occupations.
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Figure 2
(a) Schematic view of the approach of Refs. [29, 30]. The system is formed by the energy levels of a single DQD (red) with sweeps induced by the microwave (gray). The cavity transmission is affected mainly when the DQD quasienergies match the cavity frequency. (b) Resulting transmission amplitude $| S_{21} |$ . The black arrow marks out regions in which the transmission is larger than unity, which indicates that the DQD-cavity coupling exceeds the linear-response regime. (c) Theory of this Letter. The full DQD-cavity compound reacts to the excitation by the incoming fields. Red and green lines refer to the lowest DQD and cavity excitation energy, respectively. At the center (mixed color), the interaction hybridizes these states. (d) Corresponding transmission amplitude which obeys $| S_{21} | \leq 1$ . The data are computed for microwave power $P_{j} = - 40 dBm$ which corresponds to the driving amplitude $A_{d, j} = 20.2 μ eV$ . The other parameters are $2 t_{j} / ℏ = 5.2 GHz$ , $g_{j} / 2 π = 85 MHz$ , $f_{d} = 1.4 GHz$ .
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Figure 3
(a) Measured transmission $| S_{21} |$ as a function of detuning $ε_{0, 1}$ and driving power $P_{1}$ for ${DQD}_{1}$ at $2 t_{1} / h \approx 5.2$ with $f_{d} = 1.4 GHz$ . (b) Corresponding theoretical result. The inhomogeneous broadening is considered by a convolution with a Gaussian of width $σ_{ε} = 4 μ eV$ along the $ε_{0, 1}$ axis and $σ_{P} = 0.1 dB$ along the $P_{1}$ axis [22, 28, 54].
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Figure 4
Transmission $| S_{21} |$ as a function of probe frequency $ω_{p} / 2 π$ and detuning $ε_{0, 1}$ for (a) the ${DQD}_{1}$ -cavity system and (b) the two-DQD-cavity system. In (b), $ε_{0, 2}$ is simultaneously varied in the range of $(- 68.3, 68.3) μ eV$ , while $P_{1} = - 39.9$ and $P_{2} = - 42 dBm$ are fixed. Insets: the energy level schematic diagram of the hybrid system. Red, blue, and green colors refer to the states $| e ⟩_{1} | g ⟩_{2} | 0 ⟩$ , $| g ⟩_{1} | e ⟩_{2} | 0 ⟩$ , $| g ⟩_{1} | g ⟩_{2} | 1 ⟩$ , respectively, where $| g ⟩_{j}$ and $| e ⟩_{j}$ denote the ground and excited state of ${DQD}_{j}$ and $| n ⟩$ the $n$ -photon cavity state. (c),(d) Theoretical results with the inhomogeneous broadening used in Fig. 3.
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