Controllable Switching between Superradiant and Subradiant States in a 10-qubit Superconducting Circuit

Zhen Wang, Hekang Li, Wei Feng, Xiaohui Song, Chao Song, Wuxin Liu, Qiujiang Guo, Xu Zhang, Hang Dong, Dongning Zheng, H. Wang, and Da-Wei Wang

Phys. Rev. Lett. 124, 013601 – Published 2 January 2020

Abstract

Superradiance and subradiance concerning enhanced and inhibited collective radiation of an ensemble of atoms have been a central topic in quantum optics. However, precise generation and control of these states remain challenging. Here we deterministically generate up to 10-qubit superradiant and 8-qubit subradiant states, each containing a single excitation, in a superconducting quantum circuit with multiple qubits interconnected by a cavity resonator. The $\sqrt{N}$ -scaling enhancement of the coupling strength between the superradiant states and the cavity is validated. By applying an appropriate phase gate on each qubit, we are able to switch the single collective excitation between superradiant and subradiant states. While the subradiant states containing a single excitation are forbidden from emitting photons, we demonstrate that they can still absorb photons from the resonator. However, for an even number of qubits, a singlet state with half of the qubits being excited can neither emit nor absorb photons, which is verified with 4 qubits. This study is a step forward in coherent control of collective radiation and has promising applications in quantum information processing.

Received 23 July 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.013601

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Superconducting quantum optics Superradiance & subradiance

Coherent control Dicke model Tavis-Cummings model

Atomic, Molecular & Optical

Authors & Affiliations

Zhen Wang ¹, Hekang Li ², Wei Feng ¹, Xiaohui Song², Chao Song ¹, Wuxin Liu ¹, Qiujiang Guo¹, Xu Zhang ¹, Hang Dong¹, Dongning Zheng ^2,3,*, H. Wang ^1,†, and Da-Wei Wang ^1,3,‡

¹Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
²Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
³CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

^*dzheng@iphy.ac.cn
^†hhwang@zju.edu.cn
^‡dwwang@zju.edu.cn

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Vol. 124, Iss. 1 — 10 January 2020

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Images

Figure 1
(a) Image of the device where 10 qubits, shown as line shapes, are capacitively coupled to the central bus resonator. Each qubit has a $Z$ line for frequency biasing, an $X Y$ line for microwave excitation, and a readout resonator for qubit state measurement. A ten-tone microwave signal, which targets the resonance frequencies of all readout resonators, is passed through the launch pads “in” and “out” as labeled for the multiqubit readout. The scale bar on the bottom-left corner indicates 1 mm. (b) Pulse sequences used to generate and characterize the single-excitation superradiant or subradiant states, where the horizontal axis is for time and the vertical axis represents frequency. For $Q_{0}$ with frequency $ω_{0}$ , the sinusoid with a Gaussian envelope is a microwave pulse acting as a $π$ -rotational gate. The two rectangular $Z$ pulses with durations of $t_{iSWAP}$ ( $\approx π / 2 g$ ) are iswap gates: The first one transfers an excitation quantum from $Q_{0}$ to $R$ and the second one is for measurement of the resonator population. For $Q_{1}$ to $Q_{N}$ , the big rectangular $Z$ pulses (blue) simultaneously bring all qubits into resonance with $R$ : The first set has a duration of $\approx π / 2 \sqrt{N} g$ while the second set takes duration values continuously from 0 to 100 ns for observation of the collective swapping dynamics between the $N$ qubits and $R$ . The small rectangular $Z$ pulses (red) are phase gates with durations of 100 ns for switching the superradiant to subradiant states. The switching time is reduced to 10 ns in a later cooldown [37].
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Figure 2
(a) Collective swapping dynamics after the $N$ qubits in superradiance are tuned into resonance with the resonator in vacuum. Shown are the population for the $| 1 ⟩$ state, $P_{1}$ , of each qubit and that for the first excited state of resonator $R$ , measured as functions of the swapping time using the pulse sequence shown in Fig. 1. $N = 1$ to 10 from up to down. For $N = 10$ , we infer the resonator population by subtracting the $P_{1}$ sum of all 10 qubits from unity, instead of directly measuring $R$ using $Q_{0}$ and an iswap gate. (b) Collective coupling strength (dots) vs $N$ obtained by fitting the oscillation curves in (a) for the Rabi frequency. Line is a fit according to the $\sqrt{N}$ scaling. (c) Collective swapping dynamics between the $N$ qubits ( $N = 2$ to 8 from up to down) in subradiance and $R$ . The same data are replotted with logarithmic scale in the Supplemental Material [37]. $P_{1}$ of each qubit is measured to be around $1 / N$ (left) and that for the first excited state of $R$ remains almost zero (right), where the observable small fluctuations are likely due to the imperfection of the initial state, the slight inhomogeneity in $g_{j}$ and the qubit-qubit crosstalk couplings (typically less than 0.2 MHz).
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Figure 3
(a) Pulse sequences used to implement the switching operation from subradiance to superradiance for $N = 2$ . The first set of single-qubit phase gates (both the top and bottom panels), small rectangular Z pulses (red), is for generating subradiant states while the second set (the bottom panel) is inserted and configured for switching to superradiance. The collective swapping process is witnessed by tuning the $N$ qubits into resonance with $R$ using a set of big rectangular pulses (blue) followed by simultaneous readout of the $N$ qubits and $R$ . (b) Experimental results using the pulse sequences in (a) as indicated. The appearance of Rabi oscillations at 100 ns signifies the entrance from subradiance to superradiance. The small oscillations during $t_{D}$ can be suppressed by improving the initial state fidelity [37]. (c) Experimental results of the resonator photon number as a function of the swap time using pulse sequences similar to those in (a), which demonstrate controllable switching operations from subradiance to superradiance with $N$ from 3 to 8.
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Figure 4
(a) Collective swapping dynamics for the single-excitation subradiant state after the 4 qubits are tuned into resonance with the resonator in vacuum. Shown are the population for the $| 1 ⟩$ state, $P_{1}$ , of each of qubit and that for the first excited state of resonator $R$ , measured as functions of the swapping time using the pulse sequence shown in Fig. 1. Variations in $P_{1}$ are likely due to the slight inhomogeneity in $g_{j}$ and the qubit-qubit crosstalk couplings that are not taken into account. Here the data are obtained using a similar experimental sequence as that in Fig. 2 for $N = 4$ . (b) Collective swapping dynamics showing the well-defined Rabi oscillations for the single-excitation subradiant state after the 4 qubits are tuned into resonance with $R$ that initially hosts a single photon. (c) Collective swapping dynamics for the 4 qubits in $| ψ_{S} ⟩$ while $R$ is initialized in vacuum. (d) Collective swapping dynamics for the 4 qubits in $| ψ_{S} ⟩$ while $R$ initially hosts a single photon.
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