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Applied Physics Letters

Realization of dark state in a three-dimensional transmon superconducting qutrit

Yuhao Liu, Dong Lan, Xinsheng Tan, Jie Zhao, Peng Zhao, Mengmeng Li, Ke Zhang, Kunzhe Dai, Zhiyuan Li, Qiang Liu, Shudong Huang, Guangming Xue, Peng Xu, Haifeng Yu, Shi-Liang Zhu, Yang Yu

Published Nov 16, 2015• 9 citations
Publisher

Abstract

We realize the dark state in a three-dimensional transmon superconducting qutrit that consists of three cascading energy levels: |0⟩, |1⟩, and |2⟩. When the system is simultaneously driven with two tone microwaves on resonance with |0⟩, |1⟩ and |1⟩, |2⟩, respectively, it is found that the state of the system will generally evolve in time domain. However, the qutrit state is frozen-out if it is initialized in a dark state for corresponding drive amplitudes. We observe this freeze-out phenomenon by changing the amplitude of the microwaves while fixing the initial state or vice versa.

DOI
10.1063/1.4936206

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We realize the dark state in a three-dimensional transmon superconducting qutrit that consists of three cascading energy levels: |0⟩, |1⟩, and |2⟩. When the system is simultaneously driven with two tone microwaves on resonance with |0⟩, |1⟩ and |1⟩, |2⟩, respectively, it is found that the state of the system will generally evolve in time domain. However, the qutrit state is frozen-out if it is initialized in a dark state for corresponding drive amplitudes. We observe this freeze-out phenomenon by changing the amplitude of the microwaves while fixing the initial state or vice versa.
We have observed the Autler-Townes doublet in a superconducting Al/AlOX{}_{X}X​/Al transmon qubit that acts as an artificial atom embedded in a three-dimensional Cu microwave cavity at a temperature of 22 mK. Using pulsed microwave spectroscopy, the three lowest transmon levels are isolated, eliminating unwanted effects of higher qubit modes and cavity modes. The long coherence time ($\ensuremath{\sim}$$40\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{s}$) of the transmon enables us to observe a clear Autler-Townes splitting at drive amplitudes much smaller than the transmon level anharmonicity (177 MHz). Three-level density matrix simulations with no free parameters provide excellent fits to the data. At maximum separation, the fidelity of a dark state achieved in this experiment is estimated to be 99.699.6%--99.9%99.6.
Superconducting microwave links have enabled deterministic state transfer and remote entanglement between qubits, but deterministic links have so far operated with an effectively two-dimensional transmitted Hilbert space. Here we demonstrate a superconducting qutrit link between two independently packaged nodes connected by a microwave channel. Each node combines a transmon qutrit, a transmission resonator, and a tunable Purcell-filter interface, allowing the two remote microwave-photon interfaces to be matched in both frequency and bandwidth. We implement two transition-selective photon-mediated operations that transfer the ∣e⟩|e\rangle∣e⟩ and ∣f⟩|f\rangle∣f⟩ qutrit components in distinct temporal modes of the same channel. We tomographically characterize arbitrary qutrit-state transfer, obtaining a mean transferred-state fidelity of 83.68% and a qutrit process fidelity of 77.12%, exceeding both the classical qutrit-transfer benchmark and the best possible average fidelity of an effective qubit channel used to transmit an arbitrary qutrit. Using partial-transfer operations, we reconstruct a remote two-qutrit state with negativity 0.730, a tomography-inferred dense-coding capacity of 2.273 bits, and a tomography-inferred Collins-Gisin-Linden-Massar-Popescu (CGLMP) parameter I3=2.332I_3=2.332I3​=2.332, all beyond the corresponding qubit or local bounds. These results demonstrate a superconducting microwave link that uses the native three-level structure of transmons as a genuine high-dimensional communication resource.
Quantum networks will enable extraordinary capabilities for communicating and processing quantum information. These networks require a reliable means of storage, retrieval, and manipulation of quantum states at the network nodes. A node receives one or more coherent inputs and sends a conditional output to the next cascaded node in the network through a quantum channel. Here, we demonstrate this basic functionality by using the quantum interference mechanism of electromagnetically induced transparency in a transmon qubit coupled to a superconducting resonator. First, we apply a microwave bias, i.e., drive, to the qubit-cavity system to prepare a Λ-type three-level system of polariton states. Second, we input two interchangeable microwave signals, i.e., a probe tone and a control tone, and observe that transmission of the probe tone is conditional upon the presence of the control tone that switches the state of the device with up to 99.73% transmission extinction. Importantly, our electromagnetically induced transparency scheme uses all dipole allowed transitions. We infer high dark state preparation fidelities of >99.39% and negative group velocities of up to -0.52±0.09 km/s based on our data.
Superconducting quantum multilevel systems coupled to resonators have recently been considered in some applications such as microwave lasing and high-fidelity quantum logical gates. In this work, using an rf-SQUID type phase qudit coupled to a microwave coplanar waveguide resonator, we study both theoretically and experimentally the energy spectrum of the system when the qudit level spacings are varied around the resonator frequency by changing the magnetic flux applied to the qudit loop. We show that the experimental result can be well described by a theoretical model that extends from the usual two-level Jaynes-Cummings system to the present four-level system. It is also shown that due to the small anharmonicity of the phase device a simplified model capturing the leading state interactions fits the experimental spectra very well. Furthermore we use the Lindblad master equation containing various relaxation and dephasing processes to calculate the level populations in the simpler qutrit-resonator system, which allows a clear understanding of the dynamics of the system under the microwave drive. Our results help to better understand and perform the experiments of coupled multilevel and resonator systems and can be applied in the case of transmon or Xmon qudits having similar anharmonicity to the present phase device.
In the circuit quantum electrodynamics architecture, both the resonance frequency and the coupling of superconducting qubits to microwave field modes can be controlled via external electric and magnetic fields to explore qubit-photon dynamics in a wide parameter range. Here, we experimentally demonstrate and analyze a scheme for tuning the coupling between a transmon qubit and a microwave resonator using a single coherent drive tone. We treat the transmon as a three-level system, with the qubit subspace defined by the ground and the second excited states. If the drive frequency matches the difference between the resonator and the qubit frequencies, a Jaynes-Cummings-type interaction is induced, which is tunable in both amplitude and phase. We show that coupling strengths of about 10 MHz can be achieved in our setup, limited only by the anharmonicity of the transmon qubit. This scheme has been successfully used to generate microwave photons with a controlled temporal shape [M. Pechal et al., Phys. Rev. X 4, 041010 (2014)] and can be directly implemented with superconducting quantum devices featuring larger anharmonicity for higher coupling strengths.