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arXiv:2101.09532 · Physical Review Letters

Propagating Wigner-Negative States Generated from the Steady-State Emission of a Superconducting Qubit

Yong Lu, Ingrid Strandberg, Fernando Quijandría, Göran Johansson, Simone Gasparinetti, Per Delsing

Published Jun 25, 2021• 31 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate the steady-state generation of propagating Wigner-negative states from a continuously driven superconducting qubit. We reconstruct the Wigner function of the radiation emitted into propagating modes defined by their temporal envelopes, using digital filtering. For an optimized temporal filter, we observe a large Wigner logarithmic negativity, in excess of 0.08, in agreement with theory. The fidelity between the theoretical predictions and the states generated experimentally is up to 99%, reaching state-of-the-art realizations in the microwave frequency domain. Our results provide a new way to generate and control nonclassical states, and may enable promising applications such as quantum networks and quantum computation based on waveguide quantum electrodynamics.

DOI
10.1103/physrevlett.126.253602

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We experimentally demonstrate the steady-state generation of propagating Wigner-negative states from a continuously driven superconducting qubit. We reconstruct the Wigner function of the radiation emitted into propagating modes defined by their temporal envelopes, using digital filtering. For an optimized temporal filter, we observe a large Wigner logarithmic negativity, in excess of 0.08, in agreement with theory. The fidelity between the theoretical predictions and the states generated experimentally is up to 99%, reaching state-of-the-art realizations in the microwave frequency domain. Our results provide a new way to generate and control nonclassical states, and may enable promising applications such as quantum networks and quantum computation based on waveguide quantum electrodynamics.
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Propagating modes of light with negative-valued Wigner distributions are of fundamental interest in quantum optics and represent a key resource in the pursuit of optics-based quantum information technologies. Most schemes proposed or implemented for the generation of such modes are probabilistic in nature and rely on heralding by detection of a photon or on conditional methods where photons are separated from the original field mode by a beam splitter. In this Letter we demonstrate theoretically, using a cascaded-quantum-systems model, the possibility of deterministic generation of Wigner-negativity in temporal modes of the steady-state emission of a two-level system driven by finite-bandwidth quadrature-squeezed light. Optimal negativity is obtained for a squeezing bandwidth similar to the linewidth of the transition of the two-level system. While the Wigner distribution associated with the incident squeezed light is Gaussian and everywhere positive, the Wigner functions of the outgoing temporal modes show distinct similarities and overlap with a superposition of displaced squeezed states.
The ability to generate entangled states of light is a key primitive for quantum communication and distributed quantum computation. Continuously driven sources, including those based on spontaneous parametric downconversion, are usually probabilistic, whereas deterministic sources require accurate timing of the control fields. Here, we experimentally generate entangled photonic modes by continuously exciting a quantum emitter - a superconducting qubit - with a coherent drive, taking advantage of mode matching in the time and frequency domain. Using joint quantum state tomography and logarithmic negativity, we show that entanglement is generated between modes extracted from the two sidebands of the resonance fluorescence spectrum. Because the entangled photonic modes are perfectly orthogonal, they can be transferred into distinct quantum memories. Our approach can be utilized to distribute entanglement at a high rate in various physical platforms, with applications in waveguide quantum electrodynamics, distributed quantum computing, and quantum networks.
Generating the negative Wigner functions where the corresponding Wigner states are nonclassical has been recognized as a powerful tool for successfully performing quantum information and computing protocols beyond the scope of classical computers. Here, we present the possibility to generate and engineer the negative Wigner function at a steady state using parametric (two-photon) driving and homodyne-based feedback in a quantum van der Pol (vdP) oscillator. Specifically, we employ a quantum master equation approach for calculating the Wigner function of the vdP oscillator field in phase space and, furthermore, quantifying its negativity content. We clearly show that the negative-value magnitudes, regions, and shapes of the Wigner function can be effectively tuned by the parametric driving phase and the parametric driving amplitude, as well as the feedback coefficient within a large range. We identify different contributions of these involved parameters to the Wigner-function negativity. In the present scheme, more complex quantum coherence and interference phenomena are introduced via the parametric driving and feedback, which stabilizes the phase of the vdP oscillator field and renders the capability to generate the negative Wigner function. Therefore, the enhanced Wigner-function negativity can be achieved under these optimized system parameters. Our in-depth study provides insight into the formation and in situ control of the desirable Wigner nonclassical states. The obtained results are not limited to the vdP oscillator systems and should be generally applicable to other coherent coupled systems within the reach of modern experimental facilities.
In this work we demonstrate numerically that the nonlinearity provided by a continuously driven two-level system allows for the generation of Wigner-negative states of the electromagnetic field confined in one spatial dimension. Wigner-negative states, also known as Wigner nonclassical states, are desirable for quantum information protocols beyond the scope of classical computers. Focusing on the steady-state emission from the two-level system, we find the largest negativity at the drive strength where the coherent reflection vanishes.
We show that a Kerr-nonlinear cavity coupled to an incoherently pumped two-level qubit can stabilize a nonclassical steady state with pronounced Wigner negativity. Without the qubit, two-photon drive and dissipation preserve photon-number parity and confine vacuum-initiated dynamics to the even-parity Fock subspace, preventing the emergence of odd-parity-induced central Wigner negativity. The qubit opens a frequency-selective injection channel into the odd-parity Fock subspace, while Kerr nonlinearity suppresses unwanted higher-order transitions, driving the system toward a steady state dominated by the single-photon Fock state that can approach a nearly pure state in the optimal regime. The resulting Wigner negativity remains robust over broad experimentally relevant loss and dephasing regimes, providing a route to the dissipative stabilization of nonclassical light in cavity quantum electrodynamics platforms.