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arXiv:1209.0441 · Physical Review Letters

Observation of Entanglement between Itinerant Microwave Photons and a Superconducting Qubit

Christopher Eichler, Claus Lang, J. M. Fink, Joonas Govenius, Stefan Filipp, Andreas J. Wallraff

Published Dec 10, 2012• 105 citations
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Abstract

A localized qubit entangled with a propagating quantum field is well suited to study nonlocal aspects of quantum mechanics and may also provide a channel to communicate between spatially separated nodes in a quantum network. Here, we report the on-demand generation and characterization of Bell-type entangled states between a superconducting qubit and propagating microwave fields composed of zero-, one-, and two-photon Fock states. Using low noise linear amplification and efficient data acquisition we extract all relevant correlations between the qubit and the photon states and demonstrate entanglement with high fidelity.

DOI
10.1103/physrevlett.109.240501

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A localized qubit entangled with a propagating quantum field is well suited to study nonlocal aspects of quantum mechanics and may also provide a channel to communicate between spatially separated nodes in a quantum network. Here, we report the on-demand generation and characterization of Bell-type entangled states between a superconducting qubit and propagating microwave fields composed of zero-, one-, and two-photon Fock states. Using low noise linear amplification and efficient data acquisition we extract all relevant correlations between the qubit and the photon states and demonstrate entanglement with high fidelity.
Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasiprobability distributions and statistical moments for one-channel and two-channel detection. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms. Our theoretical investigations are supported by the presentation of experimental data, for which microwave quantum fields beyond the single-photon and Gaussian level have been prepared and reconstructed.
By combining a squeezed propagating microwave field and an unsqueezed vacuum field on a hybrid (microwave beam splitter), we generate entanglement between the two output modes. We verify that we have generated entangled states by making independent and efficient single-quadrature measurements of the two output modes. We observe the entanglement witness ${E}_{\mathrm{W}}=\ensuremath{-}0.{263}_{\ensuremath{-}0.036}^{+0.001}$ and the negativity $N=0.{0824}_{\ensuremath{-}0.0004}^{+0.01}$ with measurement efficiencies at least $26\ifmmode\pm\else\textpm\fi{}0.1%$ and $41\ifmmode\pm\else\textpm\fi{}0.2%$ for channels 1 and 2, respectively. These measurements show that the output two-mode state violates the separability criterion and therefore demonstrates entanglement. This shared entanglement between propagating microwaves provides an important resource for building quantum networks with superconducting microwave systems.
In this thesis, I demonstrate and evaluate an on-demand source of single propagating microwaves photons. Working in the context of a quantum network, nodes are connected via propagating, nonclassical states of the electromagnetic field. As such, preparing and detecting propagating quantum states is an essential task. I work with one particular node consisting of a microfabricated, effective two level system coupled to a microwave resonator and study its ability to produce propagating nonclassical states, such as single photon states. In principle, states generated by this node could be sent to other such nodes. However, I send them into a Josephson parametric amplifier (JPA) to characterize the source. In particular, I discuss how to design and couple the two components that form my source: a fixed frequency transmon qubit and a 3D superconducting waveguide cavity. I demonstrate the ability to control of the dynamics of this combined system and implement a single photon generation protocol, which utilizes a single microwave control field that is far detuned from the photon emission frequency. To characterize the generation, I perform tomography on the propagating photon state to determine its density matrix ρ. I perform repeated JPA-backed, linear measurements of the propagating state. Based on the histograms of my measurements, I infer a maximum single photon component ρ₁₁ = 0.36 ± 0.01. I characterize the imperfections of the photon generation and detection, including detection inefficiency and measurement backaction. I find that within uncertainty my measurements match my expectation.
We present a scalable quantum-bus-based device for generating the entanglement on microwave photons (MPs) in distant superconducting resonators (SRs). Different from the processors in previous works with some resonators coupled to a superconducting qubit (SQ), our device is composed of some 1D SRs rjr_jrj​ which are coupled to the quantum bus (another common resonator RRR) in its different positions simply, assisted by superconducting quantum interferometer devices. By using the technique for catching and releasing a MP state in a 1D SR, it can work as an entanglement generator or a node in quantum communication. To demonstrate the performance of this device, we propose a one-step scheme to generate high-fidelity Bell states on MPs in two distant SRs. It works in the dispersive regime of rjr_jrj​ and RRR, which enables us to extend it to generate high-fidelity multi-Bell states on different resonator pairs simultaneously.
Using modern micro and nano-fabrication techniques combined with superconducting materials we realize quantum electronic circuits in which we create, store, and manipulate individual microwave photons. The strong interaction of photons with superconducting quantum two-level systems allows us to probe fundamental quantum effects of microwave radiation and also to develop components for applications in quantum technology. Previously we have realized on-demand single photon sources which we have characterized using correlation function measurements [1] and full quantum state tomography [2]. For this purpose we have developed efficient methods to separate the quantum signals of interest from the noise added by the linear amplifiers used for quadrature amplitude detection [3]. We now regularly employ superconducting parametric amplifiers [4] to perform nearly quantum limited detection of propagating electromagnetic fields. These enable us to probe the entanglement which we generate on demand between stationary qubits and microwave photons freely propagating down a transmission line [5]. Using two independent microwave single photon sources, we have recently performed Hong-Ou-Mandel experiments at microwave frequencies [6] and have probed the coherence of two-mode multi-photon states at the out-put of a beam-splitter. The non-local nature of such states may prove to be useful for distributing entanglement in future small-scale quantum networks.
Measurement has traditionally been viewed as a means to restore classical behavior to a quantum system: a coherent superposition, once observed, transforms into a single classical state. However, it is possible to design a measurement that instead projects into an entangled state, thereby purifying, rather than destroying, quantum correlations. We use continuous measurement to generate entanglement between two superconducting qubits that are separated by more than a meter of cable, demonstrating that quantum information can be transferred over the metallic wires that comprise a low-loss channel for microwave photon propagation. We further generate a faithful, time-resolved record of single quantum trajectories. Studying the statistics of these trajectories and of the ensemble of measurements provides insight into the dynamics of measurement-induced entanglement in an extended quantum network.