Observation of Entanglement between Itinerant Microwave Photons and a Superconducting Qubit

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.

Figure 1

Schematic of the experimental setup. (a) A transmon qubit with individual charge drive line (red) at frequency ${\omega }_{ge}$ and flux control line (green) is strongly coupled to a resonator with a weakly coupled input port (${\gamma }_{\mathrm{in}}/\kappa \approx 0.001$) driven at frequency ${\omega }_r$ for qubit readout (orange). The output port is strongly coupled into a transmission line (violet) and amplified with a Josephson parametric amplifier (light blue) pumped at ${\omega }_p$ through a directional coupler with adjustable phase and attenuation for pump tone cancellation. The signal reflected off the parametric amplifier passes through a chain of circulators into a low-noise semiconductor amplifier after which its two quadratures $X$, $P$ are detected. (b) False color optical micrograph of the sample. The transmon qubit (enlarged) consists of two capacitively coupled islands connected by a pair of Josephson junctions. (c) False color micrograph of the Josephson parametric amplifier. The array of Josephson junctions (enlarged) at the end of the quarter wavelength resonator (light blue) provides the nonlinearity. (d) Pulse sequence used for the experiment: (i) state preparation, (ii) field measurement, and (iii) qubit readout (see text for details). (e) Measured probability distribution $p(Q)$ of the qubit readout quadrature $Q$ in arbitrary units (a.u.) for prepared ground (blue), excited (red), and Bell (dashed white) states.

Figure 2

Photon-qubit correlations for a prepared Bell state. (a) Qubit state population conditioned on the measured photon field quadratures $X$ and $P$ for the indicated Bloch vector components. $\{X,P\}$ pairs for which no measurement results occurred are shown in gray. White circles indicate the standard deviation of the photon field distribution ${\delta }_m$. (i)–(iii) $⟨{\sigma }_z⟩$ for the reference states $|0g⟩$, $|0e⟩$, and the Bell state $|\psi ⟩$. For better visibility only, the data in subpanel (iii) are offset by their total mean $\approx 0.1$, compensating for the qubit decay during photon detection. (iv), (v) $⟨{\sigma }_x⟩$ and $⟨{\sigma }_y⟩$ for the Bell state $|\psi ⟩$. (b) Expectation values $⟨(a^{†}{)}^n{a}^m{\sigma }_i⟩$ extracted from the qubit-photon field correlations shown in (a) and the measured photon field distribution. The real (imaginary) parts of these measured moments are shown in red (blue) and compared to the ideal Bell state (wire frame). The error bars are extracted from the standard deviation of repeated measurements. (c) Real part of the measured (solid) and ideal (wire frame) density matrix $\rho$ for the Bell state $|\psi ⟩$ with fidelity $F=⟨\psi |\rho |\psi ⟩=83\%$ and for the state $|\varphi ⟩=[(|1⟩+|2⟩)|g⟩+(|1⟩-|2⟩)|e⟩]/2$ with fidelity $F=80\%$ in (d).