C. Eichler

Observation of resonant photon blockade at microwave frequencies using correlation function measurements.

Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured by using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra.

Deterministic quantum teleportation with feed-forward in a solid state system

Transferring the state of an information carrier from a sender to a receiver is an essential primitive in both classical and quantum communication and information processing. In a quantum process known as teleportation the unknown state of a quantum bit can be relayed to a distant party using shared entanglement and classical information. Here we present experiments in a solid-state system based on superconducting quantum circuits demonstrating the teleportation of the state of a qubit at the macroscopic scale. In our experiments teleportation is realized deterministically with high efficiency and achieves a high rate of transferred qubit states. This constitutes a significant step towards the realization of repeaters for quantum communication at microwave frequencies and broadens the tool set for quantum information processing with superconducting circuits.Engineered macroscopic quantum systems based on superconducting electronic circuits are attractive for experimentally exploring diverse questions in quantum information science. At the current state of the art, quantum bits (qubits) are fabricated, initialized, controlled, read out and coupled to each other in simple circuits. This enables the realization of basic logic gates, the creation of complex entangled states and the demonstration of algorithms or error correction. Using different variants of low-noise parametric amplifiers, dispersive quantum non-demolition single-shot readout of single-qubit states with high fidelity has enabled continuous and discrete feedback control of single qubits. Here we realize full deterministic quantum teleportation with feed-forward in a chip-based superconducting circuit architecture. We use a set of two parametric amplifiers for both joint two-qubit and individual qubit single-shot readout, combined with flexible real-time digital electronics. Our device uses a crossed quantum bus technology that allows us to create complex networks with arbitrary connecting topology in a planar architecture. The deterministic teleportation process succeeds with order unit probability for any input state, as we prepare maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two-qubit measurement with high efficiency and high fidelity. We teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 104 s−1, exceeding other reported implementations. The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.

Observation of Two-Mode Squeezing in the Microwave Frequency Domain

Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. As an important step towards the observation of entanglement between propagating microwave photons we demonstrate the experimental state reconstruction of two field modes in the microwave domain. In particular, we generate two-mode correlated states with a Josephson parametric amplifier and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix and reconstruct the four-dimensional Wigner function. We demonstrate strong correlations between the quadrature amplitude noise in the two modes. Under ideal conditions two-mode squeezing below the standard quantum limit should be observable in future experiments.

Experimental State Tomography of Itinerant Single Microwave Photons

A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the Wigner function of itinerant single photon Fock states and their superposition with the vacuum using linear amplifiers and quadrature amplitude detectors. We have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier by analyzing the moments of the measured amplitude distribution up to 4th order. This work is expected to enable studies of propagating microwaves in the context of linear quantum optics.

Correlations, indistinguishability and entanglement in Hong–Ou–Mandel experiments at microwave frequencies

Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a controllable delay, in time-resolved second-order crossand auto-correlation function measurements. Using quadrature amplitude detection we are able to resolve different photon numbers and detect coherence in and between the output arms. This measurement scheme allows us to observe the HOM effect and, in addition, to fully characterize the two-mode entanglement of the spatially separated beam splitter output modes. Our experiments constitute a first step towards using two-photon interference at microwave frequencies for quantum communication and information processing, e.g. for distributing entanglement between nodes of a quantum network [2, 3] and for linear optics quantum computation [4, 5]. Presently, HOM two-photon interference has been demonstrated exclusively using photons at optical or telecom wavelengths. Experiments were performed with photons emitted from a single source using parametric downconversion [1], trapped ions [3], atoms [6], quantum dots [7] and single molecules [8]. The HOM effect has also been observed with two independent sources [9–15] realizing indistinguishable single-photon states which are required as a resource in quantum networks or linear optics quantum computation. Such experiments have also been performed using donor impurities as sources [16] including NV-centers in diamond [17, 18]. Furthermore, the HOM effect has been employed to create entanglement between ions [19] in spatially separated traps, and to realize a controlled-NOT gate in a small-scale photonic network [20]. Here, we demonstrate the HOM interference of two indistinguishable microwave photons emitted from independent triggered sources realized in superconducting circuits. In each source A (B) a transmon-type qubit is strongly coupled with rate g/2π = 169 (177) MHz to a transmission line resonator, see Fig. 1a. To create a single photon using one of the sources, we coherently excite the qubit into a state α |g〉 + β |e〉 using a resonant microwave pulse. Then, we swap the qubit state into the resonator mode  (B̂) by tuning the qubit transition frequency for half a vacuum-Rabi period into resonance with the resonator. This creates the state α |0〉 + β |1〉 in the resonator, which for β = 1 corresponds to a single-photon Fock state [22]. The photon then decays exponentially with Lorentzian spectrum through the strongly coupled output port of the resonator into the input mode â′ (b̂′) of the beam splitter at a rate κ/2π = 4.1 (4.6) MHz, see Fig. 1. The two photons then interfere at the beam splitter and are emitted into the output modes â and b̂, see Fig. 1a. Using the dispersive interaction between qubit and resonator, we tune the emission frequencies of the two sources to an identical value of νr = 7.2506 GHz. This is achieved by adjusting the qubit transition frequencies νa to 8.575 (8.970) GHz with a static magnetic flux applied to the SQUID-loop of each qubit. For our experiments, we sequentially create 20 single photons in each source at a rate 1/tr = 1/512 ns ∼ 1.95 MHz in a sequence repeated every 12.5μs.

Observation of Dicke superradiance for two artificial atoms in a cavity with high decay rate

An individual excited two-level system decays to its ground state in a process known as spontaneous emission. The probability of detecting the emitted photon decreases exponentially with the time passed since its excitation. In 1954, Dicke first considered the more subtle situation in which two emitters decay in close proximity to each other. He argued that the emission dynamics of a single two-level system is altered by the presence of a second one, even if it is in its ground state. Here, we present a close to ideal realization of Dickes original two-spin Gedankenexperiment, using a system of two individually controllable superconducting qubits weakly coupled to a fast decaying microwave cavity. The two-emitter case of superradiance is explicitly demonstrated both in time-resolved measurements of the emitted power and by fully reconstructing the density matrix of the emitted field in the photon number basis.

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.

Microwave-Controlled Generation of Shaped Single Photons in Circuit Quantum Electrodynamics

Large-scale quantum information processors or quantum communication networks will require reliable exchange of information between spatially separated nodes. The links connecting these nodes can be established using traveling photons that need to be absorbed at the receiving node with high efficiency. This is achievable by shaping the temporal profile of the photons and absorbing them at the receiver by time reversing the emission process. Here, we demonstrate a scheme for creating shaped microwave photons using a superconducting transmon-type three-level system coupled to a transmission line resonator. In a second-order process induced by a modulated microwave drive, we controllably transfer a single excitation from the third level of the transmon to the resonator and shape the emitted photon. We reconstruct the density matrices of the created single-photon states and show that the photons are antibunched. We also create multipeaked photons with a controlled amplitude and phase. In contrast to similar existing schemes, the one we present here is based solely on microwave drives, enabling operation with fixed frequency transmons.

Characterizing quantum microwave radiation and its entanglement with superconducting qubits using linear detectors

Recent progress in the development of superconducting circuits has allowed for realizing 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 quasi-probability distributions and statistical moments. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms.

Controlling the dynamic range of a Josephson parametric amplifier

One of the central challenges in the development of parametric amplifiers is the control of the dynamic range relative to its gain and bandwidth, which typically limits quantum limited amplification to signals which contain only a few photons per inverse bandwidth. Here, we discuss the control of the dynamic range of Josephson parametric amplifiers by using Josephson junction arrays. We discuss gain, bandwidth, noise, and dynamic range properties of both a transmission line and a lumped element based parametric amplifier. Based on these investigations we derive useful design criteria, which may find broad application in the development of practical parametric amplifiers.