We show experimentally that a dc-biased Josephson junction in series with two microwave resonators emits entangled beams of microwaves leaking out of the resonators. In the absenceof a stationary phase reference for characterizing the entanglement of the outgoing beams, we measure second-order coherence functions for proving entanglement up to an emission rate of 2.5 billion photon pairs per second. The experimental results are found in quantitative agreement with theory, proving that the low frequency noise of the dc bias is the main limitation for the coherence time of the entangled beams. This agreement allows us to evaluate the entropy of entanglement of the resonators, and to identify the improvements that could bring this device closer to a useful bright source of entangled microwaves for quantum-technological applications.
The interaction between superconducting qubits and one-dimensional microwave transmission lines has been studied experimentally and theoretically in the past two decades. In this work,we investigate the spontaneous emission of an initially excited artificial atom which is capacitively coupled to a semi-infinite transmission line, shorted at one end. This configuration can be viewed as an atom in front of a mirror. The distance between the atom and the mirror introduces a time-delay in the system, which we take into account fully. When the delay time equals an integer number of atom oscillation periods, the atom converges into a dark state after an initial decay period. The dark state is an effect of destructive interference between the reflected part of the field and the part directly emitted by the atom. Based on circuit quantization, we derive linearized equations of motion for the system and use these for a semiclassical analysis of the transient dynamics. We also make a rigorous connection to the quantum optics system-reservoir approach and compare these two methods to describe the dynamics. We find that both approaches are equivalent for transmission lines with a low characteristic impedance, while they differ when this impedance is higher than the typical impedance of the superconducting artificial atom.
Spontaneous parametric downconversion (SPDC) has been a key enabling technology in exploring quantum phenomena and their applications for decades. For instance, traditional SPDC, whichsplits a high energy pump photon into two lower energy photons, is a common way to produce entangled photon pairs. Since the early realizations of SPDC, researchers have thought to generalize it to higher order, e.g., to produce entangled photon triplets. However, directly generating photon triplets through a single SPDC process has remained elusive. Here, using a flux-pumped superconducting parametric cavity, we demonstrate direct three-photon SPDC, with photon triplets generated in a single cavity mode or split between multiple modes. With strong pumping, the states can be quite bright, with flux densities exceeding 60 photon/s/Hz. The observed states are strongly non-Gaussian, which has important implications for potential applications. In the single-mode case, we observe a triangular star-shaped distribution of quadrature voltages, indicative of the long-predicted „star state“. The observed star state shows strong third-order correlations, as expected for a state generated by a cubic Hamiltonian. By pumping at the sum frequency of multiple modes, we observe strong three-body correlations between multiple modes, strikingly, in the absence of second-order correlations. We further analyze the third-order correlations under mode transformations by the symplectic symmetry group, showing that the observed transformation properties serve to „fingerprint“ the specific cubic Hamiltonian that generates them. The observed non-Gaussian, third-order correlations represent an important step forward in quantum optics and may have a strong impact on quantum communication with microwave fields as well as continuous-variable quantum computation.
In this Letter, we demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by parametrically pumping a multimode superconductingcavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. The Gaussian output states are fully characterized by measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated using an in situ microwave calibration source, a shot noise tunnel junction. Applying a variety of entanglement measures, we demonstrate both full inseparability and genuine tripartite entanglement of the states. Our method is easily extensible to more modes.
Quantum fluctuations of the vacuum are both a surprising and fundamental phenomenon of nature. Understood as virtual photons flitting in and out of existence, they still have a veryreal impact, \emph{e.g.}, in the Casimir effects and the lifetimes of atoms. Engineering vacuum fluctuations is therefore becoming increasingly important to emerging technologies. Here, we shape vacuum fluctuations using a „mirror“, creating regions in space where they are suppressed. As we then effectively move an artificial atom in and out of these regions, measuring the atomic lifetime tells us the strength of the fluctuations. The weakest fluctuation strength we observe is 0.02 quanta, a factor of 50 below what would be expected without the mirror, demonstrating that we can hide the atom from the vacuum.
We propose and analyze a circuit that implements a nonlinear coupling between two superconducting microwave resonators. The resonators are coupled through a superconducting quantuminterference device (SQUID) that terminates one of the resonators. This produces a nonlinear interaction on the standard optomechanical form, where the quadrature of one resonator couples to the photon number of the other resonator. The circuit therefore allows for all-electrical realizations of analogs to optomechanical systems, with coupling that can be both strong and tunable. We estimate the coupling strengths that should be attainable with the proposed device, and we find that the device is a promising candidate for realizing the single-photon strong-coupling regime. As a potential application, we discuss implementations of networks of nonlinearly-coupled microwave resonators, which could be used in microwave-photon based quantum simulation.
The phenomenon of quantum fluctuations, consisting in virtual particles emerging from vacuum, is central to understanding important effects in nature – for instance, the Lambshift of atomic spectra and the anomalous magnetic moment of the electron. It was also suggested that a mirror undergoing relativistic motion could convert virtual into real photons. This phenomenon, denominated dynamical Casimir effect (DCE), has been observed in recent experiments with superconducting circuits. Here, we show that the physics underlying the DCE may generate multipartite quantum correlations. To achieve it, we propose a circuit quantum electrodynamics (cQED) scenario involving superconducting quantum interference devices (SQUIDs), cavities, and superconducting qubits, also called artificial atoms. Our results predict the generation of highly entangled states for two and three superconducting qubits in different geometric configurations with realistic parameters. This proposal paves the way for a scalable method of multipartite entanglement generation in cavity networks through dynamical Casimir physics.
We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of thehomodyne record, the feedback controller reverts the stochastic quantum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with measurement efficiency η~≈0.5, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.
The ability to detect the presence of a single, travelling photon without destroying it has been a long standing project in optics and is fundamental for applications in quantum informationand measurement. The realization of such a detector has been complicated by the fact that photon- photon interactions are very weak at optical frequencies. At microwave frequencies, very strong photon-photon interactions have been demonstrated. Here however, the single-photon detector has been elusive due to the low energy of the microwave photon. In this article, we present a realistic proposal for quantum nondemolition measurements of a single propagating microwave photon. The detector design is built on a of chain of artificial atoms connected through circulators which break time-reversal symmetry, making both signal and probe photons propagate in one direction only. Our analysis is based on the theory of cascaded quantum systems and quantum trajectories which takes the full dynamics of the atom-field interaction into account. We show that a signal-to-noise ratio above one can be realized with current state of the art microwave technology.
We study a superconducting charge qubit coupled to an intensive electromagnetic field and probe changes in the resonance frequency of the formed dressed states. At large driving strengths,exceeding the qubit energy-level splitting, this reveals the well known Landau-Zener-St\“uckelberg (LZS) interference structure of a longitudinally driven two-level system. For even stronger drives we observe a significant change in the LZS pattern and contrast. We attribute this to photon-assisted quasiparticle tunneling in the qubit. This results in the recovery of the qubit parity, eliminating effects of quasiparticle poisoning and leads to an enhanced interferometric response. The interference pattern becomes robust to quasiparticle poisoning and has a good potential for accurate charge sensing.