One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. Although initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences--for instance, producing the Lamb shift of atomic spectra and modifying the magnetic moment of the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed whether it might be possible to more directly observe the virtual particles that compose the quantum vacuum. Forty years ago, it was suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. The phenomenon, later termed the dynamical Casimir effect, has not been demonstrated previously. Here we observe the dynamical Casimir effect in a superconducting circuit consisting of a coplanar transmission line with a tunable electrical length. The rate of change of the electrical length can be made very fast (a substantial fraction of the speed of light) by modulating the inductance of a superconducting quantum interference device at high frequencies (>10 gigahertz). In addition to observing the creation of real photons, we detect two-mode squeezing in the emitted radiation, which is a signature of the quantum character of the generation process.

We propose and demonstrate a read-out technique for a superconducting qubit by dispersively coupling it with a Josephson parametric oscillator. We employ a tunable quarter wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with 185±15 photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot read-out performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing.

A quantum coherent interface between optical and microwave photons can be used as a basic building block within a future quantum information network. The interface is envisioned as an ensemble of rare-earth ions coupled to a superconducting resonator, allowing for coherent transfer between optical and microwave photons. Towards this end, we have realized a hybrid device coupling a Er 3+ doped Y2SiO5 crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewdith of down to 75 MHz. * Electronic address: staudt@chalmers.se 1 H.

We characterize a novel Josephson parametric amplifier based on a flux-tunable quarter-wavelength resonator. The fundamental resonance frequency is ∼1 GHz, but we use higher modes of the resonator for our measurements. An on-chip tuning line allows for magnetic flux pumping of the amplifier. We investigate and compare degenerate parametric amplification, involving a single mode, and nondegenerate parametric amplification, using a pair of modes. We show that we reach quantum-limited noise performance in both cases, and we show that the added noise can be less than 0.5 added photons in the case of low gain.

We describe a circuit model for a flux-driven SQUID. This is useful for developing insight into how these devices perform as active elements in parametric amplifiers. The key concept is that frequency mixing in a flux-pumped SQUID allows for the appearance of an effective negative resistance. In the three-wave, degenerate case treated here, a negative resistance appears only over a certain range of allowed input signal phase. This model readily lends itself to testable predictions of more complicated circuits. Systems closely related to these amplifiers are also providing new physics, such as photon measurements of fast-tunable resonators 13 and the observation of the dynamical Casimir effect 14 . Since topics related to the manipulation of coherent states of light have traditionally been associated with quantum optics, a quantum-optics formalism dominates the commonly encountered explanations of these systems. However, under suitably small-signal limits, a truly nonlinear reactance may be modeled simply as a timevarying reactance. Under this approximation, the principle of superposition holds and we have the standard lexicon of linear analytical techniques available to us, such as Fourier analysis. In fact, "classical" parametric amplifiers were often treated in this linearized manner in literature 15-17 generated during the 1960s and 70s. While this literature was commonly depicting circuits utilizing varactor diodes as active elements, it remains a general premise that a parametrically driven nonlinear reactance leads to frequency mixing.In this work, a linearized method of analysis allows us to depict the effects of amplification using simple, intuitive models of equivalent electrical circuit elements. We examine the case of a three-wave degenerate parametric amplifier based on a dc Superconducting QUantum Interference Device (SQUID). Although outside the scope a) Electronic mail: kyle.sundqvist@gmail.com of this work it is also possible to consider the nondegenerate case, were an idler tone is introduced and considered separately from a signal tone.The parametric interaction is supplied by the SQUID, acting as a tunable, nonlinear inductance. By way of a mutual inductance to a control line, a time-varying magnetic flux, Φ ac , is applied to the SQUID and acts as our pump.We will show how the application of a dc and an ac pump flux allows us to treat the SQUID electrically as the well-known Josephson inductance, in parallel to a special circuit element which we introduce as "the pumpistor." We find that the pumpistor defined under these conditions leads to a phase sensitive impedance, where the phase angle between the pump and signal tones becomes important. In particular the pumpistor can act as a negative resistance, producing gain. Thus, our treatment presents a simple, analytical, albeit classical understanding of the phase sensitivity associated with degenerate parametric amplification.Our circuit model of a flux-pumped SQUID allows us to analyze much more complicated circuits in a straightforward way. ...

We have developed and tested a doubly tunable resonator, with the intention to simulate fast motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide half-wavelength microwave resonator, with fundamental resonant frequency ∼ 5 GHz. Both of its ends are terminated by dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows tuning of the resonant frequency by approximately 700 MHz. By using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to twice that of the resonator's fundamental mode. We observe photon generation, at the fundamental frequency, above a certain pump amplitude threshold. By varying the relative phase of the two pumps we are able to control the photon generation threshold, in good agreement with a theoretical model for the modulation of the boundary conditions. At the same time, some of our observations deviate from the theoretical predictions, which we attribute to parasitic couplings, resulting in current driving of the SQUIDs.

We demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by our parametrically pumping a multimode superconducting cavity. 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 our measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated by our 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.

We investigate nondegenerate parametric oscillations in a superconducting microwave multimode resonator that is terminated by a superconducting quantum interference device (SQUID). The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonant tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.