Michael Roger Andre Simoen

Observation of the dynamical Casimir effect in a superconducting circuit

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.

Single-shot read-out of a superconducting qubit using a Josephson parametric oscillator

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.

Coupling of an erbium spin ensemble to a superconducting resonator

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 Er3 +-doped Y2SiO5 crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewidth of down to 75 MHz.

Characterization of a multimode coplanar waveguide parametric amplifier

We characterize a 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.

The pumpistor: A linearized model of a flux-pumped superconducting quantum interference device for use as a negative-resistance parametric amplifier

We describe a circuit model for a flux-driven Superconducting QUantum Interference Device (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.

Simple, robust, and on-demand generation of single and correlated photons

We propose two different setups to generate single photons on demand using an atom in front of a mirror, along with either a beam splitter or a tunable coupling. We show that photon-generation efficiency of ?99% is straightforward to achieve. The proposed schemes are simple and easily tunable in frequency. The operation is relatively insensitive to dephasing and can be easily extended to generate correlated pairs of photons. They can also, in principle, be used to generate any photonic qubit of the form ?0+?1 in arbitrary wave packets, making them very attractive for quantum communication applications.

An On-Chip Mach-Zehnder Interferometer in the Microwave Regime

The design, simulation and measurements of an on-chip Mach-Zehnder interferometer operating in the microwave regime are described. Using microwave signals in microfabricated superconducting Al waveguides, the concept of an interferometer is transferred from optics to on-chip. Tuning of the path length of one of the interferometer arms is executed through the tunable inductance of a SQUID. By placing one or more SQUIDs in the waveguide structure and by varying the magnetic flux through the SQUID loop, the total SQUID inductance can be tuned. In this way, a phase difference leading to destructive or constructive interference at the interferometer output can be achieved. Thorough software simulations were performed to determine the different design parameters, assign a desired working frequency and provide a reference for comparison with experimental results. Measurements at 300 mK show an effective working frequency close to the simulations, with a deviation smaller than 0.05 GHz. The behavior of the interferometer is very similar to the simulations as well. The on-off ratio exceeds 40 dB.

Nondegenerate parametric oscillations in a tunable superconducting resonator

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 s how 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.

Microwave photon generation in a doubly tunable superconducting resonator

We have created a doubly tunable resonator, with the intention to simulate relativistic motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide microwave resonator, with fundamental resonant frequency ω 1 / (2 π ) ~ 5 GHz. Both of its ends are terminated to ground via dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows the tuning of ω 1 / (2 π ) by approximately 700 MHz. Using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to 2 ω 1 . We observe photon generation, at ω 1 , above a certain pump amplitude threshold. By varying the relative phase of the two pumps we are able to control this threshold, in good agreement with a theoretical model. 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

Experimental test of the entanglement of radiation generated by the dynamical Casimir effect

In the dynamical Casimir effect (DCE), a boundary condition for the electromagnetic field is changed rapidly, resulting in generation of pairs of photons [1]. This was experimentally demonstrated in 2011 [2]. Both generation of photons and two-mode squeezing were observed. Quantum theory predicts that the photon pairs are entangled and that the resulting electromagnetic field is in a nonclassical state at zero temperature. Johansson et al. [3] recently suggested how to test entanglement of the DCE radiation by evaluating the log negativity. Here we present such an experimental test. We have measured a sample consisting of an open transmission line terminated by a superconducting quantum interference device (SQUID). The electrical length of the transmission line can be modulated, by changing the magnetic flux through the SQUID loop. Broadband radiation of photon pairs is observed along with strong two mode squeezing. The system is characterized at a temperature of <; 20 mK, and the signal level is calibrated using the SQUID as a shot-noise source. We investigate the cross-correlations for the field at two different frequencies and we recover the covariance matrix. From this matrix we determine the log negativity, which shows weakly positive values indicating that the two modes are entangled. A source of entangled photons can be useful in quantum information applications, for instance to entangle qubits [4].