Squeezed states of the electromagnetic field have been generated by nondegenerate four-wave mixing due to Na atoms in an optical cavity. The optical noise in the cavity, comprised of primarily vacuum fluctuations and a small component of spontaneous emission from the pumped Na atoms, is amplified in one quadrature of the optical field and deamplified in the other quadrature. These quadrature components are measured with a balanced homodyne detector. The total noise level in the deamplified quadrature drops below the vacuum noise level.

Observation of squeezed states generated by four-wave mixing in an optical cavity

We have measured probability distributions of quadrature-field amplitude for both vacuum and quadrature-squeezed states of a mode of the electromagnetic field. From these measurements we demonstrate the technique of optical homodyne tomography to determine the Wigner distribution and the density matrix of the mode. This provides a complete quantum mechanical characterization of the measured mode.

Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum.

Microwave photonics with superconducting quantum circuits

Quantum-mechanical effects at the macroscopic level were first explored in Josephson-junction-based superconducting circuits in the 1980s. In recent decades, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to gate-based digital quantum information processing with superconducting circuits. In addition, circuit QED provides a framework for the study of hybrid quantum systems, such as quantum dots, magnons, Rydberg atoms, surface acoustic waves, and mechanical systems interacting with microwave photons. Here the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focusing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system are reviewed. Also discussed is coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, important use cases of these ideas in quantum information processing and in quantum optics are discussed. Circuit QED realizes a broad set of concepts that open up new possibilities for the study of quantum physics at the macro scale with superconducting circuits and applications to quantum information science in the widest sense.

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Circuit quantum electrodynamics

In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field.

We have demonstrated (47\ifmmode\pm\else\textpm\fi{}8)% squeezing of vacuum-fluctuation noise using a Josephson-parametric amplifier operated at 19.16 GHz. The amplifier was operated at 30 mK and has a double-sideband noise temperature of 0.446 K. This is comparable to the vacuum noise floor h\ensuremath{\nu}/2k=0.460 K.

Observation of zero-point noise squeezing via a Josephson-parametric amplifier.

We have obtained parametric gain at 19 GHz from a distributed Josephson junction parametric amplifier whose active gain medium consists of a series array of 1000 Josephson junctions embedded in a coplanar waveguide. When cooled to 1.7 K the amplifier provides 16 dB gain in a mode where the internally generated double sideband noise referred to input is 0.5±0.1 K. This noise is consistent with Nyquist noise generated from the losses. An instantaneous bandwidth of 125 MHz has been observed with a peak gain of 12 dB. The 3 dB compression point with a peak gain of 14.6 dB is ‐90.5 dB and the dynamic range is 38 dB.

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A low-noise series-array Josephson junction parametric amplifier

A systematic study of noise in a nondegenerate Josephson-parametric amplifier as it passes through the threshold for oscillation was performed. Below the threshold all the noise is accounted for by equilibrium fluctuations of the losses. Well above the threshold the noise is 3 dB larger than the below-threshold value and is again accounted for by noise from the losses. In the region near the threshold, the noise can become quite large. The behavior of the noise is in qualitative agreement with that expected for a generic system undergoing a Hopf bifurcation.

Behavior of noise in a nondegenerate Josephson-parametric amplifier

The noise-rise phenomenon is a long-standing problem that was first observed in Josephson-junction-parametric amplifiers over ten years ago. We present here a case where noise-rise data from a Josephson junction is successfully explained, using a theory based on the universal properties of a dynamical system operated near a bifurcation point. The experiment and theory presented here is for a bifurcation of the Hopf type, a case not discussed previously. The predicted behavior is qualitatively different from that of previously studied bifurcations.

Noise rise in nondegenerate parametric amplifiers.

We report the observation of substantial amplification due to multiwave (more than four) mixing in a Josephson-parametric amplifier. Amplification was achieved with subharmonic pumping at 2/3, 2/3, and 2/7 of the signal frequency near 19 GHz. The processes responsible for the amplification were, correspondingly, five-, seven-, and nine-wave mixing. For the case of five-wave mixing we have observed amplification in excess of 35 dB and noise referred to input of a few degrees kelvin before the amplifier undergoes a pitchfork instability. The noise rise at the pitchfork bifurcation was also studied and compared with theory

R. Movshovich

Papers

Observation of zero-point noise squeezing via a Josephson-parametric amplifier.

A low-noise series-array Josephson junction parametric amplifier

Behavior of noise in a nondegenerate Josephson-parametric amplifier

Noise rise in nondegenerate parametric amplifiers.

Subharmonic pumping of a Josephson-parametric amplifier and the pitchfork instability.