The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and atomic, molecular, optical--quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, the basics of weak continuous measurements are described. Particular attention is given to the treatment of the standard quantum limit on linear amplifiers and position detectors within a general linear-response framework. This approach is shown how it relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics and its application to the case of electrical circuits is illustrated, including mesoscopic detectors and resonant cavity detectors.

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Introduction to quantum noise, measurement, and amplification

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.

The aim of this review is to provide quantum engineers with an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits. Over the past twenty years, the field has matured from a predominantly basic research endeavor to a one that increasingly explores the engineering of larger-scale superconducting quantum systems. Here, we review several foundational elements—qubit design, noise properties, qubit control, and readout techniques—developed during this period, bridging fundamental concepts in circuit quantum electrodynamics and contemporary, state-of-the-art applications in gate-model quantum computation.

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A quantum engineer's guide to superconducting qubits

Microwave photonics with superconducting quantum circuits

We present the results of an experimental effort to generate squeezed microwave radiation using the phase-sensitive gain of a Josephson parametric amplifier. To facilitate the interpretation of the experimental results, we first present a discussion of the theory of microwave squeezing via Josephson parametric amplifiers. This is followed by a detailed description of the device fabricated for our experiment. Experimental results are then presented for the device used in both the doubly degenerate or four-photon mode and for the degenerate or three-photon mode. We have observed parametric deamplification of signals by more than 8 dB. We have demonstrated squeezing of 4.2-K thermal noise. When operated at 0.1 K, the amplifier exhibits an excess noise of 0.28 K when referred to the input. This is smaller than the vacuum fluctuation noise level \ensuremath{\Elzxh}\ensuremath{\omega}/2k=0.47 K. The amplifier is thus quieter than a linear phase-insensitive amplifier in principle can be.

Observation of parametric amplification and deamplification in a Josephson parametric amplifier

We have demonstrated 42% squeezing of 4.2-K thermal noise using a Josephson-parametric amplifier operated at 19.4 GHz. The amplifier has been operated at 0.1 K with an excess noise of 0.28 K referred to the input port. This is less than the vacuum fluctuation noise h\ensuremath{\nu}/2k=0.47 K at 19.4 GHz. The amplifier thus is less noise than a linear phase-insensitive amplifier such as a maser could in principle be.

Observation of 4.2-K equilibrium-noise squeezing via a Josephson-parametric amplifier.

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.

The authors observed the squeezing of 4.2 K thermal noise using a Josephson parametric amplifier operated in the degenerate mode at 19.4 GHz. A 42% reduction in the equilibrium noise was observed. The amplifier has also been operated at 0.1 K with an excess noise of 0.28 K referred to the amplifier's input port. This is less than the vacuum fluctuation noise of 0.47 K at the amplifier's input. Recently the amplifier has been operated in a nonchaotic mode with a signal gain in excess of 16 dB. >

Observation of 4.2 equilibrium noise squeezing via a Josephson-parametric amplifier

We report the performance of a Josephson Voltage-controlled oscillator consisting of a tunnel junction shunted by a small inductor in series with a small bias resistor (a resistive SQUID circuit). The circuit displayed regions of stability, bifurcation, and chaos as a function of bias conditions and circuit parameters. We measured narrow band coupled power levels of 25 pW in the fundamental mode and 50 pW in the first subharmonic mode over a 10% frequency band at approximately 9 GHz. Linewidths were dominated by the thermal noise of the bias resistor. These results are in qualitative agreement with numerical simulations, which also show progressive bifurcations from fundamental to chaotic trajectories.

A. D. Smith

Papers

Observation of parametric amplification and deamplification in a Josephson parametric amplifier

Observation of 4.2-K equilibrium-noise squeezing via a Josephson-parametric amplifier.

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

Observation of 4.2 equilibrium noise squeezing via a Josephson-parametric amplifier

Chaos and bifurcation in Josephson voltage-controlled oscillators