We discuss a general method for constructing nonreciprocal, cavity-based photonic devices, based on matching a given coherent interaction with its corresponding dissipative counterpart; our method generalizes the basic structure used in the theory of cascaded quantum systems and can render an extremely wide class of interactions directional. In contrast to standard interference-based schemes, our approach allows directional behavior over a wide bandwidth. We show how it can be used to devise isolators and directional, quantum-limited amplifiers. We discuss in detail how this general method allows the construction of a directional, noise-free phase-sensitive amplifier that is not limited by any fundamental gain-bandwidth constraint. Our approach is particularly well suited to implementations using superconducting microwave circuits and optomechanical systems.

Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic magnetic flux, which in combination with dissipative coupling to the mechanical bath, leads to nonreciprocal transport of photons with 35 dB of isolation. Additionally, optical pumping with blue-detuned light manifests as a particle non-conserving interaction between photons and phonons, resulting in directional optical amplification of 12 dB in the isolator through direction. These results indicate the feasibility of utilizing optomechanical circuits to create a more general class of nonreciprocal optical devices, and further, to enable novel topological phases for both light and sound on a microchip.

Quantum electromechanical systems offer a unique opportunity to probe quantum noise properties in macroscopic devices, properties that ultimately stem from Heisenberg's uncertainty relations. A simple example of this behavior is expected to occur in a microwave parametric transducer, where mechanical motion generates motional sidebands corresponding to the up-and-down frequency conversion of microwave photons. Because of quantum vacuum noise, the rates of these processes are expected to be unequal. We measure this fundamental imbalance in a microwave transducer coupled to a radiofrequency mechanical mode, cooled near the ground state of motion. We also discuss the subtle origin of this imbalance: depending on the measurement scheme, the imbalance is most naturally attributed to the quantum fluctuations of either the mechanical mode or of the electromagnetic field.

We describe a new kind of phase-preserving quantum amplifier which utilizes dissipative interactions in a parametrically-coupled three-mode bosonic system. The use of dissipative interactions provides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. We show that the scheme is simple enough to be implemented both in optomechanical systems and in superconducting microwave circuits.PACS numbers: 42.65. Yj, 03.65.Ta, 42.50.Wk, 07.10.Cm Introduction-The past few years have seen a resurgence of interest in amplifiers working near the fundamental limits set by quantum mechanics [1], in contexts varying from quantum information processing in circuits [2][3][4], to radio astronomy [5], to ultra-sensitive force detection (e.g., for gravity wave detection [6]). The standard paradigm for a quantum-limited, phasepreserving amplifier is the non-degenerate parametric amplifier (NDPA) [7][8][9][10], which is based on a coherent interaction involving three bosonic modes (pump, signal and idler). This interaction simply converts a pump mode photon into two photons, one in the signal mode, the other in the idler mode. The result is that weak signals incident on the signal mode are amplified, with the minimum possible added noise. There has been remarkable progress in realizing such amplifiers using superconducting circuits [11][12][13][14][15][16][17][18]. This in turn has enabled a number of breakthroughs, from the measurement of mechanical motion near the quantum limit [19], to the measurement of quantum jumps of a superconducting qubit [20,21] and the implementation of quantum feedback schemes [22,23].Despite their many advantages, standard cavity-based parametric amplifiers suffer from the limitation of having a fixed gain-bandwidth product: as one increases the gain of the amplifier, one also reduces the range of signal frequencies over which there is amplification. This is a fundamental consequence of the amplification mechanism, which involves introducing effective negative damping to the signal mode. The consequent reduced damping rate determines the amplification, but also sets the amplification bandwidth (see, e.g., [3]). This tradeoff between gain and bandwidth can severely limit the utility of cavity-based parametric amplifiers in many applications. Traveling-wave parametric amplifiers (TWPAs) [24,25] do not use cavities and are in principle not limited in the same way. In practice however, good device performance and bandwidth of TWPAs is limited by the requirement of phase-matching (though see Ref. 26 for recent progress in the microwave domain).In this work, we introduce a new approach for quantum-limited amplification based now on three local-