1It has recently become possible to encode the quantum state of superconducting qubits and the position of nanomechanical oscillators into the states of microwave fields 1,2 . However, to make an ideal measurement of the state of a qubit, or to detect the position of a mechanical oscillator with quantum-limited sensitivity requires an amplifier that adds no noise. If an amplifier adds less than half a quantum of noise, it can also squeeze the quantum noise of the electromagnetic vacuum. Highly squeezed states of the vacuum serve as an important quantum information resource. They can be used to generate entanglement or to realize back-action-evading measurements of position 3,4 . Here we introduce a general purpose parametric device, which operates in a frequency band between 4 and 8 GHz. It is a subquantum-limited microwave amplifier, it amplifies quantum noise above the added noise of commercial amplifiers, and it squeezes quantum fluctuations by 10 dB.With the emergence of quantum information processing with electrical circuits, there is a renewed interest in Josephson parametric devices 5,6,7,8,9 . Previous work with Josephson parametric amplifiers demonstrated that they can operate with subquantum-limited added noise and modestly squeeze vacuum noise 10,11,12,13,14 . Earlier realizations of Josephson parametric amplifiers (JPAs) were only capable of amplifying signals in a narrow frequency range, were not operated with large enough gain to make the noise of the following, conventional amplifier negligible or were too lossy to be subquantum limited 5 . For related reasons, the degree of squeezing of the vacuum noise was never larger than 3 dB. We create a new type of parametric amplifier in which we embed a tunable, low-loss, and nonlinear metamaterial in a microwave cavity. The tunability of the metamaterial allows us to adjust the amplified band between 4 and 8 GHz, and the cavity isolates the gain medium from low-frequency noise, providing the stability required to achieve high gains and large squeezing.A single mode of a microwave field with angular frequency ω can be decomposed in two orthogonal components, referred to as quadratureŝ V (t) ∝X 1 cos ωt +X 2 sin ωt whereX 1 andX 2 are conjugate quantum variables obeying the commutation relation [X 1 ,X 2 ] = i/2. The proportionality constant depends on the details of the mode 15,16,17 .As a consequence of the commutation relation, the uncertainties inX 1 andX 2 are subject 2 to the Heisenberg constraint ∆X 1 ∆X 2 ≥ 1/4, where ∆X 2 j is the variance of the quadrature amplitudeX j . A mode is "squeezed" if for one of the quadratures ∆X j < 1/2 (ref. 17). An amplifier that transforms both input quadratures by multiplying them by a gain √ G must add at least half a quantum of noise for the output signal to obey the commutation relation 18 ; if it adds exactly half a quantum of noise, it is quantum limited. On the other hand, an amplifier which transforms the input signal by multiplying one quadrature by √ G and multiplying the other quadrature by 1/ √ G would...

Nanomechanical oscillators are at the heart of ultrasensitive detectors of force, mass and motion. As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. If the imprecision of a measurement of the displacement of an oscillator is pushed below a scale set by the standard quantum limit, the measurement must perturb the motion of the oscillator by an amount larger than that scale. Here we show a displacement measurement with an imprecision below the standard quantum limit scale. We achieve this imprecision by measuring the motion of a nanomechanical oscillator with a nearly shot-noise limited microwave interferometer. As the interferometer is naturally operated at cryogenic temperatures, the thermal motion of the oscillator is minimized, yielding an excellent force detector with a sensitivity of 0.51 aN Hz(-1/2). This measurement is a critical step towards observing quantum behaviour in a mechanical object.

We create a Josephson parametric amplifier from a transmission line resonator whose inner conductor is made from a series SQUID array. By changing the magnetic flux through the SQUID loops, we are able to adjust the circuit's resonance frequency and, consenquently, the center of the amplified band, between 4 and 7.8 GHz. We observe that the amplifier has gains as large as 28 dB and infer that it adds less than twice the input vacuum noise.