Amplifiers are ubiquitous in electronics and play a fundamental role in a wide range of scientific measurements. From a user's perspective, an ideal amplifier has very low noise, operates over a broad frequency range, and has a high dynamic range -it is capable of handling strong signals with little distortion.Unfortunately, it is difficult to obtain all of these characteristics simultaneously.For example, modern transistor amplifiers offer multi-octave bandwidths and excellent dynamic range. However, their noise remains far above the fundamental limit set by the uncertainty principle of quantum mechanics.[1] Parametric amplifiers, which predate transistor amplifiers and are widely used in optics, exploit a nonlinear response to transfer power from a strong pump tone to a weak signal.If the nonlinearity is purely reactive, i.e. nondissipative, in theory the amplifier noise can reach the quantum-mechanical limit.[2] Indeed, microwave frequency superconducting Josephson parametric amplifiers [3, 4] do approach the quantum limit, but generally are narrow band and have very limited dynamic range. In this paper, we describe a superconducting parametric amplifier that overcomes these limitations. The amplifier is very simple, consisting only of a patterned metal film on a dielectric substrate, and relies on the nonlinear kinetic inductance of a superconducting transmission line. We measure gain extending over 2 GHz on either side of an 11.56 GHz pump tone, and we place an upper limit 1 arXiv:1201.2392v1 [cond-mat.supr-con] 11 Jan 2012 on the added noise of the amplifier of 3.4 photons at 9.4 GHz. Furthermore, the dynamic range is very large, comparable to microwave transistor amplifiers, and the concept can be applied throughout the microwave, millimeter-wave and submillimeter-wave bands.Over the past decade, the combination of high-performance superconducting microresonators and low-noise, microwave frequency cryogenic transistor amplifier readouts has proven to be particularly powerful for a wide range of applications including photon detection and quantum information experiments. [5][6][7] These developments have generated strong renewed interest in superconducting amplifiers that achieve even lower readout noise. [8][9][10][11][12].Most of these devices are parametric amplifiers that make use of the nonlinear inductance of the Josephson junction, which is almost ideally reactive with little dissipation below the critical current I c . As a result, Josephson paramps can be exquisitely sensitive, approaching the standard quantum limit of half a photon ω/2 of added noise power per unit bandwidth in the standard case when both quadratures of a signal at frequency ω are amplified equally.Here is Planck's constant divided by 2π. Even less noise is possible in situations when only one quadrature is amplified. [1]. In comparison, the added noise of cryogenic transistor amplifiers is typically 10-20 times the quantum limit.[13] However, the dynamic range of Josephson paramps is regulated by the Josephson energy E J = I c ...

Titanium nitride (TiN x ) films are ideal for use in superconducting microresonator detectors because: a) the critical temperature varies with composition (0 < T c < 5 K); b) the normal-state resistivity is large, ρ n ∼ 100 µΩ cm, facilitating efficient photon absorption and providing a large kinetic inductance and detector responsivity; and c) TiN films are very hard and mechanically robust. Resonators using reactively sputtered TiN films show remarkably low loss (Q i > 10 7 ) and have noise properties similar to resonators made using other materials, while the quasiparticle lifetimes are reasonably long, 10−200 µs. TiN microresonators should therefore reach sensitivities well below 10 −19 W Hz −1/2 .

If driven sufficiently strongly, superconducting microresonators exhibit nonlinear behavior including response bifurcation. This behavior can arise from a variety of physical mechanisms including heating effects, grain boundaries or weak links, vortex penetration, or through the intrinsic nonlinearity of the kinetic inductance. Although microresonators used for photon detection are usually driven fairly hard in order to optimize their sensitivity, most experiments to date have not explored detector performance beyond the onset of bifurcation. Here, we present measurements of a lumped-element superconducting microresonator designed for use as a farinfrared detector and operated deep into the nonlinear regime. The 1 GHz resonator was fabricated from a 22 nm thick titanium nitride film with a critical temperature of 2 K and a normal-state resistivity of 100 lX cm. We measured the response of the device when illuminated with 6.4 pW optical loading using microwave readout powers that ranged from the low-power, linear regime to 18 dB beyond the onset of bifurcation. Over this entire range, the nonlinear behavior is well described by a nonlinear kinetic inductance. The best noise-equivalent power of 2 Â 10 À16 W=Hz 1=2 at 10 Hz was measured at the highest readout power, and represents a $10 fold improvement compared with operating below the onset of bifurcation. V C 2013 American Institute of Physics. [http://dx

The energy resolution of a single photon counting Microwave Kinetic Inductance Detector (MKID) can be degraded by noise coming from the primary low temperature amplifier in the detector's readout system. Until recently, quantum limited amplifiers have been incompatible with these detectors due to dynamic range, power, and bandwidth constraints. However, we show that a kinetic inductance based traveling wave parametric amplifier can be used for this application and reaches the quantum limit. The total system noise for this readout scheme was equal to ∼2.1 in units of quanta. For incident photons in the 800 to 1300 nm range, the amplifier increased the average resolving power of the detector from ∼6.7 to 9.3 at which point the resolution becomes limited by noise on the pulse height of the signal. Noise measurements suggest that a resolving power of up to 25 is possible if redesigned detectors can remove this additional noise source.Optical MKIDs 1 are superconducting, single photon counting, energy resolving sensors which are sensitive to radiation in the ultraviolet to near infrared range. Advantages over semiconductor detectors in this wavelength band include the absence of false counts (read noise, dark current, and cosmic rays), intrinsic spectral resolution, high speed, and radiation hardness. Other superconducting detectors have shown promise at these wavelengths, 2,3 but they are difficult to chain together into large arrays. Optical MKIDs, however, are naturally frequency domain multiplexed, which has enabled full-scale instruments at the Palomar observatory 4,5 and Subaru telescope. 6 In the future, these detectors will be included in a balloon borne mission. 7 Photon counting MKIDs operate differently than MKIDs designed for longer wavelength detection in the bolometric regime. Instead of measuring a constant flux of photons, they record individual photon events similarly to an X-ray calorimeter. To achieve a measurable detector response for a single photon event they tend to be smaller and able to handle less signal power than their longer wavelength bolometric counterparts. In these conditions, amplifier noise can be comparable in magnitude to the detector phase noise that originates from microscopic two-level system (TLS) states on the surface or between layers of the device. 8 The TLS noise can be mitigated through careful sample preparation, 9 fabrication, 10,11 and device design 12-14 while the effect of amplifier noise can be addressed by designing detectors that can handle higher signal powers. 15,16 These routes are actively pursued, but, for optical MKIDs, improving the main readout amplifier's noise floor offers an additional path to lowering the total system noise.Quantum mechanics imposes an uncertainty relationship between the two quadratures of an electromagnetic signal. 17 This relationship results in a lower limit to the noise that a high gain, phase-preserving, linear amplifier adds to its input signal, equal to that of the electromagnetic zero-point fluctuations (A = 1 /2). To readout a...

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