Cryogenic detectors are extremely sensitive and have a wide variety of applications (particularly in astronomy), but are difficult to integrate into large arrays like a modern CCD (charge-coupled device) camera. As current detectors of the cosmic microwave background (CMB) already have sensitivities comparable to the noise arising from the random arrival of CMB photons, the further gains in sensitivity needed to probe the very early Universe will have to arise from large arrays. A similar situation is encountered at other wavelengths. Single-pixel X-ray detectors now have a resolving power of DeltaE < 5 eV for single 6-keV photons, and future X-ray astronomy missions anticipate the need for 1,000-pixel arrays. Here we report the demonstration of a superconducting detector that is easily fabricated and can readily be incorporated into such an array. Its sensitivity is already within an order of magnitude of that needed for CMB observations, and its energy resolution is similarly close to the targets required for future X-ray astronomy missions.

The authors have measured noise in thin-film superconducting coplanar waveguide resonators. This noise appears entirely as phase noise, equivalent to a jitter of the resonance frequency. In contrast, amplitude fluctuations are not observed at the sensitivity of their measurement. The ratio between the noise power in the phase and amplitude directions is large, in excess of 30 dB. These results have important implications for resonant readouts of various devices such as detectors, amplifiers, and qubits. They suggest that the phase noise is due to two-level systems in dielectric materials. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2711770͔ Thin-film superconducting microwave resonators are of interest for a number of applications, including the multiplexed readout of single electron transistors, 1 microwave kinetic inductance detectors ͑MKIDs͒, 2,3 normal metalinsulator-superconductor tunnel junction detectors, 4 superconducting quantum interference devices, 5,6 and qubits. 7,8 The device to be measured presents a variable dissipative or reactive load to the resonator, influencing the resonator quality factor Q r or frequency f r , respectively. Changes to both Q r and f r may be determined simultaneously by sensing the amplitude and phase of a microwave probe signal. 2 While several early demonstrations used hand-assembled lumpedelement circuits, 1,4,5 frequency-domain multiplexing of large arrays generally will require compact microlithographed high-Q r resonators. 1 Such resonators are also needed for strong coupling to charge qubits. 7 Noise in microlithographed resonators has been observed 2,3 and can be a limiting factor for device performance but is not well understood. In this letter, we report measurements of resonator noise, show how the noise spectra separate into amplitude and phase components, and discuss the physical origin of the noise.We studied quarter-wavelength coplanar waveguide ͑CPW͒ resonators 2 ͓Fig. 1͑a͔͒ with center strip widths w of 0.6-6 m and gaps g between the center strip and ground planes of 0.4-4 m, and with impedances Z 0 Ϸ 50 ⍀. Resonator lengths of 3 -7 mm produce resonance frequencies f r between 4 and 10 GHz. Frequency multiplexed arrays of up to 100 resonators are coupled to a single CPW feedline. The CPW circuits are patterned from a film of either Al ͑T c = 1.2 K͒ or Nb ͑T c = 9.2 K͒ on a crystalline substrate, either sapphire, Si, or Ge. The surfaces of the semiconductor substrates are not intentionally oxidized, although a native oxide due to air exposure is expected to be present.A microwave synthesizer at frequency f is used to excite a resonator. The transmitted signal is amplified with a cryogenic high electron mobility transistor ͑HEMT͒ amplifier and is compared to the original signal using an IQ mixer, whose output voltages I and Q are proportional to the in-phase and quadrature amplitudes of the transmitted signal 2,3 ͑see Fig. 2 inset͒. As f is varied, the output = ͓I , Q͔ T ͑the superscript T represents the transpose͒ traces out a resonance circle ͓Fi...

We present measurements of the temperature-dependent frequency shift of five niobium superconducting coplanar waveguide microresonators with center strip widths ranging from 3 to 50 m, taken at temperatures in the range of 100-800 mK, far below the 9.2 K transition temperature of niobium. These data agree well with the two-level system ͑TLS͒ theory. Fits to this theory provide information on the number of TLSs that interact with each resonator geometry. The geometrical scaling indicates a surface distribution of TLSs and the data are consistent with a TLS surface layer thickness of the order of a few nanometers, as might be expected for a native oxide layer. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2906373͔Superconducting microresonators have attracted substantial interest for low temperature detector applications due to the possibility of large-scale microwave frequency multiplexing.1-7 Such resonators are also being used in quantum computing experiments [8][9][10] and for sensing nanomechanical motion. 11 We previously reported that excess frequency noise is universally observed in these resonators and suggested that two-level systems ͑TLSs͒ in dielectric materials 14,15 may be responsible for this noise.12 TLS effects are also observed in superconducting qubits.9 The TLS hypothesis is strongly supported by the observed temperature dependence of the noise and also by the observation of temperature-dependent resonance frequency shifts that closely agree with the TLS theory. 13 To make further progress, it is essential to constrain the location of the TLSs, to determine whether they exist in the bulk substrate or in surface layers, perhaps oxides on the exposed metal or substrate surfaces, or in the interface layers between the metal films and the substrate. In this paper, we provide direct experimental evidence for a surface distribution of TLSs.TLSs are abundant in amorphous materials 14,15 and have electric dipole moments that couple to the electric field E ជ of our resonators. For microwave frequencies and at temperatures T between 100 mK and 1 K, the resonant interaction dominates over relaxation, which leads to a temperaturedependent variation of the dielectric constant given bywhere is the frequency, ⌿ is the complex digamma function, and ␦ = Pd 2 / 3⑀ represents the TLS-induced dielectric loss tangent at T = 0 for weak nonsaturating fields. Here, P and d are the two-level density of states and dipole moment, as introduced by Phillips. 16 Equation ͑1͒ has been extensively used to derive values of Pd 2 in amorphous materials. If TLSs are present in superconducting microresonators, their contribution to the dielectric constant described by Eq. ͑1͒ could be observable as a temperature-dependent shift in the resonance frequency. Indeed, it has recently been suggested that the small anomalous low-temperature frequency shifts often observed in superconducting microresonators may be due to TLS effects, 17,18 and, in fact, excellent fits to the TLS theory can be obtained. 13 Assuming that the TLSs ar...

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 .

We present measurements of the low-temperature excess frequency noise of four niobium superconducting coplanar waveguide microresonators, with center strip widths s r ranging from 3 to 20 m. For a fixed internal power, we find that the frequency noise decreases rapidly with increasing center strip width, scaling as 1 / s r 1.6 . We show that this geometrical scaling is readily explained by a simple semiempirical model which assumes a surface distribution of independent two-level system fluctuators. These results allow the resonator geometry to be optimized for minimum noise. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2937855͔ Thin-film superconducting microresonators are of great interest for a number of applications ͑see Refs. 1-4 and references therein͒. Excess frequency noise is universally observed in these resonators 2,5,6 and is very likely caused by two-level systems ͑TLSs͒ in dielectric materials. 3,7 Indeed, the TLS hypothesis is supported by the observed dependence of the noise on resonator internal power 7,8 and temperature. 3 In a recent paper 4 ͑paper A hereafter͒, we presented measurements of the TLS-induced low-temperature frequency shifts of five niobium ͑T c = 9.2 K͒ coplanar waveguide ͑CPW͒ resonators with varying center strip widths s r . From the observed geometrical scaling of the frequency shifts ͑ϳ1 / s r ͒, we showed that the TLS must be located in a thin ͑few nanometer͒ layer on the surface of the CPW. In this letter, we propose a semiempirical TLS noise model that assumes this surface distribution, and we show that the model explains our measurements of the geometrical scaling of the noise.The device used for the experiment in this paper is exactly the same device used in paper A. In brief, the chip contains five CPW quarter-wavelength resonators ͑Z 0 Ϸ 50 ⍀, f r Ϸ 6 GHz͒ made by patterning a 120 nm thick Nb film deposited on a c-plane crystalline sapphire substrate. Each resonator is capacitively coupled to a common feedline, using a CPW coupler ͑coupling quality factor Q c ϳ 50 000͒ of length l c Х 200 m and with a common center-strip width of s c =3 m. The coupler is then widened into the resonator body, with a center-strip width of s r = 3, 5, 10, 20, or 50 m, and a length of l r ϳ 5 mm. The noise was measured using a standard IQ homodyne technique; 2,3 both the measurement setup and the analysis of the noise data are identical to our previous work. 7 The device is cooled in a dilution refrigerator to a base temperature of 55 mK. The fractional frequency noise spectra S ␦f ͑ ͒ / f r 2 of the five resonators were measured for microwave readout power P w in the range −61 to − 73 dBm; the −65 dBm spectra are shown in Fig. 1͑a͒. We clearly see that the noise has a common spectral shape but decreases as the center strip becomes wider. Unfortunately, the data for the lowest-noise ͑50 m͒ resonator are influenced by the noise floor of our cryogenic microwave amplifier, so we exclude this resonator from further discussion. The noise levels at = 2 kHz were retrieved from the n...

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

We demonstrate position and energy-resolved phonon-mediated detection of particle interactions in a silicon substrate instrumented with an array of microwave kinetic inductance detectors (MKIDs). The relative magnitude and delay of the signal received in each sensor allows the location of the interaction to be determined with 1 mm resolution at 30 keV. Using this position information, variations in the detector response with position can be removed, and an energy resolution of σ E = 0.55 keV at 30 keV was measured. Since MKIDs can be fabricated from a single deposited film and are naturally multiplexed in the frequency domain, this technology can be extended to provide highly-pixelized athermal phonon sensors for ∼1 kg scale detector elements. Such high-resolution, massive particle detectors would be applicable to rare-event searches such as the direct detection of dark matter, neutrinoless double-beta decay, or coherent neutrino-nucleus scattering.Next generation rare-event searches such as the direct detection of dark matter require large target masses (∼10 3 kg) with sub-keV energy resolution. This requires increasing the mass of current solid-state, cryogenic experiments 1,2 by 2 orders of magnitude, while maintaining the background-free operation of existing detectors. Reducing the cost and time needed to fabricate and test each detector element is necessary for such large cryogenic experiments to be feasible.Detectors that measure both the athermal phonons and ionization created by a particle interaction have demonstrated sufficient background rejection to enable next-generation experiments 3 . Microwave kinetic inductance detectors (MKIDs) 4,5 offer several advantages for providing athermal phonon sensors in large experiments relative to the transition edge sensor (TES)-based designs currently in use 1,2,6 . MKIDs can be patterned from a single deposited aluminum film, with large (>10 µm) features, significantly reducing fabrication time and complexity. Since MKIDs are naturally multiplexed in the frequency domain, hundreds of sensors can be read out on a single coaxial cable, enabling a more granular phonon sensor that is expected to provide enhanced background rejection. In addition to dark matter direct detection, high-resolution, massive particle detectors are applicable to the detection of neutrinoless double-beta decay 7 and coherent neutrino-nucleus scattering 8 .Previous designs 9-11 attempted to absorb the incident energy in large-area collectors coupled to smaller volume, distributed MKIDs. Although separating the absorber and sensor allowed increased sensitivity by concentrating the absorbed energy, test devices suffered from poor transmission of quasiparticles from the absorber to sensor. Here we present a simplified design that eliminates the absorber by directly collecting the energy using large-area MKIDs. A similar design developed independently by Swenson et al. 12 has been used a) Electronic mail: davidm@caltech.edu to demonstrate time-resolved phonon-mediated detection of high-energy int...