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...

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...