The interaction of matter and light is one of the fundamental processes occurring in nature, and its most elementary form is realized when a single atom interacts with a single photon. Reaching this regime has been a major focus of research in atomic physics and quantum optics for several decades and has generated the field of cavity quantum electrodynamics. Here we perform an experiment in which a superconducting two-level system, playing the role of an artificial atom, is coupled to an on-chip cavity consisting of a superconducting transmission line resonator. We show that the strong coupling regime can be attained in a solid-state system, and we experimentally observe the coherent interaction of a superconducting two-level system with a single microwave photon. The concept of circuit quantum electrodynamics opens many new possibilities for studying the strong interaction of light and matter. This system can also be exploited for quantum information processing and quantum communication and may lead to new approaches for single photon generation and detection.

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...

We measure the coherence of a new superconducting qubit, the low-impedance flux qubit, finding T * 2 ∼ T1 ∼ 1.5µs. It is a three-junction flux qubit, but the ratio of junction critical currents is chosen to make the qubit's potential have a single well form. The low impedance of its large shunting capacitance protects it from decoherence. This qubit has a moderate anharmonicity, whose sign is reversed compared with all other popular qubit designs. The qubit is capacitively coupled to a high-Q resonator in a λ/2 configuration, which permits the qubit's state to be read out dispersively. PACS numbers:While there have been many successful superconducting qubit types, their large diversity suggests that the optimal qubit will be a hybrid combining favorable features of all: the tunability of the flux qubit [1][2][3], the simplicity, robustness and low impedance of the phase qubit [4][5][6] and the high coherence and compatibility with high-Q superconducting resonators of the transmon [7,8]. We have built such a hybrid, related to a suggested design of You et al. [9]. Our capacitively shunted flux qubit begins as a traditional three-junction loop[1], but is made to have low impedance by virtue of a large capacitive shunt (C s = 100fF) of the small junction. This new superconducting qubit is as coherent as the best currently reported; we measure T * 2 ∼ T 1 ∼ 1.5µs. Since the key to this qubit is the large shunting capacitance C s and therefore its low effective impedance L J /C s , we will call it the low-impedance flux qubit ( Z flux qubit). As Fig. 1(a) shows, the shunt capacitor is realized using a simple, reliable single-level interdigitated structure. We choose the ratio of the small and large junction critical currents I 0 to be around α = 0.3. For this α the qubit potential has only one minimum (see Eq. (3) below), and the qubit shows only a weak dependence of the qubit frequency ω 01 on applied flux Φ. As for the original flux qubit, a "sweet spot" exists at which the qubit is to first order insensitive to Φ, giving rise to long dephasing times, but even away from this degeneracy point our frequency sensitivity is about a factor of 30 smaller than in the traditional flux qubit. Our flux sensitivity is comparable to that of the phase qubit (∂ω 01 /∂Φ ∼ 30 GHz/Φ 0 ) which permits tunability without completely destroying phase coherence, despite the presence of significant flux noise amplitude on the order of S Φ = 1 − 2µΦ 0 / √ Hz. Modeling indicates that our qubit at the sweet spot still has appreciable anharmonicity, with |ω 12 − ω 01 |/2π in the neighborhood of several 100 MHz (or about 2 − 10% of the qubit resonance frequency, depending on α), but interestingly, with ω 12 > ω 01 , the opposite of any important qubit except the flux qubit. Such anharmonicity leads to a situation where all of the lowest energy levels for a two-qubit system would be those of the computational manifold |0 and |1 , which will facilitate coupled qubit experiments. The reduced impedance of this qubit has several advantages. Qubits...

We present measurements of the temperature and power dependence of the resonance frequency and frequency noise of superconducting niobium thin-film coplanar waveguide resonators carried out at temperatures well below the superconducting transition ͑T c = 9.2 K͒. The noise decreases by nearly two orders of magnitude as the temperature is increased from 120 to 1200 mK, while the variation of the resonance frequency with temperature over this range agrees well with the standard two-level system ͑TLS͒ model for amorphous dielectrics. These results support the hypothesis that TLSs are responsible for the noise in superconducting microresonators and have important implications for resonator applications such as qubits and photon detectors. 23 have highlighted TLS effects in superconducting microcircuits. While the TLS energy splitting ⌬E has a broad distribution, 22 a resonator with frequency f r is most sensitive to TLS with ⌬E ϳ hf r . The level populations and relaxation rates of such TLS vary strongly at temperatures T ϳ hf r / 2k B , or around 100 mK for the device studied here. Furthermore, such near-resonant TLS may saturate 18 for strong resonator excitation power P w . Hence, measurements of the power and temperature variation of the resonator frequency and noise, as presented in this letter, provide a strong test of the TLS hypothesis.We studied coplanar waveguide ͑CPW͒ quarterwavelength resonators 2,18 fabricated on a high-resistivity ͑ ജ 10 k⍀ cm͒ crystalline silicon substrate by patterning a 200 nm thick niobium film using a photoresist mask and a SF 6 inductively coupled plasma etch. In this device, TLS may be present in the native oxide surface layers on the metal film or substrate. 18 The resonator is capacitively coupled to a CPW feedline ͑Fig. 1͒ that has a 10 m wide center strip and 6 m gaps between the center strip and the ground plane. For the resonator, these dimensions are 5 and 1 m, respectively. The resonator length is 5.8 mm, corresponding to f r = 4.35 GHz. The coupling strength is set lithographically 17,18 ͑see Fig. 1͒ and is characterized by the coupling-limited quality factor Q c =5ϫ 10 5 . The device was cooled using a dilution refrigerator, and its temperature was measured to Ϯ5 mK accuracy using a calibrated RuO 2 thermometer mounted on the copper sample enclosure. The microwave readout ͑Fig. 1͒ uses a standard IQ homodyne mixing technique. 2,17 The IQ mixer's complex output voltage ͑f͒ = I͑f͒ + jQ͑f͒ follows a circular trajectory in the complex plane as the microwave excitation frequency f is varied, 18 and f r and Q r are determined by complex leastsquares fitting of this trajectory to a ten-parameter model:Here ␦x = ͑f − f r ͒ / f r is the fractional frequency offset, S 21 ͑r͒ is the complex forward transmission on resonance, B 0 + B 1 ␦x allows for a linear gain variation, 0 + 1 ␦x allows a similar linear phase variation, and B 2 and 2 specify the output offset voltages of the IQ mixer. The combined noise of the resonator and readout electronics is measured by tuning the synthesi...

We propose a scheme for dispersive readout of stored energy in one mode of a nonlinear superconducting microwave ring resonator by detection of the frequency shift of a second mode coupled to the first via a Kerr nonlinearity. Symmetry is used to enhance the device responsivity while minimizing self nonlinearity of each mode. Assessment of the signal to noise ratio indicates that the scheme will function at the single photon level, allowing quantum non-demolition measurement of the photon number state of one mode. Experimental data from a simplified version of the device demonstrating the principle of operation are presented. PACS: 84.40.Dc, 85.25.Am