S. Novikov

Decoupling a Cooper-Pair Box to Enhance the Lifetime to 0.2 ms

We present results on a circuit QED experiment in which a separate transmission line is used to address a quasilumped element superconducting microwave resonator which is in turn coupled to an Al/AlO(x)/Al Cooper-pair box charge qubit. With our device, we find a strong correlation between the lifetime of the qubit and the inverse of the coupling between the qubit and the transmission line. At the smallest coupling we measured, the lifetime of the Cooper-pair box was T₁=200 μs, which represents more than a twentyfold improvement in the lifetime of the Cooper-pair box compared with previous results. These results imply that the loss tangent in the AlO(x) junction barrier must be less than about 4×10⁻⁸ at 4.5 GHz, about 4 orders of magnitude less than reported in larger area Al/AlO(x)/Al tunnel junctions.

Autler-Townes splitting in a three-dimensional transmon superconducting qubit

We have observed the Autler-Townes doublet in a superconducting Al/AlOx/Al transmon qubit that acts as an artificial atom embedded in a three-dimensional Cu microwave cavity at a temperature of 22 mK. Using pulsed microwave spectroscopy, the three lowest transmon levels are isolated, eliminating unwanted effects of higher qubit modes and cavity modes. The long coherence time (~40 us) of the transmon enables us to observe a clear Autler-Townes splitting at drive amplitudes much smaller than the transmon level anharmonicity (177 MHz). Three-level density matrix simulations with no free parameters provide excellent fits to the data. At maximum separation, the fidelity of a dark state achieved in this experiment is estimated to be 99.6-99.9%.

Observation of Autler-Townes effect in a dispersively dressed Jaynes-Cummings System

We report on the spectrum of a superconducting transmon device coupled to a planar superconducting resonator in the strong dispersive limit where discrete peaks, each corresponding to a different number of photons, are resolved. A thermal population of 5.474 GHz photons at an effective resonator temperature of T = 120 mK results in a weak n = 1 photon peak along with the n = 0 photon peak in the qubit spectrum in the absence of a coherent drive on the resonator. Two-tone spectroscopy using independent coupler and probe tones reveals an Autler–Townes splitting in the thermal n = 1 photon peak. The observed effect is explained accurately using the four lowest levels of the dispersively dressed qubit–resonator system and compared to results from numerical simulations of the steady-state master equation for the coupled system.

Singular soliton operators and indefinite metrics

We consider singular real second order 1D Schrödinger operators such that all local solutions to the eigenvalue problems are x-meromorphic for all λ. All algebrogeometrical potentials (i.e. “singular finite-gap” and “singular solitons”) satisfy to this condition. A Spectral Theory is constructed for the periodic and rapidly decreasing potentials in the classes of functionswith singularities: The corresponding operators are symmetric with respect to some natural indefinite inner product as it was discovered by the present authors. It has a finite number of negative squares in the both (periodic and rapidly decreasing) cases. The time dynamics provided by the KdV hierarchy preserves this number. The right analog of Fourier Transform on Riemann Surfaces with good multiplicative properties (the R-Fourier Transform) is a partial case of this theory. The potential has a pole in this case at x = 0 with asymptotics u ∼ g(g + 1)/x2. Here g is the genus of spectral curve.

Nonlinear microwave photon occupancy of a driven resonator strongly coupled to a transmon qubit

We measure photon occupancy in a thin-film superconducting lumped element resonator coupled to a transmon qubit at 20mK and find a nonlinear dependence on the applied microwave power. The transmon-resonator system was operated in the strong dispersive regime, where the ac Stark shift (2χ) due to a single microwave photon present in the resonator was larger than the linewidth (Γ) of the qubit transition. When the resonator was coherently driven at 5.474 325 GHz, the transition spectrum of the transmon at 4.982 GHz revealed well-resolved peaks, each corresponding to an individual photon number-state of the resonator. From the relative peak heights we obtain the occupancy of the photon states and the average photon occupancy n¯ of the resonator. We observe a nonlinear variation of n¯ with the applied drive power Prf for n¯<5 and compare our results to numerical simulations of the system-bath master equation in the steady state, as well as to a semiclassical model for the resonator that includes the Jaynes-Cummings interaction between the transmon and the resonator. We find good quantitative agreement using both models and analysis reveals that the nonlinear behavior is principally due to shifts in the resonant frequency caused by a qubit-induced Jaynes-Cummings nonlinearity.

Spectroscopy of a Cooper-pair box coupled to a two-level system via charge and critical current

We report on the quadrupling of the transition spectrum of an Al/AlOx/Al Cooper-pair box (CPB) charge qubit in the 4.0-7.3 GHz frequency range. The qubit was coupled to a quasi-lumped element Al superconducting resonator and measured at a temperature of 25 mK. We obtained good matches between the observed spectrum and the spectra calculated from a model Hamiltonian containing two distinct low excitation energy two-level systems (TLS) coupled to the CPB. In our model, each TLS has a charge that tunnels between two sites in a local potential and induces a change in the CPB critical current. By fitting the model to the spectrum, we have extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a surprisingly large fractional change (30-40%) in the critical current (12 nA). This large change is consistent with a Josephson junction with a non-uniform tunnel barrier containing a few dominant conduction channels and a TLS that modulates one of them.

Decoherence in a pair of long-lived Cooper-pair boxes

We have investigated the decoherence of quantum states in two Al/AlOx/Al Cooper-pair boxes coupled to lumped element superconducting inductor-capacitor resonators. At 25 mK, the first qubit had an energy relaxation time T1 that varied from 30 μs to 200 μs between 4 and 8 GHz and displayed an inverse correlation between T1 and the coupling to the microwave drive line. The Ramsey fringe decay times T2* were in the [200–500] ns range while the spin echo envelope decay times Techo varied from 2.4–3.3 μs, consistent with 1/f charge noise with a high frequency cutoff of 0.2 MHz. A second Cooper-pair box qubit with similar parameters showed T1=4−30 μs between 4 and 7.3 GHz, and that the T1 and the coupling were again inversely correlated. Although the lifetime of the second device was shorter than that of the first device, the dependence on coupling in both devices suggests that further reduction in coupling should lead to improved qubit performance.