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arXiv:1108.2705 · Physical Review B

Coherent control of a superconducting qubit with dynamically tunable qubit-cavity coupling

Anthony J. Hoffman, Srikanth J. Srinivasan, Jay Gambetta, Andrew Houck

Published Nov 14, 2011• 47 citations
arXivHTMLPDF

Abstract

We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths showing that the qubit transition can be turned off by a factor of more than 1500. We show how the qubit can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe ${T}_{1}$ and ${T}_{2}$ times of 1.6 and 1.9 $\ensuremath{\mu}$s, respectively. This work demonstrates how this qubit can be incorporated into quantum architectures.

DOI
10.1103/physrevb.84.184515

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We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths showing that the qubit transition can be turned off by a factor of more than 1500. We show how the qubit can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe T1{T}_{1}T1​ and T2{T}_{2}T2​ times of 1.6 and 1.9 \ensuremathμ\ensuremath{\mu}\ensuremathμs, respectively. This work demonstrates how this qubit can be incorporated into quantum architectures.
In this work, we study a series of tunable flux qubits inductively coupled to a coplanar waveguide resonator fabricated on a sapphire substrate. Each qubit includes an asymmetric superconducting quantum interference device, which is controlled by the application of an external magnetic field and acts as a tunable Josephson junction. The tunability of the qubits is typically $\ifmmode\pm\else\textpm\fi{}3.5\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$ around their central gap frequency. The measured relaxation times are limited by dielectric losses in the substrate and can attain ${T}_{1}\ensuremath{\sim}8\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$. The echo dephasing times are limited by flux noise even at optimal points and reach ${T}_{2E}\ensuremath{\sim}4\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$, almost an order of magnitude longer than state of the art.
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Abstract Ensembles of trapped atoms interacting with on-chip microwave resonators are considered as promising systems for the realization of quantum memories, novel quantum gates, and interfaces between the microwave and optical regime. Here, we demonstrate coupling of magnetically trapped ultracold Rb ground-state atoms to a coherently driven superconducting coplanar resonator on an integrated atom chip. When the cavity is driven off-resonance from the atomic transition, the microwave field strength in the cavity can be measured through observation of the AC shift of the atomic hyperfine transition frequency. When driving the cavity in resonance with the atoms, we observe Rabi oscillations between hyperfine states, demonstrating coherent control of the atomic states through the cavity field. These observations enable the preparation of coherent atomic superposition states, which are required for the implementation of an atomic quantum memory.
We measured the relaxation and decoherence rates of a superconducting transmon qubit in a resonator-free setting. In our experiments, the qubit is coupled to an open coplanar waveguide such that the transmission of microwaves through this line depends on the qubit's state. To determine the occupation of the first excited qubit energy level, we introduced a two-pulse technique. The first applied pulse, at a frequency close to the eigenfrequency of the qubit, serves to excite the qubit. A second pulse is then used for probing the transition between the first and second excited energy levels. Utilizing this measurement technique allowed for the reconstruction of the relaxation dynamics and Rabi oscillations. Furthermore, we demonstrate the consistency between the extracted parameters and the corresponding estimations from frequency-domain measurements.
We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved with a tunable coupling design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasistatic tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single-photon exchange in 6 ns. Qubit coherence times exceeding 20 μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon nonconserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80%.
We have fabricated and characterized systems consisting of superconducting quantum bits (qubits) of the transmon type, coupled to a tunable transmission line resonator. The resonator consists of a superconducting quarter wavelength coplanar waveguide (CPW) resonator that is made tunable by terminating the transmission line to ground through a superconducting quantum interference device (SQUID). Here we present measurements on two devices where we observe Rabi oscillations as we drive the qubit, and vacuum Rabi splitting both as we tune the qubits into resonance with the resonator and as we tune the resonator into resonance with the qubits. We also observe coherent interaction between two resonant qubits. In addition, we demonstrate that we can calculate the response very accurately using a multilevel Hamiltonian.