Simultaneous Bistability of a Qubit and Resonator in Circuit Quantum Electrodynamics

Physical Review Letters American Physical Society (APS) 118 (0) 040402

TK Mavrogordatos, G Tancredi, M Elliott, MJ Peterer, A Patterson, J Rahamim, PJ Leek, E Ginossar, MH Szymańska

Thermal Excitation of Multi-Photon Dressed States in Circuit Quantum Electrodynamics

ArXiv (0)

JM Fink, M Baur, R Bianchetti, S Filipp, M Göppl, PJ Leek, L Steffen, A Blais, A Wallraff

The exceptionally strong coupling realizable between superconducting qubits and photons stored in an on-chip microwave resonator allows for the detailed study of matter-light interactions in the realm of circuit quantum electrodynamics (QED). Here we investigate the resonant interaction between a single transmon-type multilevel artificial atom and weak thermal and coherent fields. We explore up to three photon dressed states of the coupled system in a linear response heterodyne transmission measurement. The results are in good quantitative agreement with a generalized Jaynes-Cummings model. Our data indicates that the role of thermal fields in resonant cavity QED can be studied in detail using superconducting circuits.

Dynamics of dispersive single qubit read-out in circuit quantum electrodynamics

ArXiv (0)

R Bianchetti, S Filipp, M Baur, JM Fink, M Göppl, PJ Leek, L Steffen, A Blais, A Wallraff

The quantum state of a superconducting qubit nonresonantly coupled to a transmission line resonator can be determined by measuring the quadrature amplitudes of an electromagnetic field transmitted through the resonator. We present experiments in which we analyze in detail the dynamics of the transmitted field as a function of the measurement frequency for both weak continuous and pulsed measurements. We find excellent agreement between our data and calculations based on a set of Bloch-type differential equations for the cavity field derived from the dispersive Jaynes-Cummings Hamiltonian including dissipation. We show that the measured system response can be used to construct a measurement operator from which the qubit population can be inferred accurately. Such a measurement operator can be used in tomographic methods to reconstruct single and multiqubit states in ensemble-averaged measurements.

Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED

ArXiv (0)

JM Fink, R Bianchetti, M Baur, M Goeppl, L Steffen, S Filipp, PJ Leek, A Blais, A Wallraff

We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multi-qubit states and observe the discrete square root of N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such as the W-state, in a fully globally and locally controllable quantum system. Our scalable approach is interesting for solid-state quantum information processing and for fundamental multi-atom quantum optics experiments with fixed atom numbers.

Measurement of Autler-Townes and Mollow transitions in a strongly driven superconducting qubit

ArXiv (0)

M Baur, S Filipp, R Bianchetti, JM Fink, M Göppl, L Steffen, PJ Leek, A Blais, A Wallraff

We present spectroscopic measurements of the Autler-Townes doublet and the sidebands of the Mollow triplet in a driven superconducting qubit. The ground to first excited state transition of the qubit is strongly pumped while the resulting dressed qubit spectrum is probed with a weak tone. The corresponding transitions are detected using dispersive read-out of the qubit coupled off-resonantly to a microwave transmission line resonator. The observed frequencies of the Autler-Townes and Mollow spectral lines are in good agreement with a dispersive Jaynes-Cummings model taking into account higher excited qubit states and dispersive level shifts due to off-resonant drives.

Two-Qubit State Tomography using a Joint Dispersive Read-Out

ArXiv (0)

S Filipp, P Maurer, PJ Leek, M Baur, R Bianchetti, JM Fink, M Göppl, L Steffen, JM Gambetta, A Blais, A Wallraff

Quantum state tomography is an important tool in quantum information science for complete characterization of multi-qubit states and their correlations. Here we report a method to perform a joint simultaneous read-out of two superconducting qubits dispersively coupled to the same mode of a microwave transmission line resonator. The non-linear dependence of the resonator transmission on the qubit state dependent cavity frequency allows us to extract the full two-qubit correlations without the need for single shot read-out of individual qubits. We employ standard tomographic techniques to reconstruct the density matrix of two-qubit quantum states.

Using Sideband Transitions for Two-Qubit Operations in Superconducting Circuits

ArXiv (0)

PJ Leek, S Filipp, P Maurer, M Baur, R Bianchetti, JM Fink, M Göppl, L Steffen, A Wallraff

We demonstrate time resolved driving of two-photon blue sideband transitions between superconducting qubits and a transmission line resonator. Using the sidebands, we implement a pulse sequence that first entangles one qubit with the resonator, and subsequently distributes the entanglement between two qubits. We show generation of 75% fidelity Bell states by this method. The full density matrix of the two qubit system is extracted using joint measurement and quantum state tomography, and shows close agreement with numerical simulation. The scheme is potentially extendable to a scalable universal gate for quantum computation.

Coplanar Waveguide Resonators for Circuit Quantum Electrodynamics

ArXiv (0)

M Göppl, A Fragner, M Baur, R Bianchetti, S Filipp, JM Fink, PJ Leek, G Puebla, L Steffen, A Wallraff

We have designed and fabricated superconducting coplanar waveguide resonators with fundamental frequencies from 2 to $9 \rm{GHz}$ and loaded quality factors ranging from a few hundreds to a several hundred thousands reached at temperatures of $20 \rm{mK}$. The loaded quality factors are controlled by appropriately designed input and output coupling capacitors. The measured transmission spectra are analyzed using both a lumped element model and a distributed element transmission matrix method. The experimentally determined resonance frequencies, quality factors and insertion losses are fully and consistently characterized by the two models for all measured devices. Such resonators find prominent applications in quantum optics and quantum information processing with superconducting electronic circuits and in single photon detectors and parametric amplifiers.