[Show abstract][Hide abstract] ABSTRACT: At optical frequencies the radiation produced by a source, such as a laser, a black body or a single-photon emitter, is frequently characterized by analysing the temporal correlations of emitted photons using single-photon counters. At microwave frequencies, however, there are no efficient single-photon counters yet. Instead, well-developed linear amplifiers allow for efficient measurement of the amplitude of an electromagnetic field. Here, we demonstrate first-and second-order correlation function measurements of a pulsed microwave-frequency single-photon source integrated on the same chip with a 50/50 beam splitter followed by linear amplifiers and quadrature amplitude detectors. We clearly observe single-photon coherence in first-order and photon antibunching in second-order correlation function measurements of the propagating fields.
[Show abstract][Hide abstract] ABSTRACT: Microwave cavities with high quality factors enable coherent coupling of distant quantum systems. Virtual photons lead to a transverse interaction between qubits when they are nonresonant with the cavity but resonant with each other. We experimentally investigate the inverse scaling of the interqubit coupling with the detuning from a cavity mode and its proportionality to the qubit-cavity interaction strength. We demonstrate that the enhanced coupling at higher frequencies is mediated by multiple higher-harmonic cavity modes. Moreover, we observe dark states of the coupled qubit-qubit system and analyze their relation to the symmetry of the applied driving field at different frequencies.
Full-text · Article · Jun 2011 · Physical Review A
[Show abstract][Hide abstract] ABSTRACT: Superconducting circuits have been successfully established as systems to prepare and investigate microwave light fields at the quantum level. In contrast to optical experiments where light is detected using photon counters, microwaves are usually measured with well developed linear amplifiers. This makes measurements of correlation functions - one of the important tools in optics - harder to achieve because they traditionally rely on photon counters and beam splitters. Here, we demonstrate a system where we can prepare on demand single microwave photons in a cavity and detect them at the two outputs of the cavity using linear amplifiers. Together with efficient data processing, this allows us to measure different observables of the cavity photons, including the first-order correlation function. Using these techniques we demonstrate cooling of a thermal background field in the cavity.
Full-text · Article · Jan 2011 · Journal of Physics Conference Series
[Show abstract][Hide abstract] ABSTRACT: Microwave cavities with high quality factors enable coherent coupling of
distant quantum systems. Virtual photons lead to a transverse exchange
interaction between qubits, when they are non-resonant with the cavity but
resonant with each other. We experimentally probe the inverse scaling of the
inter-qubit coupling with the detuning from a cavity mode and its
proportionality to the qubit-cavity interaction strength. We demonstrate that
the enhanced coupling at higher frequencies is mediated by multiple
higher-harmonic cavity modes. Moreover, in the case of resonant qubits, the
symmetry properties of the system lead to an allowed two-photon transition to
the doubly excited qubit state and the formation of a dark state.
[Show abstract][Hide abstract] ABSTRACT: A number of superconducting qubits, such as the transmon or the phase qubit, have an energy level structure with small anharmonicity. This allows for convenient access of higher excited states with similar frequencies. However, special care has to be taken to avoid unwanted higher-level populations when using short control pulses. Here we demonstrate the preparation of arbitrary three level superposition states using optimal control techniques in a transmon. Performing dispersive readout, we extract the populations of all three levels of the qutrit and study the coherence of its excited states. Finally we demonstrate full quantum state tomography of the prepared qutrit states and evaluate the fidelities of a set of states, finding on average 95%.
Full-text · Article · Nov 2010 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: The Silences of the Archives, the Reknown of the Story.
The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, before captivated judges and a guilty feeling Bertrande de Rols. The historian wanted to go beyond the known story in order to discover the world of the heroes. This research led to disappointments and surprizes as documents were discovered concerning the environment of Artigat’s inhabitants and bearing directly on the main characters thanks to notarial contracts. Along the way, study of the works of Coras and Lesueur took a new direction. Coming back to the affair a quarter century later did not result in finding new documents (some are perhaps still buried in Spanish archives), but by going back over her tracks, the historian could only be struck by the silences of the archives that refuse to reveal their secrets and, at the same time, by the possible openings they suggest, by the intuition that almost invisible threads link here and there characters and events.
Full-text · Article · Oct 2010 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: Coherent control of higher than two-dimensional quantum systems can considerably improve present techniques for quantum information processing. In particular, superconducting quantum circuits can be operated in a regime with closely spaced energy levels, where arbitrary superposition states can be prepared by applying appropriately shaped microwave pulses at different frequencies. We employ dispersive read-out  to discriminate the population of upper energy levels of superconducting transmon circuits coupled to a coplanar microwave resonator. This allows us to determine the dynamics in the restricted two-dimensional qubit subspace and assess the population transfer to the third level. Finally, we fully characterize arbitrary three-dimensional qutrit states by a complete tomographic measurement.[4pt]  R. Bianchetti et al., Phys. Rev. A 80, 043840 (2009).
[Show abstract][Hide abstract] ABSTRACT: We present the realization of a cavity quantum electrodynamics setup in which photons of strongly different lifetimes are engineered in different harmonic modes of the same cavity. We achieve this in a superconducting transmission line resonator with superconducting qubits coupled to the different modes. One cavity mode is strongly coupled to a detection line for qubit state readout, while a second long lifetime mode is used for photon storage and coherent quantum operations. We demonstrate sideband-based measurement of photon coherence, generation of n photon Fock states and the scaling of the sideband Rabi frequency with square root of n using a scheme that may be extended to realize sideband-based two-qubit logic gates.
Full-text · Article · Mar 2010 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: 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. Comment: ArXiv version of manuscript to be published in the Physica Scripta topical issue on the Nobel Symposium 141: Qubits for Future Quantum Computers(2009), 13 pages, 6 figures, hi-res version at http://qudev.ethz.ch/content/science/PubsPapers.html
[Show abstract][Hide abstract] ABSTRACT: 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.
Full-text · Article · Oct 2009 · Physical Review A
[Show abstract][Hide abstract] ABSTRACT: 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 multiqubit states and observe the discrete square root 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 multiatom quantum optics experiments with fixed atom numbers.
Full-text · Article · Aug 2009 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: 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 readout 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.
[Show abstract][Hide abstract] ABSTRACT: Quantum state tomography is an important tool in quantum information science for complete characterization of multiqubit states and their correlations. Here we report a method to perform a joint simultaneous readout of two superconducting qubits dispersively coupled to the same mode of a microwave transmission line resonator. The nonlinear 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 readout of individual qubits. We employ standard tomographic techniques to reconstruct the density matrix of two-qubit quantum states.
Full-text · Article · Jun 2009 · Physical Review Letters
[Show abstract][Hide abstract] ABSTRACT: The already very active field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has recently gained additional momentum by the advent of experiments with semiconducting and superconducting systems. In these solid state implementations, novel quantum optics experiments are enabled by the possibility to engineer many of the characteristic parameters at will. In cavity QED, the observation of the vacuum Rabi mode splitting is a hallmark experiment aimed at probing the nature of matter-light interaction on the level of a single quantum. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous, long sought for spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED setup, in which ultra strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high quality on-chip microwave cavity.
[Show abstract][Hide abstract] ABSTRACT: In a circuit quantum electrodynamics setup the qubit state is inferred from the response of the coupled qubit-cavity system to a microwave signal applied close to the cavity resonance. We experimentally investigate the frequency dependence of the response for both weak continuous and pulsed measurement signals. We find excellent agreement with theoretical predictions from a generalized Jaynes-Cummings model which includes dissipation and dephasing. The quantitative understanding of the system response is used to optimize the measurement frequency maximizing the signal-to-noise ratio. This allows for an accurate determination of the qubit excited state population from the measured field response.
[Show abstract][Hide abstract] ABSTRACT: High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.
Full-text · Article · Jan 2009 · Journal of Applied Physics
[Show abstract][Hide abstract] ABSTRACT: 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. Comment: 4 pages, 5 figures, version with high resolution figures available at http://qudev.ethz.ch/content/science/PubsPapers.html
[Show abstract][Hide abstract] ABSTRACT: Quantum theory predicts that empty space is not truly empty. Even in the absence of any particles or radiation, in pure vacuum, virtual particles are constantly created and annihilated. In an electromagnetic field, the presence of virtual photons manifests itself as a small renormalization of the energy of a quantum system, known as the Lamb shift. We present an experimental observation of the Lamb shift in a solid-state system. The strong dispersive coupling of a superconducting electronic circuit acting as a quantum bit (qubit) to the vacuum field in a transmission-line resonator leads to measurable Lamb shifts of up to 1.4% of the qubit transition frequency. The qubit is also observed to couple more strongly to the vacuum field than to a single photon inside the cavity, an effect that is explained by taking into account the limited anharmonicity of the higher excited qubit states.
[Show abstract][Hide abstract] ABSTRACT: The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting and superconducting systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter-light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication.
[Show abstract][Hide abstract] ABSTRACT: In quantum information science, the phase of a wave function plays an important role in encoding information. Although most experiments in this field rely on dynamic effects to manipulate this information, an alternative approach is to use geometric phase, which has been argued to have potential fault tolerance. We demonstrated the controlled accumulation of a geometric phase, Berry's phase, in a superconducting qubit; we manipulated the qubit geometrically by means of microwave radiation and observed the accumulated phase in an interference experiment. We found excellent agreement with Berry's predictions and also observed a geometry-dependent contribution to dephasing.