M. Baur

Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system

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.

Implementation of a Toffoli gate with superconducting circuits

The Toffoli gate is a three-quantum-bit (three-qubit) operation that inverts the state of a target qubit conditioned on the state of two control qubits. It makes universal reversible classical computation possible and, together with a Hadamard gate, forms a universal set of gates in quantum computation. It is also a key element in quantum error correction schemes. The Toffoli gate has been implemented in nuclear magnetic resonance, linear optics and ion trap systems. Experiments with superconducting qubits have also shown significant progress recently: two-qubit algorithms and two-qubit process tomography have been implemented, three-qubit entangled states have been prepared, first steps towards quantum teleportation have been taken and work on quantum computing architectures has been done. Implementation of the Toffoli gate with only single- and two-qubit gates requires six controlled-NOT gates and ten single-qubit operations, and has not been realized in any system owing to current limits on coherence. Here we implement a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubits, we have significantly reduced the number of elementary gates needed for the implementation of the Toffoli gate, relative to that required in theoretical proposals using only two-level systems. Using full process tomography and Monte Carlo process certification, we completely characterize the Toffoli gate acting on three independent qubits, measuring a fidelity of 68.5 ± 0.5 per cent. A similar approach to realizing characteristic features of a Toffoli-class gate has been demonstrated with two qubits and a resonator and achieved a limited characterization considering only the phase fidelity. Our results reinforce the potential of macroscopic superconducting qubits for the implementation of complex quantum operations with the possibility of quantum error correction.

Observation of resonant photon blockade at microwave frequencies using correlation function measurements.

Creating a train of single photons and monitoring its propagation and interaction is challenging in most physical systems, as photons generally interact very weakly with other systems. However, when confining microwave frequency photons in a transmission line resonator, effective photon-photon interactions can be mediated by qubits embedded in the resonator. Here, we observe the phenomenon of photon blockade through second-order correlation function measurements. The experiments clearly demonstrate antibunching in a continuously pumped source of single microwave photons measured by using microwave beam splitters, linear amplifiers, and quadrature amplitude detectors. We also investigate resonance fluorescence and Rayleigh scattering in Mollow-triplet-like spectra.

Deterministic quantum teleportation with feed-forward in a solid state system

Transferring the state of an information carrier from a sender to a receiver is an essential primitive in both classical and quantum communication and information processing. In a quantum process known as teleportation the unknown state of a quantum bit can be relayed to a distant party using shared entanglement and classical information. Here we present experiments in a solid-state system based on superconducting quantum circuits demonstrating the teleportation of the state of a qubit at the macroscopic scale. In our experiments teleportation is realized deterministically with high efficiency and achieves a high rate of transferred qubit states. This constitutes a significant step towards the realization of repeaters for quantum communication at microwave frequencies and broadens the tool set for quantum information processing with superconducting circuits.Engineered macroscopic quantum systems based on superconducting electronic circuits are attractive for experimentally exploring diverse questions in quantum information science. At the current state of the art, quantum bits (qubits) are fabricated, initialized, controlled, read out and coupled to each other in simple circuits. This enables the realization of basic logic gates, the creation of complex entangled states and the demonstration of algorithms or error correction. Using different variants of low-noise parametric amplifiers, dispersive quantum non-demolition single-shot readout of single-qubit states with high fidelity has enabled continuous and discrete feedback control of single qubits. Here we realize full deterministic quantum teleportation with feed-forward in a chip-based superconducting circuit architecture. We use a set of two parametric amplifiers for both joint two-qubit and individual qubit single-shot readout, combined with flexible real-time digital electronics. Our device uses a crossed quantum bus technology that allows us to create complex networks with arbitrary connecting topology in a planar architecture. The deterministic teleportation process succeeds with order unit probability for any input state, as we prepare maximally entangled two-qubit states as a resource and distinguish all Bell states in a single two-qubit measurement with high efficiency and high fidelity. We teleport quantum states between two macroscopic systems separated by 6 mm at a rate of 104 s−1, exceeding other reported implementations. The low transmission loss of superconducting waveguides is likely to enable the range of this and other schemes to be extended to significantly larger distances, enabling tests of non-locality and the realization of elements for quantum communication at microwave frequencies. The demonstrated feed-forward may also find application in error correction schemes.

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

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.

Measurement of Autler-Townes and Mollow Transitions in a Strongly Driven Superconducting Qubit

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.

Cavity Quantum Electrodynamics with Separate Photon Storage and Qubit Readout Modes

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.

Resolving Vacuum Fluctuations in an Electrical Circuit by Measuring the Lamb Shift

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.

Benchmarking a Quantum Teleportation Protocol in Superconducting Circuits Using Tomography and an Entanglement Witness

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three-qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 88%.

Quantum-To-Classical Transition in Cavity Quantum Electrodynamics

The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupation-or effective temperature-is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantum-to-classical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements.