Is there a no-go theorem for superradiant quantum phase transitions in cavity and circuit QED ?

In cavity quantum electrodynamics (QED), the interaction between an atomic transition and the cavity field is measured by the vacuum Rabi frequency $\Omega_0$. The analogous term "circuit QED" has been introduced for Josephson junctions, because superconducting circuits behave as artificial atoms coupled to the bosonic field of a resonator. In the regime with $\Omega_0$ comparable to the two-level transition frequency, "superradiant" quantum phase transitions for the cavity vacuum have been predicted, e.g. within the Dicke model. Here, we prove that if the time-independent light-matter Hamiltonian is considered, a superradiant quantum critical point is forbidden for electric dipole atomic transitions due to the oscillator strength sum rule. In circuit QED, the capacitive coupling is analogous to the electric dipole one: yet, such no-go property can be circumvented by Cooper pair boxes capacitively coupled to a resonator, due to their peculiar Hilbert space topology and a violation of the corresponding sum rule

Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box

Under appropriate conditions, superconducting electronic circuits behave quantum mechanically, with properties that can be designed and controlled at will. We have realized an experiment in which a superconducting two-level system, playing the role of an artificial atom, is strongly coupled to a single photon stored in an on-chip cavity. We show that the atom-photon coupling in this circuit can be made strong enough for coherent effects to dominate over dissipation, even in a solid state environment. This new regime of matter light interaction in a circuit can be exploited for quantum information processing and quantum communication. It may also lead to new approaches for single photon generation and detection.Comment: 8 pages, 4 figures, accepted for publication in Nature, embargo does apply, version with high resolution figures available at: http://www.eng.yale.edu/rslab/Andreas/content/science/PubsPapers.htm

Culture shapes how we look at faces

Background: Face processing, amongst many basic visual skills, is thought to be invariant across all humans. From as early as 1965, studies of eye movements have consistently revealed a systematic triangular sequence of fixations over the eyes and the mouth, suggesting that faces elicit a universal, biologically-determined information extraction pattern. Methodology/Principal Findings: Here we monitored the eye movements of Western Caucasian and East Asian observers while they learned, recognized, and categorized by race Western Caucasian and East Asian faces. Western Caucasian observers reproduced a scattered triangular pattern of fixations for faces of both races and across tasks. Contrary to intuition, East Asian observers focused more on the central region of the face. Conclusions/Significance: These results demonstrate that face processing can no longer be considered as arising from a universal series of perceptual events. The strategy employed to extract visual information from faces differs across cultures

Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System

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.Comment: ArXiv version of manuscript published in Nature in July 2008, 5 pages, 5 figures, hi-res version at http://www.finkjohannes.com/SqrtNArxivPreprint.pd

Coherent quantum state storage and transfer between two phase qubits via a resonant cavity

A network of quantum-mechanical systems showing long lived phase coherence of its quantum states could be used for processing quantum information. As with classical information processing, a quantum processor requires information bits (qubits) that can be independently addressed and read out, long-term memory elements to store arbitrary quantum states, and the ability to transfer quantum information through a coherent communication bus accessible to a large number of qubits. Superconducting qubits made with scalable microfabrication techniques are a promising candidate for the realization of a large scale quantum information processor. Although these systems have successfully passed tests of coherent coupling for up to four qubits, communication of individual quantum states between qubits via a quantum bus has not yet been demonstrated. Here, we perform an experiment demonstrating the ability to coherently transfer quantum states between two superconducting Josephson phase qubits through a rudimentary quantum bus formed by a single, on chip, superconducting transmission line resonant cavity of length 7 mm. After preparing an initial quantum state with the first qubit, this quantum information is transferred and stored as a nonclassical photon state of the resonant cavity, then retrieved at a later time by the second qubit connected to the opposite end of the cavity. Beyond simple communication, these results suggest that a high quality factor superconducting cavity could also function as a long term memory element. The basic architecture presented here is scalable, offering the possibility for the coherent communication between a large number of superconducting qubits.Comment: 17 pages, 4 figures (to appear in Nature

Nonlinear response of the vacuum Rabi resonance

On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By employing a cavity to confine the field, the strength of this interaction can be increased many orders of magnitude to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit QED and quantum-dot systems. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity - an effect known as vacuum Rabi splitting. The circuit QED architecture is ideally suited for going beyond this linear response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet, and the appearance of additional peaks with the characteristic sqrt(n) spacing of the Jaynes-Cummings ladder. These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Comment: 6 pages, 4 figures. Supplementary Material and Supplementary Movies are available at http://www.eng.yale.edu/rslab/publications.htm

Resolving photon number states in a superconducting circuit

Electromagnetic signals are always composed of photons, though in the circuit domain those signals are carried as voltages and currents on wires, and the discreteness of the photon's energy is usually not evident. However, by coupling a superconducting qubit to signals on a microwave transmission line, it is possible to construct an integrated circuit where the presence or absence of even a single photon can have a dramatic effect. This system is called circuit quantum electrodynamics (QED) because it is the circuit equivalent of the atom-photon interaction in cavity QED. Previously, circuit QED devices were shown to reach the resonant strong coupling regime, where a single qubit can absorb and re-emit a single photon many times. Here, we report a circuit QED experiment which achieves the strong dispersive limit, a new regime of cavity QED in which a single photon has a large effect on the qubit or atom without ever being absorbed. The hallmark of this strong dispersive regime is that the qubit transition can be resolved into a separate spectral line for each photon number state of the microwave field. The strength of each line is a measure of the probability to find the corresponding photon number in the cavity. This effect has been used to distinguish between coherent and thermal fields and could be used to create a photon statistics analyzer. Since no photons are absorbed by this process, one should be able to generate non-classical states of light by measurement and perform qubit-photon conditional logic, the basis of a logic bus for a quantum computer.Comment: 6 pages, 4 figures, hi-res version at http://www.eng.yale.edu/rslab/papers/numbersplitting_hires.pd

Tripartite interactions between two phase qubits and a resonant cavity

The creation and manipulation of multipartite entangled states is important for advancements in quantum computation and communication, and for testing our fundamental understanding of quantum mechanics and precision measurements. Multipartite entanglement has been achieved by use of various forms of quantum bits (qubits), such as trapped ions, photons, and atoms passing through microwave cavities. Quantum systems based on superconducting circuits have been used to control pair-wise interactions of qubits, either directly, through a quantum bus, or via controllable coupling. Here, we describe the first demonstration of coherent interactions of three directly coupled superconducting quantum systems, two phase qubits and a resonant cavity. We introduce a simple Bloch-sphere-like representation to help one visualize the unitary evolution of this tripartite system as it shares a single microwave photon. With careful control and timing of the initial conditions, this leads to a protocol for creating a rich variety of entangled states. Experimentally, we provide evidence for the deterministic evolution from a simple product state, through a tripartite W-state, into a bipartite Bell-state. These experiments are another step towards deterministically generating multipartite entanglement in superconducting systems with more than two qubits

Single-shot qubit readout in circuit Quantum Electrodynamics

The future development of quantum information using superconducting circuits requires Josephson qubits [1] with long coherence times combined to a high-fidelity readout. Major progress in the control of coherence has recently been achieved using circuit quantum electrodynamics (cQED) architectures [2, 3], where the qubit is embedded in a coplanar waveguide resonator (CPWR) which both provides a well controlled electromagnetic environment and serves as qubit readout. In particular a new qubit design, the transmon, yields reproducibly long coherence times [4, 5]. However, a high-fidelity single-shot readout of the transmon, highly desirable for running simple quantum algorithms or measur- ing quantum correlations in multi-qubit experiments, is still lacking. In this work, we demonstrate a new transmon circuit where the CPWR is turned into a sample-and-hold detector, namely a Josephson Bifurcation Amplifer (JBA) [6, 7], which allows both fast measurement and single-shot discrimination of the qubit states. We report Rabi oscillations with a high visibility of 94% together with dephasing and relaxation times longer than 0:5 \mu\s. By performing two subsequent measurements, we also demonstrate that this new readout does not induce extra qubit relaxation.Comment: 14 pages including 4 figures, preprint forma