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

Natural TTS Synthesis by Conditioning WaveNet on Mel Spectrogram Predictions

This paper describes Tacotron 2, a neural network architecture for speech synthesis directly from text. The system is composed of a recurrent sequence-to-sequence feature prediction network that maps character embeddings to mel-scale spectrograms, followed by a modified WaveNet model acting as a vocoder to synthesize timedomain waveforms from those spectrograms. Our model achieves a mean opinion score (MOS) of $4.53$ comparable to a MOS of $4.58$ for professionally recorded speech. To validate our design choices, we present ablation studies of key components of our system and evaluate the impact of using mel spectrograms as the input to WaveNet instead of linguistic, duration, and $F_0$ features. We further demonstrate that using a compact acoustic intermediate representation enables significant simplification of the WaveNet architecture.Comment: Accepted to ICASSP 201

Noiseless nonreciprocity in a parametric active device

Nonreciprocal devices such as circulators and isolators belong to an important class of microwave components employed in applications like the measurement of mesoscopic circuits at cryogenic temperatures. The measurement protocols usually involve an amplification chain which relies on circulators to separate input and output channels and to suppress backaction from different stages on the sample under test. In these devices the usual reciprocal symmetry of circuits is broken by the phenomenon of Faraday rotation based on magnetic materials and fields. However, magnets are averse to on-chip integration, and magnetic fields are deleterious to delicate superconducting devices. Here we present a new proposal combining two stages of parametric modulation emulating the action of a circulator. It is devoid of magnetic components and suitable for on-chip integration. As the design is free of any dissipative elements and based on reversible operation, the device operates noiselessly, giving it an important advantage over other nonreciprocal active devices for quantum information processing applications.Comment: 17 pages, 4 figures + 12 pages Supplementary Informatio

Energy spectra of quantum rings

Ring geometries have fascinated experimental and theoretical physicists over many years. Open rings connected to leads allow the observation of the Aharonov-Bohm effect, a paradigm of quantum mechanical phase coherence. The phase coherence of transport through a quantum dot embedded in one arm of an open ring has been demonstrated. The energy spectrum of closed rings has only recently been analysed by optical experiments and is the basis for the prediction of persistent currents and related experiments. Here we report magnetotransport experiments on a ring-shaped semiconductor quantum dot in the Coulomb blockade regime. The measurements allow us to extract the discrete energy levels of a realistic ring, which are found to agree well with theoretical expectations. Such an agreement, so far only found for few-electron quantum dots, is here extended to a many-electron system. In a semiclassical language our results indicate that electron motion is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots.Comment: 10 pages, 4 figure

Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime

In cavity quantum electrodynamics (QED), light-matter interaction is probed at its most fundamental level, where individual atoms are coupled to single photons stored in three-dimensional cavities. This unique possibility to experimentally explore the foundations of quantum physics has greatly evolved with the advent of circuit QED, where on-chip superconducting qubits and oscillators play the roles of two-level atoms and cavities, respectively. In the strong coupling limit, atom and cavity can exchange a photon frequently before coherence is lost. This important regime has been reached both in cavity and circuit QED, but the design flexibility and engineering potential of the latter allowed for increasing the ratio between the atom-cavity coupling rate and the cavity transition frequency above the percent level. While these experiments are well described by the renowned Jaynes-Cummings model, novel physics is expected in the ultrastrong coupling limit. Here, we report on the first experimental realization of a superconducting circuit QED system in the ultrastrong coupling limit and present direct evidence for the breakdown of the Jaynes-Cummings model.Comment: 5 pages, 3 figure

Quantum Non-demolition Detection of Single Microwave Photons in a Circuit

Thorough control of quantum measurement is key to the development of quantum information technologies. Many measurements are destructive, removing more information from the system than they obtain. Quantum non-demolition (QND) measurements allow repeated measurements that give the same eigenvalue. They could be used for several quantum information processing tasks such as error correction, preparation by measurement, and one-way quantum computing. Achieving QND measurements of photons is especially challenging because the detector must be completely transparent to the photons while still acquiring information about them. Recent progress in manipulating microwave photons in superconducting circuits has increased demand for a QND detector which operates in the gigahertz frequency range. Here we demonstrate a QND detection scheme which measures the number of photons inside a high quality-factor microwave cavity on a chip. This scheme maps a photon number onto a qubit state in a single-shot via qubit-photon logic gates. We verify the operation of the device by analyzing the average correlations of repeated measurements, and show that it is 90% QND. It differs from previously reported detectors because its sensitivity is strongly selective to chosen photon number states. This scheme could be used to monitor the state of a photon-based memory in a quantum computer.Comment: 5 pages, 4 figures, includes supplementary materia

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

A preliminary report of an educational intervention in practice management

BACKGROUND: Practice management education continues to evolve, and little information exists regarding its curriculum design and effectiveness for resident education. We report the results of an exploratory study of a practice management curriculum for primary care residents. METHODS: After performing a needs assessment with a group of primary care residents at Wright State University, we designed a monthly seminar series covering twelve practice management topics. The curriculum consisted of interactive lectures and practice-based application, whenever possible. We descriptively evaluated two cognitive components (practice management knowledge and skills) and the residents' evaluation of the curriculum. RESULTS: The mean correct on the knowledge test for this group of residents was 74% (n = 12) and 91% (n = 12) before and after the curriculum, respectively. The mean scores for the practice management skill assessments were 2.62 before (n = 12), and 3.65 after (n = 12) the curriculum (modified Likert, 1 = strongly disagree, 5 = strongly agree). The residents rated the curriculum consistently high. CONCLUSIONS: This exploratory study suggests that this curriculum may be useful in developing knowledge and skills in practice management for primary care residents. This study suggests further research into evaluation of this curriculum may be informative for practice-based education

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

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