Response of the Strongly-Driven Jaynes-Cummings Oscillator

We analyze the Jaynes-Cummings model of quantum optics, in the strong-dispersive regime. In the bad cavity limit and on timescales short compared to the atomic coherence time, the dynamics are those of a nonlinear oscillator. A steady-state non-perturbative semiclassical analysis exhibits a finite region of bistability delimited by a pair of critical points, unlike the usual dispersive bistability from a Kerr nonlinearity. This analysis explains our quantum trajectory simulations that show qualitative agreement with recent experiments from the field of circuit quantum electrodynamics.Comment: 5 pages, 3 figure

Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities

In dispersive readout schemes, qubit-induced nonlinearity typically limits the measurement fidelity by reducing the signal-to-noise ratio (SNR) when the measurement power is increased. Contrary to seeing the nonlinearity as a problem, here we propose to use it to our advantage in a regime where it can increase the SNR. We show analytically that such a regime exists if the qubit has a many-level structure. We also show how this physics can account for the high-fidelity avalanchelike measurement recently reported by Reed {\it et al.} [arXiv:1004.4323v1].Comment: 4 pages, 5 figure

Improved qubit bifurcation readout in the straddling regime of circuit QED

We study bifurcation measurement of a multi-level superconducting qubit using a nonlinear resonator biased in the straddling regime, where the resonator frequency sits between two qubit transition frequencies. We find that high-fidelity bifurcation measurements are possible because of the enhanced qubit-state-dependent pull of the resonator frequency, the behavior of qubit-induced nonlinearities and the reduced Purcell decay rate of the qubit that can be realized in this regime. Numerical simulations find up to a threefold improvement in qubit readout fidelity when operating in, rather than outside of, the straddling regime. High-fidelity measurements can be obtained at much smaller qubit-resonator couplings than current typical experimental realizations, reducing spectral crowding and potentially simplifying the implementation of multi-qubit devices.Comment: 9 pages, 6 figure

Quantum Heating of a nonlinear resonator probed by a superconducting qubit

We measure the quantum fluctuations of a pumped nonlinear resonator, using a superconducting artificial atom as an in-situ probe. The qubit excitation spectrum gives access to the frequency and temperature of the intracavity field fluctuations. These are found to be in agreement with theoretical predictions; in particular we experimentally observe the phenomenon of quantum heating

Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise

We observe measurement-induced qubit state mixing in a transmon qubit dispersively coupled to a planar readout cavity. Our results indicate that dephasing noise at the qubit-readout detuning frequency is up-converted by readout photons to cause spurious qubit state transitions, thus limiting the nondemolition character of the readout. Furthermore, we use the qubit transition rate as a tool to extract an equivalent flux noise spectral density at f ~ 1 GHz and find agreement with values extrapolated from a $1/f^\alpha$ fit to the measured flux noise spectral density below 1 Hz.Comment: 5 pages, 4 figures. Final journal versio

Circuit QED with a Nonlinear Resonator : ac-Stark Shift and Dephasing

We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.Comment: Paper : 4 pages, 3 figures; Supplementary material : 1 page, 1 figur

Non-linear dispersive regime of cavity QED: The dressed dephasing model

Systems in the dispersive regime of cavity quantum electrodynamics (QED) are approaching the limits of validity of the dispersive approximation. We present a model which takes into account nonlinear corrections to the dressing of the atom by the field. We find that in the presence of pure dephasing, photons populating the cavity act as a heat bath on the atom, inducing incoherent relaxation and excitation. These effects are shown to reduce the achievable signal-to-noise ratio in cavity QED realizations where the atom is measured indirectly through cavity transmission and in particular in circuit QED.Comment: 4 pages, 2 figure

QuantMig:The use of migration scenarios in future characterisations: A systematic review and typology

BackgroundMigration plays an increasingly important role in shaping the demographic profiles of developed countries and receives ample attention in society at large as well as among policymakers. To understand how migration flows might evolve in the future, the QuantMig project set the goal of producing migration scenarios to support European migration policy. To do so, we need to make clear with what purpose scenarios are developed, how they are developed, and on which flows they focus. Other questions concern whether they are designed to describe the most likely future or a possible future, whether they are extrapolating trends observed in the past (assuming no fundamental changes in policies), or whether they are designed to describe desirable futures (migration as a panacea for ageing societies) or undesirable futures (massive inflow of immigration from developing countries). To produce the best possible migration scenarios, it is essential to get an overview of the literature. Migration scenarios have been used in a variety of future characterisations including forecasts, projections, and foresights. However, the term migration scenario is rarely well-defined or used consistently. Before developing a set of own scenarios, this document takes the necessary step of providing an overview of the existing literature and provide a definition and typology of migration scenarios. Based on this work, alternative ways of exploring the future of migration (for example in a vignette survey) will be discussed that lay out the bases for the extension of the work in the next deliverables of the work package. MethodsThis document looks at how migration scenarios are used in the literature presenting characterisations of societies’ futures. Relevant documents are systematically retrieved and assigned to one of six categories part of a pre-established typology. The typology rests on the focus (either migration or another aspect of societies influenced by migration) and purpose (either to predict the future, explore the future, or establish how a specific target can be reached) of each future characterisation. Subsequently, the techniques used for generating migration scenarios are described in terms of the approach taken (quantitative or qualitative) and how data is generated and transformed into meaningful output. Finally, the specific geographical context and characteristics of migration and migrants included in the scenarios are explored. ResultsA total of 107 documents were analysed. More than half presented migration scenarios that were developed to answer questions not about migration itself, but about its influence on a population’s future growth, age composition, or economic performance, among others. Future characterisations had most often prediction as purpose, being for example population forecasts, while many others had exploration as purpose, where the sensitivity of a given phenomenon to different migration assumptions is assessed. Most scenarios rest on a quantitative approach rather than on a narrative, but the latter has clearly expanded in the last years. Migration scenarios that follow a quantitative approach often rest on past migration trends to characterise the future, but seldom provide likelihoods that a given scenario will realise. Migration scenarios that follow a qualitative approach, on the other hand, often rest on experts and stakeholders’ views for input, or rely on previously developed storylines. Finally, quantitative scenarios often concentrate on net migration figures inside of a single, usually economically developed country, while qualitative scenarios are more likely to consider bidirectional flows between two (world) regions. ConclusionsThere was an increase over time in the use of qualitative scenarios to characterise the future of migration. However, these scenarios were seldom used to translate storylines into quantitative outputs that specifically aim at predicting future migration flows. Ways to achieve this are discussed, including more advanced data collection techniques among experts and stakeholders, and the consideration of multiple types of migration

Collective modes of CP(3) Skyrmion crystals in quantum Hall ferromagnets

The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseudospin, or both intertwined. In this article, we present a comprehensive numerical study of the collective excitations of these textured crystals using the GRPA. For the pure spin case, at finite Zeeman coupling the state is a Skyrmion crystal with a gapless phonon mode, and a separate Goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent Skyrmions break up, and the resulting state is a meron crystal with 4 gapless modes. In contrast, a pure pseudospin Skyrme crystal at finite tunneling has only the phonon mode. For Delta_SAS=0, the state evolves into a meron crystal and supports an extra gapless U(1) mode in addition to the phonon. For a CP(3) Skyrmion crystal, we find a U(1) gapless mode in the presence of the symmetry-breaking fields. In addition, a second mode with a very small gap is present in the spectrum.Comment: 16 pages and 12 eps figure