We study effective light-matter interactions in a circuit QED system consisting of a single LC resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that in addition to the usual collective qubit-photon coupling the resulting Hamiltonian contains direct qubit-qubit interactions, which have a drastic effect on the ground and excited state properties of such circuits in the ultrastrong coupling regime. In contrast to a superradiant phase transition expected from the standard Dicke model, we find an opposite mechanism, which at very strong interactions completely decouples the photon mode and projects the qubits into a highly entangled ground state. These findings resolve previous controversies over the existence of superradiant phases in circuit QED, but they more generally show that the physics of two-or multi-atom cavity QED settings can differ significantly from what is commonly assumed.

The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed beyond the rotating wave approximation using matrix product states. It is found that the scattering is strongly influenced by the single-and multiphoton dressed bound states present in the system. In the ultrastrong coupling regime a new channel for inelastic scattering appears, where an incident photon deposits energy into the qubit, exciting a photon-bound state, and escaping with a lower frequency. This single-photon nonlinear frequency conversion process can reach up to 50% efficiency. Other remarkable features in the scattering induced by counterrotating terms are a blueshift of the reflection resonance and a Fano resonance due to long-lived excited states. Introduction.-As light-matter interaction controls an immense variety of physical processes, its modification usually leads to new phenomena. One strategy to increase this interaction is to confine the electromagnetic field in waveguides and make it interact with few level systems. It is possible nowadays to reach in this way the situation where the coherent light-matter coupling predominates over decoherence processes (the so-called strong-coupling regime), and to generate, manipulate, and store a single (or a few) photon. The ability of performing tasks with just one photon has already been demonstrated [1,2], opening the path for proposals such as optical transistors [3][4][5], singlephoton routers [6], one-photon lasers [7], qubit-mediated entanglement [8], or efficient photodetectors [9].All these results have been analyzed within the rotatingwave approximation (RWA) for the photon-dipole interaction [10]. The RWA only considers the processes where light and matter exchange excitations, which is valid when the couplings are much smaller than the typical photon and qubit energies. For sufficiently strong couplings, processes involving spontaneous creation and annihilation of pairs of excitations are relevant and the RWA picture breaks down [11]. This regime of ultrastrong coupling opens the door to new physics [12,13], which is within reach for many different experimental implementations [14].From the theoretical viewpoint, within the RWA the scattering of multiphoton wave packets by qubits is a complex problem [15][16][17][18][19][20], but the one-photon scattering is trivial. Beyond the RWA, computing the scattering of even one flying photon is difficult as subspaces with different photon numbers mix in the dynamics. This converts the problem into a many-body one for which only partial solutions exist for models that consider linear (unbounded)

In this paper we study the application of the Sobolev gradients technique to the problem of minimizing several Schrödinger functionals related to timely and difficult nonlinear problems in quantum mechanics and nonlinear optics. We show that these gradients act as preconditioners over traditional choices of descent directions in minimization methods and show a computationally inexpensive way to obtain them using a discrete Fourier basis and a fast Fourier transform. We show that the Sobolev preconditioning provides a great convergence improvement over traditional techniques for finding solutions with minimal energy as well as stationary states and suggest a generalization of the method using arbitrary linear operators.

We demonstrate that it is possible to implement a quantum perceptron with a sigmoid activation function as an efficient, reversible many-body unitary operation. When inserted in a neural network, the perceptron's response is parameterized by the potential exerted by other neurons. We prove that such a quantum neural network is a universal approximator of continuous functions, with at least the same power as classical neural networks. While engineering general perceptrons is a challenging control problem -also defined in this work-, the ubiquitous sigmoid-response neuron can be implemented as a quasi-adiabatic passage with an Ising model. In this construct, the scaling of resources is favorable with respect to the total network size and is dominated by the number of layers. We expect that our sigmoid perceptron will have applications also in quantum sensing or variational estimation of many-body Hamiltonians. arXiv:1801.00934v2 [quant-ph]

In this paper, we study a general nonlinear Schrödinger equation with a time-dependent harmonic potential. Despite the lack of translational invariance, we find a symmetry transformation that, up from any solution, produces infinitely many others that are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave packet, but also the shape of the solution is independent of the behavior of the center of the wave. Our findings have implications on the dynamics of Bose-Einstein condensates in magnetic traps.