We solve the mixing-demixing transition in repulsive one-dimensional bose-bose mixtures. This is done numerically by means of the continuous matrix product states variational ansatz. We show that the effective low-energy bosonization theory is able t
o detect the transition whenever the Luttinger parameters are exactly computed. We further characterize the transition by calculating the ground-state energy density, the field-field fluctuations and the density correlations.
The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and its linear
limit for the scattered photons as a function of $N$, $M$, qubit inter distance and light-matter coupling. The quantum evolution is numerically solved via the Matrix Product States technique. Both the time evolution for the field and qubits is computed. The nonlinear character (as a function of $N/M$) depends on the computed observable. While perfect reflection is obtained for $N/M cong 1$, photon-photon correlations are still resolved for ratios $N/M= 2/20$. Inter-qubit distance enhances the nonlinear response. Moving to the ultrastrong coupling regime, we observe that inelastic processes are emph{robust} against the number of qubits and that the qubit-qubit interaction mediated by the photons is qualitatively modified. The theory developed in this work modelises experiments in circuit QED, photonic crystals and dielectric waveguides.
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 r
otating wave approximation using Matrix Product States. It is found that the scattering is strongly influenced by the single- and multi-photon 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 counter-rotating terms are a blueshift of the reflection resonance and a Fano resonance due to long-lived excited states
Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rhythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical c
onsensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.
Based on a circuit QED qubit-cavity array a source of two-mode entangled microwave radiation is designed. Our scheme is rooted in the combination of external driving, collective phenomena and dissipation. On top of that the reflexion symmetry is brok
en via external driving permitting the appearance of chiral emission. Our findings go beyond the applications and are relevant for fundamental physics, since we show how to implement quantum lattice models exhibiting criticality driven by dissipation.
We investigate creation, manipulation, and steering of entanglement in spin chains from the viewpoint of quantum communication between distant parties. We demonstrate how global parametric driving of the spin-spin coupling and/or local time-dependent
Zeeman fields produce a large amount of entanglement between the first and the last spin of the chain. This occurs whenever the driving frequency meets a resonance condition, identified as entanglement resonance. Our approach marks a promising step towards an efficient quantum state transfer or teleportation in solid state system. Following the reasoning of Zueco et al. [1], we propose generation and routing of multipartite entangled states by use of symmetric tree-like structures of spin chains. Furthermore, we study the effect of decoherence on the resulting spin entanglement between the corresponding terminal spins.
