Three-Josephson Junctions Flux Qubit Couplings

  1. María Hita-Pérez,
  2. Gabriel Jaumà,
  3. Manuel Pino,
  4. and Juan José García-Ripoll
We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics
of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a SQUID. Those two elements allow to engineer qubits Hamiltonians with XX, YY and ZZ interactions, including ultra-strongly coupled ones. We present an exhaustive numerical study for two three-Josephson junctions flux qubit that can be directly used in experimental work. The method developed here, namely the numerical tool to extract qubit effective Hamiltonians at strong coupling, can be applied to replicate our analysis for general systems of many qubits and any type of coupling.

Ultrastrong capacitive coupling of flux qubits

  1. María Hita-Pérez,
  2. Gabriel Jaumà,
  3. Manuel Pino,
  4. and Juan José García-Ripoll
A flux qubit can interact strongly when it is capacitively coupled to other circuit elements. This interaction can be separated in two parts, one acting on the qubit subspaces and one
in which excited states mediate the interaction. The first term dominates the interaction between the flux qubit and an LC-resonator, leading to ultrastrong couplings of the form σy(a+a†), which complement the inductive σxi(a†−a) coupling. However, when coupling two flux qubits capacitively, all terms need to be taken into account, leading to complex non-stoquastic ultrastrong interaction of the σyσy, σzσz and σxσx type. Our theory explains all these interactions, describing them in terms of general circuit properties—coupling capacitances, qubit gaps, inductive, Josephson and capactive energies—, that apply to a wide variety of circuits and flux qubit designs.

Quantum emulation of molecular force fields: A blueprint for a superconducting architecture

  1. Diego G. Olivares,
  2. Borja Peropadre,
  3. Joonsuk Huh,
  4. and Juan José García-Ripoll
In this work, we propose a flexible architecture of microwave resonators with tuneable couplings to perform quantum simulations of molecular chemistry problems. The architecture builds
on the experience of the D-Wave design, working with nearly harmonic circuits instead of with qubits. This architecture, or modifications of it, can be used to emulate molecular processes such as vibronic transitions. Furthermore, we discuss several aspects of these emulations, such as dynamical ranges of the physical parameters, quenching times necessary for diabaticity and finally the possibility of implementing anharmonic corrections to the force fields by exploiting certain nonlinear features of superconducting devices.

Inhibition of ground-state superradiance and light-matter decoupling in circuit QED

  1. Tuomas Jaako,
  2. Ze-Liang Xiang,
  3. Juan José Garcia-Ripoll,
  4. and Peter Rabl
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 prevent the otherwise expected superradiant phase transition in the ground state of this system. Moreover, these qubit-qubit interactions are responsible for an opposite mechanism, which at very strong couplings completely decouples the photon mode and projects the qubits into a highly entangled ground state. These findings shed new light on the controversy over the existence of superradiant phase transitions in cavity and circuit QED systems, and show that the physics of ultrastrong light-matter interactions in two- or multi-qubit settings differ drastically from the more familiar one qubit case.

Dynamical polaron ansatz: a theoretical tool for the ultra-strong coupling regime of circuit QED

  1. Guillermo Díaz-Camacho,
  2. Alejandro Bermudez,
  3. and Juan José García-Ripoll
In this work we develop a semi-analytical variational ansatz to study the properties of few photon excitations interacting with a collection of quantum emitters in regimes that go beyond
the rotating wave approximation. This method can be used to approximate both the static and dynamical properties of a superconducting qubit in an open transmission line, including the spontaneous emission spectrum and the resonances in scattering experiments. The approximations are quantitatively accurate for rather strong couplings, as shown by a direct comparison to Matrix-Product-State numerical methods, and provide also a good qualitative description for stronger couplings well beyond the Markovian regime.

Entangled microwaves as a resource for entangling spatially separate solid-state qubits: superconducting qubits, NV centers and magnetic molecules

  1. Angela Viviana Gómez,
  2. Ferney Javier Rodríguez,
  3. Luis Quiroga,
  4. and Juan José García-Ripoll
Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits
or two qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Our results provide evidence that this entanglement transfer by dissipation is feasible yielding to a steady-state amount of entanglement in the bipartite quantum system which can be optimized for a wide range of realistic physical systems that include state-of-the-art experiments with NV centers in diamond, superconducting qubits or even magnetic molecules embedded in a crystalline matrix.

Spin-boson model with an engineered reservoir in circuit quantum electrodynamics

  1. Max Haeberlein,
  2. Frank Deppe,
  3. Andreas Kurcz,
  4. Jan Goetz,
  5. Alexander Baust,
  6. Peter Eder,
  7. Kirill Fedorov,
  8. Michael Fischer,
  9. Edwin P. Menzel,
  10. Manuel J. Schwarz,
  11. Friedrich Wulschner,
  12. Edwar Xie,
  13. Ling Zhong,
  14. Enrique Solano,
  15. Achim Marx,
  16. Juan José García-Ripoll,
  17. and Rudolf Gross
A superconducting qubit coupled to an open transmission line represents an implementation of the spin-boson model with a broadband environment. We show that this environment can be
engineered by introducing partial reflectors into the transmission line, allowing to shape the spectral function, J({\omega}), of the spin-boson model. The spectral function can be accessed by measuring the resonance fluorescence of the qubit, which provides information on both the engineered environment and the coupling between qubit and transmission line. The spectral function of a transmission line without partial reflectors is found to be Ohmic over a wide frequency range, whereas a peaked spectral density is found for the shaped environment. Our work lays the ground for future quantum simulations of other, more involved, impurity models with superconducting circuits.

Driven Spin-Boson Luttinger Liquids

  1. Andreas Kurz,
  2. Juan Jose Garcia-Ripoll,
  3. and Alejandro Bermudez
We introduce a lattice model of interacting spins and bosons that leads to Luttinger-liquid physics, and allows for quantitative tests of the theory of bosonization by means of trapped-ion
or superconducting-circuit experiments. By using a variational bosonization ansatz, we calculate the power-law decay of spin and boson correlation functions, and study their dependence on a single tunable parameter, namely a bosonic driving. For small drivings, Matrix-Product-States (MPS) numerical methods are shown to be efficient and validate our ansatz. Conversely, even static MPS become inefficient for large-driving regimes, such that the experiment can potentially outperform classical numerics, achieving one of the goals of quantum simulations.

Stationary discrete solitons in circuit QED

  1. Uta Naether,
  2. Fernando Quijandría,
  3. Juan José García-Ripoll,
  4. and David Zueco
We demonstrate that stationary localized solutions (discrete solitons) exist in a one dimensional Bose-Hubbard lattices with gain and loss in the semiclassical regime. Stationary solutions,
by defi- nition, are robust and do not demand for state preparation. Losses, unavoidable in experiments, are not a drawback, but a necessary ingredient for these modes to exist. The semiclassical calculations are complemented with their classical limit and dynamics based on a Gutzwiller Ansatz. We argue that circuit QED architectures are ideal platforms for realizing the physics developed here. Finally, within the input-output formalism, we explain how to experimentally access the different phases, including the solitons, of the chain.

Light-matter decoupling and A^2 term detection in superconducting circuits

  1. Juan José García-Ripoll,
  2. Borja Peropadre,
  3. and Simone De Liberato
We study the spontaneous emission of a qubit interacting with a one-dimensional waveguide through a realistic minimal-coupling interaction. We show that the diamagnetic term A2 leads
to an effective decoupling of a single qubit from the electromagnetic field. This effects is observable at any range of qubit-photon couplings. For this we study a setup consisting of a transmon that is suspended over a transmission line. We prove that the relative strength of the A2 term is controlled with the qubit-line separation and show that, as a consequence, the spontaneous emission rate of the suspended transmon onto the line can increase with such separation, instead of decreasing.