Photon Condensation and Enhanced Magnetism in Cavity QED.

A system of magnetic molecules coupled to microwave cavities (LC resonators) undergoes the equilibrium superradiant phase transition. The transition is experimentally observable. The effect of the coupling is first illustrated by the vacuum-induced ferromagnetic order in a quantum Ising model and then by the modification of the magnetic phase diagram of Fe_{8} dipolar crystals, exemplifying the cooperation between intrinsic and photon-induced spin-spin interactions. Finally, a transmission experiment is shown to resolve the transition, measuring the quantum electrodynamical control of magnetism.

Influence of non-Markovian dynamics in equilibrium uncertainty-relations.

Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that in quantum mechanics, these deviations originate from the uncertainty principle and are supported by the non-Markovian character of the dynamics. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum; therefore, quantum mechanics inhibits the system thermal-equilibrium-state from being described by the canonical Boltzmann's distribution. We show for a wide class of systems, systems interacting via central forces with pairwise-self-interacting environments; this general observation is in sharp contrast to the classical case, for which the thermal equilibrium distribution, irrespective of the interaction strength, is exactly characterized by the canonical Boltzmann distribution; therefore, no dependence on the bath power spectrum is present. We define an effective coupling to the environment that depends on all energy scales in the system and reservoir interaction. Sample computations in regimes predicted by this effective coupling are demonstrated. For example, for the case of strong effective coupling, deviations from standard thermodynamics are present and for the case of weak effective coupling, quantum features such as stationary entanglement are possible at high temperatures.

Quantum chaos in an ultrastrongly coupled bosonic junction.

The semiclassical and quantum dynamics of two ultrastrongly coupled nonlinear resonators cannot be explained using the discrete nonlinear Schrödinger equation or the Bose-Hubbard model, respectively. Instead, a model beyond the rotating wave approximation must be studied. In the semiclassical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both semiclassical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.

Scanning Spin Probe Based on Magnonic Vortex Quantum Cavities.

Performing nanoscale scanning electron paramagnetic resonance (EPR) requires three essential ingredients: First, a static magnetic field together with field gradients to Zeeman split the electronic energy levels with spatial resolution; second, a radio frequency (rf) magnetic field capable of inducing spin transitions; finally, a sensitive detection method to quantify the energy absorbed by spins. This is usually achieved by combining externally applied magnetic fields with inductive coils or cavities, fluorescent defects, or scanning probes. Here, we theoretically propose the realization of an EPR scanning sensor merging all three characteristics into a single device: the vortex core stabilized in ferromagnetic thin-film discs. On one hand, the vortex ground state generates a significant static magnetic field and field gradients. On the other hand, the precessional motion of the vortex core around its equilibrium position produces a circularly polarized oscillating magnetic field, which is enough to produce spin transitions. Finally, the spin-magnon coupling broadens the vortex gyrotropic frequency, suggesting a direct measure of the presence of unpaired electrons. Moreover, the vortex core can be displaced by simply using external magnetic fields of a few mT, enabling EPR scanning microscopy with large spatial resolution. Our numerical simulations show that, by using low damping magnets, it is theoretically possible to detect single spins located on the disc's surface. Vortex nanocavities could also attain strong coupling to individual spin molecular qubits with potential applications to mediate qubit-qubit interactions or to implement qubit readout protocols.

Circuit QED bright source for chiral entangled light based on dissipation.

We present a scalable and tunable framework for the quantum simulation of critical dissipative models based on a circuit QED cavity array interacting with driven superconducting qubits. We will show that the strongly correlated many-body state of the cavities can be mapped into the state of propagating photons in a transmission line. This allows not only for an efficient way of accessing the correlations in the many-body system, but also provides a bright source of chiral entangled light where directionality and entanglement are assisted by collective phenomena and breaking of reflection symmetry.

Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit.

We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin. The spin Hamiltonian and its parameters, as well as the spin dynamics, have been determined via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals. We find low temperature spin coherence times of micro-seconds and spin relaxation times longer than a second. For sufficiently strong magnetic fields (B > 0.1 T, corresponding to resonance frequencies of 9-10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. The presence of multiple equispaced nuclear spin levels then merely provides 8 alternatives to define the '1' and '0' basis states. For lower magnetic fields (B < 0.1 T), and lower frequencies (<2 GHz), we find spectroscopic signatures of a sizeable electronuclear entanglement. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, we show that each molecule fulfills the conditions to act as a universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings widen the catalogue of chemically designed systems able to implement non-trivial quantum functionalities, such as quantum simulations and, especially, quantum error correction at the molecular level.

Chemical tuning of spin clock transitions in molecular monomers based on nuclear spin-free Ni(ii).

We report the existence of a sizeable quantum tunnelling splitting between the two lowest electronic spin levels of mononuclear Ni complexes. The level anti-crossing, or magnetic "clock transition", associated with this gap has been directly monitored by heat capacity experiments. The comparison of these results with those obtained for a Co derivative, for which tunnelling is forbidden by symmetry, shows that the clock transition leads to an effective suppression of intermolecular spin-spin interactions. In addition, we show that the quantum tunnelling splitting admits a chemical tuning via the modification of the ligand shell that determines the crystal field and the magnetic anisotropy. These properties are crucial to realize model spin qubits that combine the necessary resilience against decoherence, a proper interfacing with other qubits and with the control circuitry and the ability to initialize them by cooling.

Bringing entanglement to the high temperature limit.

Decoherence due to contact with a hot environment typically restricts quantum phenomena to the low temperature limit, k_{B}T/ℏω≪1 (ℏω is the typical energy of the system). Here we report the existence of a nonequilibrium state for two coupled, parametrically driven, dissipative harmonic oscillators which, contrary to generalized intuition, has stationary entanglement at high temperatures. This clarifies the role of temperature and could lighten the burden on quantum experiments requiring delicate precooling setups.

A dissymmetric [Gd2] coordination molecular dimer hosting six addressable spin qubits.

Artificial magnetic molecules can host several spin qubits, which could then implement small-scale algorithms. In order to become of practical use, such molecular spin processors need to increase the available computational space and warrant universal operations. Here, we design, synthesize and fully characterize dissymetric molecular dimers hosting either one or two Gadolinium(III) ions. The strong sensitivity of Gadolinium magnetic anisotropy to its local coordination gives rise to different zero-field splittings at each metal site. As a result, the [LaGd] and [GdLu] complexes provide realizations of distinct spin qudits with eight unequally spaced levels. In the [Gd2] dimer, these properties are combined with a Gd-Gd magnetic interaction, sufficiently strong to lift all level degeneracies, yet sufficiently weak to keep all levels within an experimentally accessible energy window. The spin Hamiltonian of this dimer allows a complete set of operations to act as a 64-dimensional all-electron spin qudit, or, equivalently, as six addressable qubits. Electron paramagnetic resonance experiments show that resonant transitions between different spin states can be coherently controlled, with coherence times TM of the order of 1 µs limited by hyperfine interactions. Coordination complexes with embedded quantum functionalities are promising building blocks for quantum computation and simulation hybrid platforms.

Enhanced Molecular Spin-Photon Coupling at Superconducting Nanoconstrictions.

We combine top-down and bottom-up nanolithography to optimize the coupling of small molecular spin ensembles to 1.4 GHz on-chip superconducting resonators. Nanoscopic constrictions, fabricated with a focused ion beam at the central transmission line, locally concentrate the microwave magnetic field. Drops of free-radical molecules have been deposited from solution onto the circuits. For the smallest ones, the molecules were delivered at the relevant circuit areas by means of an atomic force microscope. The number of spins Neff effectively coupled to each device was accurately determined combining Scanning Electron and Atomic Force Microscopies. The collective spin-photon coupling constant has been determined for samples with Neff ranging between 2 × 106 and 1012 spins, and for temperatures down to 44 mK. The results show the well-known collective enhancement of the coupling proportional to the square root of Neff. The average coupling of individual spins is enhanced by more than 4 orders of magnitude (from 4 mHz up to above 180 Hz), when the transmission line width is reduced from 400 µm down to 42 nm, and reaches maximum values near 1 kHz for molecules located on the smallest nanoconstrictions.

Nonlinear quantum optics in the (ultra)strong light-matter coupling.

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. The time evolutions for both the field and qubits are computed. The nonlinear character (as a function of N/M) depends on the computed observable. While perfect reflection is obtained for N/M≅1, photon-photon correlations are still resolved for ratios N/M=non-zero. Inter-qubit distance enhances the nonlinear response. Moving to the ultrastrong coupling regime, we observe that inelastic processes are 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 models experiments in circuit QED, photonic crystals and dielectric waveguides.

Synchronization in a semiclassical Kuramoto model.

Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus 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.

Quantum navigation and ranking in complex networks.

Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.

Time-resolved measurement of a charge qubit.

We propose a scheme for monitoring coherent quantum dynamics with good time-resolution and low backaction, which relies on the response of the considered quantum system to high-frequency ac driving. An approximate analytical solution of the corresponding quantum master equation reveals that the phase of an outgoing signal, which can directly be measured in an experiment with lock-in technique, is proportional to the expectation value of a particular system observable. This result is corroborated by the numerical solution of the master equation for a charge qubit realized with a Cooper-pair box, where we focus on monitoring coherent oscillations.

Modified Ehrenfest Formalism for Efficient Large-Scale ab initio Molecular Dynamics.

We present in detail the recently derived ab initio molecular dynamics (AIMD) formalism [Alonso et al. Phys. Rev. Lett. 2008, 101, 096403], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work, we provide the formal details of the new method, describe its implementation, and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave function representation, making it suitable for inclusion in any AIMD software package.