International audienceA quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits for long times, is a key element for quantum information processing. Electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above 1 s. Benefiting from these long coherence times requires one to apply the refocusing techniques used in magnetic resonance, a major challenge in the context of hybrid quantum circuits. Here, we report the first implementation of such a scheme, using ensembles of nitrogen-vacancy centers in diamond coupled to a superconducting resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of the nitrogen-vacancy spins into their ground state by optical pumping and their refocusing by Hahn-echo sequences. This enables the storage of multiple microwave pulses at the picowatt level and their retrieval after up to 35 μs, a 3 orders of magnitude improvement compared to previous experiments

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Rényi entropy of a partial observation to a subsystem consisting of contiguous sites in the limit of large size. (2008)]. A striking feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size. This logarithmic behavior originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyze the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long-range pairing.

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We study the Rényi entanglement entropy of an interval in a periodic fermionic chain for a general eigenstate of a free, translational invariant Hamiltonian. In order to analytically compute the entropy we use two technical tools. The first one is used to reduce logarithmically the complexity of the problem and the second one to compute the Rényi entropy of the chosen subsystem. We introduce new strategies to perform the computations, derive new expressions for the entropy of these general states and show the perfect agreement of the analytical computations and the numerical outcome. Finally we discuss the physical interpretation of our results and generalise them to compute the entanglement entropy for a fragment of a fermionic ladder.

In this paper we complete the study on the asymptotic behaviour of the entanglement entropy for Kitaev chains with long range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for the asymptotic growth of the entropy appear. The coefficient of the leading term is not universal any more and the connection with conformal field theories is lost.We perform a numerical and analytical approach to the problem showing a perfect agreement. In order to carry out the analytical study, a new technique for computing the asymptotic behaviour of block Toeplitz determinants with discontinuous symbols has been developed.

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The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this formalism is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.The use of the symmetries of a system is one of the most fruitful techniques in physics, specially for quantum systems. Among the consequences of symmetry in quantum physics are: selection rules, relations between matrix elements of observables, degeneracies in energy and, specially, the existence of conservation laws which are guarantied by the Noether's theorem or by its equivalent, the Ehrenfest equation. In particular, the evolution of the expectation values of an operator B is given by the Heisenberg equationthat says that for any group of symmetry whose elements (or generators in the associated Lie algebra) commute with the Hamiltonian H, if such operators do not depend explicitly on time t, their expectation value on any physical state must be constant with t.Even for the case when the symmetry is not exact (it is explicitly broken), the Heisenberg equation (1) gives us how do evolve with time the expectation values of the corresponding generators. This has been largely used, for example, in particle physics where the flavor symmetry is explicitly broken by mass terms, or in nuclear physics where isospin symmetry is broken by the Coulomb interaction between protons and by the up-down quark mass difference.However, there are some cases where although the symmetry is exact at the classical level, it is not preserved in the corresponding quantum theory. This is the anomalous symmetry

The quantum planar rotor is chosen as a model to test different approximate techniques, emphasizing the analogies between this simple system and the non-Abelian quantum gauge field theories (instantons, 6 vacuum, etc.). In particular, variational and perturbative methods, path-integral techniques, and Monte Carlo simulations are applied. It is pointed out that the maximal destructive interference between instantons takes place in the 6vacuum realization of the interacting rotor system with 6= 1/2, where the tunneling effects are shown to be severely diminished. 1852