Entanglement and Disentanglement in Circuit QED Architectures

We propose a protocol for creating entanglement within a dissipative circuit QED network architecture that consists of two electromagnetic circuits (cavities) and two superconducting qubits. The system interacts with a quantum environment, giving rise to decoherence and dissipation. We discuss the preparation of two separate entangled cavity-qubit states via Landau-Zener sweeps, after which the cavities interact via a tunable "quantum switch" which is realized with an ancilla qubit. Moreover, we discuss the decay of the resulting entangled two-cavity state due to the influence of the environment, where we focus on the entanglement decay.Comment: 7 pages, 5 figure

Functional renormalization group analysis of Dzyaloshinsky Moriya and Heisenberg spin interactions on the kagome lattice

We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated $J_1$-$J_2$ kagome-Heisenberg model using the pseudo-fermion functional-renormalization-group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of non-collinear magnetic orders of the $J_1$-$J_2$ Heisenberg model ($\mathbf{q}=0$, $\sqrt{3}\times\sqrt{3}$, and cuboc orders) and shrink the extents of magnetically disordered phases. We discuss our results in the light of the mineral {\it herbertsmithite} which has been experimentally predicted to host a quantum spin liquid at low temperatures. Our PFFRG data indicates that this material lies in close proximity to a quantum critical point. In parts of the experimentally relevant parameter regime for {\it herbertsmithite}, the spin-correlation profile is found to be in good qualitative agreement with recent inelastic-neutron-scattering data

Effects of two loop contributions in the pseudofermion functional renormalization group method for quantum spin systems

We implement an extension of the pseudofermion functional renormalization group method for quantum spin systems that takes into account two loop diagrammatic contributions. An efficient numerical treatment of the additional terms is achieved within a nested graph construction which recombines different one loop interaction channels. In order to be fully self consistent with respect to self energy corrections, we also include certain three loop terms of Katanin type. We first apply this formalism to the antiferromagnetic J1 amp; 8722;J2 Heisenberg model on the square lattice and benchmark our results against the previous one loop plus Katanin approach. Even though the renormalization group RG equations undergo significant modifications when including the two loop terms, the magnetic phase diagram, comprising N el ordered and collinear ordered phases separated by a magnetically disordered regime, remains remarkably unchanged. Only the boundary position between the disordered and the collinear phases is found to be moderately affected by two loop terms. On the other hand, critical RG scales, which we associate with critical temperatures Tc, are reduced by a factor of 2 indicating that the two loop diagrams play a significant role in enforcing the Mermin Wagner theorem. Improved estimates for critical temperatures are also obtained for the Heisenberg ferromagnet on the three dimensional simple cubic lattice where errors in Tc are reduced by 34 . These findings have important implications for the quantum phase diagrams calculated within the previous one loop plus Katanin approach which turn out to be already well converge

Matrix measures and random walks

In this paper we study the connection between matrix measures and random walks with a tridiagonal block transition matrix. We derive sufficient conditions such that the blocks of the n-step transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by means of this matrix measure. In many cases this measure is supported in the interval [-1, 1]. The results are illustrated by several examples including random walks on a grid and the embedded chain of a queuing system. --Markov chain,block tridiagonal transition matrix,spectral measure,matrix measure,quasi birth and death processes,canonical moments

Nonequilibrium phases in hybrid arrays with flux qubits and NV centers

We propose a startling hybrid quantum architecture for simulating a localization-delocalization transition. The concept is based on an array of superconducting flux qubits which are coupled to a diamond crystal containing nitrogen-vacancy (NV) centers. The underlying description is a Jaynes-Cummings-lattice in the strong-coupling regime. However, in contrast to well-studied coupled cavity arrays the interaction between lattice sites is mediated here by the qubit rather than by the oscillator degrees of freedom. Nevertheless, we point out that a transition between a localized and a delocalized phase occurs in this system as well. We demonstrate the possibility of monitoring this transition in a non-equilibrium scenario, including decoherence effects. The proposed scheme allows the monitoring of localization-delocalization transitions in Jaynes-Cummings-lattices by use of currently available experimental technology. Contrary to cavity-coupled lattices, our proposed recourse to stylized qubit networks facilitates (i) to investigate localization-delocalization transitions in arbitrary dimensions and (ii) to tune the inter-site coupling in-situ.Comment: Version to be published in Phys. Rev.

Numerical treatment of spin systems with unrestricted spin length S: A functional renormalization group study

We develop a generalized pseudofermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case S=1/2 to the classical limit S→∞. Within this framework, spins of magnitude S are realized by implementing M=2S copies of spin-1/2 degrees of freedom on each lattice site. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudofermion constraint in previous spin-1/2 PFFRG studies. We apply this method to the antiferromagnetic J1−J2 honeycomb Heisenberg model with nearest-neighbor J1>0 and second-neighbor J2>0 interactions. Mapping out the phase diagram in the J2/J1−S plane, we find that upon increasing S, quantum fluctuations are rapidly decreasing. In particular, already at S=1 we find no indication for a magnetically disordered phase. In the limit S→∞, the known phase diagram of the classical system is exactly reproduced. More generally, we prove that for S→∞ the PFFRG approach is identical to the Luttinger-Tisza method

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.Comment: 4 pages, 3 figure

Anomalous expansion and phonon damping due to the Co spin-state transition in RCoO_3 with R = La, Pr, Nd and Eu

We present a combined study of the thermal expansion and the thermal conductivity of the perovskite series RCoO_3 with R = La, Nd, Pr and Eu. The well-known spin-state transition in LaCoO_3 is strongly affected by the exchange of the R ions due to their different ionic radii, i.e. chemical pressure. This can be monitored in detail by measurements of the thermal expansion, which is a highly sensitive probe for detecting spin-state transitions. The Co ions in the higher spin state act as additional scattering centers for phonons, therefore suppressing the phonon thermal conductivity. Based on the analysis of the interplay between spin-state transition and heat transport, we present a quantitative model of the thermal conductivity for the entire series. In PrCoO_3, an additional scattering effect is active at low temperatures. This effect arises from the crystal field splitting of the 4f multiplet, which allows for resonant scattering of phonons between the various 4f levels.Comment: 15 pages including 5 figure