arXiv subjects

Juan Atalaya

Publications and source records attributed to Juan Atalaya.

41 records · Page 3Linked to original sources

arXiv2017

Simultaneous continuous measurement of non-commuting observables: quantum state correlations

We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlators are defined for an ensemble of qubit trajectories, which has the same fixed initial state and can also be optionally constrained by a fixed final state. We develop a stochastic path integral description for the continuous quantum measurement and use it to calculate the considered correlators. Exact analytic results are possible in the case of ideal measurements of equal strength and are also shown to agree with solutions obtained using the Fokker-Planck equation. For a more general case with decoherence effects and inefficiency, we use a diagrammatic approach to find the correlators perturbatively in the quantum efficiency. We also calculate the state correlators for the quantum trajectories which are extracted from readout signals measured in a transmon qubit experiment, by means of the quantum Bayesian state update. We find an excellent agreement between the correlators based on the experimental data and those obtained from our analytical and numerical results.

quant-ph↗

arXiv2017

Correlators in simultaneous measurement of non-commuting qubit observables

We consider the simultaneous and continuous measurement of qubit observables $σ_z$ and $σ_z\cosφ+ σ_x\sinφ$, focusing on the temporal correlations of the two output signals. Using quantum Bayesian theory, we derive analytical expressions for the correlators, which we find to be in very good agreement with experimentally measured output signals. We further discuss how the correlators can be applied to parameter estimation, and use them to infer a small residual qubit Hamiltonian arising from calibration inaccuracy in the experimental data.

quant-ph↗

arXiv2016

Bacon-Shor code with continuous measurement of non-commuting operators

We analyze the operation of a four-qubit Bacon-Shor code with simultaneous continuous measurement of non-commuting gauge operators. The error syndrome in this case is monitored via time-averaged cross-correlators of the output signals. We find the logical error rate for several models of decoherence, and also find the termination rate for this quantum error detecting code. The code operation is comparable to that based on projective measurements when the collapse timescale due to continuous measurements is an order of magnitude less than the time period between the projective measurements. An advantage of the continuous-measurement implementation is the absence of time-dependence in the code operation, with passive continuous monitoring of the error syndrome.

quant-ph↗

arXiv2014

Flux $1/f^α$ noise in 2D Heisenberg spin glasses: effects of weak anisotropic interactions

We study the dynamics of a two-dimensional ensemble of randomly distributed classical Heisenberg spins with isotropic RKKY and weaker anisotropic dipole-dipole couplings. Such ensembles may give rise to the flux noise observed in SQUIDs with a $1/f^α$ power spectrum ($α\lesssim 1$). We solve numerically the Landau-Lifshiftz-Gilbert equations of motion in the dissipationless limit. We find that Ising type fluctuators, which arise from spin clustering close to a spin-glass critical behavior with $T_c =0$, give rise to $1/f^α$ noise. Even weak anisotropic interactions lead to a crossover from the Heisenberg-type criticality to the much stronger Ising-type criticality. The temperature dependent exponent $α(T) \lesssim 1$ grows and approaches unity when the temperature is lowered. This mechanism acts in parallel to the spin diffusion mechanism. Whereas the latter is sensitive to the device geometry, the spin-clustering mechanism is largely geometry independent.

cond-mat.mes-hall↗

arXiv2008

Continuum elastic modeling of graphene resonators

Starting from an atomistic approach we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. The descriptions are validated by applying them to square graphene-based resonators with clamped edges and studying numerically their mechanical responses. Both static and dynamic responses are treated. We find that already for deflections of the order of 0.5Å a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be used to accurately describe the dynamics of graphene membranes.

cond-mat.other↗