An Ising-Glauber Spin Cluster Model for Temperature Dependent Magnetization Noise in SQUIDs

Clusters of interacting two-level-systems (TLS),likely due to $F^+$ centers at the metal-insulator interface, are shown to self consistently lead to $1/f^{\alpha }$ magnetization noise in SQUIDs. By introducing a correlation-function calculation method and without any a priori assumptions on the distribution of fluctuation rates, it is shown why the flux noise is only weakly temperature dependent with $\alpha\lesssim 1$, while the inductance noise has a huge temperature dependence seen in experiment, even though the mechanism producing both spectra is the same. Though both ferromagnetic- RKKY and short-range-interactions (SRI) lead to strong flux-inductance-noise cross-correlations seen in experiment, the flux noise varies a lot with temperature for SRI. Hence it is unlikely that the TLS's time reversal symmetry is broken by the same mechanism which mediates surface ferromagnetism in nanoparticles and thin films of the same insulator materials

1/f Flux Noise in low-Tc_c SQUIDs due to Superparamagnetic Phase Transitions in Defect Clusters

It is shown here that $1/f^\alpha$ flux noise in conventional low-T$_c$ SQUIDs is a result of low temperature superparamagnetic phase transitions in small clusters of strongly correlated color center defects. The spins in each cluster interact via long-range ferromagnetic interactions. Due to its small size, the cluster behaves like a 'random-telegraphic' macro-spin when transitioning to the superparamagnetic phase. This results in $1/f^{\alpha}$ noise when ensemble averaged over a random distribution of clusters. This model is self-consistent and explains all related experimental results which includes $\alpha\sim 0.8$ independent of system-size. The experimental flux-inductance-noise spectrum is explained through three-point correlation calculations and time reversal symmetry breaking arguments. Also, unlike the flux noise, it is shown why the second-spectrum inductance noise is inherently temperature dependent due to the fluctuation-dissipation theorem. A correlation-function calculation methodology using Ising-Glauber dynamics was key for obtaining these results

A Couped-Qubit Tavis Cummings Scheme for Prolonging Quantum Coherence

Qubit-qubit interactions can significantly boost quantum coherence times for Bell states. The coherence-time-enhancements are however not monotonic and there exists a phase where further increasing the interaction is unhelpful. A resonator in a suggested circuit QED type implementation of the Tavis-Cummings(Dicke) model, is shown to shift this transition point depending on the number of loaded photons. This allows the resonator to amplify the coherence enhancements in certain regimes. The interactions also induce unusual collapse and revival type behavior for the entanglement dynamics. A new and exact open quantum systems formalism -- the quasi-Hamiltonians for the Dicke model thus reveals how a Bell state in a resonator can be protected against $1/f$ noise from randomly fluctuating two level systems. Simple circuit level details are given for flux qubits

Fast Quantum Control for Weakly Nonlinear Qubits: On Two-Quadrature Adiabatic Gates

Adiabatic or slowly varying gate operations are typically required in order to remain within the qubit subspace in an anharmonic oscillator. However significant speed ups are possible by using the two quadrature derivative-removal-by-adiabatic-gate(DRAG) technique, where a second time derivative pulse component burns a spectral hole near an unwanted transition. It is shown here, that simultaneous optimization of the detuning and the pulse norm in addition, further reduces leakage errors and significantly improve gate fidelities. However, with this optimization accounting for the AC Stark shift, there is a low spectral weight pulse envelope regime, where DRAG is almost not needed and where the two state error fidelities are stable against pulse jitter. Explicit time evolution calculations are carried out in the lab frame for truncated multi-level Transmon qubit models obtained from a tight-binding model

Strong Cavity-Pseudospin Coupling in Monolayer Transition Metal Dichalcogenides: Spontaneous Spin-Oscillations and Magnetometry

Strong coupling between the electronic states of monolayer transition metal dichalcogenides (TMDC) such as MoS$_2$, MoSe$_2$, WS$_2$, or WSe$_2$, and a two-dimensional (2D) photonic cavity gives rise to several exotic effects. The Dirac type Hamiltonian for a 2D gapped semiconductor with large spin-orbit coupling facilitates pure Jaynes-Cummings type coupling in the presence of a single mode electric field. The presence of an additional circularly polarized beam of light gives rise to valley and spin dependent cavity-QED properties. The cavity causes the TMDC monolayer to act as an on-chip coherent light source and a spontaneous spin-oscillator. In addition, a TMDC monolayer in a cavity is a sensitive magnetic field sensor for an in-plane magnetic field

Magnetization Noise Induced Collapse and Revival of Rabi Oscillations in circuit QED

We use a quasi Hamiltonian formalism to describe the dissipative dynamics of a circuit QED qubit that is affected by several fluctuating two level systems with a 1/f noise power spectrum. The qubit-resonator interactions are described by the Jaynes Cummings model. We argue that the presence of pure dephasing noise in such a qubit-resonator system will also induce an energy relaxation mechanism via a fluctuating dipole coupling term. This random modulation of the coupling is seen to lead to rich physical behavior. For non-Markovian noise, the coupling can either worsen or alleviate decoherence depending on the initial conditions. The magnetization noise leads to behavior resembling the collapse and revival of Rabi oscillations. For a broad distribution of noise couplings, the frequency of these oscillations depends on the mean noise strength. We describe this behavior semi-analytically and find it to be independent of the number of fluctuators. This phenomenon could be used as an in situ probe of the noise characteristics

Electronic Structure and Optical Properties of the Lonsdaleite Phase of Si, Ge and diamond

Crystalline semiconductors may exist in different polytypic phases with significantly different electronic and optical properties. In this paper, we calculate the electronic structure and optical properties of diamond, Si and Ge in the lonsdaleite (hexagonal-diamond) phase. We use an empirical pseudopotentials method based on transferable model potentials, including spin-orbit interactions. We obtain band structures, densities of states and complex dielectric functions calculated in the dipole approximation for light polarized perpendicular and parallel to the c-axis of the crystal. We find strong polarization dependent optical anisotropy. Simple analytical expressions are provided for the dispersion relations. We find that in the lonsdaleite phase, diamond and Si remain indirect gap semiconductors while Ge is transformed into a direct gap semiconductor with a significantly smaller band gap

Dynamically corrected gates for qubits with always-on Ising couplings: Error model and fault-tolerance with the toric code

We describe how a universal set of dynamically-corrected quantum gates can be implemented using sequences of shaped decoupling pulses on any qubit network forming a sparse bipartite graph with always-on Ising interactions. These interactions are constantly decoupled except when they are needed for two-qubit gates. We analytically study the error operators associated with the constructed gates up to third order in the Magnus expansion, analyze these errors numerically in the unitary time evolution of small qubit clusters, and give a bound on high-order errors for qubits on a large square lattice. We prove that with a large enough toric code the present gate set can be used to implement a fault-tolerant quantum memory

Universal set of Dynamically Protected Gates for Bipartite Qubit Networks II: Soft Pulse Implementation of the [[5,1,3]] Quantum Error Correcting Code

We model repetitive quantum error correction (QEC) with the single-error-correcting five-qubit code on a network of individually-controlled qubits with always-on Ising couplings, using our previously designed universal set of quantum gates based on sequences of shaped decoupling pulses. In addition to serving as accurate quantum gates, the sequences also provide dynamical decoupling (DD) of low-frequency phase noise. The simulation involves integrating unitary dynamics of six qubits over the duration of tens of thousands of control pulses, using classical stochastic phase noise as a source of decoherence. The combined DD/QEC protocol dramatically improves the coherence, with the QEC alone responsible for more than an order of magnitude infidelity reduction.Comment: 12 pages, 9 figure

Control of Majorana Edge Modes by a g-factor Engineered Nanowire Spin Transistor

We propose the manipulation of Majorana edge states via hybridization and spin currents in a nanowire spin transistor. The spin transistor is based on a heterostructure nanowire comprising of semiconductors with large and small g-factors that form the topological and non-topological regions respectively. The hybridization of bound edge states results in spin currents and $4\pi$-periodic torques, as a function of the relative magnetic field angle -- an effect which is dual to the fractional Josephson effect. We establish relation between torques and spin-currents in the non-topological region where the magnetic field is almost zero and spin is conserved along the spin-orbit field direction. The angular momentum transfer could be detected by sensitive magnetic resonance force microscopy techniques