Electrometry Using Coherent Exchange Oscillations in a Singlet-Triplet-Qubit

Two level systems that can be reliably controlled and measured hold promise in both metrology and as qubits for quantum information science (QIS). When prepared in a superposition of two states and allowed to evolve freely, the state of the system precesses with a frequency proportional to the splitting between the states. In QIS,this precession forms the basis for universal control of the qubit,and in metrology the frequency of the precession provides a sensitive measurement of the splitting. However, on a timescale of the coherence time, $T_2$, the qubit loses its quantum information due to interactions with its noisy environment, causing qubit oscillations to decay and setting a limit on the fidelity of quantum control and the precision of qubit-based measurements. Understanding how the qubit couples to its environment and the dynamics of the noise in the environment are therefore key to effective QIS experiments and metrology. Here we show measurements of the level splitting and dephasing due to voltage noise of a GaAs singlet-triplet qubit during exchange oscillations. Using free evolution and Hahn echo experiments we probe the low frequency and high frequency environmental fluctuations, respectively. The measured fluctuations at high frequencies are small, allowing the qubit to be used as a charge sensor with a sensitivity of $2 \times 10^{-8} e/\sqrt{\mathrm{Hz}}$, two orders of magnitude better than the quantum limit for an RF single electron transistor (RF-SET). We find that the dephasing is due to non-Markovian voltage fluctuations in both regimes and exhibits an unexpected temperature dependence. Based on these measurements we provide recommendations for improving $T_2$ in future experiments, allowing for higher fidelity operations and improved charge sensitivity

Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits

Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform inter-qubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor due to their potential for scalability and miniaturization. However, their weak interactions with the environment, which leads to their long coherence times, makes inter-qubit operations challenging. We perform a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography we measure the full density matrix of the system and determine the concurrence and the fidelity of the generated state, providing proof of entanglement

Anomalous structure in the single particle spectrum of the fractional quantum Hall effect

The two-dimensional electron system (2DES) is a unique laboratory for the physics of interacting particles. Application of a large magnetic field produces massively degenerate quantum levels known as Landau levels. Within a Landau level the kinetic energy of the electrons is suppressed, and electron-electron interactions set the only energy scale. Coulomb interactions break the degeneracy of the Landau levels and can cause the electrons to order into complex ground states. In the high energy single particle spectrum of this system, we observe salient and unexpected structure that extends across a wide range of Landau level filling fractions. The structure appears only when the 2DES is cooled to very low temperature, indicating that it arises from delicate ground state correlations. We characterize this structure by its evolution with changing electron density and applied magnetic field. We present two possible models for understanding these observations. Some of the energies of the features agree qualitatively with what might be expected for composite Fermions, which have proven effective for interpreting other experiments in this regime. At the same time, a simple model with electrons localized on ordered lattice sites also generates structure similar to those observed in the experiment. Neither of these models alone is sufficient to explain the observations across the entire range of densities measured. The discovery of this unexpected prominent structure in the single particle spectrum of an otherwise thoroughly studied system suggests that there exist core features of the 2DES that have yet to be understood.Comment: 15 pages, 10 figure

Effect of Oscillating Landau Bandwidth on the Integer Quantum Hall Effect in a Unidirectional Lateral Superlattice

We have measured activation gaps for odd-integer quantum Hall states in a unidirectional lateral superlattice (ULSL) -- a two-dimensional electron gas (2DEG) subjected to a unidirectional periodic modulation of the electrostatic potential. By comparing the activation gaps with those simultaneously measured in the adjacent section of the same 2DEG sample without modulation, we find that the gaps are reduced in the ULSL by an amount corresponding to the width acquired by the Landau levels through the introduction of the modulation. The decrement of the activation gap varies with the magnetic field following the variation of the Landau bandwidth due to the commensurability effect. Notably, the decrement vanishes at the flat band conditions.Comment: 7 pages, 6 figures, minor revisio

High Resolution Spectroscopy of Two-Dimensional Electron Systems

Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunneling, yield measurements of the "single particle" density of states (SPDOS) spectrum of a system. The SPDOS is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proven difficult to probe spectroscopically. Here we present an improved version of time domain capacitance spectroscopy (TDCS) that now allows us to measure the SPDOS of a 2DES with unprecedented fidelity and resolution. Using TDCS, we perform measurements of a cold 2DES, providing the first direct measurements of the single-particle exchange-enhanced spin gap and single particle lifetimes in the quantum Hall system, as well as the first observations of exchange splitting of Landau levels not at the Fermi surface. The measurements reveal the difficult to reach and beautiful structure present in this highly correlated system far from the Fermi surface.Comment: There are formatting and minor textual differences between this version and the published version in Nature (follow the DOI link below

Scaling properties of protein family phylogenies

One of the classical questions in evolutionary biology is how evolutionary processes are coupled at the gene and species level. With this motivation, we compare the topological properties (mainly the depth scaling, as a characterization of balance) of a large set of protein phylogenies with a set of species phylogenies. The comparative analysis shows that both sets of phylogenies share remarkably similar scaling behavior, suggesting the universality of branching rules and of the evolutionary processes that drive biological diversification from gene to species level. In order to explain such generality, we propose a simple model which allows us to estimate the proportion of evolvability/robustness needed to approximate the scaling behavior observed in the phylogenies, highlighting the relevance of the robustness of a biological system (species or protein) in the scaling properties of the phylogenetic trees. Thus, the rules that govern the incapability of a biological system to diversify are equally relevant both at the gene and at the species level.Comment: Replaced with final published versio

The effect of oscillating Fermi energy on the line shape of the Shubnikov-de Haas oscillation in a two dimensional electron gas

The line shape of the Shubnikov-de Haas (SdH) oscillation has been analyzed in detail for a GaAs/AlGaAs two-dimensional electron gas. The line shape, or equivalently the behavior of the Fourier components, of the experimentally observed SdH oscillation is well reproduced by the sinusoidal density of states at the Fermi energy that oscillates with a magnetic field in a saw-tooth shape to keep the electron density constant. This suggests that the broadening of each Landau level by disorder is better described by a Gaussian than by a Lorentzian.Comment: 7 pages,6 figures, minor revision