arXiv subjects

Robert Joynt

Publications and source records attributed to Robert Joynt.

At least 73 records · Page 4Linked to original sources

arXiv2011

Topology of Entanglement Evolution of Two Qubits

The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described by the function ~n(t), where ~n is the 15-dimensional polarization vector. This representation is particularly useful because the components of ~n are direct physical observables, there is a meaningful notion of orthogonality, and the concurrence C can be computed for any point in the space. We analyze the topology of the space S of separable states (those having C = 0), and the often lower-dimensional linear dynamical subspace D that is characteristic of a specific physical model. This allows us to give a rigorous characterization of the four possible kinds of entanglement evolution. Which evolution is realized depends on the dimensionality of D and of D \cap S, the position of the asymptotic point of the evolution, and whether or not the evolution is "distance-Markovian", a notion we define. We give several examples to illustrate the general principles, and to give a method to compute critical points. We construct a model that shows all four behaviors.

quant-ph↗

arXiv2011

Disappearance of entanglement: a topological point of view

We give a topological classification of the evolution of entanglement, particularly the different ways the entanglement can disappear. Four categories exhaust all possibilities given the initial quantum state is entangled and the final one is not. Exponential decay of entanglement, entanglement sudden death and sudden birth can all be understood and visualized in the associated geometrical picture - the polarization vector representation. The entanglement evolution categories of any model are determined by the topology of the state space, the limiting state and the memory effect of the environment. Transitions between these types of behaviors as a function of physical parameters are also possible. These transitions are thus of topological nature. We illustrate the general concepts with a visualizable model.

quant-ph↗

arXiv2011

Quasi-Hamiltonian Method for Computation of Decoherence Rates

For many implementations of quantum computing, 1/f and other types of broad-spectrum noise are an important source of decoherence. An important step forward would be the ability to back out the characteristics of this noise from qubit measurements and to see if it leads to new physical effects. For certain types of qubits, the working point of the qubit can be varied. Using a new mathematical method that is suited to treat all working points, we present theoretical results that show how this degree of freedom can be used to extract noise parameters and to predict a new effect: noise-induced looping on the Bloch sphere. We analyze data on superconducting qubits to show that they are very near the parameter regime where this looping should be observed.

quant-ph↗

arXiv2011

Cooling of cryogenic electron bilayers via the Coulomb interaction

Heat dissipation in current-carrying cryogenic nanostructures is problematic because the phonon density of states decreases strongly as energy decreases. We show that the Coulomb interaction can prove a valuable resource for carrier cooling via coupling to a nearby, cold electron reservoir. Specifically, we consider the geometry of an electron bilayer in a silicon-based heterostructure, and analyze the power transfer. We show that across a range of temperatures, separations, and sheet densities, the electron-electron interaction dominates the phonon heat-dissipation modes as the main cooling mechanism. Coulomb cooling is most effective at low densities, when phonon cooling is least effective in silicon, making it especially relevant for experiments attempting to perform coherent manipulations of single spins.

cond-mat.mes-hall↗

arXiv2011

Pauli spin blockade and lifetime-enhanced transport in a Si/SiGe double quantum dot

We analyze electron transport data through a Si/SiGe double quantum dot in terms of spin blockade and lifetime-enhanced transport (LET), which is transport through excited states that is enabled by long spin relaxation times. We present a series of low-bias voltage measurements showing the sudden appearance of a strong tail of current that we argue is an unambiguous signature of LET appearing when the bias voltage becomes greater than the singlet-triplet splitting for the (2,0) electron state. We present eight independent data sets, four in the forward bias (spin-blockade) regime and four in the reverse bias (lifetime-enhanced transport) regime, and show that all eight data sets can be fit to one consistent set of parameters. We also perform a detailed analysis of the reverse bias (LET) regime, using transport rate equations that include both singlet and triplet transport channels. The model also includes the energy dependent tunneling of electrons across the quantum barriers, and resonant and inelastic tunneling effects. In this way, we obtain excellent fits to the experimental data, and we obtain quantitative estimates for the tunneling rates and transport currents throughout the reverse bias regime. We provide a physical understanding of the different blockade regimes and present detailed predictions for the conditions under which LET may be observed.

cond-mat.mes-hall↗

arXiv2011

Suppression of Decoherence and Disentanglement by the Exchange Interaction

Entangled qubit pairs can serve as a quantum memory or as a resource for quantum communication. The utility of such pairs is measured by how long they take to disentangle or decohere. To answer the question of whether qubit-qubit interactions can prolong entanglement, we calculate the dissipative dynamics of a pair of qubits coupled via the exchange interaction in the presence of random telegraph noise and $1/f$ noise. We show that for maximally entangled (Bell) states, the exchange interaction generally suppresses decoherence and disentanglement. This suppression is more apparent for random telegraph noise if the noise is non-Markovian, whereas for $1/f$ noise the exchange interaction should be comparable in magnitude to strongest noise source. The entangled singlet-triplet superposition state of 2 qubits ($ψ_{\pm}$ Bell state) can be protected by the interaction, while for the triplet-triplet state ($ϕ_{\pm}$ Bell state), it is less effective. Thus the former is more suitable for encoding quantum information.

cond-mat.mes-hall↗

arXiv2010

Disentanglement and decoherence from classical non-Markovian noise: Random telegraph noise

We calculate the two-qubit disentanglement due to classical random telegraph noise using the quasi-Hamiltonian method. This allows us to obtain analytical results even for strong coupling and mixed noise, important when the qubits have tunable working point. We determine when entanglement sudden death and revival occur as functions of qubit working point, noise coupling strength and initial state entanglement. For extended Werner states, we show that the concurrence is related to the difference of two functions: one is related to dephasing and the other longitudinal relaxation. A physical intepretation based on the generalized Bloch vector is given: revival only occurs for strongly-coupled noise and comes from the angular motion of the vector.

quant-ph↗

arXiv2010

Two-particle quantum walks applied to the graph isomorphism problem

We show that the quantum dynamics of interacting and noninteracting quantum particles are fundamentally different in the context of solving a particular computational problem. Specifically, we consider the graph isomorphism problem, in which one wishes to determine whether two graphs are isomorphic (related to each other by a relabeling of the graph vertices), and focus on a class of graphs with particularly high symmetry called strongly regular graphs (SRG's). We study the Green's functions that characterize the dynamical evolution single-particle and two-particle quantum walks on pairs of non-isomorphic SRG's and show that interacting particles can distinguish non-isomorphic graphs that noninteracting particles cannot. We obtain the following specific results: (1) We prove that quantum walks of two noninteracting particles, Fermions or Bosons, cannot distinguish certain pairs of non-isomorphic SRG's. (2) We demonstrate numerically that two interacting Bosons are more powerful than single particles and two noninteracting particles, in that quantum walks of interacting bosons distinguish all non-isomorphic pairs of SRGs that we examined. By utilizing high-throughput computing to perform over 500 million direct comparisons between evolution operators, we checked all tabulated pairs of non-isomorphic SRGs, including graphs with up to 64 vertices. (3) By performing a short-time expansion of the evolution operator, we derive distinguishing operators that provide analytic insight into the power of the interacting two-particle quantum walk.

quant-ph↗

arXiv2009

Looping on the Bloch sphere: Oscillatory effects in dephasing of qubits subject to broad-spectrum noise

quant-ph↗

arXiv2008

Exact solution of a model of qubit dephasing due to telegraph noise

We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be applied to a qubit subject to an arbitrary combination of dephasing and relaxational telegraph noise, in contrast to existing non-perturbative methods that treat only one or the other of these limits. We present 3 applications: 1) We obtain the full qubit dynamics on time scales short compared with the enviromental correlation times. In the strong coupling cases this reveals unexpected oscillations and induced magnetization components; 2) We find in strong coupling case strong violations of the widely used relation 1/T$_2$ = 1/2T$_1$ + 1/T$_ϕ$, which is a result of perturbation theory; 3) We discuss the effects of bang-bang and spin-echo controls of the qubit dynamics in general settings of the telegraph noises. %The result shows that these methods are not very effective in %reducing decoherence arising from a single telegraph noise. Finally, we discuss the extension of the method to the cases of many telegraph noise sources and multiple qubits. The method still works when white noise is also present.

quant-ph↗

arXiv2007

Spin-Valley Kondo Effect in Multi-electron Silicon Quantum Dots

We study the spin-valley Kondo effect of a silicon quantum dot occupied by $% \mathcal{N}$ electrons, with $\mathcal{N}$ up to four. We show that the Kondo resonance appears in the $\mathcal{N}=1,2,3$ Coulomb blockade regimes, but not in the $\mathcal{N}=4$ one, in contrast to the spin-1/2 Kondo effect, which only occurs at $\mathcal{N}=$ odd. Assuming large orbital level spacings, the energy states of the dot can be simply characterized by fourfold spin-valley degrees of freedom. The density of states (DOS) is obtained as a function of temperature and applied magnetic field using a finite-U equation-of-motion approach. The structure in the DOS can be detected in transport experiments. The Kondo resonance is split by the Zeeman splitting and valley splitting for double- and triple-electron Si dots, in a similar fashion to single-electron ones. The peak structure and splitting patterns are much richer for the spin-valley Kondo effect than for the pure spin Kondo effect.

cond-mat.mtrl-sci↗

arXiv2007

Controllable valley splitting in silicon quantum devices

Silicon has many attractive properties for quantum computing, and the quantum dot architecture is appealing because of its controllability and scalability. However, the multiple valleys in the silicon conduction band are potentially a serious source of decoherence for spin-based quantum dot qubits. Only when these valleys are split by a large energy does one obtain well-defined and long-lived spin states appropriate for quantum computing. Here we show that the small valley splittings observed in previous experiments on Si/SiGe heterostructures result from atomic steps at the quantum well interface. Lateral confinement in a quantum point contact limits the electron wavefunctions to several steps, and enhances the valley splitting substantially, up to 1.5 meV. The combination of electronic and magnetic confinement produces a valley splitting larger than the spin splitting, which is controllable over a wide range. These results improve the outlook for realizing spin qubits with long coherence times in silicon-based devices.

cond-mat.mes-hall↗

arXiv2007

Energy Level Statistics of Quantum Dots

We investigate the charging energy level statistics of disordered interacting electrons in quantum dots by numerical calculations using the Hartree approximation. The aim is to obtain a global picture of the statistics as a function of disorder and interaction strengths. We find Poisson statistics at very strong disorder, Wigner- Dyson statistics for weak disorder and interactions, and a Gaussian intermediate regime. These regimes are as expected from previous studies and fundamental considerations, but we also find interesting and rather broad crossover regimes. In particular, intermediate between the Gaussian and Poisson regimes we find a two-sided exponential distribution for the energy level spacings. In comparing with experiment, we find that this distribution may be realized in some quantum dots.

cond-mat.dis-nn↗

arXiv2007

Exact solution of qubit decoherence models by a transfer matrix method

We present a new method for the solution of the behavior of an ensemble of qubits in a random time-dependent external field. The forward evolution in time is governed by a transfer matrix. The elements of this matrix determine the various decoherence times. The method provides an exact solution in cases where the noise is piecewise constant in time. We show that it applies, for example, to a realistic model of decoherence of electron spins in semiconductors. Results are obtained for the non-perturbative regimes of the models, and we see a transition from weak relaxation to overdamped behavior as a function of noise anisotropy.

quant-ph↗

arXiv2007

Valley Kondo Effect in Silicon Quantum Dots

Recent progress in the fabrication of quantum dots using silicon opens the prospect of observing the Kondo effect associated with the valley degree of freedom. We compute the dot density of states using an Anderson model with infinite Coulomb interaction $U$, whose structure mimics the nonlinear conductance through a dot. The density of states is obtained as a function of temperature and applied magnetic field in the Kondo regime using an equation-of-motion approach. We show that there is a very complex peak structure near the Fermi energy, with several signatures that distinguish this spin-valley Kondo effect from the usual spin Kondo effect seen in GaAs dots. We also show that the valley index is generally not conserved when electrons tunnel into a silicon dot, though the extent of this non-conservation is expected to be sample-dependent. We identify features of the conductance that should enable experimenters to understand the interplay of Zeeman splitting and valley splitting, as well as the dependence of tunneling on the valley degree of freedom.

cond-mat.str-el↗

arXiv2006

Spectroscopy of Valley Splitting in a Silicon/Silicon-Germanium Two-Dimensional Electron Gas

The lifting of the two-fold degeneracy of the conduction valleys in a strained silicon quantum well is critical for spin quantum computing. Here, we obtain an accurate measurement of the splitting of the valley states in the low-field region of interest, using the microwave spectroscopy technique of electron valley resonance (EVR). We compare our results with conventional methods, observing a linear magnetic field dependence of the valley splitting, and a strong low-field suppression, consistent with recent theory. The resonance linewidth shows a marked enhancement above $T\simeq 300$ mK.

cond-mat.mes-hall↗

arXiv2006

Detection and measurement of the Dzyaloshinskii-Moriya interaction in double quantum dot systems

Spins in quantum dots can act as the qubit for quantum computation. In this context we point out that spins on neighboring dots will experience an anisotropic form of the exchange coupling, called the Dzyaloshinskii-Moriya (DM) interaction, which mixes the spin singlet and triplet states. This will have an important effect on both qubit interactions and spin-dependent tunneling. We show that the interaction depends strongly on the direction of the external field, which gives an unambiguous signature of this effect. We further propose a new experiment using coupled quantum dots to detect and characterize the DM interaction.

cond-mat.mtrl-sci↗

arXiv2005

Quantum dots in Si/SiGe 2DEGs with Schottky top-gated leads

We report on the fabrication and characterization of quantum dot devices in a Schottky-gated silicon/silicon-germanium two-dimensional electron gas (2DEG). The dots are confined laterally inside an etch-defined channel, while their potential is modulated by an etch-defined 2DEG gate in the plane of the dot. For the first time in this material, Schottky top gates are used to define and tune the tunnel barriers of the dot. The leakage current from the gates is reduced by minimizing their active area. Further suppression of the leakage is achieved by increasing the etch depth of the channel. The top gates are used to put the dot into the Coulomb blockade regime, and conductance oscillations are observed as the voltage on the side gate is varied.

cond-mat.mes-hall↗