arXiv subjects

Zhan Shi

Publications and source records attributed to Zhan Shi.

At least 127 records · Page 7Linked to original sources

arXiv2013

Fast coherent manipulation of three-electron states in a double quantum dot

A fundamental goal in the manipulation of quantum systems is the achievement of many coherent oscillations within the characteristic dephasing time T2*[1]. Most manipulations of electron spins in quantum dots have focused on the construction and control of two-state quantum systems, or qubits, in which each quantum dot is occupied by a single electron[2-7]. Here we perform quantum manipulations on a system with more electrons per quantum dot, in a double dot with three electrons. We demonstrate that tailored pulse sequences can be used to induce coherent rotations between 3-electron quantum states. Certain pulse sequences yield coherent oscillations with a very high figure of merit (the ratio of coherence time to rotation time) of >100. The presence of the third electron enables very fast rotations to all possible states, in contrast to the case when only two electrons are used, in which some rotations are slow. The minimum oscillation frequency we observe is >5 GHz.

cond-mat.mes-hall↗

arXiv2013

Coherent Quantum Oscillations in a Silicon Charge Qubit

Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2* ranges from 127ps to ~2.1ns; it depends substantially on how the energy difference of the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise(charge noise that changes the asymmetry of the qubit's double-well potential). In the regime with the shortest T2*, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127ps to 760ps, demonstrating that low-frequency noise processes are an important dephasing mechanism.

cond-mat.mes-hall↗

arXiv2011

Tunable singlet-triplet splitting in a few-electron Si/SiGe quantum dot

We measure the excited-state spectrum of a Si/SiGe quantum dot as a function of in-plane magnetic field, and we identify the spin of the lowest three eigenstates in an effective two-electron regime. The singlet-triplet splitting is an essential parameter describing spin qubits, and we extract this splitting from the data. We find it to be tunable by lateral displacement of the dot, which is realized by changing two gate voltages on opposite sides of the device. We present calculations showing the data are consistent with a spectrum in which the first excited state of the dot is a valley-orbit state.

cond-mat.mes-hall↗

arXiv2011

Single-shot measurement of triplet-singlet relaxation in a Si/SiGe double quantum dot

We investigate the lifetime of two-electron spin states in a few-electron Si/SiGe double dot. At the transition between the (1,1) and (0,2) charge occupations, Pauli spin blockade provides a readout mechanism for the spin state. We use the statistics of repeated single-shot measurements to extract the lifetimes of multiple states simultaneously. At zero magnetic field, we find that all three triplet states have equal lifetimes, as expected, and this time is ~10 ms. At non-zero field, the T0 lifetime is unchanged, whereas the T- lifetime increases monotonically with field, reaching 3 seconds at 1 T.

cond-mat.mes-hall↗

arXiv2011

A fast "hybrid" silicon double quantum dot qubit

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers $S^2=3/4$ ($S=\half$) and $S_z = -\half$, with the two different states being singlet and triplet in the doubly occupied dot. The architecture is relatively simple to fabricate, a universal set of fast operations can be implemented electrically, and the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.

quant-ph↗

arXiv2011

Almost sure convergence for stochastically biased random walks on trees

We are interested in the biased random walk on a supercritical Galton--Watson tree in the sense of Lyons, Pemantle and Peres, and study a phenomenon of slow movement. In order to observe such a slow movement, the bias needs to be random; the resulting random walk is then a tree-valued random walk in random environment. We investigate the recurrent case, and prove, under suitable general integrability assumptions, that upon the system's non-extinction, the maximal displacement of the walk in the first n steps, divided by (log n)^3, converges almost surely to a known positive constant.

math.PR↗

arXiv2010

Tunable spin-selective loading of a silicon spin qubit

The remarkable properties of silicon have made it the central material for the fabrication of current microelectronic devices. Silicon's fundamental properties also make it an attractive option for the development of devices for spintronics and quantum information processing. The ability to manipulate and measure spins of single electrons is crucial for these applications. Here we report the manipulation and measurement of a single spin in a quantum dot fabricated in a silicon/silicon-germanium heterostructure. We demonstrate that the rate of loading of electrons into the device can be tuned over an order of magnitude using a gate voltage, that the spin state of the loaded electron depends systematically on the loading voltage level, and that this tunability arises because electron spins can be loaded through excited orbital states of the quantum dot. The longitudinal spin relaxation time T1 is measured using single-shot pulsed techniques and found to be ~3 seconds at a field of 1.85 Tesla. The demonstration of single spin measurement as well as a long spin relaxation time and tunability of the loading are all favorable properties for spintronics and quantum information processing applications.

cond-mat.mes-hall↗

arXiv2010

Weak convergence for the minimal position in a branching random walk: a simple proof

Consider the boundary case in a one-dimensional super-critical branching random walk. It is known that upon the survival of the system, the minimal position after $n$ steps behaves in probability like ${3\over 2} \log n$ when $n\to \infty$. We give a simple and self-contained proof of this result, based exclusively on elementary properties of sums of i.i.d. real-valued random variables.

math.PR↗

arXiv2010

Asymptotics for the survival probability in a killed branching random walk

Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope $γ-ε$, where $γ$ denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when $ε\to 0$, the probability in question decays like $\exp\{- {β+ o(1)\over ε^{1/2}}\}$, where $β$ is a positive constant depending on the distribution of the branching random walk. In the special case of i.i.d. Bernoulli$(p)$ random variables (with $0<p<{1\over 2}$) assigned on a rooted binary tree, this answers an open question of Robin Pemantle.

math.PR↗

arXiv2009

Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees

We establish a second-order almost sure limit theorem for the minimal position in a one-dimensional super-critical branching random walk, and also prove a martingale convergence theorem which answers a question of Biggins and Kyprianou [9]. Our method applies furthermore to the study of directed polymers on a disordered tree. In particular, we give a rigorous proof of a phase transition phenomenon for the partition function (from the point of view of convergence in probability), already described by Derrida and Spohn [17]. Surprisingly, this phase transition phenomenon disappears in the sense of upper almost sure limits.

math.PR↗

arXiv2009

The infinite valley for a recurrent random walk in random environment

We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the - suitably centered - empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time of the RWRE and also determine the exact constant in the almost sure upper limit of the maximal local time.

math.PR↗

arXiv2007

A weakness in strong localization for Sinai's walk

Sinai's walk is a recurrent one-dimensional nearest-neighbor random walk in random environment. It is known for a phenomenon of strong localization, namely, the walk spends almost all time at or near the bottom of deep valleys of the potential. Our main result shows a weakness of this localization phenomenon: with probability one, the zones where the walk stays for the most time can be far away from the sites where the walk spends the most time. In particular, this gives a negative answer to a problem of Erdős and Révész [Mathematical Structures--Computational Mathematics--Mathematical Modelling 2 (1984) 152--157], originally formulated for the usual homogeneous random walk.

math.PR↗

arXiv2006

Slow movement of random walk in random environment on a regular tree

We consider a recurrent random walk in random environment on a regular tree. Under suitable general assumptions upon the distribution of the environment, we show that the walk exhibits an unusual slow movement: the order of magnitude of the walk in the first $n$ steps is $(\log n)^3$.

math.PR↗

arXiv2006

Small Deviations of Gaussian Random Fields in $L_q$--Spaces

We investigate small deviation properties of Gaussian random fields in the space $L_q(\R^N,μ)$ where $μ$ is an arbitrary finite compactly supported Borel measure. Of special interest are hereby "thin" measures $μ$, i.e., those which are singular with respect to the $N$--dimensional Lebesgue measure; the so--called self--similar measures providing a class of typical examples. For a large class of random fields (including, among others, fractional Brownian motions), we describe the behavior of small deviation probabilities via numerical characteristics of $μ$, called mixed entropy, characterizing size and regularity of $μ$. For the particularly interesting case of self--similar measures $μ$, the asymptotic behavior of the mixed entropy is evaluated explicitly. As a consequence, we get the asymptotic of the small deviation for $N$--parameter fractional Brownian motions with respect to $L_q(\R^N,μ)$--norms. While the upper estimates for the small deviation probabilities are proved by purely probabilistic methods, the lower bounds are established by analytic tools concerning Kolmogorov and entropy numbers of Hölder operators.

math.PR↗

arXiv2006

A subdiffusive behaviour of recurrent random walk in random environment on a regular tree

We are interested in the random walk in random environment on an infinite tree. Lyons and Pemantle [11] give a precise recurrence/transience criterion. Our paper focuses on the almost sure asymptotic behaviours of a recurrent random walk $(X\_n)$ in random environment on a regular tree, which is closely related to Mandelbrot [13]'s multiplicative cascade. We prove, under some general assumptions upon the distribution of the environment, the existence of a new exponent $ν\in (0, {1\over 2}]$ such that $\max\_{0\le i \le n} |X\_i|$ behaves asymptotically like $n^ν$. The value of $ν$ is explicitly formulated in terms of the distribution of the environment.

math.PR↗

arXiv2006

Valleys and the maximum local time for random walk in random environment

Let $ξ(n, x)$ be the local time at $x$ for a recurrent one-dimensional random walk in random environment after $n$ steps, and consider the maximum $ξ^*(n) = \max_x ξ(n,x)$. It is known that $\limsup ξ^*(n)/n$ is a positive constant a.s. We prove that $\liminf_n (\log\log\log n)ξ^*(n)/n$ is a positive constant a.s.; this answers a question of P. Révész (1990). The proof is based on an analysis of the {\em valleys /} in the environment, defined as the potential wells of record depth. In particular, we show that almost surely, at any time $n$ large enough, the random walker has spent almost all of its lifetime in the two deepest valleys of the environment it has encountered. We also prove a uniform exponential tail bound for the ratio of the expected total occupation time of a valley and the expected local time at its bottom.

math.PR↗

arXiv2005

Annealed deviations of random walk in random scenery

Let $(Z_n)_{n\in\N}$ be a $d$-dimensional {\it random walk in random scenery}, i.e., $Z_n=\sum_{k=0}^{n-1}Y(S_k)$ with $(S_k)_{k\in\N_0}$ a random walk in $\Z^d$ and $(Y(z))_{z\in\Z^d}$ an i.i.d. scenery, independent of the walk. The walker's steps have mean zero and finite variance. We identify the speed and the rate of the logarithmic decay of $¶(\frac 1n Z_n>b_n)$ for various choices of sequences $(b_n)_n$ in $[1,\infty)$. Depending on $(b_n)_n$ and the upper tails of the scenery, we identify different regimes for the speed of decay and different variational formulas for the rate functions. In contrast to recent work \cite{AC02} by A. Asselah and F. Castell, we consider sceneries {\it unbounded} to infinity. It turns out that there are interesting connections to large deviation properties of self-intersections of the walk, which have been studied recently by X. Chen \cite{C03}.

math.PR↗

arXiv2005

Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation

We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L_n at any fixed time prior to the critical time. The asymptotic behavior of L_n is also analyzed for sequences of times tending to the critical time. A phenomenon of phase transition shows up, namely, for small initial particle speeds (``cold'' gas) L_n has logarithmic order of growth while higher speeds (``warm'' gas) yield polynomial rates for L_n.

cond-mat.stat-mech↗