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W. De Roeck

Publications and source records attributed to W. De Roeck.

At least 19 recordsLinked to original sources

A trilinear quantum dot architecture for semiconductor spin qubits

Semiconductor quantum dot spin qubits hold significant potential for scaling to millions of qubits for practical quantum computing applications, as their structure highly resembles the structure of conventional transistors. Since classical semiconductor manufacturing technology has reached an unprecedented level of maturity, reliably mass-producing CMOS chips with hundreds of billions of components, conventional wisdom dictates that leveraging CMOS technologies for quantum dot qubits can result in upscaled quantum processors with thousands or even millions of interconnected qubits. However, the interconnect requirements for quantum circuits are very different from those for classical circuits, where for each qubit individual control and readout wiring could be needed. Although significant developments have been demonstrated on small scale systems, qubit numbers remain limited, to a large extent due to the lack of scalable qubit interconnect schemes. Here, we present a trilinear quantum dot array that is simple in physical layout while allowing individual wiring to each quantum dot. By means of electron shuttling, the trilinear architecture provides qubit connectivity that is equivalent to or even surpasses that of 2D square lattice. Assuming the current qubit fidelities of small-scale devices can be extrapolated to large-scale arrays, medium-length shuttling arrays on the order of tens of microns would allow million-scale qubit systems, while maintaining manageable overheads. We also present a scalable control scheme, where the qubit chip is 3D-integrated with a low-power switch-based cryoCMOS circuit for parallel qubit operation with limited control inputs. As our trilinear quantum dot array is fully compatible with existing semiconductor technologies, this qubit architecture represents one possible framework for future research and development of large-scale spin qubit systems.

quant-ph

Stability of the uniqueness regime for ferromagnetic Glauber dynamics under non-equilibrium perturbations

In this paper, we prove a general result concerning finite-range, attractive interacting particle systems on $\{-1, 1\}^{\mathbb{Z}^d}$. If the particle system has a unique stationary measure and, in a precise sense, relaxes to this stationary measure at an exponential rate then any small perturbation of the dynamics also has a unique stationary measure to which it relaxes at an exponential rate. To augment this result, we study the particular case of Glauber dynamics for the Ising model. We show that for any non-zero external field the dynamics converges to its unique invariant measure at an exponential rate. Previously, this was only known for $β<β_c$ and $β$ sufficiently large. As a consequence, Glauber dynamics is stable to small, non-equilibrium perturbations in the entire uniqueness phase.

math-ph

Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems

We establish some general dynamical properties of lattice many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasi-conserved extensive quantity $H_*$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well-approximated by the evolution with the Hamiltonian $H_*$ up to time $τ_*$, which is exponentially long in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where $H_*$ is ergodic, the driven system prethermalizes to a thermal state described by $H_*$ at intermediate times $t\lesssim τ_*$, eventually heating up to an infinite-temperature state at times $t\sim τ_*$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.

cond-mat.stat-mech

Minimal velocity estimates and soft mode bounds for the massless spin-boson model

We consider generalised versions of the spin-boson model at small coupling. We assume the spin (or atom) to sit at the origin $0 \in \mathbb{R}^d$ and the propagation speed $v_p$ of free bosons to be constant, i.e.\ independent of momentum. In particular, the bosons are massless. We prove detailed bounds on the mean number of bosons contained in the ball $\{|x| \leq v_p t \}$. In particular, we prove that, as $t \to \infty$, this number tends to an asymptotic value that can be naturally identified as the mean number of bosons bound to the atom in the ground state. Physically, this means that bosons that are not bound to the atom, are travelling outwards at a speed that is not lower than $v_p$, hence the term 'minimal velocity estimate'. Additionally, we prove bounds on the number of emitted bosons with low momentum (soft mode bounds). This paper is an extension of our earlier work in 'Approach to ground state and time-independent photon bound for massless spin-boson models' (arXiv:1109.5582, Ann. H. Poincare, 2012). Together with the results in that paper, the bounds of the present paper suffice to prove asymptotic completeness, as we describe in 'Asymptotic completeness for the massless spin-boson model'(arXiv:1301.2357).

math-ph

Diffusion for a quantum particle coupled to phonons in $d\geq 3$

We prove diffusion for a quantum particle coupled to a field of bosons (phonons or photons). The importance of this result lies in the fact that our model is fully Hamiltonian and randomness enters only via the initial (thermal) state of the bosons. This model is closely related to the one considered in [De Roeck, Fröhlich 2011], but various restrictive assumptions of the latter have been eliminated. In particular, depending on the dispersion relation of the bosons, the present result holds in dimension $d \geq 3$.

math-ph

Asymptotic completeness for the massless spin-boson model

We consider generalized versions of the massless spin-boson model. Building on the recent work in 'Approach to ground state and time-independent photon bound for massless spin-boson models' (arXiv:1109.5582, Annales H. Poincare, 2012) and 'Propagation bounds and soft photon bounds for the massless spin-boson model' (submitted to arXiv jointly with the present paper), we prove asymptotic completeness.

math-ph

Approach to ground state and time-independent photon bound for massless spin-boson models

It is widely believed that an atom interacting with the electromagnetic field (with total initial energy well-below the ionization threshold) relaxes to its ground state while its excess energy is emitted as radiation. Hence, for large times, the state of the atom+field system should consist of the atom in its ground state, and a few free photons that travel off to spatial infinity. Mathematically, this picture is captured by the notion of asymptotic completeness. Despite some recent progress on the spectral theory of such systems, a proof of relaxation to the ground state and asymptotic completeness was/is still missing, except in some special cases (massive photons, small perturbations of harmonic potentials). In this paper, we partially fill this gap by proving relaxation to an invariant state in the case where the atom is modelled by a finite-level system. If the coupling to the field is sufficiently infrared-regular so that the coupled system admits a ground state, then this invariant state necessarily corresponds to the ground state. Assuming slightly more infrared regularity, we show that the number of emitted photons remains bounded in time. We hope that these results bring a proof of asymptotic completeness within reach.

math-ph

From the Anderson model on a strip to the DMPK equation and random matrix theory

We study weakly disordered quantum wires whose width is large compared to the Fermi wavelength. It is conjectured that such wires diplay universal metallic behaviour as long as their length is shorter than the localization length (which increases with the width). The random matrix theory that accounts for this behaviour - the DMPK theory- rests on assumptions that are in general not satisfied by realistic microscopic models. Starting from the Anderson model on a strip, we show that a twofold scaling limit nevertheless allows to recover rigorously the fundaments of DMPK theory, thus opening a way to settle some conjectures on universal metallic behaviour.

math-ph

Diffusion of a massive quantum particle coupled to a quasi-free thermal medium

We consider a heavy quantum particle with an internal degree of freedom moving on the $d$-dimensional lattice $\bbZ^d$ (e.g., a heavy atom with finitely many excited states). The particle is coupled to a thermal medium (bath) consisting of free relativistic bosons through an interaction of strength $\la$ linear in creation and annihilation operators. The mass of the quantum particle is assumed to be of order $\la^{-2}$, and we assume that the internal degree of freedom is coupled "effectively" to the thermal medium. We prove that the motion of the quantum particle is diffusive in $d\geq 4$ and for $\la$ small enough.

math-ph

Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

We show that, in a model where a non-relativistic particle is coupled to a quantized relativistic scalar Bose field, the embedded mass shell of the particle dissolves in the continuum when the interaction is turned on, provided the coupling constant is sufficiently small. More precisely, under the assumption that the fiber eigenvectors corresponding to the putative mass shell are differentiable as functions of the total momentum of the system, we show that a mass shell could exist only at a strictly positive distance from the unperturbed embedded mass shell near the boundary of the energy-momentum spectrum.

math-ph

'Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion

Recently, several authors studied small quantum systems weakly coupled to free boson or fermion fields at positive temperature. All the approaches we are aware of employ complex deformations of Liouvillians or Mourre theory (the infinitesimal version of the former). We present an approach based on polymer expansions of statistical mechanics. Despite the fact that our approach is elementary, our results are slightly sharper than those contained in the literature up to now. We show that, whenever the small quantum system is known to admit a Markov approximation (Pauli master equation \emph{aka} Lindblad equation) in the weak coupling limit, and the Markov approximation is exponentially mixing, then the weakly coupled system approaches a unique invariant state that is perturbatively close to its Markov approximation.

math-ph

A note on the non-commutative Laplace-Varadhan integral lemma

We continue the study of the free energy of quantum lattice spin systems where to the local Hamiltonian $H$ an arbitrary mean field term is added, a polynomial function of the arithmetic mean of some local observables $X$ and $Y$ that do not necessarily commute. By slightly extending a recent paper by Hiai, Mosonyi, Ohno and Petz [9], we prove in general that the free energy is given by a variational principle over the range of the operators $X$ and $Y$. As in [9], the result is a noncommutative extension of the Laplace-Varadhan asymptotic formula.

math-ph

Quantum Brownian Motion in a Simple Model System

We consider a quantum particle coupled (with strength $\la$) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we prove that the long-time behavior of the particle is diffusive for small, but finite $\la$. Our proof relies on an expansion around the kinetic scaling limit ($\la \searrow 0$, while time and space scale as $\la^{-2}$) in which the particle satisfies a Boltzmann equation. We also show an equipartition theorem: the distribution of the kinetic energy of the particle tends to a Maxwell-Boltzmann distribution, up to a correction of $O(\la^2)$.

math-ph

Reduced and Extended Weak Coupling Limit

We give an extended review of recent work on the extended weak coupling limit. Background material on completely positive semigroups and their unitary dilations is given, as well as a particularly easy construction of `quadratic noises'.

math-ph

Quantum Macrostates, Equivalence of Ensembles and an H-Theorem

Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several observables. We propose an implementation of ideas that go back to John von Neumann's writing about the macroscopic measurement. We apply our scheme to the relation between macroscopic autonomy and an H-theorem, and to the problem of equivalence of ensembles. In particular, we show how the latter is related to the asymptotic equipartition theorem. The main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate, as the size of the system gets larger, on the macroscopic values for the different macroscopic observables. Deviations from that law are governed by the entropy.

math-ph

H-Theorems from Autonomous Equations

The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy. If for a Hamiltonian dynamics for many particles, at all times the present macrostate determines the future macrostate, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autonomous macroscopic evolution (sharp only in the limit of infinite scale separation); and to evaluate the presumed necessity of a Markov property for the macroscopic evolution.

cond-mat.stat-mech

An extension of the Kac ring model

We introduce a unitary dynamics for quantum spins which is an extension of a model introduced by Mark Kac to clarify the phenomenon of relaxation to equilibrium. When the number of spins gets very large, the magnetization satisfies an autonomous equation as function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proven as a law of large numbers with respect to a class of initial data. The corresponding Gibbs-von Neumann entropy is also computed and its monotonicity in time discussed.

cond-mat.stat-mech