Cyril Petitjean
Université de Liège, Physics, Post-Doc
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We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the... more
We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of ...
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Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. We study this phenomena in graphene in presence of a... more
Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. We study this phenomena in graphene in presence of a strong perpendicular magnetic field on top of a spin-orbit (SO) induced QSH phase. We show that, below the SO gap, the QSH phase is virtually unaffected by the presence of the magnetic field. Above the SO gap, the QH phase is restored. An electrostatic gate placed on top of the system allows to create a QSH-QH junction which is characterized by the existence of a spin-polarized chiral state, propagating along the topological interface. We find that such a setup naturally provides an extremely sensitive spin-polarized current switch.
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We discuss the current induced magnetization dynamics of spin valves F0|N|SyF where the free layer is a synthetic ferrimagnet SyF made of two ferromagnetic layers F1 and F2 coupled by RKKY exchange coupling. In the interesting situation... more
We discuss the current induced magnetization dynamics of spin valves F0|N|SyF where the free layer is a synthetic ferrimagnet SyF made of two ferromagnetic layers F1 and F2 coupled by RKKY exchange coupling. In the interesting situation where the magnetic moment of the outer layer F2 dominates the magnetization of the ferrimagnet, we find that the sign of the effective spin torque exerted on the free middle layer F1 is controlled by the strength of the RKKY coupling: for weak coupling one recovers the usual situation where spin torque tends to, say, anti-align the magnetization of F1 with respect to the pinned layer F0. However for large coupling the situation is reversed and the spin torque tends to align F1 with respect to F0. Careful numerical simulations in the intermediate coupling regime reveal that the competition between these two incompatible limits leads generically to spin torque oscillator (STO) behavior. The STO is found in the absence of magnetic field, with very signi...
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We investigate the time-dependent variance of the fidelity with which an initial narrow wave packet is reconstructed after its dynamics is time reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show... more
We investigate the time-dependent variance of the fidelity with which an initial narrow wave packet is reconstructed after its dynamics is time reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time t(c) , after which it decays. To leading order in the effective Planck's constant Planck's(eff) , this decay is given by the sum of a classical term approximately same as exp [-2lambdat] , a quantum term approximately same as 2Planck's(eff) exp [-Gamma t] , and a mixed term approximately 2 exp [- (Gamma+lambda) t] . Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent lambda in a larger parameter range. Our results are confirmed by numerical simulations.
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We investigate the effect of dephasing/decoherence on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, λ_F/L << 1. We use the trajectory-based... more
We investigate the effect of dephasing/decoherence on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, λ_F/L << 1. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from: (i) an external closed quantum chaotic environment, (ii) a classical source of noise, (iii) a voltage probe, i.e. an additional current-conserving terminal. We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an exponential suppression of weak-localization ∝[-τ̃/τ_ϕ], with the dephasing rate τ_ϕ^-1. The parameter τ̃ depends strongly on the source of dephasing. For a voltage probe, τ̃ is of order the Ehrenfest time ∝ [L/λ_F ]. In contrast, for a chaotic environment or a classical source of...
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We study the one-dimensional (1D) transport properties of an ultracold gas of Bose-Einstein condensed atoms through Aharonov-Bohm (AB) rings. Our system consists of a BoseEinstein condensate (BEC) that is outcoupled from a magnetic trap... more
We study the one-dimensional (1D) transport properties of an ultracold gas of Bose-Einstein condensed atoms through Aharonov-Bohm (AB) rings. Our system consists of a BoseEinstein condensate (BEC) that is outcoupled from a magnetic trap into a 1D waveguide which is made of two semiinfinite leads that join a ring geometry exposed to a synthetic magnetic flux φ. We specifically investigate the effects both of a disorder potential and of a small atom-atom contact interaction strength on the AB oscillations. The main numerical tools that we use for this purpose are a mean-field Gross-Pitaevskii (GP) description and the truncated Wigner (tW) method. We find that a correlated disorder suppress the AB oscillations leaving thereby place to weaker amplitude, half period oscillations on transmission, namely the Aronov-Al’tshuler-Spivak (AAS) oscillations. The competition between disorder and interaction leads to a flip of the transmission at the AB flux φ = π. This flip could be a possible pr...
Laboratoire de Physique des Solides, CNRS, Universit´e Paris Sud, UMR 8502, Bˆatiment 510, F-91405 Orsay Cedex, France(Dated: September 19, 2011)We develop a three dimensional semiclassical theory which generalizes the Valet-Fert model... more
Laboratoire de Physique des Solides, CNRS, Universit´e Paris Sud, UMR 8502, Bˆatiment 510, F-91405 Orsay Cedex, France(Dated: September 19, 2011)We develop a three dimensional semiclassical theory which generalizes the Valet-Fert model inorder to account for non-collinear systems with magnetic texture, including e.g. domain walls ormagnetic vortices. The theory allows for spin transverse to the magnetization to penetrate in-side the ferromagnet over a finite length and properly accounts for the Sharvin resistances. Forferromagnetic-normal-ferromagnetic multilayers where the current is injected in the plane of thelayers (CIP), we predict the existence of a non zero mesoscopic CIP Giant Magneto-Resistance(GMR) at the diffusive level. This mesoscopic CIP-GMR, which adds to the usual ballistic contri-butions, has a non monotonic spatial variation and is reminiscent of conductance quantization inthe layers. Furthermore, we study the spin transfer torque in spin valve nanopillars. We find th...
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Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. In graphene, the peculiar" relativistic" nature... more
Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. In graphene, the peculiar" relativistic" nature of the Quantum Hall effect (with its two Landau levels pinned at the Dirac point) allows to have the QH and the QSH phases sharing the same spectrum, which itself opens the possibility for, say, QH-QSH transitions induced by a gate voltage. In the first part of this talk, I will discuss a proposition to induce ...
Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. In graphene, the peculiar" relativistic" nature... more
Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. In graphene, the peculiar" relativistic" nature of the Quantum Hall effect (with its two Landau levels pinned at the Dirac point) allows to have the QH and the QSH phases sharing the same spectrum, which itself opens the possibility for, say, QH-QSH transitions induced by a gate voltage. In the first part of this talk, I will discuss a proposition to induce ...
We discuss the current induced magnetization dynamics of spin valves F0|N|SyF where the free layer is a synthetic ferrimagnet SyF made of two ferromagnetic layers F1 and F2 coupled by RKKY exchange coupling. When the magnetic moment of... more
We discuss the current induced magnetization dynamics of spin valves F0|N|SyF where the free layer is a synthetic ferrimagnet SyF made of two ferromagnetic layers F1 and F2 coupled by RKKY exchange coupling. When the magnetic moment of the outer layer F2 dominates the magnetization of the SyF, the sign of the effective spin torque exerted on the layer F1 is controlled by the coupling’s strength: for weak coupling the spin torque tends to antialign F1’s magnetization with respect to the pinned layer F0. At large coupling the situation is reversed and tends to align F1 with respect to F0. At intermediate coupling, numerical simulations reveal that the competition between these two incompatible limits leads generically to spin torque oscillator (STO) behavior. The STO is found at zero magnetic field, with very significant amplitude of oscillations and frequencies up to 50 GHz or higher.
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This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems in the short wavelength limit. We formulate and attempt to answer three fundamental questions: (i) What drives a dynamical quantum system... more
This review summarizes and amplifies on recent investigations of coupled quantum dynamical systems in the short wavelength limit. We formulate and attempt to answer three fundamental questions: (i) What drives a dynamical quantum system to behave classically ? (ii) What deter-mines the rate at which two coupled quantum–mechanical systems become entangled ? (iii) How does irreversibility occur in quantum systems with few degrees of freedom ? We embed these three questions in the broader context of the quantum–classical correspondence, which motivates the use of short–wavelength approximations to quantum mechanics such as the trajectory-based semiclas-sical methods and random matrix theory. Doing so, we propose a novel investigative procedure towards decoherence and the emergence of classicality out of quantumness in dynamical systems coupled to external degrees of freedom. We reproduce known results derived using master equation or Lindblad approaches but also generate novel ones. In...
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... Thèse, unige:481. Titre Quantum reversibility, decoherence and transport in dynamical systems Auteur Petitjean, Cyril Jean-Pierre Stéphane Soutenance Thèse de doctorat : Univ. Genève, 2007. - Sc. 3861. - 2007/06/11 Directeur ...
Research Interests: Physics, Condensed Matter Physics, Quantum Physics, Dynamical Systems, Quantum Mechanics, and 18 moreQuantum Chaos, Quantum entanglement, Integer quantum hall effect, Dynamics, Instability, Random Matrix Theory, Entanglement, Time Reversal, Chaotic Dynamical System in Ecology, Decoherence, Phase Space, Quantum Dynamics, Lyapunov exponent, Trajectories, Quantum Harmonic Oscillator, Dynamic System, Degree of Freedom, and Master Equation
We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket is reconstructed after its dynamics is time-reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show... more
We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket is reconstructed after its dynamics is time-reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time $t_c$, after which it decays. To leading order in the effective Planck's constant $\hbar_{\rm eff}$, this decay is given by the sum of a classical term $\simeq \exp[-2 \lambda t]$, a quantum term $\simeq 2 \hbar_{\rm eff} \exp[-\Gamma t]$ and a mixed term $\simeq 2 \exp[-(\Gamma+\lambda)t]$. Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent $\lambda$ in a larger parameter range. Our results are confirmed by numerical simulations.
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In Echo experiments, imperfect time-reversal operations are performed on a subset of the total number of degrees of freedom. To capture the physics of these experiments, we introduce a partial fidelity, the Boltzmann echo, where only part... more
In Echo experiments, imperfect time-reversal operations are performed on a subset of the total number of degrees of freedom. To capture the physics of these experiments, we introduce a partial fidelity, the Boltzmann echo, where only part of the system's degrees of freedom can be time-reversed. We present a semiclassical calculation of the Boltzmann echo. We show that, as the time-reversal operation is performed more and more accurately, the decay rate of the Boltzmann echo saturates at a value given by the decoherence rate of the controlled degrees of freedom due to their coupling to uncontrolled ones. We connect these results with NMR spin echo experiments.
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We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an... more
We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an exponential suppression of weak-localization $\propto \exp[-\tilde{\tau}/\tau_\phi]$, with the dephasing rate $\tau_\phi^{-1}$. The parameter $\tilde{\tau}$ depends strongly on the source of dephasing. For a voltage probe, $\tilde{\tau}$ is of order the Ehrenfest time $\propto \ln [L/\lambda_F ]$. In contrast, for a chaotic environment or a classical source of noise, it has the correlation length $\xi$ of the coupling/noise potential replacing the Fermi wavelength $\lambda_F $. We explicitly show that the Fano factor for shot noise is unaffected by decoherence. We connect these results to earlier works on dephasing due to electron-electron interactions, and numerically confirm our findings.
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Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the... more
Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time an electron hits the superconducting part it is retroreflected as a hole (and vice-versa). Using a semiclassical framework for systems with chaotic dynamics, we show how this reflection, along with the interference due to subtle correlations between the classical paths of electrons and holes inside the system, are ultimately responsible for the gap formation. The treatment can be extended to include the effects of a symmetry breaking magnetic field in the normal part of the billiard or an Andreev billiard connected to two phase shifted superconductors. Therefore we are able to see how these effects can remold and eventually suppress the gap. Furthermore the semiclassical framework is able to cover the effect of a finite Ehrenfest time which also causes the gap to shrink. However for intermediate values this leads to the appearance of a second hard gap - a clear signature of the Ehrenfest time.
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The connection of a superconductor to a chaotic ballistic quantum dot leads to interesting phenomena, most notably the appearance of a hard gap in its excitation spectrum. Here we treat such an Andreev billiard semiclassically where the... more
The connection of a superconductor to a chaotic ballistic quantum dot leads to interesting phenomena, most notably the appearance of a hard gap in its excitation spectrum. Here we treat such an Andreev billiard semiclassically where the density of states is expressed in terms of the classical trajectories of electrons (and holes) that leave and return to the superconductor. We show how classical orbit correlations lead to the formation of the hard gap, as predicted by random matrix theory in the limit of negligible Ehrenfest time $\tE$, and how the influence of a finite $\tE$ causes the gap to shrink. Furthermore, for intermediate $\tE$ we predict a second gap below $E=\pi\hbar /2\tE$ which would presumably be the clearest signature yet of $\tE$-effects.
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We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened... more
We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime.
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Due to the progress made in the control and the manipulation of mesoscopic structures driven by high frequency periodic voltages, the ac regime has been recently experimentally investigated [1] and consequently its theoretical interest... more
Due to the progress made in the control and the manipulation of mesoscopic structures driven by high frequency periodic voltages, the ac regime has been recently experimentally investigated [1] and consequently its theoretical interest has been renewed. We consider here, a quantum chaotic cavity that is coupled via tunnel barriers and gates to a macroscopic circuit which contains ac-sources [2]. By extending to the ac-transport, the recent trajectory-based semiclassical theory of quantum chaotic transport in presence of tunnel barrier [3], we derive for arbitrary tunneling rates and arbitrary positive Ehrenfest time, the averaged and the weak-localization correction to the screened conductance. Then we use these results to investigate the effect of dephasing on the relaxation resistance of a chaotic capacitor in the linear low frequency regime. This last investigation are in principle relevant to the recent measure of the admittance at zero magnetic flux of a mesoscopic capacitor [1,4].References[2][t]1cm#1[t]14cm#2 [1] J. Gabelli et al., Science 313, 499 (2006).[2] C. Petitjean et al, in preparation (2008).[3] R.S. Whitney, Phys. Rev. B, 75, 235404 (2007).[4] S. Nigg and M. B"uttiker, Phys. Rev. B 77, 085312 (2008).
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Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the... more
Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time an electron hits the superconducting part it is retroreflected as a hole (and vice-versa). Using a semiclassical framework for systems with chaotic dynamics, we show how this reflection, along with the interference due to subtle correlations between the classical paths of electrons and holes inside the system, are ultimately responsible for the gap formation. The treatment can be extended to include the effects of a symmetry breaking magnetic field in the normal part of the billiard or an Andreev billiard connected to two phase shifted superconductors. Therefore we are able to see how these effects can remold and eventually suppress the gap. Furthermore the semiclassical framework is able to cover the effect of a finite Ehrenfest time which also causes the gap to shrink. However for intermediate values this leads to the appearance of a second hard gap - a clear signature of the Ehrenfest time.