Papers by Cyril Petitjean
By coupling a superconductor to a quantum cavity or dot one may decide whether its classical coun... more By coupling a superconductor to a quantum cavity or dot one may decide whether its classical counterpart has integrable or chaotic dynamics by looking at the density of states. Random matrix theory (RMT) predicts a true gap of the order of the Thoules energy E T if the classical motion is chaotic and an exponential damping in the case of integrable motion. We use semiclassical techniques developed in the recent years to reproduce the RMT predictions.
New Journal of Physics, 2018
The dynamical transition of an atomic Bose-Einstein condensate from a spatially periodic state to... more The dynamical transition of an atomic Bose-Einstein condensate from a spatially periodic state to a staggered state with alternating sign in its wavefunction is experimentally studied using a onedimensional phase modulated optical lattice. We observe the crossover from quantum to thermal fluctuations as the triggering mechanism for the nucleation of staggered states. In good quantitative agreement with numerical simulations based on the truncated Wigner method, we experimentally investigate how the nucleation time varies with the renormalized tunneling rate, the atomic density, and the driving frequency. The effective inverted energy band in the driven lattice is identified as the key ingredient which explains the emergence of gap solitons as observed in numerics and the possibility to nucleate staggered states from interband excitations as reported experimentally.
We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregu... 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 ...
Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when go... 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.
We discuss the current induced magnetization dynamics of spin valves F0|N|SyF where the free laye... 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...
PHYSICAL REVIEW LETTERS, 2010
The connection of a superconductor to a chaotic ballistic quantum dot leads to interesting phenom... 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 τE, and how the influence of a finite τE causes the gap to shrink. Furthermore, for intermediate τE we predict a second gap below E = π /2τE which would presumably be the clearest signature yet of τE-effects.
Physical Review Letters, 2006
We show how a classically vanishing interaction generates entanglement between two initially none... more We show how a classically vanishing interaction generates entanglement between two initially nonentangled particles, without affecting their classical dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate at the Lyapunov exponent of the classical dynamics as the interaction strength increases. In the saturation regime, the one-particle Wigner function follows classical dynamics better and better as one goes deeper and deeper in the semiclassical limit. This demonstrates that quantum-classical correspondence at the microscopic level requires neither high temperatures, nor coupling to a large number of external degrees of freedom.
Physical Review Letters, 2006
Physical Review Letters, 2007
Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which ... more Motivated by neutron scattering experiments, we investigate the decay of the fidelity with which a wave packet is reconstructed by a perfect time-reversal operation performed after a phase space displacement. In the semiclassical limit, we show that the decay rate is generically given by the Lyapunov exponent of the classical dynamics. For small displacements, we additionally show that, following a short-time Lyapunov decay, the decay freezes well above the ergodic value because of quantum effects. Our analytical results are corroborated by numerical simulations.
Physical Review E, 2005
We investigate the time-dependent variance of the fidelity with which an initial narrow wave pack... 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.
Physical Review B, 2008
We investigate the effect of dephasing/decoherence on quantum transport through open chaotic ball... 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, λF/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 ∝ exp[-τ /τ φ ], with the dephasing rate τ -1 φ . The parameter τ depends strongly on the source of dephasing. For a voltage probe, τ is of order the Ehrenfest time ∝ ln[L/λF]. In contrast, for a chaotic environment or a classical source of noise, it has the correlation length ξ of the coupling/noise potential replacing the Fermi wavelength λF. 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.
Physical Review B, 2011
Quantum cavities or dots have markedly different properties depending on whether their classical ... 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, is 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.
We investigate the effect of dephasing/decoherence on quantum transport through open chaotic ball... 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...
We study the one-dimensional (1D) transport properties of an ultracold gas of Bose-Einstein conde... 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...
arXiv: Mesoscale and Nanoscale Physics, 2011
Laboratoire de Physique des Solides, CNRS, Universit´e Paris Sud, UMR 8502, Bˆatiment 510, F-9140... 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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Papers by Cyril Petitjean