arXiv subjects

Philippe Jacquod

Publications and source records attributed to Philippe Jacquod.

At least 73 records · Page 4Linked to original sources

arXiv2008

Dephasing in quantum chaotic transport: a semiclassical approach

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 $\propto \exp[-\tildeτ/τ_ϕ]$, with the dephasing rate $τ_ϕ^{-1}$. The parameter $\tildeτ$ depends strongly on the source of dephasing. For a voltage probe, $\tildeτ$ is of order the Ehrenfest time $\propto \ln [L/λ_F ]$. 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 $λ_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.

cond-mat.mes-hall↗

arXiv2007

Dephasing in the semiclassical limit is system-dependent

We investigate dephasing in open quantum chaotic systems in the limit of large system size to Fermi wavelength ratio, $L/λ_F >> 1$. We semiclassically calculate the weak localization correction $g^{wl}$ to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe. In addition to the universal algebraic suppression $g^{wl} \propto (1+τ_D/τ_ϕ)^{-1}$ with the dwell time $τ_D$ through the cavity and the dephasing rate $τ_ϕ^{-1}$, we find an exponential suppression of weak localization by a factor $\propto \exp[-\tildeτ/τ_ϕ]$, with a system-dependent $\tildeτ$. In the dephasing probe model, $\tildeτ$ coincides with the Ehrenfest time, $\tildeτ \propto \ln [L/λ_F]$, for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, $\tildeτ \propto \ln [L/ξ]$ depends on the correlation length $ξ$ of the coupling potential instead of $λ_F$.

cond-mat.mes-hall↗

arXiv2007

Displacement Echoes: Classical Decay and Quantum Freeze

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.

quant-ph↗

arXiv2006

Shot noise in semiclassical chaotic cavities

We construct a trajectory-based semiclassical theory of shot noise in clean chaotic cavities. In the universal regime of vanishing Ehrenfest time $\tE$, we reproduce the random matrix theory result, and show that the Fano factor is exponentially suppressed as $\tE$ increases. We demonstrate how our theory preserves the unitarity of the scattering matrix even in the regime of finite $\tE$. We discuss the range of validity of our semiclassical approach and point out subtleties relevant to the recent semiclassical treatment of shot noise in the universal regime by Braun et al. [cond-mat/0511292].

cond-mat.mes-hall↗

arXiv2006

Quantum Reversibility and Echoes in Interacting Systems

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.

quant-ph↗

arXiv2005

Chaos, Coherence and the Double-Slit Experiment

We investigate the influence that classical dynamics has on interference patterns in coherence experiments. We calculate the time-integrated probability current through an absorbing screen and the conductance through a doubly connected ballistic cavity, both in an Aharonov-Bohm geometry with forward scattering only. We show how interference fringes in the probability current generically disappear in the case of a chaotic system with small openings, and how they may persist in the case of an integrable cavity. Simultaneously, the typical, sample dependent amplitude of the flux-sensitive part $g(ϕ)$ of the conductance survives in all cases, and becomes universal in the case of a chaotic cavity. In presence of dephasing by fluctuations of the electric potential in one arm of the Aharonov-Bohm loop, we find an exponential damping of the flux-dependent part of the conductance, $g(ϕ) \propto \exp[-τ_{\rm L}/τ_ϕ]$, in term of the traversal time $τ_{\rm L}$ through the arm and the dephasing time $τ_ϕ$. This extends previous works on dephasing in ballistic systems to the case of many conducting channels.

cond-mat.mes-hall↗

arXiv2005

Quantum-to-classical correspondence in open chaotic systems

We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time tau_E. The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by random-matrix theory. In the semiclassical limit, tau_E becomes parametrically larger than the scattering time off the boundaries and the dwell time in the system. This results in the emergence of an increasing number of deterministic transport and escape modes, which induce strong deviations from random-matrix universality. We discuss these deviations for a variety of physical phenomena, including shot noise, conductance fluctuations, decay of quasibound states, and the mesoscopic proximity effect in Andreev billiards.

cond-mat.mes-hall↗

arXiv2005

Suppression of Shot-Noise in Quantum Cavities: Chaos vs. Disorder

We investigate the behavior of the shot-noise power through quantum mechanical cavities in the semiclassical limit of small electronic wavelength. In the absence of impurity scattering, the Fano factor $F$, giving the noise to current ratio, was previously found to disappear as more and more classical, hence deterministic and noiseless transmission channels open up. We investigate the behavior of $F$ as diffractive impurities are added inside the cavity. We find that $F$ recovers its universal value provided (i) impurities cover the full cavity so that only a set of zero measure of classical trajectories may avoid them, and (ii) the impurity scattering rate exceeds the inverse dwell time through the cavity. If condition (i) is not satisfied, $F$ saturates below its universal value, even in the limit of strong scattering. Our results corroborate the validity of the two-phase fluid model according to which the electronic flow splits into two well separated components, a classical deterministic fluid and a stochastic quantum-mechanical fluid. Only the latter carries shot-noise.

cond-mat.mes-hall↗

arXiv2005

Mesoscopic Fluctuations of the Loschmidt Echo

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 $\simeq \exp[-2 λt]$, a quantum term $\simeq 2 \hbar_{\rm eff} \exp[-Γt]$ and a mixed term $\simeq 2 \exp[-(Γ+λ)t]$. Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent $λ$ in a larger parameter range. Our results are confirmed by numerical simulations.

quant-ph↗

arXiv2004

Semiclassical time-evolution of the reduced density matrix and dynamically assisted generation of entanglement for bipartite quantum systems

Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix $ρ_1$, obtained by integrating out the degrees of freedom of one of the particles. To quantify the generation of entanglement, we calculate the purity ${\cal P}(t)={\rm Tr}[ρ_1(t)^2]$. We find that entanglement generation sensitively depends (i) on the interaction potential, especially on its strength and range, and (ii) on the nature of the underlying classical dynamics. Under general statistical assumptions, and for short-scaled interaction potentials, we find that ${\cal P}(t)$ decays exponentially fast if the two particles are required to interact in a chaotic environment, whereas it decays only algebraically in a regular system. In the chaotic case, the decay rate is given by the golden rule spreading of one-particle states due to the two-particle coupling, but cannot exceed the system's Lyapunov exponent.

quant-ph↗

arXiv2003

Modes of wave-chaotic dielectric resonators

Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial structure, and cannot be classified through mode indices which would require additional constants of motion in the ray dynamics. Understanding and controlling the emission properties of such resonators requires the investigation of the correspondence between classical phase space structures of the ray motion inside the resonator and resonant solutions of the wave equations. We first discuss the breakdown of the conventional eikonal approximation in the short wavelength limit, and motivate the use of phase-space ray tracing and phase space distributions. Next, we introduce an efficient numerical method to calculate the quasi-bound modes of dielectric resonators, which requires only two diagonalizations per N states, where N is approximately equal to the number of half-wavelengths along the perimeter. The relationship between classical phase space structures and modes is displayed via the Husimi projection technique. Observables related to the emission pattern of the resonator are calculated with high efficiency.

physics.optics↗

arXiv2003

Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator

We investigate the quasiparticle density of states in disordered d-wave superconductors. By constructing a quantum map describing the quasiparticle dynamics in such a medium, we explore deviations of the density of states from its universal form ($\propto E$), and show that additional low-energy quasiparticle states exist provided (i) the range of the impurity potential is much larger than the Fermi wavelength [allowing to use recently developed semiclassical methods]; (ii) classical trajectories exist along which the pair-potential changes sign; and (iii) the diffractive scattering length is longer than the superconducting coherence length. In the classically chaotic regime, universal random matrix theory behavior is restored by quantum dynamical diffraction which shifts the low energy states away from zero energy, and the quasiparticle density of states exhibits a linear pseudogap below an energy threshold $E^* \ll Δ_0$.

cond-mat.supr-con↗

arXiv2002

Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U=infinity eigenstates bases respectively. This implies the existence of a duality point U_d where the eigenstates have the same spreading in both bases. U_d is surrounded by an interval of finite width which is characterized by a non Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.

cond-mat.dis-nn↗

arXiv2002

Magnetism and Transport for Two-Dimensional Electrons : Absence of Stoner Ferromagnetism and Positive In-Plane Magnetoresistance in the Metallic Phase

We calculate the interaction kernel K for two-dimensional diffusive electrons. The screening of the Coulomb interaction together with the Fermi statistics induces a spin selection rule for electron-electron scattering so that in leading order in the inverse conductance only pairs of electrons with antiparallel spins do scatter. At low temperature, this results in a larger coherence length for fully polarized electrons and thus in a positive in-plane magnetoresistance. An applied in-plane magnetic field also induces a nonmonotonous behavior of K at finite temperature. Alternatively, the vanishing of the scattering in the triplet channel strongly reduces ferromagnetism deep in the metallic regime. These effects weaken as the density of charge carriers is reduced.

cond-mat.mes-hall↗

arXiv2001

Ground-State Magnetization for Interacting Fermions in a Disordered Potential : Kinetic Energy, Exchange Interaction and Off-Diagonal Fluctuations

We study a model of interacting fermions in a disordered potential, which is assumed to generate uniformly fluctuating interaction matrix elements. We show that the ground state magnetization is systematically decreased by off-diagonal fluctuations of the interaction matrix elements. This effect is neglected in the Stoner picture of itinerant ferromagnetism in which the ground-state magnetization is simply determined by the balance between ferromagnetic exchange and kinetic energy, and increasing the interaction strength always favors ferromagnetism. The physical origin of the demagnetizing effect of interaction fluctuations is the larger number of final states available for interaction-induced scattering in the lower spin sectors of the Hilbert space. We analyze the energetic role played by these fluctuations in the limits of small and large interaction $U$. In the small $U$ limit we do second-order perturbation theory and identify explicitly transitions which are allowed for minimal spin and forbidden for higher spin. These transitions then on average lower the energy of the minimal spin ground state with respect to higher spin. For large interactions $U$ we amplify on our earlier work [Ph. Jacquod and A.D. Stone, Phys. Rev. Lett. 84, 3938 (2000)] which showed that minimal spin is favored due to a larger broadening of the many-body density of states in the low-spin sectors. Numerical results are presented in both limits.

cond-mat.mes-hall↗

arXiv2001

Fast Ground-State Reordering from Off-Diagonal Fluctuations of Interaction

It is shown that off-diagonal fluctuations of interaction lead to the breakdown of perturbation theory in the immediate vicinity of the ground-state of a fermionic system at a rate inversely proportional to the number of considered particles. This rate is parametrically much faster than previously expected. It is shown that this follows from the coherent addition of many small second order contributions to the energy of low-lying levels.

cond-mat↗

arXiv2000

Ground-State Magnetization in Disordered Systems : Exchange vs. Off-Diagonal Interaction Fluctuations

In a Hartree-Fock picture, itinerant ferromagnetism results from a competition between kinetic and exchange energy, with the magnetized state being favored at large interaction strength. In a recent paper \cite{spings} we showed that in contrast to this average effect, fluctuations of off-diagonal interaction matrix elements systematically reduce the ground-state magnetization. When the interaction dominates, the occurence of a non-zero ground-state magnetization depends on the ratio $λ$ between average exchange energy and the fluctuation amplitude of the off-diagonal matrix elements, and a nonzero critical value $λ_c$ is necessary to magnetize the ground-state. We extend these results by numerical studies of $λ$ for standard tight-binding models which indicate a regime of intermediate disorder where off-diagonal fluctuations should play an important role for ground-state magnetization. We also emphasize the presence of strong correlations between minimal eigenvalues of different magnetization blocks which further reduce the probability of a nonzero ground-state spin.

cond-mat.mes-hall↗

arXiv2000

Suppression of Ground-State Magnetization in Finite-Sized Systems Due to Off-Diagonal Interaction Fluctuations

We study a generic model of interacting fermions in a finite-sized disordered system. We show that the off-diagonal interaction matrix elements induce density of states fluctuations which generically favor a minimum spin ground state at large interaction amplitude, $U$. This effect competes with the exchange effect which favors large magnetization at large $U$, and it suppresses this exchange magnetization in a large parameter range. When off-diagonal fluctuations dominate, the model predicts a spin gap which is larger for odd-spin ground states as for even-spin, suggesting a simple experimental signature of this off-diagonal effect in Coulomb blockade transport measurements.

cond-mat.mes-hall↗