Complete nonlinear polarization control in an optical fiber system.

International audience; We consider the counterpropagating interaction of a signal and a pump beam in an isotropic optical fiber. On the basis of recently developed mathematical techniques, we show that an arbitrary state of polarization of the signal beam can be converted into any other desired state of polarization. On the other hand, an unpolarized signal beam may be repolarized into two specific states of polarization, without loss of energy. Both processes of repolarization and polarization conversion may be controlled by adjusting the polarization state of the backward pump.

Thermalization of incoherent nonlinear waves

International audience

Atom-photon, atom-atom and photon-photon entanglement preparation via fractional adiabatic passage

We propose a relatively robust scheme to generate maximally entangled states of (i) an atom and a cavity photon, (ii) two atoms in their ground states, and (iii) two photons in two spatially separate high-Q cavities. It is based on the interaction via fractional adiabatic passage of a three-level atom traveling through a cavity mode and a laser beam. The presence of optical phases is emphasized.

Decoherence-free creation of atom-atom entanglement in cavity via fractional adiabatic passage

We propose a robust and decoherence insensitive scheme to generate controllable entangled states of two three-level atoms interacting with an optical cavity and a laser beam. Losses due to atomic spontaneous transitions and to cavity decay are efficiently suppressed by employing fractional adiabatic passage and appropriately designed atom-field couplings. In this scheme the two atoms traverse the cavity-mode and the laser beam in opposite directions as opposed to other entanglement schemes in which the atoms are required to have fixed locations inside a cavity. We also show that the coherence of a traveling atom can be transferred to the other one without populating the cavity-mode.

Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics

We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime.

Kolmogorov-Arnold-Moser–Renormalization-Group Analysis of Stability in Hamiltonian Flows

We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.

Fast SWAP gate by adiabatic passage

We present a process for the construction of a SWAP gate which does not require a composition of elementary gates from a universal set. We propose to employ direct techniques adapted to the preparation of this specific gate. The mechanism, based on adiabatic passage, constitutes a decoherence-free method in the sense that spontaneous emission and cavity damping are avoided.

Manifestation of Hamiltonian Monodromy in Nonlinear Wave Systems

International audience; We show that the concept of dynamical monodromy plays a natural fundamental role in the spatiotemporal dynamics of counterpropagating nonlinear wave systems. By means of an adiabatic change of the boundary conditions imposed to the wave system, we show that Hamiltonian monodromy manifests itself through the spontaneous formation of a topological phase singularity (2 - or -phase defect) in the nonlinear waves. This manifestation of dynamical Hamiltonian monodromy is illustrated by generic nonlinear wave models. In particular, we predict that its measurement can be realized in a direct way in the framework of a nonlinear optics experiment.

Time-dependent unitary perturbation theory for intense laser-driven molecular orientation

We apply a time-dependent perturbation theory based on unitary transformations combined with averaging techniques, on molecular orientation dynamics by ultrashort pulses. We test the validity and the accuracy of this approach on LiCl described within a rigid-rotor model and find that it is more accurate than other approximations. Furthermore, it is shown that a noticeable orientation can be achieved for experimentally standard short laser pulses of zero time average. In this case, we determine the dynamically relevant parameters by using the perturbative propagator, that is derived from this scheme, and we investigate the temperature effects on the molecular orientation dynamics.

Nonintrusive monitoring and quantitative analysis of strong laser-field-induced impulsive alignment

We report the observation of impulsive alignment of $\mathrm{C}{\mathrm{O}}_{2}$ molecules produced through their interaction with a nonresonant, strong laser pulse. The periodic alignment is monitored using a polarization technique generally employed in optical Kerr effect experiments; the birefringence produced by alignment of the molecular sample is measured with a weak pulse, time-delayed with respect to the alignment pulse. The technique provides a signal proportional to $⟨{\mathrm{cos}}^{2}\phantom{\rule{0.2em}{0ex}}\ensuremath{\theta}⟩\ensuremath{-}\frac{1}{3}$, where $\ensuremath{\theta}$ is the polar angle between the molecular axis and the strong-field polarization axis. Experimen…

Dynamical Stark Effect in the nu(2)/nu(4) Vibrational Polyad of SiH(4): Theory and Observation.

We report a theoretical and experimental investigation of the dynamical Stark effect in a tetrahedral molecule, silane (SiH(4)). We use a tetrahedral formalism and Floquet theory to calculate the absorption spectra for the molecule dressed by an intense nonresonant pulsed laser. Experimentally, the dynamical Stark effect is observed for transitions of the nu(2)/nu(4) vibrational polyad of SiH(4) by means of nanosecond diode laser absorption spectroscopy and a Nd:YAG laser excitation. Copyright 2000 Academic Press.

Peculiarities of coherent optical oscillation in Sn_2P_2S_6 crystals

We show analytically and numerically that the unusual photorefractive nonlinear response of Sn2P2S6 crystals leads to a variety of new features of coherent optical oscillation. In addition to the explanation of the known peculiarities, new features are predicted.

A universal all-fiber omnipolarizer

The all-optical control of light polarization is nowadays a fundamental issue which finds important applications in optical networks. In this field, the research has moved on the development of nonlinear methods of re-polarization of a partially coherent and initially depolarized light [1]. The main drawback of most of these devices is that they suffer from a large amount of output Relative-Intensity-Noise (RIN). However, a class of polarizers have been recently proposed which is based on the nonlinear interaction between two optical beams counter-propagating in a fiber [2]: in these devices the arbitrary state of polarization (SOP) of one of the two beams (signal) is attracted towards a sp…

Generation of multiphoton Fock states by bichromatic adiabatic passage: Topological analysis

We propose a robust scheme to generate multi-photon Fock states in an atom-maser-cavity system using adiabatic passage techniques and topological properties of the dressed eigenenergy surfaces. The mechanism is an exchange of photons from the maser field into the initially empty cavity by bichromatic adiabatic passage. The number of exchanged photons depends on the design of the adiabatic dynamics through and around the conical intersections of dressed eigenenergy surfaces.

Algebraic time-reversal operation

International audience; We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) U(4) K(4) = A(4) ^ S(4) S(4) Td. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the time inversion symmetry. As a result we can determine the TR behavior of purely algebraic operators.

Quantum averaging for driven systems with resonances

Abstract We discuss the effects of resonances in driven quantum systems within the context of quantum averaging techniques in the Floquet representation. We consider in particular iterative methods of KAM type and the extensions needed to take into account resonances. The approach consists in separating the coupling terms into resonant and nonresonant components at a given scale of time and intensity. The nonresonant part can be treated with perturbative techniques, which we formulate in terms of KAM-type unitary transformations that are close to the identity. These can be interpreted as averaging procedures with respect to the dynamics defined by effective uncoupled Hamiltonians. The reson…

Adiabatic invariant change due to separatrix crossing at sweeping through a Feshbach resonance in a nonlinear two-mode system.

Optical flip-flop memory and data packet switching operation based on polarization bistability in a telecommunication optical fiber

We report the experimental observation of bistability and hysteresis phenomena of the polarization signal in a telecommunication optical fiber. This process occurs in a counterpropagating configuration in which the optical beam nonlinearly interacts with its own Bragg-reflected replica at the fiber output. The proof of principle of optical flip–flop memory and 10  Gbit/s routing operation is also reported based on this polarization bistability. Finally, we also provide a general physical understanding of this behavior on the basis of a geometrical analysis of an effective model of the dynamics. Good quantitative agreement between theory and experiment is obtained.

Laser control for the optimal evolution of pure quantum states

Starting from an initial pure quantum state, we present a strategy for reaching a target state corresponding to the extremum (maximum or minimum) of a given observable. We show that a sequence of pulses of moderate intensity, applied at times when the average of the observable reaches its local or global extremum, constitutes a strategy transferable to different control issues. Among them, post-pulse molecular alignment and orientation are presented as examples. The robustness of such strategies with respect to experimentally relevant parameters is also examined.

Critical Attractor and Universality in a Renormalization Scheme for Three Frequency Hamiltonian Systems

We study an approximate renormalization-group transformation to analyze the breakup of invariant tori for three degrees of freedom Hamiltonian systems. The scheme is implemented for the spiral mean torus. We find numerically that the critical surface is the stable manifold of a critical nonperiodic attractor. We compute scaling exponents associated with this fixed set, and find that they can be expected to be universal.

Floquet spectrum for two-level systems in quasiperiodic time-dependent fields

We study the time evolution ofN-level quantum systems under quasiperiodic time-dependent perturbations. The problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged Hilbert space, or equivalently of a generalized Floquet operator. We discuss criteria for the appearance of pure point as well as continuous spectrum, corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior. We discuss two types of mechanisms that lead to instability. The first one is due to near resonances, while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation. We tre…

Grid methods and Hilbert space basis for simulations of quantum dynamics

We discuss spatial grid methods adapted to the structure of Hilbert spaces, used to simulate quantum mechanical systems. We review the construction of Finite Basis Representation (FBR) and the Discrete Variable Representation (DVR). A mixed representation (pseudo-spectral method) is constructed through a quadrature relation linking both bases.

Relaxation of counter-propagating waves and singular Hamiltonian tori

International audience

Topology of adiabatic passage

We examine the topology of eigenenergy surfaces characterizing the population transfer processes based on adiabatic passage. We show that this topology is the essential feature for the analysis of the population transfers and the prediction of its final result. We reinterpret diverse known processes, such as stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic passage and Stark-chirped rapid adiabatic passage. Moreover, using this picture, we display new related possibilities of transfer. In particular, we show that we can selectively control the level that will be populated in STIRAP process in $\ensuremath{\Lambda}$ or V systems by the choice of the peak amplitudes or …

Enhanced alignment and orientation of polar molecules by vibrational resonant adiabatic passage

The authors show that polar molecules can be adiabatically aligned and oriented by laser pulses more efficiently when the laser frequencies are vibrationally resonant. The aligned molecules are found in a superposition of vibrational pendular states, each associated with the alignment of the rotor in one vibrational state. The authors construct the dressed potential associated with this mechanism. Values of detunings and field amplitudes are given to optimize the degree of alignment and orientation for the CO molecule.

Adiabatic creation of entangled states by a bichromatic field designed from the topology of the dressed eigenenergies

Preparation of entangled pairs of coupled two-state systems driven by a bichromatic external field is studied. We use a system of two coupled spin-1/2 that can be translated into a three-state ladder model whose intermediate state represents the entangled state. We show that this entangled state can be prepared in a robust way with appropriate fields. Their frequencies and envelopes are derived from the topological properties of the model.

Two-laser multiphoton adiabatic passage in the frame of the Floquet theory. Applications to (1+1) and (2+1) STIRAP

We develop an adiabatic two-mode Floquet theory to analyse multiphoton coherent population transfer in N-level systems by two delayed laser pulses, which is a generalization of the three-state stimulated Raman adiabatic passage (STIRAP). The main point is that, under conditions of non-crossing and adiabaticity, the outcome and feasibility of a STIRAP process can be determined by the analysis of two features: (i) the lifting of degeneracy of dressed states at the beginning and at the end of the laser pulses, and (ii) the connectivity of these degeneracy-lifted branches in the quasienergy diagram. Both features can be determined by stationnary perturbation theory in the Floquet representation…

State-selective chirped adiabatic passage on dynamically laser-aligned molecules

We show that rovibrational state selectivity can be achieved by chirped adiabatic passage of molecules that are adiabatically aligned by a nonresonant laser field. We develop the tools to design the appropriate frequency and amplitude modulations that allow us to select a given route in the Hilbert space that leads to a final complete excitation of the chosen state, by infrared or by Raman processes. This method allows us to select a given vibrational state in a well-defined rotational $J$ state.

Hamiltonian tools for the analysis of optical polarization control

Import JabRef; International audience; The study of the polarization dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest, from both the theoretical and experimental points of view. This system exhibits a phenomenon of polarization attraction, which can be used to achieve a complete polarization of an initially unpolarized signal beam, almost without any loss of energy. Along the same way, an arbitrary polarization state of the signal beam can be controlled and converted into any other desired state of polarization, by adjusting the polarization state of the counterpropagating pump beam. These properties have been demonstrate…

Strong lowering of the mirrorless optical oscillation threshold by angular mismatches for nonlocal photorefractive nonlinearity.

We show that the introduction of an angular mismatch for the pump waves results, in the case of nonlocal photorefractive nonlinearity, in a strong almost twofold decrease of the threshold value of the coupling strength for the mirrorless optical oscillation. This surprising feature will lead to a strong modification of the threshold and near-threshold behavior of a vast variety of optical oscillators based on the photorefractive phase conjugation and involving finite-size light beams.

Orientation of Polar Molecules by Laser Induced Adiabatic Passage

International audience; We show that two overlapping linearly polarized laser pulses of frequencies ω and its second harmonic 2ω can strongly orient linear polar molecules, by adiabatic passage along dressed states. The resulting robust orientation can be interpreted as a laser-induced localization in the effective double well potential created by the fields, which induces a preliminary molecular alignment. The direction of the orientation can be selected by the relative phase of the fields.

Reaching optimally oriented molecular states by laser kicks

We present a strategy for post-pulse orientation aiming both at efficiency and maximal duration within a rotational period. We first identify the optimally oriented states which fulfill both requirements. We show that a sequence of half-cycle pulses of moderate intensity can be devised for reaching these target states.

Nonlinear pulse deceleration using photorefractive four-wave mixing

We investigate the possibilities of the backward four-wave coupling based on the nonlocal photorefractive response for the nonlinear deceleration of light pulses. The presence of an additional external variable parameter—the pump intensity ratio—allows to improve the output characteristics of the decelerated pulses compared to those typical of the two-wave coupling. In particular, large delay times of the output pulses can be achieved without their strong amplification. This positive distinctive feature of the pulse deceleration occurs far from threshold of the mirrorless optical oscillation.

Optical flip-flop memory and routing operation based on polarization bistability in optical fiber

A polarization bistability and hysteresis cycle phenomenon is demonstrated in optical fibers thanks to a counter-propagating four-wave mixing interaction. Based on this process, we successfully report the proof-of-principle of an optical flip-flop memory and a 10-Gbit/s routing operation.

Anomalous thermalization of nonlinear wave systems

We report theoretically and experimentally in an optical system a process of anomalous thermalization of one-dimensional nonlinear Hamiltonian waves. It is characterized by an irreversible evolution of the waves towards a specific equilibrium state of a fundamental different nature than the expected thermodynamic equilibrium state. A kinetic approach of the problem reveals that this phenomenon is due to the existence of a local invariant in frequency space. A novel family of equilibrium distributions is discovered, which is found in quantitative agreement with the numerical simulations.

INFLUENCE OF UNEQUAL OSCILLATOR STRENGTHS ON STIMULATED RAMAN ADIABATIC PASSAGE THROUGH BRIGHT STATE

In the present work an analytical and numerical analysis of the b -STIRAP process in a medium with unequal oscillator strengths is performed. It is shown that the length of population transfer can be considerably increased by an appropriate choice of the dipole transitions.

Optimization of population transfer by adiabatic passage

We examine the adiabatic limit of population transfer in two-level models driven by a chirped laser field. We show that the nonadiabatic correction is minimized when the adiabatic eigenenergies associated to the dynamics are parallel. In the diagram of the difference of the eigenenergy surfaces as a function of the parameters, this corresponds to an adiabatic passage along a level line. The analytical arguments are based on the Dykhne-Davis-Pechukas treatment. We illustrate this behavior with various examples.

Pulse-driven near-resonant quantum adiabatic dynamics: lifting of quasi-degeneracy

We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power law rising. This allows us to determine approximative formulas for the lineshape of resonant excitation by various forms of pulses such as truncated trig-pulses. We also analyze and explain the various superpositions of states that can be obtained by the Half Stark Chirped Rapid Adiabat…

Uniform analytic description of dephasing effects in two-state transitions

We describe the effect of pure dephasing upon the time-dependent dynamics of two-state quantum systems in the framework of a Lindblad equation for the time evolution of the density matrix. A uniform approximate formula is derived, which modifies the corresponding lossless transition probability by an exponential factor containing the dephasing rate and the interaction parameters. This formula is asymptotically exact in both the diabatic and adiabatic limits; comparison with numerical results shows that it is highly accurate also in the intermediate range. Several two-state models are considered in more detail, including the Landau-Zener, Rosen-Zener, Allen-Eberly, and Demkov-Kunike models, …

Strange attractor for the renormalization flow for invariant tori of Hamiltonian systems with two generic frequencies

We analyze the stability of invariant tori for Hamiltonian systems with two degrees of freedom by constructing a transformation that combines Kolmogorov-Arnold-Moser theory and renormalization-group techniques. This transformation is based on the continued fraction expansion of the frequency of the torus. We apply this transformation numerically for arbitrary frequencies that contain bounded entries in the continued fraction expansion. We give a global picture of renormalization flow for the stability of invariant tori, and we show that the properties of critical (and near critical) tori can be obtained by analyzing renormalization dynamics around a single hyperbolic strange attractor. We c…

Dynamics of four-wave-mixing oscillators with quasi-phase-matching

The effect of pump-wave misalignment on the oscillation spectra of a semilinear photorefractive oscillator is studied numerically and compared with the results of experiments performed with ${\text{BaTiO}}_{3}:\text{Co}$ and ${\text{KNbO}}_{3}:\text{Ag},\text{Fe}$ crystals.

Field-free two-direction alignment alternation of linear molecules by elliptic laser pulses

We show that a linear molecule subjected to a short specific elliptically polarized laser field yields postpulse revivals exhibiting alignment alternatively located along the orthogonal axis and the major axis of the ellipse. The effect is experimentally demonstrated by measuring the optical Kerr effect along two different axes. The conditions ensuring an optimal field-free alternation of high alignments along both directions are derived.

Thermalisation anormale d'ondes non linéaires

Optimized time-dependent perturbation theory for pulse-driven quantum dynamics in atomic or molecular systems

We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this formulation to a unitary superconvergent technique and improve the accuracy by several orders of magnitude with respect to the Magnus expansion.

Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses

We present a general and versatile technique of population transfer based on {\it parallel adiabatic passage} by femtosecond shaped pulses. Their amplitude and phase are specifically designed to optimize the adiabatic passage corresponding to parallel eigenvalues at all times. We show that this technique allows the robust adiabatic population transfer in a Raman system with the total pulse area as low as 3 $\pi$, corresponding to a fluence of one order of magnitude below the conventional stimulated Raman adiabatic passage process. This process of short duration, typically pico- and subpicosecond, is easily implementable with the modern pulse shaper technology and opens the possibility of ul…

Alignement moléculaire sous impulsions laser ultracourtes

Talk given by O. Faucher; National audience

Control of Quantum Dynamics by Laser Pulses: Adiabatic Floquet Theory

Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems

We consider a class of Hamiltonians with three degrees of freedom that can be mapped into quasi-periodically driven pendulums. The purpose of this paper is to determine the threshold of the break-up of invariant tori with a specific frequency vector. We apply two techniques: the frequency map analysis and renormalization-group methods. The renormalization transformation acting on a Hamiltonian is a canonical change of coordinates which is a combination of a partial elimination of the irrelevant modes of the Hamiltonian and a rescaling of phase space around the considered torus. We give numerical evidence that the critical coupling at which the renormalization transformation starts to diverg…

Target states and control of molecular alignment in a dissipative medium

Received 17 August 2006; published 14 November 2006We investigate how and to what extent molecular alignment can be controlled in a dissipative medium by asuitable train of laser pulses. We focus primarily on the extension of a scheme of control originally constructedfor unitary evolution. The procedure is applied to control the alignment of CO molecules in an Ar gas. Theparameters of the train of kicks—i.e., the intensity of each kick and the delay between them—are eitherobtained by a systematic procedure maximum strategy or by optimization by evolutionary algorithms.DOI: 10.1103/PhysRevA.74.053411 PACS number s : 32.80.Lg, 33.80. b, 42.50.Hz

Slowing down of light pulses using backward-wave four-wave mixing with local response

The slowing down of light pulses is achieved using backward-wave four-wave mixing in a medium with local response. A Bi12TiO20 crystal with an external dc field is used in the experiment as a proof-of-concept material. The delay and shape transformation of output pulses are studied and compared for the transmitted and phase conjugate channels. It is shown that the phase conjugate pulse achieves a longer delay under typical experimental conditions with equal intensities of the pump beams. This advantage of the phase conjugate beam is especially pronounced for short pulses with half-widths smaller than the response time of the medium. The agreement of the experimental results with numerical c…

Effects of an environment on a cavity-quantum-electrodynamics system controlled by bichromatic adiabatic passage

International audience; We present a theoretical investigation of a cavity-QED system controlled by bichromatic adiabatic passage in a dissipative environment. We analyze the production of a controlled Fock state in the cavity by a traveling atom simultaneously coupled by a laser field, and the leakage of the corresponding photons from the cavity.

Efficient and Long-Lived Field-Free Orientation of Molecules by a Single Hybrid Short Pulse

We show that a combination of a half-cycle pulse and a short nonresonant laser pulse produces a strongly enhanced postpulse orientation. Robust transients that display both efficient and long-lived orientation are obtained. The mechanism is analyzed in terms of optimal oriented target states in finite Hilbert subspaces and shows that hybrid pulses can prove useful for other control issues.

Wave turbulence and thermalization of random nonlinear waves

International audience

Multivalued solutions for the output intensity of a semilinear photorefractive oscillator and stability analysis

The analysis of pump-ratio dependences of the output intensity for a semilinear photorefractive coherent oscillator reveals two domains of multivalued solutions for sufficiently large coupling strength ensured by the crystal. We show that even in a strictly degenerate case the nonzero output intensity can be reached in a broad range of pump ratios r from 10−6 to infinity, including the interval where both pump intensities coincide or are very close to each other. This does not contradict the existence of the known gap in the oscillation threshold near the equal intensities of two pump waves: in this particular region the oscillation is not self-starting. The output intensities for frequency…

Postpulse molecular alignment measured by a weak field polarization technique

We report a direct nonintrusive observation of alignment and planar delocalization of ${\mathrm{C}\mathrm{O}}_{2}$ after an intense linearly polarized femtosecond laser pulse excitation. The effects are measured by a polarization technique involving a perturbative probe that itself does not induce appreciable alignment. We show that this technique allows one to measure a signal proportional to $⟨{cos}^{2}\ensuremath{\theta}⟩\ensuremath{-}1/3$, with $\ensuremath{\theta}$ the angle between the molecular axis and the laser polarization. Simulations that support this analysis allow one to characterize the experimentally observed alignment and planar delocalization quantitatively.

Absolute instability in backward wave four-wave mixing: spatial effects

The spatial distribution of new beams generated above the threshold of absolute instability of two counterpropagating incoherent light waves is studied and compared with the results of calculation.

Superluminal pulse propagation in a non-linear Lambda -type atomic medium

International audience; The propagation of two optical pulses in a non-linear -type atomic medium is considered. The analytical solution to the self-consistent Maxwell-Schrödinger equations in the adiabatic following condition is obtained. Superluminal effects during propagation of pulses in the medium are studied.

The Demkov-Kunike model in the coherent magneto- and photoassociation of ultracold atoms.

Optimization of adiabatic passage with dephasing

International audience

All-optical regeneration of polarization of a 40 Gbit/s return-to-zero telecommunication signal

International audience; We report all-optical regeneration of the state of polarization of a 40 Gbit/s return-to-zero telecommunication signal. The device discussed here consists of a 6.2-km-long nonzero dispersion-shifted fiber, with low polarization mode dispersion, pumped from the output end by a backward propagating wave coming from either an external continuous source or a reflection of the signal. An initially scrambled signal acquires a degree of polarization close to 100% toward the polarization generator output. All-optical regeneration is confirmed by means of polarization and bit-error-rate measurements as well as real-time observation of the eye diagrams. We show that the physic…

Implementation of single-qubit quantum gates by adiabatic passage and static laser phases

International audience; We propose and analyse experimentally feasible implementations of single-qubit quantum gates based on stimulated Raman adiabatic passage (STIRAP) between magnetic sublevels in atoms coupled by elliptically polarized pulsed laser fields, in part based on a proposal by Kis and Renzoni [Z. Kis, F. Renzoni, Phys. Rev. A 65 (2002) 032318]. These techniques require only the control of the relative phase of the driving fields but do not involve any dynamical or geometric phases, which makes it independent of the other interaction details: detuning, pulse shapes, pulse areas and pulse durations. The suggested techniques are immune to spontaneous emission since the qubit mani…

Anomalous thermalization of nonlinear optical waves

We report theoretically and experimentally an anomalous thermalization process characterized by an irreversible evolution of the waves towards a novel family of equilibrium states of a fundamental different nature than the standard thermodynamic equilibrium state.

Stimulated Raman Adiabatic Passage via bright state in Lambda medium of unequal oscillator strengths

International audience; We consider the population transfer process in a Lambda-type atomic medium of unequal oscillator strengths by stimulated Raman adiabatic passage via bright-state (b-STIRAP) taking into account propagation effects. Using both analytic and numerical methods we show that the population transfer efficiency is sensitive to the ratio q(p)/q(s) of the transition oscillator strengths. We find that the case q(p) > q(s) is more detrimental for population transfer process as compared to the case where q(p) <= q(s). For this case it is possible to increase medium dimensions while permitting efficient population transfer. A criterion determining the interaction adiabaticity in th…

Opération de renversement du temps appliquée a un hamiltonien algébrique adapté aux molécules tétraédriques.

Nous analysons la formulation de l'opération de renversement du temps (RVT) dans le cadre de l'approche algébrique des molécules tétraèdriques locales. Cette approche est basée sur les propriétés mathématiques de la chaîne de groupes U(5) <-- U(4) <-- K(4) = A(4) ^ S(4) <-- S(4) = Td (1) adaptée au système moléculaire étudié. Nous déterminons la forme générale de la transformation RVT pour une réalisation purement algébrique de tous les opérateurs, en imposant que les représentations irréductibles associées à a la chaîne (1) soient invariantes dans la symétrie RVT. Le résultat essentiel est que nous déduisons le comportement dans l'opération RVT de tous les opérateurs de notre formalisme, n…

Pulse-driven quantum dynamics beyond the impulsive regime

We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.

Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension

International audience; We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.

Quantum emitter states dressed by the plasmon modes of a metal nanoparticle in the strong coupling regim

The quantum control of emitters is a key issue for quantum information processing at the nanoscale. This generally necessitates the strong coupling of emitters to a high Q-cavity for efficient manipulation of the atoms and field dynamics (cavity quantum electrodynamics or cQED). Since almost a decade, strong efforts are put to transpose cQED concepts to plasmonics in order to profit of the strong mode confinement of surface plasmons polaritons. Despite the intrinsic presence of lossy channels leading to strong decoherence in plasmonics systems, it has been experimentally proven that it is possible to reach the strong coupling regim [1].

Control of field-free molecular alignment by phase-shaped laser pulses

We report an experimental study of the control of molecular alignment of ${\mathrm{N}}_{2}$ by use of spectrally modulated pulses at an intensity regime below the intrinsic saturation of the alignment. By manipulating the relative timing of the alignment revival pattern arising from the even subset of the thermal ensemble as compared to the odd subset, we demonstrate that the angular distribution of the aligned molecule can be converted into planar delocalization at specific times. We also show that the angular focusing of the molecular axis can be switched off by applying a specific bipulse.

Self-polarization effect in the middle point of an optical fiber

In this paper, we report both numerically and experimentally an unexpected phenomenon of self-polarization occurring in the middle point of an isotropic optical fiber when two uncorrelated partially polarized waves are simultaneously injected at the ends of the fiber. More precisely, we demonstrate that two counterpropagating waves of equal intensity exhibit a spontaneous organization of their polarization states around two pools of attraction just in the middle point of propagation, and then both recover a partially polarized state at their respective fiber outputs. The self-polarization effect then remains hidden within the optical fiber in the sense that no apparent sign of this process …

Renormalization-group analysis for the transition to chaos in Hamiltonian systems

Abstract We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of…

Optimized adiabatic passage with dephasing

We study adiabatic population transfer with dephasing in two-level models driven by a chirped driving field. We show that the population transfer is maximized when the dynamics follows specific ellipses as trajectories in the parameter space. We determine the optimal parameters and estimate the losses in a closed form. These estimates show a similar robustness as for the standard lossless adiabatic processes with respect to variations of the parameters.

Line of polarization attraction in highly birefringent optical fibers

We investigate the phenomenon of polarization attraction in a highly birefringent fiber. This polarization process originates from the nonlinear interaction of two counter-propagating beams. We show that all polarization states of the forward (signal) beam are attracted toward a specific line of polarization states on the surface of the Poincare sphere, whose characteristics are determined by the polarization state of the injected backward (pump) beam. This phenomenon of polarization attraction takes place without any loss of energy for the signal beam. The stability of different stationary solutions is also discussed through intensive numerical simulations. On the basis of mathematical tec…

Field-free molecular alignment induced by elliptically polarized laser pulses: Noninvasive three-dimensional characterization

International audience; An investigation of field-free molecular alignment produced by elliptically polarized laser pulses is reported. Experiments are conducted in CO2 at room temperature. A noninvasive all-optical technique, based on the cross defocusing of a probe pulse, is used to measure the alignment along two orthogonal directions which is sufficient to provide a three-dimensional characterization. The field-free molecular alignment produced by a laser of elliptical polarization is in good agreement in terms of amplitude and shape with theoretical predictions. It turns out to be almost equivalent to the superposition of the effects that one would obtain with two individual cross-pola…

Hamiltonian monodromy from a Gauss-Manin monodromy

International audience

Adiabatic evolution for systems with infinitely many eigenvalue crossings

International audience; We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings.

Domains of Convergence of Kam Type Iterations for Eigenvalue Problems

The KAM technique was first introduced to deal with small denominator problems appearing in perturbation of invariant tori in classical mechanics [1, 2]. Similar methods were later applied to many different problems, like e.g. eigenvalue problems for time dependent problems in the Floquet representation [3, 4, 5, 6]. Most of the known results are valid for sufficiently small perturbation of some simple (integrable) system. The phenomena arising for large perturbations, in particular critical perturbations at which a given torus loses its stability, have been discussed in the framework of some approximate schemes inspired in renormalization group ideas [7, 8, 9]. In this framework, an iterat…

A universal optical all-fiber omnipolarizer

International audience; Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear- and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarizatio…

Quantum plasmonics with multi-emitters: application to stimulated Raman adiabatic passage

We construct a mode-selective effective model describing the interaction of the localised surface plasmon polaritons (LSPs) supported by a spherical metal nanoparticle (MNP) with N quantum emitters (QEs) in an arbitrary geometric arrangement. Simplifying previously presented procedures, we develop a formulation in which the field response in the presence of the MNP can be decomposed into orthogonal modes, expanding the Green tensor of the system in the spherical vector harmonics basis and using the generalized global Löwdin orthogonalization algorithm. We investigate the possibility of using the LSPs as mediators of an efficient control of population transfer between two QEs. We show that a…

All-Optical Polarization Control for Telecom Applications

We describe a phenomenon of self-organization of the light state-of-polarization in optical fibers based on a nonlinear cross-polarization interaction between an incident signal and its backward replica. Several proof-of-principles for telecom applications are reported.

Resonances in classical and quantum hamiltonian systems

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Eigenfunction expansions for time dependent hamiltonians

We describe a generalization of Floquet theory for non periodic time dependent Hamiltonians. It allows to express the time evolution in terms of an expansion in eigenfunctions of a generalized quasienergy operator. We discuss a conjecture on the extension of the adiabatic theorem to this type of systems, which gives a procedure for the physical preparation of Floquet states. *** DIRECT SUPPORT *** A3418380 00004

Polarization control in spun and telecommunication optical fibers

International audience; We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical analysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are d…

Optimal adiabatic passage by shaped pulses: Efficiency and robustness

We explore the efficiency and robustness of population transfer in two-state systems by adiabatic passage (i) when the driving pulse is optimally designed in order to lead to parallel adiabatic passage or (ii) with a linear chirping. We show how one could practically implement the corresponding designs of the pulses in the spectral domain. We analyze the robustness of the two shapings taking into account fluctuations of the phase, amplitude, and the area of the pulse. We show the overall superiority of the parallel adiabatic passage especially when one faces the issue of a pulse area that is not well known. We show that the robustness of parallel adiabatic passage is not improved when it is…

Thermalization of random nonlinear waves: Application to optical waves

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Influence of the inter-particles elastic scattering on the quadratic-nonlinear Landau-Zener transition in photo- and magneto- association of ultracold atoms

Polarization and modal attractors in conservative counterpropagating four-wave interaction

An experimental and theoretical study of the resonant four-wave interaction scheme in the counterpropagating configuration reveals the existence of a novel attraction process in Hamiltonian systems. We show analytically that it is the specificity of the boundary conditions inherent in the counterpropagating configuration that makes attraction dynamics possible in spite of the reversible nature of the four-wave interaction. In the context of optics, this novel dynamical feature could be the basic mechanism of a universal polarizer performing total polarization conversion of unpolarized light with, in principle, 100% efficiency.

Adiabatic approximation for quantum dissipative systems: formulation, topology and superadiabatic tracking

A generalized adiabatic approximation is formulated for a two-state dissipative Hamiltonian which is valid beyond weak dissipation regimes. The history of the adiabatic passage is described by superadiabatic bases as in the nondissipative regime. The topology of the eigenvalue surfaces shows that the population transfer requires, in general, a strong coupling with respect to the dissipation rate. We present, furthermore, an extension of the Davis-Dykhne-Pechukas formula to the dissipative regime using the formalism of Stokes lines. Processes of population transfer by an external frequency-chirped pulse-shaped field are given as examples.

Fast polarization scrambler based on chaotic dynamics in optical fibers

Approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom

We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling prop…

Diffusive energy growth in classical and quantum driven oscillators

We study the long-time stability of oscillators driven by time-dependent forces originating from dynamical systems with varying degrees of randomness. The asymptotic energy growth is related to ergodic properties of the dynamical system: when the autocorrelation of the force decays sufficiently fast one typically obtains linear diffusive growth of the energy. For a system with good mixing properties we obtain a stronger result in the form of a central limit theorem. If the autocorrelation decays slowly or does not decay, the behavior can depend on subtle properties of the particular model. We study this dependence in detail for a family of quasiperiodic forces. The solution involves the ana…

Slowdown and speedup of light pulses using the self-compensating photorefractive response

We study theoretically the effects of pulse slowdown and speedup in ferroelectric Sn2P2S6 possessing a self-compensating photorefractive response. It is shown that both these effects can be implemented in one sample for sufficiently large values of the coupling strength. In contrast to other types of the photorefractive response (local and nonlocal), the output pulses do not suffer from strong spatial amplification and broadening.

Arbitrary state controlled-unitary gate by adiabatic passage

We propose a robust scheme involving atoms fixed in an optical cavity to directly implement the universal controlled-unitary gate. The present technique based on adiabatic passage uses novel dark states well suited for the controlled-rotation operation. We show that these dark states allow the robust implementation of a gate that is a generalisation of the controlled-unitary gate to the case where the control qubit can be selected to be an arbitrary state. This gate has potential applications to the rapid implementation of quantum algorithms such as of the projective measurement algorithm. This process is decoherence-free since excited atomic states and cavity modes are not populated during…

All-fiber based chaotic polarization scrambler

We present a fiber-based polarization scrambler founded on the nonlinear interaction between a signal and its backward replica generated and amplified by a reflective loop. The output polarization dynamic turns out to be chaotic.

Robust control of unstable nonlinear quantum systems

Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that, in the context of driven nonlinear Hamiltonian systems, adiabatic passage becomes highly non-robust when the target is unstable. We show this result for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point in the classical phase space featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially non-adiabatic trajectories. They localize at the approach of the target near the stable manifold of the separatrix, which drives the dynamics towards the ta…

Control of Localization and Suppression of Tunneling by Adiabatic Passage

We show that a field of frequency $\ensuremath{\omega}$ combined with its second harmonic $2\ensuremath{\omega}$ driving a double-well potential allows us to localize the wave packet by adiabatic passage, starting from the delocalized ground state. The relative phase of the fields allows us to choose the well of localization. We can suppress (and restore) the tunneling subsequently by switching on (and off) abruptly the fields at well-defined times. The mechanism relies on the fact that the dynamics is driven to an eigenstate of the Floquet Hamiltonian which is a localized state.

Bichromatic field propagation in a resonant medium: Floquet analysis

We study the propagation of a bichromatic field in a resonant medium. The two modes of the incoming fields are pulsed and delayed with respect to each other. It is shown that in the course of the propagation, new Raman sidebands will be generated. The achievable frequency spacing between the sidebands is determined from experimental data. A numerical example is shown for realistic physical parameters.

Dressed states of a quantum emitter strongly coupled to a metal nanoparticle

Hybrid molecule-plasmonic nanostructures have demonstrated their potential for surface enhanced spectroscopies, sensing, or quantum control at the nanoscale. In this Letter, we investigate the strong coupling regime and explicitly describe the hybridization between the localized plasmons of a metal nanoparticle and the excited state of a quantum emitter, offering a simple and precise understanding of the energy exchange in full analogy with cavity quantum electrodynamics treatment and a dressed atom picture. Both near-field emission and far-field radiation are discussed, revealing the richness of such optical nanosources.

A universal all-fiber Omnipolarizer

We report the experimental observation of self-polarization of light in optical fibers through a counter-propagating four-wave mixing between an incident signal and its backward replica. An efficient self-polarization of a 40-Gbit/s signal is demonstrated.

Singular tori as attractors of four-wave-interaction systems

We study the spatiotemporal dynamics of the Hamiltonian four-wave interaction in its counterpropagating configuration. The numerical simulations reveal that, under rather general conditions, the four-wave system exhibits a relaxation process toward a stationary state. Considering the Hamiltonian system associated to the stationary state, we provide a global geometrical view of all the stationary solutions of the system. The analysis reveals that the stationary state converges exponentially toward a pinched torus of the Hamiltonian system in the limit of an infinite nonlinear medium. The singular torus thus plays the role of an attractor for the spatiotemporal wave system. The topological pr…

Thermalization of the dispersive three-wave interaction

We investigate the role of dispersion effects on the long-term evolution of the nonlinear three-wave interaction. We show that the three waves exhibit, as a general rule, an irreversible evolution towards a thermodynamic equilibrium state in which they propagate with identical velocities. As a result of this thermalization process, the three-wave system is driven away from spatio-temporal resonance, so that the equilibrium state does not satisfy the (phase-matching) resonant conditions of energy and momentum conservation for the averaged frequencies. Moreover, we show that the interplay between temporal dispersion and spatial diffraction leads to the emergence of a peculiar equilibrium stat…

Quantum Nekhoroshev Theorem for Quasi-Periodic Floquet Hamiltonians

A quantum version of Nekhoroshev estimates for Floquet Hamiltonians associated to quasi-periodic time dependent perturbations is developped. If the unperturbed energy operator has a discrete spectrum and under finite Diophantine conditions, an effective Floquet Hamiltonian with pure point spectrum is constructed. For analytic perturbations, the effective time evolution remains close to the original Floquet evolution up to exponentially long times. We also treat the case of differentiable perturbations.

Two frequency oscillation of a photorefractive oscillator as a perturbation of the mirrorless oscillation

We consider the properties of the non-degenerate two frequency regime of oscillation of the semi-linear photorefractive oscillator and analyze its relation with the mirrorless oscillation. We consider the oscillator with or without a frequency shifted feedback by a vibrating mirror. This study shows that these two apparently different phenomena are closely related. We conclude from the obtained results that the two frequency oscillation can be considered as a perturbation of the mirrorless oscillation.

Four-wave-mixing coherent oscillator with frequency shifted feedback and misaligned pump waves.

The effect of the pump waves misalignment on the oscillation spectra and oscillation intensity of a semilinear photorefractive oscillator is studied numerically and compared with the results of the experiment performed with a KNbO3:Fe,Ag crystal.

Universality for the breakup of invariant tori in Hamiltonian flows

In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action variables, combines a rescaling of phase space and a partial elimination of irrelevant (non-resonant) frequencies. It is implemented numerically for the case applying to golden invariant tori. We find a nontrivial fixed point and compute the corresponding scaling and critical indices. If one compares flows to maps in the canonical way, our results are consistent with existing data on the breakup of golden invariant circles for area-preserving maps.

Floquet perturbative analysis for STIRAP beyond the rotating wave approximation

We present a perturbative analysis of Floquet eigenstates in the context of two delayed laser processes (STIRAP) in three level systems. We show the efficiency of a systematic perturbative development which can be applied as long as no non-linear resonances occur.

Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass

Recent research has been focused on the ability to manipulate a light beam in such a way to hide, namely to cloak, an event over a finite time or localization in space. The main idea is to create a hole or a gap in the spatial or time domain so as to allow for an object or data to be kept hidden for a while and then to be restored. By enlarging the field of applications of this concept to telecommunications, researchers have recently reported the possibility to hide transmitted data in an optical fibre. Here we report the first experimental demonstration of perpetual temporal spying and blinding process of optical data in fibre-optic transmission line based on polarization bypass. We succes…

Efficient adiabatic tracking of driven quantum nonlinear systems

We derive a technique of robust and efficient adiabatic passage for a driven nonlinear quantum system, describing the transfer to a molecular Bose-Einstein condensate from an atomic one by external fields. The pulse ingredients are obtained by tracking the dynamics derived from a Hamiltonian formulation, in the adiabatic limit. This leads to a nonsymmetric and nonmonotonic chirp. The efficiency of the method is demonstrated in terms of classical phase space, more specifically with the underlying fixed points and separatrices. We also prove the crucial property that this nonlinear system does not have any solution leading exactly to a complete transfer. It can only be reached asymptotically …

Convergence of KAM iterations for counterterm problems

Abstract We analyse two iterative KAM methods for counterterm problems for finite-dimensional matrices. The starting point for these methods is the KAM iteration for Hamiltonians linear in the action variable in classical mechanics. We compare their convergence properties when a perturbation parameter is varied. The first method has no fixed points beyond a critical value of the perturbation parameter. The second one has fixed points for arbitrarily large perturbations. We observe different domains of attraction separated by Julia sets.

Quantum logic gates by adiabatic passage

International audience; We present adiabatic passage techniques for the realisation of one and two-qubit quantum Gates. These methods use evolution along dark-states of the system, avoiding decoherence effects such as spontaneous emission. The advantage of these methods is their robustness: they are insensitive to the fluctuations of the parameters and to partial knowledge of the system.

Influence of third-order dispersion on the propagation of incoherent light in optical fibers

International audience; We study the influence of third-order dispersion effects on the propagation of an incoherent nonlinear wave in an optical fiber system. The wave spectrum is shown to exhibit a highly asymmetric deformation characterized by a lateral spectral shoulder and the subsequent formation of an unexpected constant spectral pedestal. A kinetic approach to the problem reveals the existence of an invariant that explains in detail the essential properties of such asymmetric spectral evolution of the wave.