Geometric Origin of the Tennis Racket Effect.

The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar approach describes the Dzhanibekov effect in which a wing nut, spinning around its central axis, suddenly makes a half-turn flip around a perpendicular axis and the monster flip, an almost impossible skateboard trick.

Optimal control of the transport of Bose-Einstein condensates with atom chips.

Using Optimal Control Theory (OCT), we design fast ramps for the controlled transport of Bose-Einstein condensates with atom chips' magnetic traps. These ramps are engineered in the context of precision atom interferometry experiments and support transport over large distances, typically of the order of 1 mm, i.e. about 1,000 times the size of the atomic clouds, yet with durations not exceeding 200 ms. We show that with such transport durations of the order of the trap period, one can recover the ground state of the final trap at the end of the transport. The performance of the OCT procedure is compared to that of a Shortcut-To-Adiabaticity (STA) protocol and the respective advantages/disadvantages of the OCT treatment over the STA one are discussed.

Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond.

The design of efficient and robust pulse sequences is a fundamental requirement in quantum control. Numerical methods can be used for this purpose, but with relatively little insight into the control mechanism. Here, we show that the free rotation of a classical rigid body plays a fundamental role in the control of two-level quantum systems by means of external electromagnetic pulses. For a state to state transfer, we derive a family of control fields depending upon two free parameters, which allow us to adjust the efficiency, the time and the robustness of the control process. As an illustrative example, we consider the quantum analog of the tennis racket effect, which is a geometric property of any classical rigid body. This effect is demonstrated experimentally for the control of a spin 1/2 particle by using techniques of Nuclear Magnetic Resonance. We also show that the dynamics of a rigid body can be used to implement one-qubit quantum gates. In particular, non-adiabatic geometric quantum phase gates can be realized based on the Montgomery phase of a rigid body. The robustness issue of the gates is discussed.

Polarization shaping for unidirectional rotational motion of molecules.

Control of the orientation of the angular momentum of linear molecules is demonstrated by means of laser polarization shaping. For this purpose, we combine two orthogonally polarized and partially time-overlapped femtosecond laser pulses so as to produce a spinning linear polarization which in turn induces unidirectional rotation of N2 molecules. The evolution of the rotational response is probed by a third laser beam that can be either linearly or circularly polarized. The physical observable is the frequency shift imparted to the probe beam as a manifestation of the angular Doppler effect. Our experimental results are confirmed by theoretical computations, which allow one to gain a deep physical insight into the laser-molecule interaction.

Optimal control of the signal-to-noise ratio per unit time of a spin 1/2 particle: the crusher gradient and the radiation damping cases.

We show to which extent the signal to noise ratio per unit time of a spin 1/2 particle can be maximized. We consider a cyclic repetition of experiments made of a measurement followed by a radio-frequency magnetic field excitation of the system, in the case of unbounded amplitude. In the periodic regime, the objective of the control problem is to design the initial state of the system and the pulse sequence which leads to the best signal to noise performance. We focus on two specific issues relevant in nuclear magnetic resonance, the crusher gradient and the radiation damping cases. Optimal control techniques are used to solve this non-standard control problem. We discuss the optimality of the Ernst angle solution, which is commonly applied in spectroscopic and medical imaging applications. In the radiation damping situation, we show that in some cases, the optimal solution differs from the Ernst one.

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 successfully characterize the performance of our system by alternatively copying and then concealing 100% of a 10-Gb s(-1) transmitted signal.

Robust quantum control by a single-shot shaped pulse.

Considering the problem of the control of a two-state quantum system by an external field, we establish a general and versatile method allowing the derivation of smooth pulses which feature the properties of high fidelity, robustness, and low area. Such shaped pulses can be interpreted as a single-shot generalization of the composite pulse-sequence technique with a time-dependent phase.

A universal optical all-fiber Omnipolarizer.

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-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validate a novel polarizing device - the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes - as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beam's intensity.

Time-optimal control of spin 1/2 particles in the presence of radiation damping and relaxation.

We consider the time-optimal control of an ensemble of uncoupled spin 1/2 particles in the presence of relaxation and radiation damping effects, whose dynamics is governed by nonlinear equations generalizing the standard linear Bloch equations. For a single spin, the optimal control strategy can be fully characterized analytically. However, in order to take into account the inhomogeneity of the static magnetic field, an ensemble of isochromats at different frequencies must be considered. For this case, numerically optimized pulse sequences are computed and the dynamics under the corresponding optimal field is experimentally demonstrated using nuclear magnetic resonance techniques.

Manifestation of Hamiltonian monodromy in nonlinear wave systems.

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 (2π- or π-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.

Complete nonlinear polarization control in an optical fiber system.

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.

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 properties of the singular torus confer a robust character to the stationary solution when the boundary conditions or the length of the nonlinear medium are modified. Furthermore, an adiabatic approach of the boundary conditions reveals that singular tori also play a major role for the description of the spatiotemporal dynamics of the wave system.

Fractional bidromy in the vibrational spectrum of HOCl.

We introduce the notion of fractional bidromy which is the combination of fractional monodromy and bidromy, two recent generalizations of Hamiltonian monodromy. We consider the vibrational spectrum of the HOCl molecule which is used as an illustrative example to show the presence of nontrivial fractional bidromy. To our knowledge, this is the first example of a molecular system where such a generalized monodromy is exhibited.

Singular extremals for the time-optimal control of dissipative spin 1/2 particles.

We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze a simple case where the control law is explicitly determined. We experimentally implement the optimal control using techniques of nuclear magnetic resonance. To our knowledge, this is the first experimental demonstration of singular extremals in quantum systems with bounded control amplitudes.

Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems.

We show that the peculiar topological properties inherent to singular tori play a major role in the spatiotemporal dynamics of counterpropagating nonlinear waves. Under rather general conditions, these Hamiltonian wave systems exhibit a relaxation process towards a stationary state. We show that this stationary state converges exponentially towards the singular torus of the associated Liouville-integrable Hamiltonian system in the limit of an infinite medium. The singular torus then appears as an attractor for the infinite dimensional dynamical system, a feature which is illustrated by several key models of spatiotemporal wave interactions.

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.

Dissociation energies of six NO2 isotopologues by laser induced fluorescence spectroscopy and zero point energy of some triatomic molecules.

We have measured the rotationless photodissociation threshold of six isotopologues of NO2 containing 14N, 15N, 16O, and 18O isotopes using laser induced fluorescence detection and jet cooled NO2 (to avoid rotational congestion). For each isotopologue, the spectrum is very dense below the dissociation energy while fluorescence disappears abruptly above it. The six dissociation energies ranged from 25 128.56 cm(-1) for 14N16O2 to 25 171.80 cm(-1) for 15N18O2. The zero point energy for the NO2 isotopologues was determined from experimental vibrational energies, application of the Dunham expansion, and from canonical perturbation theory using several potential energy surfaces. Using the experimentally determined dissociation energies and the calculated zero point energies of the parent NO2 isotopologue and of the NO product(s) we determined that there is a common De = 26 051.17+/-0.70 cm(-1) using the Born-Oppenheimer approximation. The canonical perturbation theory was then used to calculate the zero point energy of all stable isotopologues of SO2, CO2, and O3, which are compared with previous determinations.