Anatole Kenfack

Negativity of the Wigner function as an indicator of non-classicality

A measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyse this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wavepackets.

Bifurcation structure of two coupled periodically driven double-well Duffing oscillators

Abstract The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force f and its frequency Ω . We first examine the stability of the steady-state in linear response, and classify the different types of bifurcation likely to occur in this model. We then explore the complex behavior associated with these bifurcations numerically. Our results show many striking departures from the behavior of coupled driven Duffing oscillators with single-well potentials, as characterized by Kozlowski et al. [Phys. Rev. E 51 (1995) 1861]. In addition to the well-known routes to chaos already encountered in a one-dimensional Duffing oscillator, our model exhibits imbricated period-doubling of both types, symmetry-breaking, sudden chaos and a great abundance of Hopf bifurcations, many of which occur more than once for a given driving frequency. We explore the chaotic behavior of our model using two indicators, namely Lyapunov exponents and the power spectrum. Poincare cross-sections and phase portraits are also plotted to show the manifestation of coexisting periodic and chaotic attractors including the destruction of T2 tori doubling.

Controlling the Ratchet Effect for Cold Atoms

Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.

Optimal representations of quantum states by Gaussians in phase space

A two-step optimization is proposed to represent an arbitrary quantum state to the desired accuracy with the smallest number of Gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the modulus of the weight for the Gaussians. Then, the phase information contained in the Wigner distribution is used to obtain the full complex weights by considering the relative phases for pairs of Gaussians, the chords. The method is exemplified with excited states n of the harmonic and the Morse oscillators. A semiclassical interpretation of the number of Gaussians needed as a function of the quantum number n is given.

Femtosecond photodissociation of molecules facilitated by noise

We investigate the dynamics of diatomic molecules subjected to both a femtosecond midinfrared laser pulse and Gaussian white noise. The stochastic Schrodinger equation with a Morse potential is used to describe the molecular vibrations under noise and the laser pulse. For weak laser intensity, well below the dissociation threshold, it is shown that one can find an optimum amount of noise that leads to a dramatic enhancement of the dissociation probability. The enhancement landscape, which is shown as a function of both the noise and the laser strength, exhibits a global maximum. A frequency-resolved gain profile is recorded with a pump-probe setup which is experimentally realizable. With this profile we identify the linear and nonlinear multiphoton processes created by the interplay between laser and noise and assess their relative contribution to the dissociation enhancement.

Current without external bias and diode effect in shuttling transport of nanoshafts

A row of parallely ordered and coupled molecular nanoshafts is shown to develop a shuttling transport of charges at finite temperature. The appearance of a cu rrent without applying an external bias voltage is reported as well as a natura l diode effect allowing unidirectional charge transport along one field directi on while blocking the opposite direction. The zero-bias voltage current appears above a threshold of initial thermal and/or dislocation energy.

Stochastic dissociation of diatomic molecules

The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focusing on their dissociation probabilities. It is found that the quantum system is more robust than the classical one in the limit of a large number of kicks. The opposite behavior emerges for a small number of kicks. Quantum and classical dissociation probabilities do not coincide for any parameter combinations of the force. This can be attributed to a scaling property in the classical system which is broken quantum mechanically.

Absolute negative mobility induced by potential phase modulation.

We investigate the transport properties of a particle subjected to a deterministic inertial rocking system, under a constant bias, for which the phase of the symmetric spatial potential used is time modulated. We show that this modulated phase, assisted by a periodic driving force, can lead to the occurrence of the so-called absolute negative mobility (ANM), the phenomenon in which the particle surprisingly moves against the bias. Furthermore, we discover that ANM predominantly originates from chaotic-periodic transitions. While a detailed mechanism of ANM remains unclear, we show that one can manipulate the control parameters, i.e., the amplitude and the frequency of the phase, in order to enforce the motion of the particle in a given direction. Finally, for this experimentally realizable system, we devise a two-parameter current plot which may be a good guide for controlling ANM.

Husimi–Wigner representation of chaotic eigenstates

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. Physically, this factorization corresponds to the description of interacting components of a quantum system with many degrees of freedom and the sections could be generated by conceivable partial measurements. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi–Wigner representation. It occupies an intermediate ground between the drastic suppression of non-classical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of a chaotic Hamiltonian. Though less regular, the individual two-dimensional Wigner functions resemble those of semiclassically quantized states.

Dissociation and ionization of small molecules steered by external noise

We show that ionization and dissociation can be influenced separately in a molecule with appropriate external noise. Specifically, we investigate the hydrogen molecular ion under a stochastic force quantum mechanically beyond the Born–Oppenheimer approximation. We find that up to 30% of dissociation without ionization can be achieved by suitably tuning the forcing parameters.