Time-dependent Optical Potentials Research Articles

Ballistic dynamics of emergent soliton from Airy pulse in a medium with linear optical potential

We numerically investigate the propagation dynamics of Airy pulse in dispersive and nonlinear medium with time-dependent external optical potential. These time-dependent optical potentials are created by the co-propagating strong pump wave. In the presence of linear optical potential, soliton shedding from signal Airy pulse is observed, which demonstrates ballistic motion. However, emergent soliton can either be advanced or delayed depending upon the sign of the potential and the extent of temporal advancement or delay is directly proportional to the magnitude of the potential strength. In addition, the temporal shift of the emergent soliton is found to be dependent on the input pulse power. Moreover, we show ballistic motion of the emergent soliton by incorporating an initial linear phase as well as linear chirp (quadratic phase) parameters in the input Airy pulse. Furthermore, the effect of truncation factor on the propagation dynamics is explored. These results provide new insights on the manipulation of the signal Airy pulse dynamics in dispersive and nonlinear media.

Time-independent approximations for time-dependent optical potentials

We explore the possibility of modifying the Lewis–Riesenfeld method of invariants developed originally to find exact solutions for time-dependent quantum mechanical systems for the situation in which an exact invariant can be constructed, but the subsequently resulting time-independent eigenvalue system is not solvable exactly. We propose to carry out this step in an approximate fashion, such as employing standard time-independent perturbation theory or the WKB approximation, and subsequently feeding the resulting approximated expressions back into the time-dependent scheme. We illustrate the quality of this approach by contrasting an exactly solvable solution to one obtained with a perturbatively carried out second step for two types of explicitly time-dependent optical potentials.

A Realization of a Quasi-Random Walk for Atoms in Time-Dependent Optical Potentials

We consider the time dependent dynamics of an atom in a two-color pumped cavity, longitudinally through a side mirror and transversally via direct driving of the atomic dipole. The beating of the two driving frequencies leads to a time dependent effective optical potential that forces the atom into a non-trivial motion, strongly resembling a discrete random walk behavior between lattice sites. We provide both numerical and analytical analysis of such a quasi-random walk behavior.

Constrained Adiabatic Trajectory Method

The nonadiabatic temporal evolution which is associated with inelastic collisions and photoreactive processes typically produces a final state distribution that differs markedly from the initial state distribution. Nevertheless an adiabatic formalism is often used in a zeroth-order description of the processes; for time-periodic perturbations the Floquet theory has been used within an adiabatic framework to provide a compact dynamical theory which requires a basis composed of only a small number of Floquet eigenstates. The use of the generalized Floquet theory or of the concept of a super-adiabatic basis allows the adiabatic approach to be further extended to handle systems with quasi-periodic Hamiltonians. The present work proposes a new approach, in which the time duration of the interaction is artificially prolonged and special absorbing boundary conditions are introduced asymptotically over the lengthened time interval in such a way as to force the adiabaticity of the process. The method involves what can be thought of as time-dependent optical potentials. Some trial applications to semiclassical inelastic collisions and to photodissociation effects have shown that the use of the new technique permits a description of the dynamical processes which is so economical that the use of a single generalized Floquet eigenvector will suffice. The main technical feature of this constrained adiabatic trajectory method is that it converts the problem of solving the TDSE with an explicitly time-dependent potential into that of solving a static complex eigenvalue problem.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180° out of phase with the initial state.

Momentum transfer to and elementary excitations of a Bose-Einstein condensate by a time-dependent optical potential

We present results of calculations on Bose-Einstein condensed $^{87}$Rb atoms subjected to a moving standing-wave light-potential of the form $V_L(z,t) = V_0(t) \cos(q z-\omega t)$. We calculate the mean-field dynamics (the order paramter) of the condensate and determine the resulting condensate momentum in the $z$ direction, $P_z(q,\omega,V_0,t_p)$, where $V_0$ is the peak optical potential strength and $t_p$ is the pulse duration. Although the local density approximation for the Bogoliubov excitation spectral distribution is a good approximation for very low optical intensities, long pulse duration and sufficiently large values of the wavevector $q$ of the light-potential, for small $q$, short duration pulses, or for not-so-low intensities, the local density perturbative description of the excitation spectrum breaks down badly, as shown by our results.

Ballistic peaks at quantum resonance

We report studies of the motion of cold atoms in a time-dependent optical potential. The dynamics of our system are that of the quantum kicked rotor, and exhibit a wide variety of phenomena. One purely quantum effect is the quantum resonance, which occurs for well-chosen initial conditions and specific values of the period between kicks. Distinctly nonclassical behavior, such as ballistic growth in momentum, is possible at a quantum resonance. Previous experimental studies have observed these resonances, but have not clearly resolved the expected ballistic motion. We now observe ballistic motion at quantum resonances and compare our momentum distributions with theory and numerical simulations.

Development of a high-frequency cold neutron pulser for producing a time-dependent optical potential

A performance of a high-frequency cold neutron pulser (hf-CNP) consisiting of a Supersendust magnetic mirror and a magnetic coil is tested using TOF method. The test has been done using MINE installed at the C3-1-2 beam hole of the JRR3M in JAERI. “A cold neutron magnetic mirror placed in the pulsed magnetic field” is called a cold neutron pulser(CNP). The switching function of the hf-CNP could be used for producing a time-dependent magnetic potential to a neutron. The result of a test in the frequency range of kHz is reported.

Dynamical localization of ultracold sodium atoms.

We report a study of atomic motion in time-dependent optical potentials. We measure momentum transfer in parameter regimes for which the classical dynamics are chaotic, and observe the quantum suppression of chaos by dynamical localization. The high degree of control over the experimental parameters enables detailed comparisons with theoretical predictions, and opens new avenues for investigating quantum chaos.

Time-dependent optical potentials: non-Markovian and doorway approaches

The authors propose new approximations to the time-dependent optical potential coupling that part of the Hilbert space in which standard truncated close coupling equations are solved (P space) and the complementary Q space. They define a dynamical basis in P space allowing for a transparent separation of P-Q and Q-Q coupling from P-P coupling, thus ensuring that account for the latter exactly within any approximate scheme. Studying the time structure of the evolution operator in Q space, they are led to propose a non-Markovian scheme going beyond the instantaneous approximation. Alternatively, a topological study of the coupling between P and Q space leads to a doorway space approximation consisting in a dynamical extension of the P space by that part of the Q space to which it is directly coupled.

Optical potentials in ion-atom scattering

It is demonstrated that time-dependent optical potentials can by used as a tool for the global description of ionisation in ion-atom scattering.

Time-dependent optical potential for the Schrödinger solution in a truncated subspace

A time-dependent imaginary optical potential is used to approximate the Schr\"odinger time evolution in a necessarily truncated subspace. The flux of probability into the neglected space, for which the ordinary unitary subspace Schr\"odinger solution does not account, can generally be well reproduced by an optical potential that is diagonal in energy and linear in time. This is demonstrated in a number of examples including the Lipkin model, Gaussian Hamiltonians, and a schematic heavy-ion collision model.