Nonlinear matter wave dynamics in periodic and double well potentials

Abstract

Bose-Einstein condensates in designed potentials represent a model system for the investigation of nonlinear matter wave dynamics, since both the nonlinearity and the potentials can be very well controlled experimentally. The nonlinearity arising from the atom-atom interaction can be adjusted through the atom number. The potentials can be readily realized by employing the atom-light interaction leading to potentials which are proportional to light intensity. Since the techniques for manipulation of light are very well developed almost arbitrary potentials can be realized. In our experiments we employ the most simple light intensity configurations such as focused laser beam and standing light waves.The first experiment we will discuss deals with the realization of a bright atomic-gap solitonsa paradigm of nonlinear matter wave dynamics. These solitons exist in the presence of weak periodic potentials, which modify the free dispersion relation represented by the well known band structure. Preparing a condensate at the Brillouin zone edge anomalous dispersion can be realized. Thus a bright soliton can be formed since anomalous dispersion can compensate the repulsive atom-atom interaction of 87Rb. The systematic investigations reveal that the realized solitons exhibit the expected dependence of the atom number and the width of the soliton on the strength of the dispersion [1].Our experimental system allows in a very direct way to investigate also the regime of discrete nonlinear systems by just increasing the depth of the periodic potential i.e. increasing the light intensity, which leads to an array of weakly coupled condensates. In this regime also non-spreading wave packets exist, but in contrast to the gap-soliton the localization originates from the local dynamics of few wells at the edge of the wave packet. In our experiments we have observed this new localization process which leads to rectangular wave packetsnonlinear self trapping. We also confirm the predicted scaling behavior of the critical density which has to be surpassed to lead to nonlinear self trapping. Our theoretical model -discrete nonlinear Schrodinger equation with modified nonlinearity due to transverse Thomas Fermi distributioncaptures very well our observation. Furthermore it reveals clearly the importance of the local dynamics near the edges of the non-spreading wave packets [2].Combining a periodic potential with 5pgm period with a harmonic potential realized with a focussed laser beam leads to a well controllable double-well potential. Since our optical imaging system has a resolution of 2.8(2)gm, the population of the individual wells can be imaged in situ and the dynamics of the populations can be studied in real space. If the potentials are switched of and the atomic cloud is observed in time of flight (far field) the expected double slit interference pattem are observed. This allows the deduction of the relative phase between the two condensates and the fill characterization of the dynamics of the wave functions in the two mode approx...

Coherent spin mixing dynamics in a spin-1 atomic condensate

“…Intuitively, we would expect that this is a reasonable approximation as the total numbers of atom, at 1000, although not macro-scopic, is definitely 'large'. In fact, the recent double well experiment that confirmed the coherent nonlinear Josephson oscillations of the mean field theory, is at a similar level of numbers of atoms [21]. A rigorous discussion of this point in terms of the quantum phase diffusions in a spin-1 condensate is a rather involved procedure, and will not be reproduced here [30].…”

“…Unlike the pioneering studies on this subject as in Refs. [17,19], we will highlight the important role of an external magnetic field, which is present in all experiments to date.Recently, a beautiful experiment has finally observed the long predicted Josephson type coherent nonlinear oscillations with a scalar condensate in a spatial double well potential [21].Although spin mixing driven by the internal spindependent interaction (not of the nature of a Rabi oscillation as driven by an external field [22,23]), has been observed in both F = 1 and F = 2 condensates [9,12,14,24], the coherence of this process has not yet been investigated. Over-damped single oscillations in spin populations have been observed in earlier experiments [24] although their interpretation has been limited because evolution from the initial (meta-stable) states was noise-driven.…”

“…Recently, a beautiful experiment has finally observed the long predicted Josephson type coherent nonlinear oscillations with a scalar condensate in a spatial double well potential [21].…”

“…A promising future direction relies on increased atomic detection sensitivity, thus the use of smaller condensates as in the experiment of Ref. [21], with lower number densities and at lower temperatures, two favorable conditions for the single spatial mode approximation (SMA) [17,19].The initial atomic population distribution in Fig. 1 corresponds to the (equilibrium) ground state at a magnetic field (B-field) of 0.07 Gauss and with a zero magnetization (m = 0), specified by ρ 0 (0) ≈ 0.644 and θ(0) = 0 with c ≈ 0.614 Hz (these symbols are defined later).…”

“…A promising future direction relies on increased atomic detection sensitivity, thus the use of smaller condensates as in the experiment of Ref. [21], with lower number densities and at lower temperatures, two favorable conditions for the single spatial mode approximation (SMA) [17,19].…”