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arXiv:1110.6518

Onset time for energy oscillations in a two-dimensional trapped Bose gas excited by a red laser potential

Roger R. Sakhel, Asaad R. Sakhel

Published Oct 29, 2011• 0 citations
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Abstract

We explore the energy dynamics of a two dimensional (2D) harmonically trapped Bose-Einstein condensate inside a box potential, excited by a moving red-detuned laser potential (RDLP). For an RDLP velocity $v$ less than a critical value $v_c$, energy oscillations are observed to begin simultaneously with the motion of the RDLP. For $v > v_c$, these oscillations are delayed through a transient in the energy. At the end of the delay time $t_{ons}$, the energy oscillations are regenerated again, and $t_{ons}$ is found to depend on $v$ through universal relations for two cases: one for an RDLP depth sufficient to break off a BEC fragment, another for a depth insufficient to split the BEC. In the case of splitting, $t_{ons}$ exactly equals the time it takes the BEC fragment (dragged by the RDLP trough) to reach the hard wall of the box potential.

DOI
10.48550/arxiv.1110.6518

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We explore the energy dynamics of a two dimensional (2D) harmonically trapped Bose-Einstein condensate inside a box potential, excited by a moving red-detuned laser potential (RDLP). For an RDLP velocity vvv less than a critical value vcv_cvc​, energy oscillations are observed to begin simultaneously with the motion of the RDLP. For v>vcv > v_cv>vc​, these oscillations are delayed through a transient in the energy. At the end of the delay time tonst_{ons}tons​, the energy oscillations are regenerated again, and tonst_{ons}tons​ is found to depend on vvv through universal relations for two cases: one for an RDLP depth sufficient to break off a BEC fragment, another for a depth insufficient to split the BEC. In the case of splitting, tonst_{ons}tons​ exactly equals the time it takes the BEC fragment (dragged by the RDLP trough) to reach the hard wall of the box potential.
We explore the energy dynamics of a two dimensional (2D) trapped Bose-Einstein condensate (BEC) excited by a moving red-detuned laser potential (RDLP). The trap is a combination of a power-law (PL) potential cutoff by a hard-wall box potential (HWBP). It is found that by a restricted measurment of the energy within the boundaries of the HWBP, the energy demonstrates oscillations indicative of solitons. It is then demonstrated, that the geometry of the PL potential influences the lifetime of these oscillations, i.e., the lifetime of the ensuing solitons inside the HWBP. We argue that the energy dynamics in this setup are a good tool for measuring their lifetime. It is also found, that the condensate density dynamics display oscillatory patterns of a magnitude and order controlled by the velocity of the RDLP. A connection to oscillations in the chemical potential dynamics is also discussed. Essentially, we suggest future experiments for this kind of setup, which would measure the phonon energy dynamics to trace the lifetime of solitons.
We investigate numerically the momentum density and phase maps −-−in coordinate and momentum space−-− of a two dimensional Bose-Einstein condensate (BEC) excited by a moving red-detuned laser potential. The BEC is confined in a harmonic trap cutoff by hard walls. The system and excitation scheme are as in our previous work (Roger R. Sakhel {\it et al.} to appear in J. Low Temp. Phys. (2013)); but with twice the number of particles and interaction strength. We solve the time-dependent Gross-Pitaevskii equation numerically using the split-step Crank-Nicolson method in real time. It is demonstrated that the red-detuned laser has a phase-imprinting effect like a repulsive potential barrier. Signatures of excitations are extracted from the dynamics of the momentum densities and phase maps. Further, a new phase is defined in momentum space, which is used to reveal excitations. Therefore, phase maps in coordinate space and momentum space are compared for different BEC evolution times. We argue, that this momentum-space phase is especially important with regard to the studies of BEC momentum distributions. In addition, this work presents a new method of BEC interferometry and should contribute to the ongoing research in that field. One of our significant findings is the presence of substantial differences betwteen the momentum density obtained by a Fourier transform (FT) of the spatial density distribution and the one obtained from the modulus of the wavefunction in momentum space; the latter is obtained by a FT of the spatial wavefunction.
We report the observation of highly energetic self-interfering matter-wave (SIMW) patterns generated by a moving obstacle in a two-dimensional Bose-Einstein condensate (BEC) inside a power trap cut off by hard-wall box potential boundaries. The obstacle initially excites circular dispersive waves radiating away from the center of the trap which are reflected from hard-wall box boundaries at the edges of the trap. The resulting interference between outgoing waves from the center of the trap and reflected waves from the box boundaries institutes, to the best of our knowledge, unprecedented SIMW patterns. For this purpose we simulated the time-dependent Gross-Pitaevskii equation using the split-step Crank-Nicolson method and the obstacle was modelled by a moving impenetrable Gaussian potential barrier. Various trapping geometries are considered in which the dynamics of the spatial and momentum density, as well as the energy, are considered. The momentum dynamics reveal an oscillatory behavior for the condensate fraction, indicative of excitations out of and de-excitations back into the condensate state. An oscillatory pattern for the energy dynamics reveals the presence of solitons in the system. Some vortex features are also obtained.
A two-dimensional Bose-Einstein condensate (BEC) split by a radial potential barrier is investigated. We determine on an accurate many-body level the system's ground-state phase diagram as well as a time-dependent phase diagram of the splitting process. Whereas the ground state is condensed for a wide range of parameters, the time-dependent splitting process leads to substantial fragmentation. We demonstrate the dynamical fragmentation of a BEC despite its ground state being condensed. The results are analyzed using a mean-field model and suggest that a large manifold of low-lying fragmented excited states can significantly impact the dynamics of trapped two-dimensional BECs.
Abstract We investigate a quasi one-dimensional 87 R b Bose–Einstein condensate in a harmonic trap with an additional dimple trap (dT) in the center. Within a zero-temperature Gross–Pitaevskii mean-field description we provide a one-dimensional physical intuitive model, which we solve by both a time-independent variational approach and numerical calculations. With this we obtain at first equilibrium results for the emerging condensate wave function which reveal that a dimple trap potential induces a bump or a dip in case of a red- or a blue-detuned Gaussian laser beam, respectively. Afterwards, we investigate how this dT induced bump/dip-imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the generic case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the dT induced bump in the condensate wave function remains present, whereas the dip starts decaying after a characteristic time scale which decreases with increasing blue-detuned dT depth. Secondly, once the red- or blue-detuned dT is switched off, we find that bright shock-waves or gray/dark bi-soliton trains emerge which oscillate within the harmonic confinement with a characteristic frequency.
We explore the dynamics of a Bose–Einstein condensate created in the combined potential of a far-detuned laser standing wave superimposed to a 3D harmonic magnetic potential. We report the investigation of low-lying collective modes showing that the macroscopic dynamics along the optical lattice is strongly modified, resulting in a shift of the dipole and quadrupole mode frequencies depending on the height of the optical lattice, whereas the transverse breathing mode, occurring perpendicularly to the lattice axis, is not perturbed. The experimental findings are compared with the theoretical treatment that generalizes the hydrodynamic equation of superfluids for a weakly interacting Bose gas to include the effects of the periodic potential. We show that the array of condensates trapped in the optical wells and driven by the harmonic magnetic potential is equivalent to an array of Josephson junctions. In the regime of ‘small’ amplitude dipole oscillation the system performs a collective motion and we investigate the current–phase dynamics measuring the critical Josephson current. Increasing the amplitude of the dipole oscillation, we observe a transition from the coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap (‘insulator’ regime). The onset of the coherent regime breakdown is interpreted as the result of a discrete modulational instability occurring when the velocity of the centre of mass of the system is larger than a critical velocity proportional to the tunnelling rate between adjacent wells.