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arXiv:1409.7659 · Physical Review A

Wave-packet dynamics of noninteracting ultracold bosons in an amplitude-modulated parabolic optical lattice

Tomotake Yamakoshi, Shinichi Watanabe

Published Jun 12, 2015• 9 citations
arXivHTMLPDF

Abstract

The recent Aarhus experiment [Phys. Rev. A 88, 023620 (2013)] produced wave packets by applying amplitude modulation to a trapped Bose--Einstein condensate (BEC) of $^{87}\mathrm{Rb}$ using an optical lattice. The present paper renders a theoretical account of this experimental production of wave packets and their subsequent time evolution, focusing on a one-dimensional noninteracting bosonic system as a fundamental starting point for accurate quantum analysis. Since experimental manipulation requires efficient wave-packet creation, we introduce the ``single-$Q$ Rabi model'' to give a simple and reliable description of the interband transition. As a natural extension, we demonstrate enhancement of the wave-packet production by the ``two-step Rabi oscillation method'' using either one or two frequencies. The subsequent time evolution is affected by the intertwining of Bragg reflection and the Landau--Zener transition at each band gap, which is analyzed with the aid of a semiclassical theory [Phys. Rev. Lett. 110, 085302 (2013)].

DOI
10.1103/physreva.91.063614

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The recent Aarhus experiment [Phys. Rev. A 88, 023620 (2013)] produced wave packets by applying amplitude modulation to a trapped Bose--Einstein condensate (BEC) of 87Rb^{87}\mathrm{Rb}87Rb using an optical lattice. The present paper renders a theoretical account of this experimental production of wave packets and their subsequent time evolution, focusing on a one-dimensional noninteracting bosonic system as a fundamental starting point for accurate quantum analysis. Since experimental manipulation requires efficient wave-packet creation, we introduce the single-$Q$ Rabi model'' to give a simple and reliable description of the interband transition. As a natural extension, we demonstrate enhancement of the wave-packet production by the two-step Rabi oscillation method'' using either one or two frequencies. The subsequent time evolution is affected by the intertwining of Bragg reflection and the Landau--Zener transition at each band gap, which is analyzed with the aid of a semiclassical theory [Phys. Rev. Lett. 110, 085302 (2013)].
We show that a conspicuous wave packet of ultracold noninteracting bosonic atoms emerges in a one-dimensional parabolic optical lattice as in the setup of the Aarhus experiment [P. L. Pedersen, M. Gajdacz, N. Winter, A. J. Hilliard, J. F. Sherson, and J. Arlt, Phys. Rev. A 88, 023620 (2013)], given the lattice height is harmonically modulated with a particular amplitude at a resonant frequency. We show that this four-band periodic wave packet (4B PWP) executes stable timewise periodic motion for an infinitely long time. We apply the Floquet theory to analyze the parameter dependence of the 4B PWP in detail. Our analysis shows that it consists mainly of two principal Floquet eigenstates of the periodically driven Hamiltonian. The informative Husimi representation yields temporal slices of the phase space of the 4B PWP, visually identifying moments where the interband transitions take place. The provided data should aid the experiment in locating the 4B PWP.
We study the dynamics of fermions loaded in an optical lattice with a superimposed parabolic trap potential. In the recent Hamburg experiments [J. Heinze et al., Phys. Rev. Lett. 110, 085302 (2013)] on quantum simulation of photoconductivity, a modulation pulse on the optical lattice transferred part of the population of the lowest band to an excited band, leaving a hole in the particle distribution of the lowest band. The subsequent intricate dynamics of both excited particles and holes can be explained by a semiclassical approach based on the evolution of the Wigner function. Here we provide a more detailed analysis of the dynamics, taking into account the dimensionality of the system and finite-temperature effects, aiming at reproducing experimental results on longer time scales. A semiclassical wave packet is constructed more accurately than in the previous theory. As a result, semiclassical dynamics indeed reproduces experimental data and full quantum numerical calculations with a much better accuracy. In particular, the fascinating phenomenon of collapse and revival of holes is investigated in more detail. We presume that the experimental setup can be used for deeper exploration of nonlinear waves in fermionic gases.
We study dynamics of fermions loaded in an optical lattice with a superimposed parabolic trap potential. In the recent Hamburg experiments [J.Heinze et.al., Phys. Rev. Lett. 110, 085302 (2013)] on quantum simulation of photoconductivity, a modulation pulse on the optical lattice transferred part of the population of the lowest band to an excited band, leaving a hole in the particle distribution of the lowest band. Subsequent intricate dynamics of both excited particles and holes can be explained by a semiclassical approach based on the evolution of Wigner function. Here we provide a more detailed analysis of the dynamics taking into account the dimensionality of the system and finite temperature effects, aiming at reproducing experimental results on longer timescales. A semiclassical wave packet is constructed more accurately than in the previous theory. As a result, semiclassical dynamics indeed reproduces experimental data and full quantum numerical calculations with much better accuracy. In particular, fascinating phenomenon of collapse and revival of holes is investigated in a more detail. We presume the experimental setup can be used for deeper exploration of nonlinear waves in fermionic gases.
An experimental group in Beijing [Yueyang Zhai et al., Phys. Rev. A 87, 063638 (2013)] introduced the method of the standing-wave pulse sequence for efficiently preparing ultracold bosonic atoms into a specific excited band in a one-dimensional optical lattice. Here, we report on a theoretical extension of their work to the problem of one-dimensional bichromatic superlattices in order to understand a wave packet shaping process in higher bands. Varying the lattice parameters leads to the so-called Dirac point where a pair of excited bands crosses. This paper thus discusses simultaneously efficient excitation of the wave packet to the proximity of the Dirac point and its subsequent dynamics in the force field of a parabolic trap. We numerically explore optimal pulse-sequence parameters and find an optimized sequence which excites more than 99% of the atoms in an ideal situation to the first and second excited bands within 100 $\ensuremath{\mu}\mathrm{s}$. Our main finding is that the system permitting the Dirac point possesses a region of parameters where the excited energy bands become nearly parabolic, conducive to a robust wave packet with high coherence and isochronicity. We also provide an appropriate data set for future experimentation, including effects of the atom-atom interaction by way of the mean-field nonlinear term.
In this thesis I report on experiments on the quantum dynamics of matter waves in a onedimensional lattice potential. A 87Rb Bose-Einstein condensates is prepared in a one-dimensional waveguide in the lowest band of a superimposed optical lattice potential. The action of a weak lattice potential allows to modify the linear wave dispersion. We realized dispersion management by switching from normal to anomalous dispersion during the evolution. In this way the initial expansion of a wave packet is reversed to a compression and thus the effective spreading can be suppressed. By preparing a BEC at the Brillouin zone edge, we observed bright atomic gap solitons – non-spreading wave packets. They form, if the atom number and the lattice potential depth is tuned such that the effect of the repulsive atomic interaction and the anomalous dispersion cancel. For deep lattice potentials our system is described by a discrete nonlinear Schrödinger equation, whose dynamics is determined by the tunneling between adjacent lattice sites and the nonlinear phase evolution. In the main part of this thesis I report on the first experimental observation of nonlinear self-trapping for matter waves. The transition from the diffusive regime, characterized by an continuous expansion of the condensate, to the self-trapping regime is accomplished by increasing the atomic density. Due to the corresponding increase of the repulsive atomic interaction the initial expansion stops and the width of the wave packet remains finite. The comparison with a numerical analysis reveals that the effect is due to an inhibition of the site-to-site tunneling induced by the nonlinear phase evolution.
The coherent manipulation of wave packets is an important tool in many areas of physics. We demonstrate the experimental realization of quasi-free wave packets of ultra-cold atoms bound by an external harmonic trap. The wave packets are produced by modulating the intensity of an optical lattice containing a Bose-Einstein condensate. The evolution of these wave packets is monitored in-situ and their reflection on a band gap is observed. In direct analogy with pump-probe spectroscopy, a probe pulse allows for the resonant de-excitation of the wave packet into localized lattice states at a long, controllable distance of more than 100 lattice sites from the main component. This coherent control mechanism for ultra-cold atoms thus enables controlled quantum state preparation, opening exciting perspectives for quantum metrology and simulation.