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arXiv:1709.10268 · Physical Review A

Significantly stable mode of the ultracold atomic wave packet in amplitude-modulated parabolic optical lattices

Tomotake Yamakoshi, Farhan Saif, Shinichi Watanabe

Published Feb 13, 2018• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.023620

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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.

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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.
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-QQQ 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)].
Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum-classical correspondence.
Abstract Experiments with ultracold atoms in optical lattices usually involve a weak parabolic trapping potential which merely serves to confine the atoms, but otherwise remains negligible. In contrast, we suggest a different class of experiments in which the presence of a stronger trap is an essential part of the set-up. Because the trap-modified on-site energies exhibit a slowly varying level spacing, similar to that of an anharmonic oscillator, an additional time-periodic trap modulation with judiciously chosen parameters creates nonlinear resonances which enable efficient Floquet engineering. We employ a Mathieu approximation for constructing the near-resonant Floquet states in an accurate manner and demonstrate the emergence of effective ground states from the resonant trap eigenstates. Moreover, we show that the population of the Floquet states is strongly affected by the phase of a sudden turn-on of the trap modulation, which leads to significantly modified and rich dynamics. As a guideline for further studies, we argue that the deliberate population of only the resonance-induced effective ground states will allow one to realize Floquet condensates which follow classical periodic orbits, thus providing challenging future perspectives for the investigation of the quantum–classical correspondence.
Abstract The out-of-equilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. Our study reveals that the driving enforces the bosons in different wells to oscillate in-phase and to exhibit a dipole-like mode. A wide range from weak-to-strong driving frequencies is covered and a resonance-like behavior of the intra-well dynamics is discussed. In the proximity of the resonance a rich intraband excitation spectrum is observed. The single particle excitation mechanisms are studied in the framework of Floquet theory elucidating the role of the driving frequency. The impact of the interatomic repulsive interactions is examined in detail yielding a strong influence on the tunneling period and the excitation probabilities. Finally, the dependence of the resonance upon a variation of the tunable parameters of the optical lattice is examined. Our analysis is based on the ab initio multi-configuration time-dependent Hartree method for bosons.
The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.
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.