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Exact and semiclassical fermion dynamics in amplitude modulated lattices

Tomotake Yamakoshi, Shinsuke Watanabe, Shun Ohgoda, A. P. Itin

Published Mar 31, 2016• 0 citations
OpenAlex

Abstract

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.

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•Jan 1, 2010•0 citations
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.
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.
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)].
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.
We report on the experimental observation of an analog to a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. While particles in the excited band exhibit long-lived oscillations with a momentum-dependent frequency, a strikingly different behavior is observed for holes in the lowest band. An initial fast collapse is followed by subsequent periodic revivals. Both observations are fully explained by mapping the system onto a nonlinear pendulum.
Quantum gases in optical lattices offer a well-controlled and defect free environment to simulate and study phenomena from condensed matter physics. In particular, questions related to conductivity and charge carrier mobility lie at the heart of the properties of many fascinating materials like superconductors, graphene and semiconductors. The latter become conductive if irradiated with photons. This effect is called photoconductivity and results from photon-induced interband transitions of electrons, leading to the creation of electron and hole excitations, which subsequently serve as free charge carriers. Photoconductivity is widely used in technological applications such as semiconductor photodiodes and photoresistors and as a powerful probe for novel materials.
Ultracold bosonic gases in optical lattices are strongly correlated quantum systems similar to solids. The strong correlation between the electrons in a solid on the one hand, and the bosonic atoms in optical lattice on the other, exhibit various quantum phenomena like insulation, conductivity, localization of electrons and atoms, respectively. Controlled by the intensity of the lattice laser, the ultracold bosonic gas can be transferred from a regime with superfluid character for shallow lattices into a regime of strong correlations, the Mott insulator. As an additional external parameter besides the lattice depth, one can generate spatial inhomogeneities by superimposing an additional standing wave (so-called two-color superlattices), which gives rise to localization effects or the formation of a Bose-glass phase. In the present work, numerical simulations are employed in order to investigate characteristic signatures of the quantum phases in the low-energy excitation spectrum of one-dimensional systems. We simulate temporal small amplitude modulations of the optical lattice in analogy to experiments, and evaluate the response of the system from the time-evolved initial state. The lattice systems are described in the framework of the Bose-Hubbard model. For the evaluation of the time-evolved state, we employ several numerical methods. We analyze systems of small size (6 particles on 6 sites) using an exact time-evolution by integration of the time-dependent Schrödinger equation. The formulation of an importance truncation scheme enables us to retain only the relevant components of the model space in the strongly correlated regime and, thus, allows for the investigation of systems with 10 particles on 10 sites using exact time-evolution. Based on this method, we present results of the Mott-insulating regime as well as for the Bose-glass phase. Furthermore, we employ particle-hole methods, which allow for the treatment of systems with experimental lattice sizes and particle numbers. Starting from the equation of motion method we adapt the Tamm-Dancoff approximation as well as the random-phase approximation for the occupation number representation of the Bose-Hubbard model. We present results of simulations of up to 50 particles on 50 sites and discuss the impact of the lattice depth on the low-energy excitations (U-resonance). Moreover, the impact of a two-color superlattice and the variation of its amplitude is investigated.