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arXiv:1306.1082 · Physical Review A

Production and manipulation of wave packets from ultracold atoms in an optical lattice

Poul L. Pedersen, Miroslav Gajdacz, N. Winter, Andrew J. Hilliard, Jacob Friis Sherson, J. Arlt

Published Aug 27, 2013• 17 citations
arXivHTMLPDF

Abstract

Within the combined potential of an optical lattice and a harmonic magnetic trap, it is possible to form matter wave packets by intensity modulation of the lattice. An analysis of the production and motion of these wave packets provides a detailed understanding of the dynamical evolution of the system. The modulation technique also allows for a controllable transfer (deexcitation) of atoms from such wave packets to a state bound by the lattice. Thus, it acts as a beam splitter for matter waves that can selectively address different bands, enabling the preparation of atoms in localized states. The combination of wave packet creation and deexcitation closely resembles the well-known method of pump-probe spectroscopy. Here, we use the deexcitation for spectroscopy of the anharmonicity of the combined potential. Finally, we demonstrate that lattice modulation can be used to excite matter wave packets to even higher momenta, producing fast wave packets with potential applications in precision measurements.

DOI
10.1103/physreva.88.023620

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Within the combined potential of an optical lattice and a harmonic magnetic trap, it is possible to form matter wave packets by intensity modulation of the lattice. An analysis of the production and motion of these wave packets provides a detailed understanding of the dynamical evolution of the system. The modulation technique also allows for a controllable transfer (deexcitation) of atoms from such wave packets to a state bound by the lattice. Thus, it acts as a beam splitter for matter waves that can selectively address different bands, enabling the preparation of atoms in localized states. The combination of wave packet creation and deexcitation closely resembles the well-known method of pump-probe spectroscopy. Here, we use the deexcitation for spectroscopy of the anharmonicity of the combined potential. Finally, we demonstrate that lattice modulation can be used to excite matter wave packets to even higher momenta, producing fast wave packets with potential applications in precision measurements.
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.
In the past fifteen years ultracold atoms confined to optical lattices, which are artificial crystals of light, have proven to be powerful tools in the study of strongly correlated many-body systems widely known from a condensed matter context. The detailed knowledge, high tunability and control of microscopic parameters has enabled the creation and control of highly non-trivial quantum systems for which a direct comparison of model calculations to experimental measurements is now possible. In order to gain precise information on the properties of ultracold gases in optical lattices, many powerful methods have been developed. In particular spectroscopic methods have enabled to probe different characteristic excitations. However, many fascinating properties of strongly interacting quantum many-body systems are not yet fully characterized. Therefore, this thesis explores further possibilities of lattice modulation spectroscopy which is a time-periodic modulation of the optical lattice amplitude. We theoretically investigate the response of different (mostly one-dimensional) cold atom systems to a lattice modulation by means of the time-dependent density matrix renormalization group method and different analytical approximations. In addition to the normal lattice modulation, we consider a superlattice modulation scheme where the lattice amplitude is modulated in a dimerized fashion, coupling to a certain class of excitations in the system. The lattice modulation spectroscopy is a versatile probe which we use to study different situations relevant for experimental applications. We show that a detection of signatures of the exotic bond order wave phase is feasible in a system of interacting fermions on a one-dimensional optical lattice with staggered energy offset. Moreover, we demonstrate that a temperature measurement of fermions confined to an optical lattice is possible as well as a determination of the interaction strength of bosonic atoms confined to a one-dimensional optical lattice. In addition, various excitations in all these systems are investigated in detail.
Motivated by recent experimental progress achieved with ultracold atoms in kilohertz-driven optical lattices, we provide a theoretical discussion of mechanisms governing the response of a particle in a cosine lattice potential to strong forcing pulses with smooth envelope. Such pulses effectuate adiabatic motion of a wave packet's momentum distribution on quasienergy surfaces created by spatiotemporal Bloch waves. Deviations from adiabaticity can then be deliberately exploited for exerting coherent control and for reaching target states which may not be accessible by other means. As one particular example, we consider an analog of the $\ensuremath{\pi}$ pulses known from optical resonance. We also suggest adapting further techniques previously developed for controlling atomic and molecular dynamics by laser pulses to the coherent control of matter waves in shaken optical lattices.
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)].
We present experimental techniques that employ an optical accordion lattice with dynamically tunable spacing to create and study bright matter-wave solitons in optical lattices. The system allows precise control of lattice parameters over a wide range of lattice spacings and depths. We detail calibration methods for the lattice parameters which are adjusted to the varying lattice spacing, and we demonstrate site-resolved atom number preparation via microwave addressing. Lattice solitons are generated through rapid quenches of the atomic interaction strength and the external trapping potential. We systematically optimize the quench parameters, such as duration and final scattering length, to maximize soliton stability. Our results provide insight into nonlinear matter-wave dynamics in discretized systems and establish a versatile platform for the controlled study of lattice solitons.
Optical lattices make it possible to trap and coherently control large ensembles of ultracold atoms. They provide the possibility to create lattice potentials that mimic the structure of solid-state systems, and to control these potentials dynamically. In this thesis, we study how dynamical manipulations of the lattice geometry can be used to perform different tasks, ranging from quantum information processing to the creation of diatomic molecules. We first examine the dynamical properties of ultracold atoms trapped in a lattice whose periodicity is dynamically doubled. We derive a model describing the dynamics of the atoms during this process, and compute the different interaction parameters of this model. We investigate different ways of using this lattice manipulation to optimise the initialisation time of a Mott-insulating state with one atom per site, and provide a scaling law related to the interaction parameters of the system. We go on to show that entangling operations between the spin of adjacent atoms are realisable with optical lattices forming arrays of double-well potentials. We study the creation of a lattice containing a spin-encoded Bell-pair in each double-well, and show that resilient, highly-entangled many-body states are realisable using lattice manipulations. We show that the creation of cluster-like states encoded on Bell-pairs can be achieved using these systems, and we provide measurement networks that allow the execution of quantum algorithms while maintaining intact the resilience of the system. Finally, we investigate the possibility to create a diatomic molecular state and simulate Fermi systems via the excitation to Rydberg levels of ground-state atoms trapped in optical lattices. We develop a method based on symbolical manipulations to compute the interaction parameters between highly-excited electrons, and evaluate them for different electronic configurations. We use these parameters to investigate the existence of diatomic molecular states with equilibrium distances comparable to typical lattice spacings. Considering the possibility to excite atoms trapped in an optical lattice to Rydberg levels such that the electronic cloud of neighbouring atoms overlap, we propose a model describing their interactions and compute its parameters. If such systems were realised, they would allow the simulation of Fermi systems at a temperature much below the Fermi temperature, thus enabling the observation of quantum phenomena hitherto inaccessible with current technology.