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Optics and Spectroscopy

Echo responses of an ensemble of cold atoms in optical lattices

S. O. Elyutin

Published Apr 1, 2005• 2 citations
Publisher

Abstract

The dynamics of an ultracold dilute boson gas in an optical lattice is described in the framework of the Bose-Hubbard model in which the parameters of the system are controlled by light. Within this model, an ensemble of Bose-Einstein condensates trapped in cells of a double optical lattice generates an echo response in the quantum-mechanical probability current. The echo signal is excited by biharmonic radiation pulses under two-photon (Raman) resonance conditions. The time profile of the echo signal and the role played by the inhomogeneous broadening and the interaction of atoms in the formation of the boson echo are discussed.

DOI
10.1134/1.1914901

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The dynamics of an ultracold dilute boson gas in an optical lattice is described in the framework of the Bose-Hubbard model in which the parameters of the system are controlled by light. Within this model, an ensemble of Bose-Einstein condensates trapped in cells of a double optical lattice generates an echo response in the quantum-mechanical probability current. The echo signal is excited by biharmonic radiation pulses under two-photon (Raman) resonance conditions. The time profile of the echo signal and the role played by the inhomogeneous broadening and the interaction of atoms in the formation of the boson echo are discussed.
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
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.
The dynamics of ultracold atoms loaded in an optical lattice (superlattice) is described in the article on the basis of the Bose-Hubbard model. Both linear and circular lattices are considered in terms of attractive and repulsive types of interaction between the bosons. The numerically observed quantum-mechanical current state of the Bose condensate atoms is due to a hopping transfer of the ultracold atoms caused by the excitation of the system by the biharmonic electromagnetic field under the Raman resonance condition. When the energy of interaction between the bosons is close to the energy of photoactivation, the boson current decreases, which may be the sign of the superfluidity-insulator phase transition. In the disordered linear chain of potentials, where the depth of optical potentials alters from one site to another, the current spreading over the sites of optical lattice is suppressed in the same way as in the Anderson localization effect.
Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice modulation. Using the time-dependent density matrix renormalization group method, we study the dynamical response due to lattice modulations in different quantum phases of the system with varying density. For the Mott-insulating state, we identify several excitation processes, which provide important information about the density profile of the gases. For the superfluid, the dynamical response can be well described in a local density approximation. This simplification can be valuable in understanding the strong-correlated superfluid in a slow-varying harmonic potential. All these spectroscopic features of an inhomogeneous system can be used as a test for the validity of the Bose-Hubbard model in a parabolic trapping potential.
Ultracold atoms in optical lattices realize simple condensed matter models. We create an ensemble of ≈60 harmonically trapped 2D Bose-Hubbard systems from a 87Rb Bose-Einstein condensate in an optical lattice and use a magnetic resonance imaging approach to select a few 2D systems for study, thereby eliminating ensemble averaging. Our identification of the transition from superfluid to Mott insulator, as a function of both atom density and lattice depth, is in excellent agreement with a universal state diagram [M. Rigol, Phys. Rev. A 79 053605 (2009)] suitable for our trapped system. In agreement with theory, our data suggest a failure of the local density approximation in the transition region.