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Journal of Qingdao University of Science and Technology

Investigation of the Loading Procedure of Ultra-cold Atomic Gases into an Optical Lattice

Songqing Hu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The thermodynamic properties of ultra-cold atomic gases during the loading procedure into optical lattices from the harmonic oscillating trap are researched.The results show that: When the T/Tc equals constant,the occupation rate of particles on the ground state in the harmonic oscillating trap is higher than that of in optical lattices,and the condensate is more stable in the harmonic oscillating trap.The internal energy of the condensate U is in proportion to Tα+1,and the specific heat C V is in proportion to Tα.The entropy of systems keeps balance during the loading process of the ultra-cold atomic gases slowly and adiabatically loaded into optical lattices from the harmonic oscillating trap.When T/Tc is less than 0.30,the occupation rate of particles on the ground state becomes higher with the loading intensity of the optical lattices increasing,and the Bose system becomes more stable.However,When T/Tc is greater than 0.70,the Bose system becomes unstable with the loading intensity of the optical lattices increasing.

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The thermodynamic properties of ultra-cold atomic gases during the loading procedure into optical lattices from the harmonic oscillating trap are researched.The results show that: When the T/Tc equals constant,the occupation rate of particles on the ground state in the harmonic oscillating trap is higher than that of in optical lattices,and the condensate is more stable in the harmonic oscillating trap.The internal energy of the condensate U is in proportion to Tα+1,and the specific heat C V is in proportion to Tα.The entropy of systems keeps balance during the loading process of the ultra-cold atomic gases slowly and adiabatically loaded into optical lattices from the harmonic oscillating trap.When T/Tc is less than 0.30,the occupation rate of particles on the ground state becomes higher with the loading intensity of the optical lattices increasing,and the Bose system becomes more stable.However,When T/Tc is greater than 0.70,the Bose system becomes unstable with the loading intensity of the optical lattices increasing.
By employing the balance condition between the lattice potential and the interatomic interaction, we study the ground state solutions of superfluid Fermi gases in Fourier-synthesized (FS) optical lattices. The average energy of the ground state, the atoms number, and the atom density distribution of the Fermi system are analytically derived along the Bose—Einstein condensation (BEC) side to the Bardeen—Cooper—Schrieffer (BCS) side. We analyze the properties of ground state solutions at both the BEC limit and unitarity in FS optical lattices. It is found that the relative phase α between the two lattice harmonics impacts greatly on the properties of the ground state of the superfluid Fermi gas. Especially in the BCS limit, when α = π/2, the average energy presents an exponential form with the increase of the potential depth of the lattice harmonics υ 2 . Meanwhile, there exits a minimal value. Moreover, due to the Fermi pressure, the atom density distribution at unitarity is more outstretched than that in the BEC limit. The average energy at unitarity is apparently larger than that in the BEC limit. The properties of the ground state solution exhibit very different behaviors when the system transits from the BEC side to the BCS side.
The entropy-temperature curves are calculated for noninteracting Bose and Fermi gases in a 3D optical lattice. These curves facilitate understanding of how adiabatic changes in the lattice depth affect the temperature, and we demonstrate regimes where the atomic sample can be significantly heated or cooled by the loading process. We assess the effects of interactions on a Bose gas in a deep optical lattice and show that interactions ultimately limit the extent of cooling that can occur during lattic loading.
We derive closed analytical expressions for the order parameter $\ensuremath{\Phi}(x)$ and for the chemical potential $\ensuremath{\mu}$ of a Bose-Einstein condensate loaded into a harmonically confined, one-dimensional optical lattice for sufficiently weak, repulsive, or attractive interaction and not too strong laser intensities. Our results are compared to exact numerical calculations in order to map out the range of validity of the perturbative analytical approach. We identify parameter values where the optical lattice compensates the interaction-induced nonlinearity, such that the condensate ground state coincides with a simple, single-particle harmonic-oscillator wave function.
This thesis describes the behaviour of cold atoms in optical lattices. In particular, it explores how transport through the energy bands of the optical lattice can be used to study quantum chaos and Bose-Einstein condensation.\n\nFirstly, this study examines the dynamics of ultra-cold sodium atoms in a one-dimensional optical lattice and a three-dimensional harmonic trap, using both semi-classical and quantum-mechanical analyses. The atoms show mixed stable-chaotic classical dynamics, which originate from the intrinsically quantum-mechanical nature of the energy band. \nThe quantised energy levels exhibit Gutzwiller fluctuations, and the wavefunctions are scarred by an unstable periodic orbit. Distinct types of wavefunction are identified and related directly to particular parts of the classical phase space via a Wigner function analysis.\n\nSecondly, this report studies the dynamics of a rubidium Bose-Einstein condensate in a one-dimensional optical lattice and three-dimensional harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semi-classical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection, and performs Bloch oscillations. After multiple Bragg reflections, solitons and vortices form which damp the centre-of-mass motion.\n\nFinally, the dynamics of Bose-Einstein condensates in optical lattices are investigated for different parameter regimes, as realised in recent experiments. The results reveal how the experiments can be understood, and identify regimes in which vortices trigger explosive expansion of the condensate.
An optical lattice is a periodic potential for atoms, created using a standing wave pattern of light. Due to the interaction between the light and the atoms, the atoms are attracted to either the nodes or the anti-nodes of the standing wave, depending on the exact wave lenght of the light. This means that if such a lattice is loaded with a sufficiently high number of ultracold atoms, a periodic array of atoms is obtained, we an interatomic distance of a few tenths of a micrometer. In order to obtain such a high number of cold atoms, one first has to create a so-called Bose-Einstein condensate. When an optical lattice is loaded from a Bose-Einstein condensate, it is possible to create a system in which every atom is in the lowest band of the lattice and there is on average one atom in each lattice site. Because the lattice potential is created with laser light, the depth of the lattice can easily be tuned by changing the intensity of the laser. When the intensity of the laser light is low, the atoms can tunnel from one site to the next. Due to this tunneling, the gas of atoms in the lattice will remain superfluid. However, if the intensity of the laser light is increased to above a certain critical value, a quantum phase transition occurs to a so-called Mott insulator. In this state, the atoms can no longer tunnel due to the fact that the on-site interaction between atoms becomes more important then the tunneling probability. In this PhD thesis, a description is given of the experimental setup that is being constructed in our group to create these systems in our lab. Also, a theoretical description is given of these systems and several important quantities our derived, such as the gap of the Mott-insulating state. Furthermore, an experiment is proposed that can be used to accurately measure this gap.
Bose–Einstein Condensation (BEC) of both the ideal and the weakly inter-acting cold alkali gases confined by anisotropic harmonic oscillator poten-tials is investigated in this paper. It is shown that the transition point is shifted towards lower temperatures because of the trapped potentials, and the specific heat below the transition point is no longer proportional to T 3/2 . Expressions of modified condensation temperature, internal energy and the specific heat are derived for the ideal trapped gases explicitly. Moreover, the effect of interactions among the atoms on the transition temperature is also given and discussed.