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arXiv:cond-mat/0702055 · Physical Review A

Coherence properties of spinor condensates at finite temperatures

Krzysztof Gawryluk, Mirosław Brewczyk, Mariusz Gajda, Kazimierz Rza̧żewski

Published Jul 18, 2007• 14 citations
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Abstract

We consider a spinor condensate of $^{87}\mathrm{Rb}$ atoms in its $F=1$ hyperfine state at finite temperatures. Putting initially all atoms in ${m}_{F}=0$ component we find that the system evolves into the state of thermal equilibrium. This state is approached in a steplike process and when established it manifests itself in distinguishable ways. The atoms in states ${m}_{F}=+1$ and ${m}_{F}=\ensuremath{-}1$ start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the system first enters the stage where the ${m}_{F}=+1$ and ${m}_{F}=\ensuremath{-}1$ spinor condensate components periodically lose and recover their mutual coherence whereas their thermal counterparts get completely dephased. For stronger spin changing collisions the system enters the regime where also the strong coherence between other components is built up.

DOI
10.1103/physreva.76.013616

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We consider a spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms in its F=1F=1F=1 hyperfine state at finite temperatures. Putting initially all atoms in mF=0{m}_{F}=0mF​=0 component we find that the system evolves into the state of thermal equilibrium. This state is approached in a steplike process and when established it manifests itself in distinguishable ways. The atoms in states mF=+1{m}_{F}=+1mF​=+1 and mF=\ensuremath−1{m}_{F}=\ensuremath{-}1mF​=\ensuremath−1 start to rotate in opposite directions breaking the chiral symmetry and showing highly regular spin textures. Also the coherence properties of the system changes dramatically. Depending on the strength of spin-changing collisions the system first enters the stage where the mF=+1{m}_{F}=+1mF​=+1 and mF=\ensuremath−1{m}_{F}=\ensuremath{-}1mF​=\ensuremath−1 spinor condensate components periodically lose and recover their mutual coherence whereas their thermal counterparts get completely dephased. For stronger spin changing collisions the system enters the regime where also the strong coherence between other components is built up.
We consider a spinor condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms in the F=1F=1F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in the mF=0{m}_{F}=0mF​=0 component, we find that the system evolves toward a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin-mixing contact potential. Our results show that because of a dynamical separation of magnetic components, the spin-mixing dynamics in the 87Rb^{87}\mathrm{Rb}87Rb condensate is governed by the dipolar interaction which plays no role in a single-component rubidium system in a magnetic trap.
We experimentally investigate and analyze the rich dynamics in F=2F=2F=2 spinor Bose-Einstein condensates of 87Rb^{87}\mathrm{R}\mathrm{b}87Rb. An interplay between mean-field driven spin dynamics and hyperfine-changing losses in addition to interactions with the thermal component is observed. In particular, we measure conversion rates in the range of ${10}^{\ensuremath{-}12}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for spin-changing collisions within the F=2F=2F=2 manifold and spin-dependent loss rates in the range of ${10}^{\ensuremath{-}13}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for hyperfine-changing collisions. We observe polar behavior in the F=2F=2F=2 ground state of 87Rb^{87}\mathrm{R}\mathrm{b}87Rb, while we find the F=1F=1F=1 ground state to be ferromagnetic. We further see a magnetization for condensates prepared with nonzero total spin.
We discuss the static and dynamic magnetic properties of cold quantum gas systems. In particular, we investigate and analyze the ground state properties and dynamics of F = 2 spinor Bose-Einstein condensates of 87Rb. The rich physics of these systems is governed by an interplay between mean-field-driven spin dynamics and hyperfine-changing losses in addition to interactions with atoms in the thermal cloud. We find conversion rates on the order of 10-12 cm3 s-1 for spin-changing collisions within the F = 2 manifold and spin-dependent loss rates on the order of 10-13 cm3 s-1 for hyperfine-changing collisions. Our data leads to the conclusion that the F = 2 ground state of 87Rb is polar, while we measure the F = 1 ground state to be ferromagnetic. As remarkable features in the spin dynamics we observe spinor oscillations and a delayed formation of new mF-condensate components.
In this thesis, we study theoretically and in experimentally the properties of spin-1 Bose-Einstein condensates with antiferromagnetic interactions realized in the ultra-cold sodium gases confined in optical dipole traps. We present in detail how to realize, diagnose and control the spinor Bose-Einstein condensates in our experiment. In order to describe the condensate, a mean-field theory is first adopted. This theory predicts a phase transition when changing the magnetic field BBB. The predictions of the mean-field theory agree very well with most of our experimental results, including the values of the critical magnetic field BcB_cBc​, asymptotic values of n0n_0n0​ (relative atom number in mF=0m_F=0mF​=0 state) at large BBB and the phase diagram of n0n_0n0​. However, for small magnetization and small magnetic fields, we find abnormally large fluctuations (super-Poissonian) of n0n_0n0​. In order to describe these large fluctuations, we develop a full quantum statistical description for the spinor condensate at finite temperature. To describe uncondensed thermal atoms (also present in the same trap), we use the ``semi-ideal" Hartree-Fock approximation to deal with the interactions between the condensate atoms and the thermal ones. The experimental results lead us to introduce two kinds of temperatures, the ``spin temperature" TsT_sTs​ and the ``kinetic temperature" TkT_kTk​ with Ts≪TkT_s\ll T_kTs​≪Tk​, characterizing respectively the fluctuaitons of the condensate spin and the thermal gas. We conclude that the system is reaching a quasi-equilibrium states, where different degrees of freedom reach equilibrium by separate mechanisms but where the mutual thermalization does not occur over the lifetime of the cloud.
We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F=1F=1F=1 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.