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Physical Review A

Collisional loss rates of sodium Bose-Einstein condensates in the F=2 state in a one-dimensional optical lattice

Hiromitsu Imai, Tomoya Akatsuka, Takashi Ode, Atsuo Morinaga

Published Jan 24, 2012• 9 citations
Publisher

Abstract

We have created stable sodium Bose-Einstein condensates in the $|F=1,{m}_{F}=\ensuremath{-}1\ensuremath{\rangle}$ state in a one-dimensional optical lattice with a lifetime of 102 $\ifmmode\pm\else\textpm\fi{}$ 42 s, which is limited by the photon scattering rate. The condensates were transferred to the upper hyperfine $F$ $=$ 2 state and the one-body and two-body loss rates were examined. Condensates in the $|2,1\ensuremath{\rangle}$ state were transferred in the optical lattice from the initially prepared condensates using a two-photon microwave--radio-frequency pulse. The two-body loss coefficients in the $|2,0\ensuremath{\rangle}$ and $|2,1\ensuremath{\rangle}$ states were found to be (2.1 $\ifmmode\pm\else\textpm\fi{}$ 1.4) $\ifmmode\times\else\texttimes\fi{}$ 10${}^{\ensuremath{-}12}$ and (7.7 $\ifmmode\pm\else\textpm\fi{}$ 1.0) $\ifmmode\times\else\texttimes\fi{}$ 10${}^{\ensuremath{-}13}$ cm${}^{3}$ s${}^{\ensuremath{-}1}$, respectively. The lifetime of the $|2,1\ensuremath{\rangle}$ state was 15 ms at the initial density of 5 $\ifmmode\times\else\texttimes\fi{}$ 10${}^{14}$ atoms/cm${}^{3}$. We constructed a Ramsey atom interferometer using BECs in the $|1,\ensuremath{-}1\ensuremath{\rangle}$, and $|2,1\ensuremath{\rangle}$ states with an interrogation time of 2 ms in the optical lattice.

DOI
10.1103/physreva.85.013633

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We have created stable sodium Bose-Einstein condensates in the ∣F=1,mF=\ensuremath−1\ensuremath⟩|F=1,{m}_{F}=\ensuremath{-}1\ensuremath{\rangle}∣F=1,mF​=\ensuremath−1\ensuremath⟩ state in a one-dimensional optical lattice with a lifetime of 102 \ifmmode±\else\textpm\fi\ifmmode\pm\else\textpm\fi{}\ifmmode±\else\textpm\fi 42 s, which is limited by the photon scattering rate. The condensates were transferred to the upper hyperfine FFF === 2 state and the one-body and two-body loss rates were examined. Condensates in the ∣2,1\ensuremath⟩|2,1\ensuremath{\rangle}∣2,1\ensuremath⟩ state were transferred in the optical lattice from the initially prepared condensates using a two-photon microwave--radio-frequency pulse. The two-body loss coefficients in the ∣2,0\ensuremath⟩|2,0\ensuremath{\rangle}∣2,0\ensuremath⟩ and ∣2,1\ensuremath⟩|2,1\ensuremath{\rangle}∣2,1\ensuremath⟩ states were found to be (2.1 \ifmmode±\else\textpm\fi\ifmmode\pm\else\textpm\fi{}\ifmmode±\else\textpm\fi 1.4) \ifmmode×\else\texttimes\fi\ifmmode\times\else\texttimes\fi{}\ifmmode×\else\texttimes\fi 10\ensuremath−12{}^{\ensuremath{-}12}\ensuremath−12 and (7.7 \ifmmode±\else\textpm\fi\ifmmode\pm\else\textpm\fi{}\ifmmode±\else\textpm\fi 1.0) \ifmmode×\else\texttimes\fi\ifmmode\times\else\texttimes\fi{}\ifmmode×\else\texttimes\fi 10\ensuremath−13{}^{\ensuremath{-}13}\ensuremath−13 cm3{}^{3}3 s\ensuremath−1{}^{\ensuremath{-}1}\ensuremath−1, respectively. The lifetime of the ∣2,1\ensuremath⟩|2,1\ensuremath{\rangle}∣2,1\ensuremath⟩ state was 15 ms at the initial density of 5 \ifmmode×\else\texttimes\fi\ifmmode\times\else\texttimes\fi{}\ifmmode×\else\texttimes\fi 1014{}^{14}14 atoms/cm3{}^{3}3. We constructed a Ramsey atom interferometer using BECs in the ∣1,\ensuremath−1\ensuremath⟩|1,\ensuremath{-}1\ensuremath{\rangle}∣1,\ensuremath−1\ensuremath⟩, and ∣2,1\ensuremath⟩|2,1\ensuremath{\rangle}∣2,1\ensuremath⟩ states with an interrogation time of 2 ms in the optical lattice.
We have investigated the properties of Bose-Einstein condensates of sodium atoms in the upper hyperfine ground state. Condensates in the high-field seeking $|F=2,{m}_{F}=\ensuremath{-}2⟩$ state were created in a large volume optical trap from initially prepared $|F=1,{m}_{F}=\ensuremath{-}1⟩$ condensates using a microwave transition at 1.77 GHz. We found condensates in the stretched state $|F=2,{m}_{F}=\ensuremath{-}2⟩$ to be stable for several seconds at densities in the range of 1014 atoms/cm3{10}^{14}\text{ }\mathrm{\text{atoms}}/{\mathrm{c}\mathrm{m}}^{3}1014 atoms/cm3. In addition, we studied the clock transition $|F=1,{m}_{F}=0⟩\ensuremath{\rightarrow}|F=2,{m}_{F}=0⟩$ in a sodium Bose-Einstein condensate and determined a density-dependent frequency shift of $(2.44\ifmmode\pm\else\textpm\fi{}0.25\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\mathrm{H}\mathrm{z}\text{ }{\mathrm{c}\mathrm{m}}^{3}$.
Bose-Einstein condensates of sodium atoms have been confined in an optical dipole trap using a single focused infrared laser beam. This eliminates the restrictions of magnetic traps for further studies of atom lasers and Bose-Einstein condensates. More than $5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ condensed atoms were transferred into the optical trap. Densities of up to $3\ifmmode\times\else\texttimes\fi{}{10}^{15}{\mathrm{cm}}^{\ensuremath{-}3}$ of Bose condensed atoms were obtained, allowing for a measurement of the three-body loss rate constant for sodium condensates as ${K}_{3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}{\mathrm{cm}}^{6}{\mathrm{s}}^{\ensuremath{-}1}$. At lower densities, the observed 1/e1/e1/e lifetime was longer than 10 s. Simultaneous confinement of Bose-Einstein condensates in several hyperfine states was demonstrated.
We load a Bose-Einstein condensate into a one-dimensional (1D) optical lattice altered through the use of radio-frequency (rf) dressing. The rf resonantly couples the three levels of the 87Rb^{87}\mathrm{Rb}87Rb F=1F=1F=1 manifold and combines with a spin-dependent ``bare'' optical lattice to result in adiabatic potentials of variable shape, depth, and spatial frequency content. We choose dressing parameters such that the altered lattice is stable over lifetimes exceeding tens of ms at higher depths than in previous work. We observe significant differences between the BEC momentum distributions of the dressed lattice as compared to the bare lattice, and find general agreement with a 1D band-structure calculation informed by the dressing parameters. Previous work using such lattices was limited by very shallow dressed lattices and strong Landau-Zener tunneling loss between adiabatic potentials, equivalent to failure of the adiabatic criterion. In this work we operate with significantly stronger rf coupling (increasing the avoided-crossing gap between adiabatic potentials), observing dressed lifetimes of interest for optical lattice-based analog solid-state physics.
Motivated by recent experimental observations [Parker, Hua, and Chin, Nat. Phys. 9, 769 (2013)], we analyze the stability of a Bose-Einstein condensate (BEC) in a one-dimensional lattice subjected to periodic shaking. In such a system there is no thermodynamic ground state, but there may be a long-lived steady state, described as an eigenstate of a ``Floquet Hamiltonian.'' We calculate how scattering processes lead to a decay of the Floquet state. We map out the phase diagram of the system and find regions where the BEC is stable and regions where the BEC is unstable against atomic collisions. We show that Parker et al. performed their experiment in the stable region, which accounts for the long lifetime of the condensate $(\ensuremath{\sim}1\mathrm{s})$. We also estimate the scattering rate of the bosons in the region where the BEC is unstable.
We report on the production of Bose–Einstein condensates of sodium atoms in the hyperfine state | F = 2 , m F = 2 ⟩ in a crossed optical dipole trap using D 2 gray molasses. We use the gray molasses sub-Doppler cooling technique to obtain an atomic sample of 3 × 10 8 at 56 µK. After the radio frequency (RF) evaporation cooling in an optically plugged magnetic trap, we transfer the atoms sample of 2.5 × 10 6 at 5.7 µK to a crossed optical dipole trap where a pure condensate with an atom number of 2 × 10 5 and lifetime of 6.3 s is obtained by further evaporation. We compare the cooling process of sodium atoms in the | 2 , 2 ⟩ and the | 1 , 1 ⟩ states by evaporation in the optical trap, and also observe the different three-body loss rates by the lifetime measurement.
The phase transition from a superfluid to a Mott insulator has been observed in a 23Na^{23}\mathrm{Na}23Na Bose-Einstein condensate. A dye laser detuned $\ensuremath{\approx}5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ red of the Na $3^{2}S\ensuremath{\rightarrow}3^{2}P_{1∕2}$ transition was used to form the three-dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the time scale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the ${\mathrm{Na}}_{2}\phantom{\rule{0.3em}{0ex}}(1)^{3}\ensuremath{\Sigma}_{g}^{+}$ state.