Sodium Bose-Einstein condensates in an optical lattice

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.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.

Physical Review AJan 24, 20129 citations

Bose-Einstein Condensates in Optical Lattices: Experiments

O. Morsch

Springer eBooksDec 29, 20070 citations

Sodium Bose-Einstein condensates in an optical lattice

K. Xu, Yingmei Liu, J. R. Abo-Shaeer +6 more

The phase transition from a superfluid to a Mott insulator has been observed in a $^{23}\mathrm{Na}$ 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.The phase transition from a superfluid to a Mott insulator has been observed in a $^{23}\mathrm{Na}$ 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.

arXiv:cond-mat/0507288Physical Review AOct 10, 200557 citations

Superfluid to Mott-insulator transition in a one-dimensional optical lattice

Wenliang Liu, Ningxuan Zheng, Jun Jian +9 more

Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.Bose–Einstein condensates (BEC) of sodium atoms are transferred into one-dimensional (1D) optical lattice potentials, formed by two laser beams with a wavelength of 1064 nm, in a shallow optical trap. The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth. A qualitative change in behavior of the BEC is observed at a lattice depth of ∼ 13.7 E r, where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.

Chinese Physics BApr 8, 20223 citations

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.

The phase transition from a superfluid to a Mott insulator has been observed in a

^{23}\mathrm{Na}

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.