Ferromagnetism in spinor bosons Ground state of spinor Bose gases Effective interactions between F=l atoms Yaya a y+vvF。Fvv 2 o Polar state 23Na C2<0 Ferromagnetic state 8/Rb Ho, Phys. Rev Lett. 81, 742(1998) Ohmi and Machida, J. Phys. Soc. pn 67, 1822(1998)
• Ground state of spinor Bose gases Effective interactions between F=1 atoms Ho, Phys. Rev. Lett. 81, 742 (1998) Ohmi and Machida, J. Phys. Soc. Jpn 67, 1822 (1998) C2>0 Polar state 23Na C2<0 Ferromagnetic state 87Rb Ferromagnetism in spinor bosons
Ferromagnetism in spinor bosons Mechanism for generating ferromagnetic couplings Spin- flip scattering Super-exchange process Magnetic dipolar interaction Burke and Boh, Phys. Rev. A 59, 1303(1999) Yang and Li, Inter: J. Mod. Phys, B 17, 1027 (2003) Gu,Phys.Re"A68,025601(2003)
• Mechanism for generating ferromagnetic couplings Spin-flip scattering Super-exchange process Magnetic dipolar interaction Burke and Boh., Phys. Rev. A 59, 1303 (1999) Yang and Li, Inter. J. Mod. Phys, B 17, 1027 (2003) Gu, Phys. Rev. A 68, 025601 (2003) Ferromagnetism in spinor bosons
Ferromagnetism in spinor bosons FM phase transition induced by FM couplings TF BEC: intrinsic phase transition in bosons Competing of Two energy scale TE&t F C FC for large I <T for small l Is that true?
• FM phase transition induced by FM couplings TF • BEC: intrinsic phase transition in bosons TC • Competing of Two energy scale TF & TC TF > TC for large I TF < TC for small I Is that true? Ferromagnetism in spinor bosons
Curie point of ferromagnetic bose gas Gu and Klemm, Phys. Rev. A 68, 031604(R)(2003) Gu, Bongs and Sengstock, Phys. Rev. A70, 063609(2004)
Curie point of ferromagnetic Bose gas Gu and Klemm, Phys. Rev. A 68, 031604(R) (2003) Gu, Bongs and Sengstock, Phys. Rev. A 70, 063609 (2004)
Phase transitions hamiltonian H=∑4414-l∫rm,s (ko) The first term describes a free Bose gas, where ax=hk/(2m) The second term describes fm couplings Mean-field approximation L drS(r)s(r) 2∫s8-2Ss)+26s =-MPdrSz+-VM where M=s)is the FM order parameter
Phase transitions • Hamiltonian The first term describes a free Bose gas, where The second term describes FM couplings • Mean-field approximation S j