Spin-dependent inelastic collisions in spin-2 Bose-Einstein - PowerPoint PPT Presentation

Grant-in Aid for Scientific Research on Priority Areas (Grant No. 450) from MEXT International Symposium on Physics of New Quantum Phases in Superclean Materials PSM 2010, Hamagin Hall “VIA MARE”, Yokohama March 11, 2010 Spin-dependent inelastic collisions in spin-2 Bose-Einstein condensates Department of physics, Gakushuin University Takuya Hirano

Scope of the presentation • Poster → Aural → broaden the scope Properties and dynamics of Bose-Einstein condensates with internal degrees of freedom Experimental achievement in Gakushuin University Present member: S. Tojo, T. Tanabe, Y. Taguchi, Y. Suzuki, M. Kurihara, Y. Masuyama Spin-dependent inelastic collisions in spin-2 Bose-Einstein condensates S. Tojo, T. Hayashi, T. Tanabe, T. Hirano, Experiment Y. Kawaguchi, H. Saito, M. Ueda Theory Phys. Rev. A 80, 042704 (2009). maybe technical, but fundamental knowledge to understand spinor BEC Theory

Research objectives: Why atomic BEC with internal degrees of freedom Internal degrees of freedom • Scalar BEC: spin state is fixed (magnetic trap) • Spinor BEC: spin degrees of freedom are librated (optical trap) F =1, 2 • hyperfine spin 87 Rb, 23 Na, 7 Li, 41 K F =2, 3 85 Rb unstable F =3, 4 133 Cs F =3 ( S =3, I =0) 52 Cr F =0 ( S =0, I =0) 4 He * , 40 Ca, 174 Yb, 176 Yb All spin states can be trapped in an optical trap Novel physics in qantum fluids with many internal degrees of freedom

Rb BEC with internal degrees of freedom m F high-field seeker low-field seeker 87 Rb F =2 -2 -1 0 +1 +2 +1 0 -1 F =1 ・ Magnetic sublevels can be coherently coupled, and their populations can be controlled. ・ Scattering lengths can be controlled by Feshbach Reaonance . ・ Phase separation of two-component BEC I would like to briefly report our experimental results on “Controlling phase-separation of binary Bose-Einstein condensates by mixed-spin-channel Feshbach resonance”

Experimental setup and spin-state manipulation Crossed Far-Off Resonant Trap (FORT) Energy level diagram of 87 Rb 5 deg. r (radial) (ground hyperfine states) g Zeeman splitting at B = 20 G z (axial) m F =+2 FORT +1 Beam B=20G (axial) F = 2 0 14.020 MHz λ : 850 nm -1 Δ=58 kHz 6.8 GHz 14.078 MHz coil for magnetic trap -2 4x10 5 atoms beam waist radius Initial state radial : 90 µ m (21Hz) -1 axial : 32 µ m (140Hz) F = 1 FORT Beam 0 (radial) Trap depth: ~ 1.0 µ K m F =+1

Spin-state manipulation Energy level diagram of 87 Rb at 20 G Time evolution and imaging m F +2 +1 0 -1 -2 F = 1 and 2 rf F = 2 Microwave 6.8GHz + rf 2.0 MHz Stern-Gerlach 2-photon transition TOF initial state method (SG) (magnetic dipole transition) 15ms for F =2 F = 1 Transmission m F 0 1 -1 0 +1 +2 +1 0 -1 -2 -1 0 +1 z |2,-1> 18ms for F =1 time-evolution g |1,+1> BECs BECs BECs or miscible immiscible? Mixture of binary BECs

Rb BEC with internal degrees of freedom m F high-field seeker low-field seeker 87 Rb F =2 -2 -1 0 +1 +2 +1 0 -1 F =1 ・ Magnetic sublevels can be coherently coupled, and their populations can be controlled. ・ Scattering lengths can be controlled by Feshbach Reaonance . ・ Phase separation of two-component BEC ・ Ground-state phase of 87 Rb BEC

Rb BEC with internal degrees of freedom m F high-field seeker low-field seeker 87 Rb F =2 -2 -1 0 +1 +2 +1 0 -1 F =1 C 2 ・ Ground-state phase of 87 Rb BEC New quantum π − phase!! 2 4 a a  = c 4 2 1 m 7 Cyclic π − + 2 4 7 a 10 a 3 a  = Ferro- c 0 2 4 2 m 7 magnetic 87 Rb C 1 Measured coefficients Antiferro- ( ) ( ) + 0.99 0.06 a π h ｱ 2 magnetic c 4 m B 1 ( ) ( ) − 0.53 ｱ 0.58 a π h 2 c 4 m B 2 Ciobanu, Yip, & Ho, PRA 61, 033607 (2000). Widera et al., New Journal of Physics 8 , 152 (2006) Koashi & Ueda, PRL84, 1066 (2000).

Diagnostics for the ground-state phase of a spin-2 Bose-Einstein condensate Saito and Ueda proposed a method magnetic field strength < 100mG to determine the ground-state phase of spin-2 87 Rb BEC at zero magnetic field using spin exchange dynamics. initial configuration m F = -2 & +2 If the F = 2 87 Rb BEC has anti- ferromagnetic properties, the mixture of m F = -2 and m F = +2 is 50 ～ 300 ms evolution one of the ground states at a zero magnetic field. [ M.Ueda & M.Koashi, PRA, 65, 063602 (2002)] m F = -2 & 0 & +2 m F = -2 & +2 If m F =0 atoms appears for the initial mixture of m F = -2 and m F = +2, then the ground state is cyclic. “ anti- “ cyclic ” ferromagnetic ” Hiroki Sato & Masahito Ueda, Phys.Rev.A 72, 053628 (2005).

Time-evolution of m F = -2 & m F = +2 BECs @ 45 mG magnetic field : 45mG Total remained atoms initial spin-state: m F =-2 & m F =+2 quadratic Stretched state Zeeman energy Trap time m F =+2 m F =-2 (ms) m F = -2 -1 -1 0 +1 0 +1 +2 m F = -2 +2 0 Two-body F =2 F =2 inelastic loss rate 8.5×10 -14 cm -3 /s 50 F =1 F =1 Relative population 100 Evolve to stable Strongly suggested as spin-states at ST et al ., Appl. Phys. “anti-ferromagnetic”... 200 almost zero B 93 , 403 (2008). magnetic field. 300 However, Several problems should be considered!! No other spin states appeared

Problem-1: Inelastic collisions of F =2 states initial configuration m F = -2 & +2 If “ cyclic ” If the inelastic collision rate of m F =0 state is much larger than that of another states, it may be difficult to observe m F =0 state when creation rate is small.

Two-body inelastic collision Hyperfine changing collision = = + F 2 , m 1 F = = + = = = = + F 2 , m 2 F 2, m 0 F 1 , m 1 F F F inelastic inelastic collision collision = = F 2, m 0 F = = − = = − F 2 , m 2 = = − F 1 , m 1 F 2 , m 1 F F F m F =0 m F =+1 m F =-1 m F =-2 +2 F =2 F =2 m F =-1 m F =+1 ∆ E ∆ E F =1 F =1 trap loss! trap loss! BEC: < 100 nk >> Recipient energy: ∆ E > 300mK Trap depth: ~ 1 µ K

Inelastic collision between different spin-states Dependence of remained atoms on population imbalance S. Tojo, e t al . APB 92, 403 (2008). Trap time: 280 ms m F =-2 m F =+2 0.07 Relative population of m F = +2 0.15 0.48 0.78 ; averaged data between 0.45 and 0.55 The total number of atoms at 0.92 balanced population is lowest.

Two-body inelastic collision rate for spin states 2-body loss for intra-spin state ( m F =0) dN 6/5 2/5 ω 15 m 踐 = − 7/5 K c N = c , 銷 2 2 2 π a ： averaged scattering lentgh 14 dt a 顏 h ω ： averaged trap frequency Söding et.al., Appl. Phys. B 69,257 (1999) 2-body loss for each inter-spin states ( m F =+2&-2) dN dN Balanced Imbalanced β = = − α K n N α β β α 2( , ) dt dt = n [ dvn ( ) r n ( )] / r N β α β Total 2-body loss at population imbalance dN = − ρ ρ 7/5 ( ) t ( ) t K c N α β 2 2 dt ρ ρ ( ) t ( ) t , ： relative population α β = = K 2 K 2 K (normalized) α β β α 2 2( , ) 2( , ) A pair with different spin states selectively decays .

Population-dependence of atom loss Calculations are in good agreement ; stretched-state initially prepared. with experiments!! ; averaged data between 0.45 and 0.55

Inelastic collision rates between spin-states By analogy with the scattering length in elastic Total spin of collision channel: collisions, two-body inelastic collisions are described  = 0, 2, 4 by two parameters, b 0 and b 2 , which correspond to channels with the total spins of 0 and 2, respectively. 2 1 + b b 2 0 7 5 3 3 7 b m = 0 7 b 2 1 2 1 7 b 7 b 2 2 m = +1 m = -1 1 2 + b b 2 0 7 5 4 4 7 b 7 b 0 0 2 2 6 6 7 b 7 b 2 2 m = +2 0 m = -2 0 4 2 + b b 2 0 7 5 stretched stretched state state

Atom number evolution : single component 0 m F = 0 & 0 Transmission 0 1 K 2(0,0) = (9.7±1.0)×10 -14 cm -3 /s -1 m F = -1 & -1 K 2(-1,-1) = (11.3±1.1)×10 -14 cm -3 /s -2 m F = -2 & -2 ( K 2(-2,-2) = (0.46±0.05)×10 -14 cm -3 /s ) ・ K 2(-2,-2) is very small Negligible inelastic collision for m F = -2, -2 (stretched state) ・ Difference between K 2(0,0) and K 2(-1,-1)

Two body inelastic collision : b 0 , b 2 • Relation between m 1 , m 2 and b 0 , b 2 2 2 + + + K ~ b 2, m m 2, m 2, m b 0, m m 2, m 2, m m m 1, 2 2 1 2 2 1 0 1 2 2 1 18 2 1 = − + 2,0 2,0 4,0 2,0 0,0 m F = 0 & 0 35 7 5 2 1 = + K b b 0,0 2 0 7 5 4 3 Evaluation of b 2 , b 0 m F = -1 & -1 − − = − − − 2, 1 2, 1 4, 2 2, 2 7 7 3 = K − 7 b − 1, 1 2 b 0 = (11.1±6.1)×10 -14 cm -3 /s − − = − 2, 2 2, 2 4, 4 m F = -2 & -2 = b 2 = (26.3±2.7)×10 -14 cm -3 /s K − 0 − 2, 2

Atom number evolution : m F = -2,0 and m F = -1,0 m F = -2 and 0 0 ms 50 ms 4 7 b 2 100 ms The possibility that the inelastic collision rate of m F =0 atoms is -2 0 much higher than that of another states is denied. miscible m F = -1 and 0 → Diagnostics by saito & ueda should work. 0 ms 50 ms 1 7 b 2 100 ms 0 -1 phase separation z axis

Atom number evolution : m F = +1,-2 and m F = -1,-2 m F = +1 and -2 0 ms 50 ms 6 7 b 100 ms 2 -2 +1 miscible m F = -1 and -2 0 ms 50 ms 0 100 ms -2 -1 phase separation z axis