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Quartetting and pairing instabilities in 1D spin 3/2 fermionic systems Congjun Wu Kavli Institute for Theoretical Physics, UCSB Ref: C. Wu, Phys. Rev. Lett. 95, 266404 (2005). Many thanks to S. C. Zhang, E. Demler, Y. P. Wang, A. J. Leggett for helpful discussions. March meeting, 03/16/2006 (10:24) 1 Multiple-particle clustering (MPC) instability • Feshbach resonance: Cooper pairing superfluidity. • Beyond Cooper pairing: In fermionic systems with multiple components, Pauli’s exclusion principle allows MPC. • More two particles form bound states. baryon (3-quark); alpha particle (2p+2n); bi-exciton (2e+2h) • Driven by logic, it is natural to expect the MPC as a possible focus for the future research. • Spin-3/2 fermions have 4-componets. 132Cs, 9Be, 135Ba, 137Ba, 201Hg. 2 Quartetting order in spin 3/2 systems • 4-fermion counterpart of Cooper pairing. SU(4) singlet: k1 k2 4-body maximally entangled states Oqt 3/ 2 (r ) 1/ 2 (r ) 1/ 2 (r ) 3/ 2 (r ) k2 k1 • Difficulty: lack of a BCS type well-controlled mean field theory. trial wavefunction in 3D SU(4) symmetric model: A. S. Stepanenko and J. M. F Gunn, cond-mat/9901317. • Quartetting v.s singlet pairing in the 1D spin 3/2 systems with the general s-wave scattering interactions. C. Wu, Phys. Rev. Lett. 95, 266404 (2005). 3 Generic spin 3/2 Hamiltonian in the continuum model • The s-wave scattering interactions and spin SU(2) symmetry. 2 2 H dx ( x)( x ) ( x) 2m 3 / 2 , 1 / 2 g0 g ( x) ( x) 2 2 2 a ( x) a ( x) a 1~ 5 3 2 1 2 1 2 3 2 • Pauli’s exclusion principle: only Ftot=0, 2 are allowed; Ftot=1, 3 are forbidden. 3 3 singlet: ( x) 00 | 2 2 ; ( x) ( x) 3 3 quintet: a ( x) 2a | 2 2 ; ( x) ( x) 4 Phase diagram: bosonization+RG g2 SU(4) g0 g2 C: Singlet pairing A: Luttinger liquid g0 B: Quartetting SU(4) g 0 g2 • Gapless charge sector. • Spin gap phases B and C: pairing v.s.quartetting. • Ising transition between B and C. • Singlet pairing in purely repulsive regime. 5 Phase B: the quartetting phase • Quartetting superfluidity v.s. CDW of quartets (2kf-CDW). Oqt 3/ 2 1/ 2 1/ 2 3 / 2 e 2i N 2 k f R L ei c c wins at K c 2; wins at K c 2. Kc: the Luttinger parameter in the charge channel. d 2 /( 2k f ) 6 Phase C: the singlet pairing phase • Singlet pairing superfluidity v.s CDW of pairs (4kf-CDW). 3/ 2 3 / 2 1/ 2 1/ 2 ei O4 k f ,cdw R R L L e 2i c c wins at K c 1 ; 2 wins at K c 12 . d 2 /( 4k f ) • Existence of singlet Cooper pair superfluidity at 1>Kc>1/2. 7 Competition between quartetting and pairing phases • Two-component superfluidity 1 3/ 23 /2 1 2 ei c Oquar 12 ei 4 c (e i v + e i v cos2 v . 2 1/ 21/ 2 c overall phase; ); v relative phase. • The relative phase channel determines the transition. 1 1 H eff {( x v ) 2 ( xv ) 2 } (1 cos 2 v 2 cos 2 v ) 2 2a • 1 2 the relative phase is locked: pairing order; 1 2 the dual field is locked: quartetting order. Ising transition: two Majorana fermions with masses: 1 2 A. J. Leggett, Prog, Theo. Phys. 36, 901(1966); H. J. Schulz, PRB 53, R2959 (1996). 8 Experiment setup and detection • Array of 1D optical tubes. • RF spectroscopy to measure the excitation gap. pair breaking: quartet breaking: M. Greiner et. al., PRL, 2001. 9 Summary • Spin 3/2 cold atomic systems provide a good starting point to study the quartetting problem. • Both singlet Cooper pairing and quartetting orders are allowed in 1D systems. • The phase transition between them is Ising-like at 1D. 10 Hidden symmetry and novel phases in spin 3/2 systems • The exact Sp(4) or SO(5) symmetry without fine-tuning. • Quintet Cooper pairing: the Alice string and topological generation of quantum entanglement. • Strong quantum fluctuations in spin 3/2 magnetic systems. Ref: C. Wu, J. P. Hu, and S. C. Zhang, Phys. Rev. Lett. 91, 186402(2003); C. Wu, Phys. Rev. Lett. 95, 266404 (2005); S. Chen, C. Wu, S. C. Zhang and Y. P. Wang, Phys. Rev. B 72, 214428 (2005); C. Wu, J. P. Hu, and S. C. Zhang, cond-mat/0512602. 11