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Quartetting and pairing instabilities in 1D spin 3/2 fermionic systems

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.

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Quartetting and pairing instabilities in 1D spin 3/2 fermionic systems

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  1. 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)

  2. 132Cs, 9Be, 135Ba, 137Ba, 201Hg. 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.

  3. Quartetting order in spin 3/2 systems • 4-fermion counterpart of Cooper pairing. SU(4) singlet: 4-body maximally entangled states • 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).

  4. Generic spin 3/2 Hamiltonian in the continuum model • The s-wave scattering interactions and spin SU(2) symmetry. • Pauli’s exclusion principle: only Ftot=0, 2 • are allowed; Ftot=1, 3 are forbidden. singlet: quintet:

  5. SU(4) C: Singlet pairing B: Quartetting SU(4) Phase diagram: bosonization+RG • Gapless charge sector. • Spin gap phases B and C: pairing v.s.quartetting. A: Luttinger liquid • Ising transition between B and C. • Singlet pairing in purely repulsive regime.

  6. Phase B: the quartetting phase • Quartetting superfluidity v.s. CDW of quartets (2kf-CDW). Kc: the Luttinger parameter in the charge channel.

  7. Phase C: the singlet pairing phase • Singlet pairing superfluidity v.s CDW of pairs (4kf-CDW). • Existence of singlet Cooper pair superfluidity at 1>Kc>1/2.

  8. overall phase; relative phase. Competition between quartetting and pairing phases • Two-component superfluidity • The relative phase channel determines the transition. • the relative phase is locked: pairing order; • the dual field is locked: quartetting order. Ising transition: two Majorana fermions with masses: A. J. Leggett, Prog, Theo. Phys. 36, 901(1966); H. J. Schulz, PRB 53, R2959 (1996).

  9. 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.

  10. 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.

  11. 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.

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