Universal trimers in spin-orbit coupled Fermi gases

Transcription

1 Universal trimers in spin-orbit coupled Fermi gases Wei Yi ( 易为 ) University of Science and Technology of China Few-body Conference, Beijing 14/04/2016 Wei Yi (USTC) Beijing, April / 20

2 Acknowledgement Institute of Physics, CAS Xiaoling Cui 崔晓玲 USTC Xingze Qiu 邱型泽 : Wei Yi (USTC) Beijing, April / 20

3 Outline Outline Synthetic spin-orbit coupling (SOC) in ultracold atoms Universal Borromean binding under Rashba SOC Stability of trimers against a spin-orbit coupled Fermi sea Summary Wei Yi (USTC) Beijing, April / 20

4 Synthetic Spin-Orbit Coupling Raman scheme for 1D SOC Atomic Gas Ω δ Raman lasers couple internal and external degrees of freedom An effective one-dimensional SOC with effective Zeeman fields H k = 2 2m ( k + k 0 xσ z ) 2 δ 2 σ z + Ω 2 σ x Y.-J. Lin, K. Jiménez-García, and I. B. Spielman, Nature 471, 83 (2011). Wei Yi (USTC) Beijing, April / 20

5 Synthetic Spin-Orbit Coupling Experiments on synthetic spin-orbit coupling in cold atoms NIST Shanxi University USTC, Purdue, WSU, IoP(CAS)... MIT Wei Yi (USTC) Beijing, April / 20

6 Synthetic Spin-Orbit Coupling Recent experimental realization of 2D SOC Huang et al., Nat. Phys. (2016) Wu et al., arxiv: Wei Yi (USTC) Beijing, April / 20

7 Synthetic Spin-Orbit Coupling Single-particle dispersion under SOC ε k ξ + ξ k Spin mixed Degenerate ground state in k-space Wei Yi (USTC) Beijing, April / 20

8 Synthetic Spin-Orbit Coupling Single-particle dispersion under SOC ε k ξ + ξ k x k Spin mixed Degenerate ground state in k-space Different types of SOC Wei Yi (USTC) Beijing, April / 20

9 Synthetic Spin-Orbit Coupling Single-particle dispersion under SOC ε k ξ + ξ k x k Spin mixed Degenerate ground state in k-space Different types of SOC Wei Yi (USTC) Beijing, April / 20

10 Synthetic Spin-Orbit Coupling Many-body physics under synthetic SOC Bose gas L L R R L L R R Hui Zhai, Rep. Prog. Phys. 78, (2015) Wei Yi (USTC) Beijing, April / 20

11 Synthetic Spin-Orbit Coupling Many-body physics under synthetic SOC Bose gas L L R R L L R R Fermi gas Hui Zhai, Rep. Prog. Phys. 78, (2015) Wei Yi (USTC) Beijing, April / 20

12 Synthetic Spin-Orbit Coupling Many-body physics under synthetic SOC Bose gas L L R R L L R R Fermi gas Hui Zhai, Rep. Prog. Phys. 78, (2015) Wei Yi (USTC) Beijing, April / 20

13 Synthetic Spin-Orbit Coupling Many-body physics under synthetic SOC Bose gas L L R R L L R R Fermi gas Hui Zhai, Rep. Prog. Phys. 78, (2015) WY, Wei Zhang, Xiaoling Cui, Sci. China: Phys. Mech. Astron. 58, (2015) Wei Yi (USTC) Beijing, April / 20

14 Synthetic Spin-Orbit Coupling SOC-enhanced three-body states Universal trimers with 3D SOC Zhe-Yu Shi, Xiaoling Cui, Hui Zhai, Phys. Rev. Lett. 112, (2014) Universal Borromean with Rashba SOC Xiaoling Cui, WY, Phys. Rev. X 4, (2014) Wei Yi (USTC) Beijing, April / 20

15 Universal Borromean binding under Rashba SOC Universal Borromean binding under Rashba SOC Two-body bound state Wei Yi (USTC) Beijing, April / 20

16 Universal Borromean binding under Rashba SOC Universal Borromean binding under Rashba SOC Two-body bound state Three-body bound state Wei Yi (USTC) Beijing, April / 20

17 Universal Borromean binding under Rashba SOC Bound-state solutions (2) ψ Q = ϕ kα b Q k a kα 0 α=± kα,qβ k (3) ψ Q = ϕ kα,qβ b Q k q a kα a qβ 0 Wei Yi (USTC) Beijing, April / 20

18 Universal Borromean binding under Rashba SOC Bound-state solutions Hamiltonian H = + k k,σ=, with φ k = arg(k x, k y ). (2) ψ Q = ϕ kα b Q k a kα 0 α=± kα,qβ k (3) ψ Q = ϕ kα,qβ b Q k q a kα a qβ 0 2 k 2 a k,σ 2m a k,σ + 2 λ ( ) k e iφ k a k, a m a k, + h.c. a 2 k 2 b k 2m b k + U b k,k,q k a k, b q k b q k a k,, Wei Yi (USTC) Beijing, April / 20

19 Universal Borromean binding under Rashba SOC Bound-state solutions In the Helicity basis (2) ψ Q = ϕ kα b Q k a kα 0 α=± kα,qβ k (3) ψ Q = ϕ kα,qβ b Q k q a kα a qβ 0 H = ξ k± a kα a kα + 2 k 2 b k 2m b k b kα=± k + U f kα,k βa kα b q k b q k a k β, kα,k β,q with ξ k± = 2 2m a ((k λ) 2 + k 2 z) 2 λ 2 2m a. Wei Yi (USTC) Beijing, April / 20

20 Universal Borromean binding under Rashba SOC Bound-state solutions (2) ψ Q = ϕ kα b Q k a kα 0 α=± kα,qβ k (3) ψ Q = ϕ kα,qβ b Q k q a kα a qβ 0 Bound-state wave functions (Q = 0, 40 K 40 K 6 Li) Wei Yi (USTC) Beijing, April / 20

21 Universal Borromean binding under Rashba SOC Bound-state solutions (2) ψ Q = ϕ kα b Q k a kα 0 α=± kα,qβ k (3) ψ Q = ϕ kα,qβ b Q k q a kα a qβ 0 Bound-state energies (Q = 0, 40 K 40 K 6 Li) Wei Yi (USTC) Beijing, April / 20

22 Universal Borromean binding under Rashba SOC Bound-state solutions (2) ψ Q = ϕ kα b Q k a kα 0 α=± kα,qβ k (3) ψ Q = ϕ kα,qβ b Q k q a kα a qβ 0 Bound-state energies (Q = 0, 40 K 40 K 6 Li) Universal Borromean Wei Yi (USTC) Beijing, April / 20

23 Universal Borromean binding under Rashba SOC Phase diagram Mass ratio η = m a /m b Borromean stable for η 0.39 Driven by symmetry of single-particle dispersion Wei Yi (USTC) Beijing, April / 20

24 Universal Borromean binding under Rashba SOC Phase diagram Mass ratio η = m a /m b Borromean stable for η 0.39 Driven by symmetry of single-particle dispersion Stability in a many-body system? Wei Yi (USTC) Beijing, April / 20

25 Stability against Fermi sea From few to many: Impurity in a spin-orbit coupled Fermi sea Effects of Fermi sea Pauli blocking: destabilizing bound states Particle-hole excitations: stabilizing bound states Wei Yi (USTC) Beijing, April / 20

26 Stability against Fermi sea From few to many: Impurity in a spin-orbit coupled Fermi sea Effects of Fermi sea Pauli blocking: destabilizing bound states Particle-hole excitations: stabilizing bound states Wei Yi (USTC) Beijing, April / 20

27 Stability against Fermi sea From few to many: Impurity in a spin-orbit coupled Fermi sea Effects of Fermi sea Pauli blocking: destabilizing bound states Particle-hole excitations: stabilizing bound states Focus on the two dimensional case for simplification Wei Yi (USTC) Beijing, April / 20

28 Stability against Fermi sea Bound states in 2D (equal mass case η = 1) (E + Eb)/Eth Dimer Trimer E b /E th Q/λ Q/λ E b /E th E b : energy of the two-body bound state without SOC Dimer always exists Universal trimer stable for E b < 1.66 Bound states with finite center-of-mass momentum Wei Yi (USTC) Beijing, April / 20

29 Stability against Fermi sea Bound-state wave functions (2) ψ 0 (3) ψ 0 (3) ψ Q -2-1 k x k y ϕk k y k x ϕk, k k y k x ϕk,2q k 2 Wei Yi (USTC) Beijing, April / 20

30 Stability against Fermi sea Bound-state wave functions (2) ψ 0 (3) ψ 0 (3) ψ Q -2-1 k x k y ϕk k y k x ϕk, k k y k x ϕk,2q k 2 Wei Yi (USTC) Beijing, April / 20

31 Stability against Fermi sea Effects of Pauli blocking: tuning the Fermi energy Ansatz for bare molecule/trimer (b) M Q = ϕ kα b Q k a kα FS kα (b) T Q = kα,qβ N 1 ϕ kα,qβ b Q k q a kα a qβ FS N 2 Wei Yi (USTC) Beijing, April / 20

32 Stability against Fermi sea Effects of Pauli blocking: tuning the Fermi energy Ansatz for bare molecule/trimer (b) M Q = ϕ kα b Q k a kα FS kα (b) T Q = kα,qβ N 1 ϕ kα,qβ b Q k q a kα a qβ FS N 2 η = 1 EF /Eth Normal M (b) T (b) E b /E th Pauli blocking the Rashba ring Wei Yi (USTC) Beijing, April / 20

33 Stability against Fermi sea Effects of Pauli blocking: tuning the Fermi energy Ansatz for bare molecule/trimer (b) M Q = ϕ kα b Q k a kα FS kα (b) T Q = kα,qβ N 1 ϕ kα,qβ b Q k q a kα a qβ FS N 2 η = EF /Eth Normal T (b) E b /E th M (b) E/Eth E b = 1.2E th M (b) T (b) E F /E th Pauli blocking the Rashba ring Wei Yi (USTC) Beijing, April / 20

34 Stability against Fermi sea Particle-hole fluctuations (polaron vs. dressed states) ( PQ = ϕ Q b Q + ) FS ϕ kα,qβ b q k a kα a qβ kα,qβ MQ = ϕ kα b Q k a kα FS kα + kα,k β,qγ T = + kα,qβ N 1 ϕ kα,k β,qγb Q k k +q a kα a k β a qγ FS N 1 ϕ kα,qβ b k q a kα a qβ FS kα,k β,k γ,qν N 2 ϕ kα,k β,k γ,qνb q k k k a kα a k β a k γ a qν FS N 2 Simplification for dressed trimer: Q = 0, q on Rashba ring N Wei Yi (USTC) Beijing, April / 20

35 Stability against Fermi sea Particle-hole fluctuations (polaron vs. dressed states) η = 1 EF /Eth T P(0) M(0) E b /E th Dressed trimer stabilized by particle-hole fluctuation Polaron wins eventually Wei Yi (USTC) Beijing, April / 20

36 Stability against Fermi sea Particle-hole fluctuations (polaron vs. dressed states) EF /Eth η = 1 T P(0) M(0) E/Eth E b 2.16E th M(0) P(0) T E b /E th E F /E th Dressed trimer stabilized by particle-hole fluctuation Polaron wins eventually Wei Yi (USTC) Beijing, April / 20

37 Stability against Fermi sea Phase diagram (E F 0.05E th ) 2 P(Q) η 1 T P(0) M(Q) M(0) E b /E th Dressed trimer stable for η > 0.38 Wei Yi (USTC) Beijing, April / 20

38 Summary Summary Effects of single-particle dispersion in few-body problems Universal Borromean in a spin-orbit coupled Fermi gas Similar universal trimers stable against a Fermi sea Quantum many-body states with exotic few-body correlations References: Xiaoling Cui, WY, Phys. Rev. X 4, (2014) Xingze Qiu, Xiaoling Cui, WY (in preparation) Wei Yi (USTC) Beijing, April / 20

39 Summary Summary Effects of single-particle dispersion in few-body problems Universal Borromean in a spin-orbit coupled Fermi gas Similar universal trimers stable against a Fermi sea Quantum many-body states with exotic few-body correlations References: Xiaoling Cui, WY, Phys. Rev. X 4, (2014) Xingze Qiu, Xiaoling Cui, WY (in preparation) THANK YOU!! Wei Yi (USTC) Beijing, April / 20