Quantum Magnetism with 7 Li Ivana Dimitrova, Jesse Amato-Grill, Niklas Jepsen, William Lunden, Wolfgang Ketterle Magnetic Ordering via Superexchange Two-component Bose-Hubbard Hamiltonian H = - X ij ,σ =↑,↓ t σ a † iσ a jσ + h.c. + 1 2 X i,σ =↑,↓ U σ n iσ (n iσ - 1) + U ↑↓ X i n i↑ n i↓ Why use 7 Li? • Fast superexchange timescales t ≈ E R 4 π V 0 E R 3/4 e - √ V 0 /E R U ≈ (k L a s ) r 8 π V 0 E R 3/4 E R For fixed V 0 E R : t 2 U = t U 2 U ∝ a s k 3 L m ∼ 150 Hz in 1D (up to a logarithmic dependence on (k L a s )) • Tunable interactions through Feshbach resonances �������� 200 400 600 800 1000 1200 1400 B ( Gauss ) - 200 - 100 100 200 a S aa ab bb bc cc calculation by Lawrence Cheuk, MIT Simulation of the Heisenberg Hamiltonian 1 Mott Insulator with n =1 atoms/site The Hubbard model maps to S = 1 2 Heisenberg model 2 Mott Insulator with n =2 atoms/site The Hubbard models maps to S =1 Heisenberg model at certain values of U ↑↑ ,U ↑↓ ,U ↓↓ 3 For N atoms/site, the Hubbard model maps to a Heisenberg model for U ↑↑ = U ↓↓ Atlman, E. et al. New Journal of Physics 5, 113.1-113.19, (2003) Adiabatic State Preparation How to get to the ground state of these model Hamiltonians? • S N k B ln(2) for 1 atom/site • Cooling in the lattice • Entropy redistribution to other parts of the system or to other degrees of freedom • Start from a low entropy state and adiabatically sweep a parameter to connect to the desired state Phase Diagram S=1/2 H = X i,j J z s z i s z j - J xy (s x i s x j + s y i s y j ) - h z X i s z i J z = t 2 U ↑↓ - t 2 U ↑↑ - t 2 U ↓↓ , J xy = t 2 2U ↑↓ Duan, L et al. Phys. Rev. Lett. 91, 090402 (2003). Machine Overview ~ 2mK ~ 1.5mK ~ 60µK ~ 90µK ~ 3µK ~ 10s nK Davis, K. et al. Phys. Rev. Lett. 75, 3969-3973 (1995). Optical Lattice: observed the superfluid-Mott Insulator transition B (Gauss) 0 500 1000 E (MHz) -2000 -1500 -1000 -500 0 500 1000 1500 2000 d c b a Optical Lattice Stability • Spin-Flip Spectroscopy • Light Intensity Noise: Add-Noise Measurement and Nufern Modifications S(f 0 ) (dB/Hz) -120 -115 -110 -105 -100 -95 Gamma=1/tau (1/s) 0 10 20 30 40 50 60 mephisto 1-arm, 10ER nufern 1-arm, 10ER 0 100 200 300 400 500 600 700 800 900 1000 −160 −150 −140 −130 −120 −110 −100 −90 Frequency (kHz) Power Spectral Density (dB/Hz) NuAmp RIN Seed (Innolight Mephisto) Noisefloor Modified NuAmp (38A) NuAmp (33A) NuAmp (39A) • AOM Frequency Scans • Lifetimes for decreasing atom numbers