Detecting atoms in a lattice with two photon raman transitions

1. Detecting atoms in a lattice with two photon raman transitions Inés de Vega, Diego Porras, Ignacio Cirac Max Planck Institute of Quantum Optics Garching (Germany)

2. Summary 3) Conclusions • Motivation: •  what is an atom lattice? •  why measuring atoms in a lattice? • Measuring atoms in a lattice: •  Time of flight experiments •  Our method

3. Richard Feynman, December 29th 1959 at the annual meeting of the American Physical Society at the California Institute of Technology (Caltech) “I am not afraid to consider the final question as to whether, ultimately---in the great future---we can arrange the atoms the way we want; the very atoms, all the way down! “

4. Richard Feynman, December 29th 1959 at the annual meeting of the American Physical Society at the California Institute of Technology (Caltech) What would the properties of materials be if we could really arrange the atoms the way we want them? […] I can't see exactly what would happen, but I can hardly doubt that when we have some control of the arrangement of things on a small scale we will get an enormously greater range of possible properties that substances can have, and of different things that we can do.

5. What is an optical lattice A standing wave in the space gives rise to a conservative force over the atoms V0 Optical potential

6. >0 Space dependent Stark shift: when Laser blue detuned >0 atoms go to the Potential minima What is an optical lattice A standing wave in the space gives rise to a conservative force over the atoms V0 Optical potential

7. Wannier functions localiced in each lattice site. What is an optical lattice Due to the periodic potential, the discrete levels in each well form Bloch bands We consider the atoms placed in the lowest Bloch band Described with creation fuction of a particle of spin α: Creation operator with bosonic (fermionic) conmutation (anticonmutation) relations

8. Gives rise to a kinetic term, with magnitude “t” Gives rise to a repulsive term, with magnitude ~ U. Atom Hamiltonian in second quantization

9. Atom Hamiltonian in second quantization Gives rise to a kinetic term, with magnitude “t” Gives rise to a repulsive term, with magnitude ~U. Spin-spin interactions (example, for atoms with J=1)

10. Atom Hamiltonian in second quantization Gives rise to a kinetic term, with magnitude “t” Gives rise to a repulsive term, with magnitude ~U. Variating parameters t and U, this hamiltonian undergoes Quantum Phase Transitions

11. t>>U :Shallow lattice (large kinetic energy), gives rise to a superfluid state T<<U :Deep lattice, strong interactions, gives rise to a Mott state. Atoms are localized in each site. • Mott state very important: • To simulate magnetic Hamiltonians (spin-spin interactions) • As a quantum register (where highly entangled states, cluster states, can be created) An optical lattice is controllable We can change the standing wave parameters: V0 and λ We can apply an external magnetic field to increase scattering length We can use state dependent potentials V0 λ B

12. Time of flight experiments Off-resonant Ramman scattering of light and more... Why measuring atoms in a lattice A lattice is a nice quantum simulator, and may be a nice implementation of a quantum computer but... ...how can we read out the information from it?

13. Time of flight • S. Fölling et al. Nature (2005) • T. Rom et al. Nature (2006)

14. Off resonance Raman scattering x Emited photon se z Laser ge y

15. Interaction between atoms and light x Emited photon se z Laser ge y Adiabatically eliminating the e> level Duan, Cirac, Zoller (2002)

16. Z-polarized laser with spin J atoms z Emited photon x Laser y J’ We detect atoms with any spin J J

17. Z-polarized laser with spin J atoms

18. Photon counting type of measure Detected correlations of photons Correlations of atom variables in momentum space x k z y

19. (2) This is our main assumption. We check the relative error between (1) and (2) with respect to the number of photons that are emitted. And if we consider T<<1/Γ we detect atom correlations in the ground states (1)

20. Checking the assumption T<<1/Γ Through the Quantum Regression Theorem this is the evolution that correlations have Even if there were some lattice sites without an atom, this function for large is approximately a delta.

21. Nyy () number photons comming from ground state Checking the assumption T<<1/Γ Number of y-polarized photons in θ for T=0.0025 This is the type of things we measure Nyy () number of photons detected

22. J/B=0.001 J/B=-0.05 J/B=-0.5 Checking the assumption T<<1/Γ

23. …we can detect any correlation!! Measuring conbinations of quadratures…

24. -More precission with respect to time of flight: Signal to noise ration in Time of flight ~ in Raman scattering~ Conclusions -Not destructive: one can perform measures of the state in the middle of an experiment and then continue -More freedom to compute different correlations and hence to detect more complex phases -3D information

25. Thank You!!