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Clock Shifts

Clock Shifts. Sourish Basu Stefan Baur Theja De Silva (Binghampton) Dan Goldbaum Kaden Hazzard. Erich Mueller Cornell University. Outline. What we want to measure A tool: Doppler free spectroscopy Capabilities Challenges Probing fermionic superfluidity near Feshbach resonance.

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Clock Shifts

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  1. Clock Shifts Sourish Basu Stefan Baur Theja De Silva (Binghampton) Dan Goldbaum Kaden Hazzard Erich Mueller Cornell University

  2. Outline • What we want to measure • A tool: Doppler free spectroscopy • Capabilities • Challenges • Probing fermionic superfluidity near Feshbach resonance

  3. Take-Home Message • RF/Microwave spectroscopy does tell you details of the many-body state • Weak coupling -- density • Strong coupling -- complicated by final-state effects • Bimodal RF spectra in trapped Fermi gases not directly connected to pairing (trap effect) Ketterle Group: Science 316, 867-870 (2007) “Pairing without Superfluidity: The Ground State of an Imbalanced Fermi Mixture”

  4. Context: Upcoming Cold Atom Physics Profound increase in complexity Ex: modeling condensed matter systems Big Question: How to probe?

  5. What we want to know • Is the system ordered? (crystaline, magnetic, superconducting, topological order) • What are the elementary excitations? • How are they related to the elementary particles?

  6. Atomic Spectroscopy I(w) [transfer rate] E w w w0 Narrow spectral line in vacuum: in principle sensitive to details of many-body state Measured hyperfine linewidth ~ 2 Hz [PRL 63, 612, 1989] Interaction energy in Fermi gas experiments: 100 kHz Possibly very powerful

  7. Sharp Spectral lines Hyperfine spectrum: nuclear spin flips (cf. NMR) “Forbidden” optical transitions: Hydrogen 1S-2S Couple weakly to environment: influenced by interactions? Does internal structure of atom depend on many-body state? (weak coupling) (weak coupling) Line shift proportional to density [Clock Shift]

  8. Center of cloud Application -- Detecting BEC BEC Density bump Spectrum gives histogram of density Solid: condensedOpen: non-condensed Exp: (Kleppner group) PRL 81, 3811 (1998) Theory: Killian, PRA 61, 033611 (2000) [OSU connection -- Oktel]

  9. Why is density histogram useful? Optical absorption: column density obscures interesting features -- ex. Mott Plateaus -- digression

  10. Bose-Mott physics Optical lattice: Kinetic energy from hopping dominates Weak interactions: atoms delocalize -- superfluid -- Poisson number distribution Energy cost of creating particle-hole pair exceeds hopping Strong interactions: suppress hopping -- insulator

  11. Phase Diagram (lines of fixed density) Incommensurate: “extra” particles delocalize

  12. Discontinuities Cusps Wedding Cakes Trap: spatially dependent m Hard to see terraces in column densities

  13. RF Spectroscopy Exp: Ketterle group [Science, 313, 649 (2006)] Thy: Hazzard and Mueller [arXiv:0708.3657] 2 1 3 4 5 Spectral shift proportional to density Discrete bumps: density plateaus

  14. Sensitivity Significant peaks, even in superfluid Q: could this be used to detect other corrugations? FFLO? CDW?

  15. Spatially resolved Column densities

  16. So simple? Spectrum knows about more than density! Jin group [Nature 424, 47 (2003)] Ex: RF dissociation - Potassium Molecules (Thermal, non-superfluid fermionic gas) Free atoms Initially weakly bound pairs in (and free atoms in these states) pairs Drive mf=-5/2 to mf=-7/2

  17. Transfer n [kHz] Related work Ex: RF dissociation - Lithium Molecules B [Gauss] All 1+2 atoms in molecular bound state (note reversal of sign of shift) Grimm group [Science 305, 1128 (2004)]Background: Ketterle group [Science 300, 1723 (2003)

  18. What is probed by RF spectroscopy? Single Component Bose system: Excite with perturbation Final state has Hamiltonian Fermi’s Golden Rule (pseudospin susceptibility)

  19. Simple Limits I Final state does not interact (V(ab)=0) • analogous to momentum resolved tunneling (or in some limits photoemission) • probe all single particle excitations Initial: ground state Final: single a-quasihole of momentum k single free b-atom Example: BCS state -- darker = larger spectral density w w k k

  20. Simple Limits II Final state interacts same as initial (V(ab)=V(bb)), and dispersion is same • Coherent spin rotation Formally can see from X acts as ladder operator

  21. General Case -- Sum Rule Mehmet O. Oktel, Thomas C. Killian, Daniel Kleppner, L. S. Levitov, Phys. Rev. A 65, 033617 (2002) Mean clock shift Ex: Born approximation point interaction

  22. Problem Not a low energy observable!!!!!! -- dif potentials = dif results Tails dominate sum rule (unmeasurable) Pethick and Stoof, PRA 64, 013618 (2001)

  23. Summary of spectroscopy • Weak coupling • peak mostly shifted (proportional to density) • long tails (probably unobservable) • final interaction = initial • Peak sharp and unshifted • General • No simple universal picture • sum rules are ambiguous • Important for experiments on strongly interacting fermionic Lithium atoms

  24. Lithium near Feshbach resonance Innsbruck expt grp +NIST theory grp, PRL 94, 103201 (2005) Strongly interacting superfluid BCS-BEC crossover -- Randeria

  25. Outline (what is RF lineshape -- and what does it tell us) • Homogeneous lineshapes within BCS model of superfluid • Crude model for trapped gas • Highly polarized limit (normal state) • Demonstrates universality of line shape

  26. Variational Model Idea: include all excitations consisting of single quasiparticles quasiholes “coherent contribution” -- should capture low energy structure a-b pairs -- excite from b to c Neglects multi-quasiparticle intermediate states [Exact if (final int)=(initial int) or if (final it)=0]

  27. Result Bound-Free Bound-Bound Many-body

  28. Typical spectra 1-2 paired drive 2-3 1-2 paired drive 1-3 (most spectral weight is in delta function)

  29. Perali, Pieri, StrinatiarXiv:0709.0817 Experiment Ketterle group: Phys. Rev. Lett. 99, 090403 (2007) Sant-Feliu update: has seen “bound-bound”

  30. Summary: Homogeneous Lineshape • Final state interactions crucial: • Is there a bound state? • Distorted spectrum if resonance in continuum • Sets scale Next: trap

  31. Inhomogeneous line shapes Most experiments show trap averaged lineshape Grimm group, Science 305, 1128 (2004) Bimodality:due to trap

  32. Where spectral weight comes from Massignan, Bruun, and Stoof, ArXiv:0709.3158 Edge of cloud Calculation in normal state: Ndown<Nup More particles at center

  33. Highly polarized limit: only one down-spin particle Generic properties Assumption: local clock shift = (homogeneous spectrum peaks there) High temp: [Virial expansion: Ho and Mueller, PRL 92, 160404 (2004)] High density: Different a

  34. Bimodality nup ndn r Center of trap: highest down-spin density -- gives broad peak Edge of trap: low density, but a lot of volume -- All contribute at same detuning -- Gives power law singularity

  35. Quantitative Nozieres and Schmidt-Rink (no adjustable params)

  36. Calculating Free Energy (Only if asked) If ndown is small, q is only function of mup and x=w-mup-mdn. Arctan vanishes for negative x [so w is large]

  37. Summary: Trap • Trap leads to bimodal spectrum (model independent) • Simple model using NSR energy: energy scales work, temp scales seem a bit off • Final state interactions: mostly scale spectrum Decreasing T/TF Decreasing a/l

  38. Summary -- Spectroscopy • Powerful probe of local properties • Density: SF-Mott • Simple when interactions are weak • Open Q’s when interactions are strong • Bimodal RF spectra are not directly related to pairing (implicit in works of Torma and Levin) Fin

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