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Thesis Defense

Thesis Defense

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Thesis Defense

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  1. CREATING A BOSE-EINSTEIN CONDENSATE OF STABLE MOLECULES USING PHOTOASSOCIATION AND FESHBACH RESONANCES Pierre Phou Advisor: Dr. Andreas Metz Physics Department Temple University April 24, 2014 Thesis Defense:

  2. Pierre Phou Acknowledgments • Previous Advisor: Dr. Matt Mackie • Graduate Students • Mannix Shinn • Undergraduate Students • Heather Boyce • Ted Delikatny • Alex Dumont • Lev Katz • Temple University, N$F

  3. Pierre Phou Outline • Background • Basic Model • Photoassociation Many Body Rate Limit • Stable Molecules I: Adiabatic Following • Stable Molecules II: Pulsed Photoassociation with Strong Magnetoassociation • Stable Molecules III: Laser-Assisted Weak Magnetoassociation and Weak Photoassociation • Conclusions

  4. Pierre Phou Why Quantum Degenerate Molecules? • Macroscopic quantum behavior • Dipolar • Quantum computing/encryption • Long-range dipole-dipole interactions • Precise control over fine and hyperfine interactions • Tighter constraints • Precise spectroscopic determination of physical constants

  5. Pierre Phou Bose-Einstein Condensates • Particles occupy same quantum state • Exhibit quantum behavior at the macroscopic level • Ultracold (~100 nK) • Dilute (~1013-15 cm-3) • Creating ultracold molecules remains difficult • Photoassociation/Magnetoassociation provide a shortcut • Create a condensate of ultracold molecules from a condensate of already ultracold atoms Rev. Mod. Phys. 71, 1

  6. Pierre Phou Rev. Mod. Phys. 82, 1225 • Magnetoassociation: • Feshbach Resonance (FR) • One atom in a colliding pair spin flips in the presence of a magnetic field tuned near a FR to form a bound molecule • Photoassociation: • Two colliding atoms absorb a photon to form a bound molecule Rev. Mod. Phys. 78, 483

  7. Pierre Phou Objectives • Form stable quantum degenerate molecules: • Using photoassociation and magnetoassociation • Including realistic complications • Spontaneous decay • Dissociation to noncondensate levels • Elastic collisions • Under more restrictive conditions • Low intensity lasers • Narrow Feshbach resonances • Strong collisions

  8. Basic Model Bound molecule Two free atoms • Using Heisenberg Equation ( ) • Approximate operators as C-numbers Equations of motion: Pierre Phou

  9. Pierre Phou Numerical Solution In matrix notation: Ψ Non-linear Schrödinger equation: • To account for the non-linearity, we use a predictor-corrector algorithm: • First, a solution is predicted • Predicted solution is then used to calculate the corrected value Recursive Algorithm: With Predictor-Corrector:

  10. Pierre Phou Photoassociation Many Body Rate Limit • Correct length scale determines Rate Limit • Unitary Model: DeBroglie Wavelength (ΛD) • Many-Body Model: Inter-particle spacing ( ) • Additions to Basic Model • Heteronuclear molecule • Spontaneous decay • Dissociation to noncondensate levels

  11. Pierre Phou Model Molecule dissociates into pair of atoms with equal and opposite momentum Spontaneous decay Ωk Ω Ω δ0 δ0 δ Γ0 Γ0 Γ

  12. Pierre Phou Equations of Motion Heteronuclear Spontaneous decay Dissociation Analytic rate: Adiabatically eliminate dissociation and molecules Scattering length determines rate limit: complex

  13. Pierre Phou Results • Numeric Rate: τ = time for Pa to drop to 1/e • Rate Constant: • What determines fundamental limit? • Photoassociation: • Dissociation: • Eventually, dissociation to noncondensate levels wins CombinedShift • Unanticipated light shift • Difference between rollover and saturation Expected

  14. Pierre Phou Unitary Rate Limit • De Broglie wavelength sets rate • De Broglie wavelength given by Thomas-Fermi radius Unitary Many-body

  15. Pierre Phou Summary • Investigated many-body rate limit • Updated model that includes spontaneous decay • Unanticipated light shift • Without shift: Rate limit maximizes • With shift: Rate limit saturates • Numerical rate of 9ωρholds for over two orders in density • Numerical result agrees with analytic result • Best agreement at dense condensate • Many-body rate limit more strict than unitary limit

  16. Pierre Phou Stable Molecules I: Adiabatic Following • Photoassociation creates excited molecules • A second laser drives molecules to the ground state • Focus on adiabatic following scheme • Fixed laser intensity, varying laser frequency • Used extensively in magnetoassociation experiments, overlooked for photoassociation • Include elastic collisions • Relevant on time scale to create stable molecules

  17. Pierre Phou Two-Laser Scheme Ω1 δ >> Γ δ χ Ω2 Δ Δ0 • Adiabatic Following: • Subject to an adiabatic change, a system that starts in the ground state remains in the ground state • Effect adiabatic change using laser frequency

  18. Pierre Phou Elastic Collisions Atoms Stable Molecules Scattering Length

  19. Pierre Phou Equations of Motion |a1> |a2> χ Δ |g>

  20. Pierre Phou Results Weak PA: I = 32 W/cm2

  21. Pierre Phou Summary • Adiabatic following is a viable method of efficient stable molecule production • Strong photoassociation: • Starting below resonance → molecules • Starting above resonance → dissociated pairs • Efficient even for weak photoassociation • Creates molecules in both directions • Robust against reasonable collision strengths • Collisions cause mean-field shift

  22. Pierre Phou Stable Molecules II: Pulsed Photoassociation with Strong Magnetoassociation • Alternative two-photon scheme: Pulsed intensity, fixed frequency • Efficient stable molecule production using technique known as stimulated rapid adiabatic passage (STIRAP) • Often requires high laser intensity • Substitute Feshbach enhancement for high laser intensity • Shown to enhance one-color photoassociation • Unclear if this will also enhance production of stable molecules (two-color PA)

  23. Pierre Phou Ω χ • Pulsed photoassociation: • Ω: Pump Pulse • Turns atoms into excited molecules • χ: Dump Pulse • Turns excited into ground molecules Feshbach molecules • Feshbach enhancement: • Couples atoms to vibrationally excited molecules (Feshbach molecules) via strong magnetoassociation • Couples to photoassociated molecules via shared dissociation

  24. Pierre Phou Full Model Feshbach molecules

  25. Pierre Phou Resonant-Interaction Model • Adiabatically eliminate dissociation • Effective cross-coupling • Adiabatically eliminate Feshbach molecules Effective Tunable Parameters:

  26. Pierre Phou Results Full Model: • Feshbach enhancement causes vicarious losses through photoassociation state • Peak improvement occurs where Feshbach detuning is large compared to Γ Resonant-Interaction: • Peaks where tunable collisions drop to zero

  27. Pierre Phou Summary • Strong magnetoassociation enhances weak photoassociation • Improves conversion of stable molecules • Enhances both intuitive and counter-intuitive pulse sequences • Disagreement between full model and resonant-interaction model • Highlights need to explicitly include levels

  28. Pierre Phou Stable Molecules III: Laser-Assisted Weak Magnetoassociation and Weak Photoassociation • Strong magnetoassociation requires wide Feshbach resonance • May not be available for desired system • Couple a laser to assist weak magnetoassociation • Offers a more flexible alternative • Bound-bound coupling has lower intensity requirement

  29. Pierre Phou Model Additional bound level Assisting laser

  30. Pierre Phou Results Tunable Coupling

  31. Pierre Phou Summary • Assisting laser improves efficiency of weak photoassociation and weak magnetoassociation • More effective at stronger collision strengths • Assisting laser allows for greater flexibility • Additional tuning parameters • Low laser requirement • Opens access to more molecular species • Species with narrow Feshbach resonances

  32. Pierre Phou Conclusions • Photoassociation and magnetoassociation provide robust methods for creating stable quantum degenerate molecules • Efficient molecule production feasible for low laser intensity and narrow Feshbach resonance • Greater flexibility and access to wider range of molecular systems

  33. Pierre Phou Outlook • Association of molecules in a trap • Inhomogeneous condensate, which should be modeled • Improve laser-assisted system • Develop adaptive algorithm to optimize parameters • Model different molecular systems • Different species, such as alkali-earth molecules • Different statistics (Fermi gases) • Efimov trimers

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