What makes a cavity good?

1. What makes a cavity good? Dan Brooks April 29, 2008 Physics 250

2. Overview • Introduction to Cavity QED • Nanomechanical Oscillators • Our Experiments

3. Some Cavity Basics • Fabry Perot Cavity • Free Spectral Range • Linewidth (2κ) • Finesse ( ) http://en.wikipedia.org/wiki/Fabry-Perot

4. Optical Cavities • Planar Cavity • Confocal Cavity • Near-Planar Cavity

5. Other Optical Cavities • Half-Planar Cavity • Toroidal Resonator T. Aoki, et. al., Nature 443, 671-674 TP Purdy, DM Stamper-Kurn - Applied Physics B 90, 401-405 (2008)

6. Cavity couples to a two-level system (i.e. an atom) • Detunings that matter • Δca= ω cavity - ω atom • Δcl= ω cavity - ω laser • ΔN = n-atom cavity shift e g

7. γ • γ = spontaneous emission • κ = cavity decay rate • g = coupling strength parameter • where d is dipole matrix element of atom • Vc is mode volume of cavity κ g

8. Dressed Atom Picture • σ are Pauli spin matrices describing atom’s state. σ+=|e><g| and σ-=|g><e| • The rotating wave approximation has been used to eliminate counter-rotating terms • The Hamiltonian has eigenvalues: • For many atoms:

9. Dressed Atom Picture Atomic Resonance Energy 0 0 Cavity Detuning (length)

10. DN=Ng2/Dc frequency shifted cavity resonance bare cavity resonance detuned probe Δcl Dressed Atom Picture Atomic Resonance Energy 0 0 KaterMurch AMO Seminar 2007 Cavity Detuning (length)

11. The good cavity limit • Strong coupling : g > 2κ,γ • Good cavity: γ, g > κ Critical photon number no =g2/2go2 = .02 Critical atom number No =2gk/go2 = .02 Single atom cooperativity C = go2/ 2gk = 50 KaterMurch AMO Seminar 2007

12. Optical Nanomechanical Resonators • The goal: • A macroscopic quantum harmonic oscillator in its ground state. • Measurement of macroscopic resonators at the quantum standard limit • Cooling of a nanomechanical resonator via radiation pressure • Cool a single vibrational mode of the resonator. D. Kleckner, D. Bouwmeester, Nature 444, 75-78 (2006) J.D. Thompson, et. al., Nature 452, 72-75 (2008) See also: S. Gigan, et al., Nature 444 67-70 (2006) O. Arcizet, et al., Nature 444 71-74 (2006)

13. Radiation Pressure Cooling • Mode vibrates at frequency ωm • Cavity responses lags at timescales κ-1 • Lag produces damping force dependent whose sign is dependent on detuning and intensity αdP/dL. • Another good cavity limit! • ωm > κ O. Arcizet, et al., Nature 444 71-74 (2006)

14. Our Experiments • Two lasers resonant with cavity • 850 nm locks cavity length and produces an optical dipole trap via Stark effect • Optical wells have trap frequency ωm= ~ 40 kHz • 780 nm probes atoms and adds additional force on atoms (when ω laser ≠ ω atom)

15. Skipping the easy part… • Sweep probe light to resonance with cavity • Site dependent force excites a collective mode of oscillation. • Results in a macroscopic nanomechanical • oscillator initially in its ground state!!!

16. The details

17. 2mm MOT Loading Conveyor Belt Cavity Locations The details 1 mm

18. The details Tom Purdy AMO Seminar 2007

19. Stamper-Kurn Group Chris, Tony, Dan, Jennie, Tom, Zhao, Friedhelm, Mukund, Dan Ryan, Kater, Sabrina, Thierry, Ed (not pictured) Enrico, Jo, Joe, Tiger http://ultracold.physics.berkeley.edu

20. References • K.L. Moore, Ultracold Atoms, Circular Waveguides, and Cavity QED with Millimeter-scale Electromagnetic Traps, Ph.D. Thesis, UC Berkeley, May 2007 • T.P. Purdy, D.M. Stamper-Kurn - Applied Physics B 90, 401-405, 2008 • J.D. Thompson, et. al., Nature 452, 72-75 (2008) • O. Arcizet, et al., Nature 444 71-74 (2006) • D. Kleckner, D. Bouwmeester, Nature 444, 75-78 (2006) • S. Gigan, et al., Nature 444 67-70 (2006) • T. Aoki, et. al., Nature 443, 671-674 (2006) • D. Budker, D. Kimball, D. DeMille, Atomic Physics, Oxford University Press (2004) • KaterMurch, AMO Seminar Apr. 18, 2007 • Tom Purdy, AMO Seminar, Nov. 28, 2007 • http://en.wikipedia.org/wiki/Fabry-Perot