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

Overview Introduction to Cavity QED Nanomechanical Oscillators Our Experiments

Cavity QEDNanomechanical OscillatorsOur Experiments Fabry Perot Cavity – Free Spectral Range – Linewidth ( 2 κ) – Finesse ( ) Some Cavity Basics

Cavity QEDNanomechanical OscillatorsOur Experiments Optical Cavities Planar Cavity Confocal Cavity Near-Planar Cavity

Cavity QEDNanomechanical OscillatorsOur Experiments Other Optical Cavities Half-Planar Cavity Toroidal Resonator T. Aoki, et. al., Nature 443, TP Purdy, DM Stamper-Kurn - Applied Physics B 90, (2008)

Cavity QEDNanomechanical OscillatorsOur Experiments e g Cavity couples to a two-level system (i.e. an atom) Detunings that matter Δ ca = ω cavity - ω atom Δ cl = ω cavity - ω laser Δ N = n-atom cavity shift

Cavity QEDNanomechanical OscillatorsOur Experiments γ = spontaneous emission κ = cavity decay rate g = coupling strength parameter – where d is dipole matrix element of atom – V c is mode volume of cavity γ g κ

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

Cavity QEDNanomechanical OscillatorsOur Experiments Dressed Atom Picture Cavity Detuning (length) Energy 0 0 Atomic Resonance

Cavity QEDNanomechanical OscillatorsOur Experiments Dressed Atom Picture Cavity Detuning (length) Energy 0 0 Atomic Resonance frequency bare cavity resonance  N =Ng 2 /  c shifted cavity resonance detuned probe Δ cl Kater Murch AMO Seminar 2007

Cavity QEDNanomechanical OscillatorsOur Experiments The good cavity limit Strong coupling : g > 2κ,γ Good cavity: γ, g > κ Critical atom number Critical photon number Single atom cooperativity n o =    2g o 2 =.02 N o =2  g o 2 =.02 C = g o 2 / 2  = 50 Kater Murch AMO Seminar 2007

Cavity QEDNanomechanical OscillatorsOur Experiments 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. J.D. Thompson, et. al., Nature 452, (2008) D. Kleckner, D. Bouwmeester, Nature 444, (2006) See also: S. Gigan, et al., Nature (2006) O. Arcizet, et al., Nature (2006)

Cavity QEDNanomechanical OscillatorsOur Experiments Radiation Pressure Cooling O. Arcizet, et al., Nature (2006) Mode vibrates at frequency ω m Cavity responses lags at timescales κ -1 Lag produces damping force dependent whose sign is dependent on detuning and intensity α dP/dL. Another good cavity limit! ω m > κ

Cavity QEDNanomechanical OscillatorsOur Experiments 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 ω m = ~ 40 kHz – 780 nm probes atoms and adds additional force on atoms (when ω laser ≠ ω atom )

Cavity QEDNanomechanical OscillatorsOur Experiments 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!!!

Cavity QEDNanomechanical OscillatorsOur Experiments The details

Cavity QEDNanomechanical OscillatorsOur Experiments The details 1 mm 2mm MOT Loading Conveyor Belt Cavity Locations

Cavity QEDNanomechanical OscillatorsOur Experiments The details Cavity ParametersOne Sided Cavity Balanced Cavity Cavity Finesse250,000450,000 Mirror Radius of Curvature5cm Cavity Length250um270um Cavity Mode Waist25um Aperture Half Width90um Cavity Half Linewidth1.2 MHz.65 MHz Maximum Coupling Strength13 MHz12 MHz Atomic Half Linewidth( 87 Rb)3 MHz Single Atom Cooperativity2337 Critical Photon Number Photon Collection Efficiency.6.25 Tom Purdy AMO Seminar 2007

Cavity QEDNanomechanical OscillatorsOur Experiments Stamper-Kurn Group Chris, Tony, Dan, Jennie, Tom, Zhao, Friedhelm, Mukund, Dan Ryan, Kater, Sabrina, Thierry, Ed (not pictured) Enrico, Jo, Joe, Tiger

Cavity QEDNanomechanical OscillatorsOur Experiments 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, , 2008 – J.D. Thompson, et. al., Nature 452, (2008) – O. Arcizet, et al., Nature (2006) – D. Kleckner, D. Bouwmeester, Nature 444, (2006) – S. Gigan, et al., Nature (2006) – T. Aoki, et. al., Nature 443, (2006) – D. Budker, D. Kimball, D. DeMille, Atomic Physics, Oxford University Press (2004) – Kater Murch, AMO Seminar Apr. 18, 2007 – Tom Purdy, AMO Seminar, Nov. 28, 2007 –