Download What makes a cavity good?

What makes a cavity good?
Dan Brooks
April 29, 2008
Physics 250
Overview
• Introduction to Cavity QED
• Nanomechanical Oscillators
• Our Experiments
Cavity QED
Nanomechanical Oscillators
Our Experiments
Some Cavity Basics
• Fabry Perot Cavity
– Free Spectral Range
– Linewidth (2κ)
– Finesse ( )
http://en.wikipedia.org/wiki/Fabry-Perot
Cavity QED
Nanomechanical Oscillators
Optical Cavities
• Planar Cavity
• Confocal Cavity
• Near-Planar Cavity
Our Experiments
Cavity QED
Nanomechanical Oscillators
Our Experiments
Other Optical Cavities
• Half-Planar Cavity
TP Purdy, DM Stamper-Kurn - Applied
Physics B 90, 401-405 (2008)
• Toroidal Resonator
T. Aoki, et. al., Nature 443, 671-674
Cavity QED
Nanomechanical Oscillators
Our Experiments
e
g
• 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
Cavity QED
Nanomechanical Oscillators
Our Experiments
γ
κ
g
• 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
Cavity QED
Nanomechanical Oscillators
Our Experiments
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:
Cavity QED
Nanomechanical Oscillators
Our Experiments
Dressed Atom Picture
Ng 2

Energy
Ng
Atomic 0
Resonance
0
Cavity Detuning (length)
Cavity QED
Nanomechanical Oscillators
Our Experiments
Dressed Atom Picture
Ng 2

Energy
N=Ng2/c
Ng
Atomic 0
Resonance
frequency
shifted cavity
resonance
bare cavity
resonance
detuned
probe Δcl
0
Cavity Detuning (length)
Kater Murch AMO Seminar 2007
Cavity QED
Nanomechanical Oscillators
Our Experiments
The good cavity limit
• Strong coupling : g > 2κ,γ
• Good cavity: γ, g > κ
Critical photon number
Critical atom number
Single atom cooperativity
no =g2/2go2 = .02
No =2gk/go2 = .02
C = go2/ 2gk = 50
Kater Murch AMO Seminar 2007
Cavity QED
Nanomechanical Oscillators
Our 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, 72-75 (2008)
See also: S. Gigan, et al., Nature 444 67-70 (2006)
O. Arcizet, et al., Nature 444 71-74 (2006)
D. Kleckner, D. Bouwmeester,
Nature 444, 75-78 (2006)
Cavity QED
Nanomechanical Oscillators
Our Experiments
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 α dP/dL.
• Another good cavity limit!
ωm > κ
O. Arcizet, et al., Nature 444 71-74 (2006)
Cavity QED
Nanomechanical Oscillators
Our 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 ωm= ~ 40 kHz
– 780 nm probes atoms and adds additional force on
atoms (when ω laser ≠ ω atom)
Cavity QED
Nanomechanical Oscillators
Our 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 QED
Nanomechanical Oscillators
The details
Our Experiments
Cavity QED
Nanomechanical Oscillators
Our Experiments
The details
1 mm
2mm
MOT
Loading
Conveyor
Belt
Cavity
Locations
Cavity QED
Nanomechanical Oscillators
Our Experiments
The details
Cavity Parameters
One
Sided
Cavity
Balanced
Cavity
Cavity Finesse
250,000
450,000
Mirror Radius of Curvature
5cm
Cavity Length
0
Cavity Mode Waist
250um
270um
25um
25um
Aperture Half Width
90um
k / 2
Cavity Half Linewidth
Atomic Half Linewidth(87Rb)
g / 2
g / 2
Single Atom Cooperativity
g 2 / 2gk
Maximum Coupling Strength
Critical Photon Number
g 2 / 2g 2
Photon Collection Efficiency
1.2 MHz
.65 MHz
13 MHz
12 MHz
3 MHz
23
37
.027
.031
.6
.25
Tom Purdy AMO Seminar 2007
Cavity QED
Nanomechanical Oscillators
Our Experiments
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
Cavity QED
Nanomechanical Oscillators
• 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)
– Kater Murch, AMO Seminar Apr. 18, 2007
– Tom Purdy, AMO Seminar, Nov. 28, 2007
– http://en.wikipedia.org/wiki/Fabry-Perot
Our Experiments