Coherent Spectroscopy of RareEarth-Ion Doped Whispering
Gallery Mode Resonators
D. L. McAuslan, D. Korystov, and J. J. Longdell
Jack Dodd Centre for Photonics and Ultra-Cold Atoms,
University of Otago, Dunedin, New Zealand.
David McAuslan – QIP-REIDS2011
Outline



Whispering Gallery Modes (WGMs).
Strong Coupling Regime of Cavity QED.
Experiments.
◦
◦
◦
◦
◦
Atom-Cavity Coupling.
Coherence Time.
Population Lifetime.
Spectral Hole Lifetime.
Optical Bistability/Normal-Mode Splitting.
David McAuslan – QIP-REIDS2011
Whispering Gallery Modes


Electric field confined to
equator.
High quality factor.
[1]


Small mode volume.
Ideal for strong coupling cavity
QED.
[1] S. Arnold et al., Opt. Lett. 28 (2003).
David McAuslan – QIP-REIDS2011
Whispering Gallery Modes
[1]
[2]
[2]
[3]
[3]
[4]
Microdisk
Microtoroid
Microsphere
Crystalline
r~10-100 μm.
Q=107.
r~20-100 μm.
Q=108.
r~10-500μm.
Q=109.
r~100-5000μm.
Q=1011.
[1] T. J. Kippenberg, PhD. Thesis (2004).
[2] A. Schliesser et al., Nature Physics 4 (2008).
[3] Y. Park et al., Nano Lett. 6 (2006).
[4] J. Hofer et al., PRA 82 (2010).
David McAuslan – QIP-REIDS2011
Strong Coupling Regime


κ – cavity decay rate:
γ – atomic population decay
rate:

γh – atomic phase decay rate:

g – coupling between atoms and cavity:
David McAuslan – QIP-REIDS2011
Strong Coupling Regime

Critical atom number:

Saturation photon number:



N0<1, n0<1.
“Good cavity” strong coupling regime: g > κ, γ, γh.
“Bad cavity” strong coupling regime: κ > g >> γ, γh.
David McAuslan – QIP-REIDS2011
Why Strong Coupling?

Reversible State Transfer

Single Atom Detection
D. L. McAuslan et al., Physical Review A 80, 062307 (2009)
David McAuslan – QIP-REIDS2011
Aim of Experiments

Measure the properties of a Pr3+:Y2SiO5
resonator.
◦
◦
◦
◦

Atom-cavity coupling.
Coherence time.
Population lifetime.
Spectral hole lifetime.
Calculate cavity QED parameters to determine
viability of strong-coupling regime.
David McAuslan – QIP-REIDS2011
Experimental Setup

Resonator:
◦ 0.05% Pr3+:Y2SiO5.
◦ r = 1.95mm.
◦ Q = 2 x 106.
LO
Probe

Sample:
◦ 0.02% Pr3+:Y2SiO5.
◦ 5x5x5mm cube.
David McAuslan – QIP-REIDS2011
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
π Pulse Length
π = 0.32μs for
Pin = 700μW
David McAuslan – QIP-REIDS2011
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
Atom-Cavity Coupling

Rabi frequency:

Atom-Cavity Coupling:

Compare to g calculated from the theoretical mode volume (V
= 5.40 x 10-13 m3 for r = 1.95mm):
David McAuslan – QIP-REIDS2011
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
Coherence Time

Through Resonator
e-2τ/T

Coupled into Resonator
2
e-2τ/T
2
David McAuslan – QIP-REIDS2011
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
Coherence Time

Through Resonator

Coupled into Resonator
e-2τ/T
2
e-2τ/T
2
T2 = 30.8 μs
David McAuslan – QIP-REIDS2011
T2 = 21.0 μs
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
Population Lifetime

Through Resonator
e-Τ/T
1
David McAuslan – QIP-REIDS2011

Coupled into Resonator
e-Τ/T
1
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
Population Lifetime

Through Resonator

Coupled into Resonator
e-Τ/T
1
T1 = 205μs
David McAuslan – QIP-REIDS2011
e-Τ/T
1
T1 = 187μs
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
Spectral Hole Lifetime
D. L. McAuslan et al., ArXiv:1104.4150 (2011)
David McAuslan – QIP-REIDS2011
Optical Bistability



Optical bistability and
normal-mode splitting
studied by Ichimura and
Goto in a Pr3+:Y2SiO5
Fabry-Perot resonator [1].
Theory modified for a
WGM resonator.
800μW
Sweep
400μW
Sweep
200μW
100μW
80μW
40μW
Fitting to experimental
data gives:
◦ g = 2π x 2.2 kHz.
[1] K. Ichimura and H. Goto, PRA 74 (2006)
David McAuslan – QIP-REIDS2011
Cavity QED Parameters

This resonator:
◦
◦
◦
◦
◦

κ = 2π x 138 MHz.
γ = 2π x 0.851 kHz.
γh= 2π x 2.34 kHz.
g = 2π x 1.73 kHz.
N0 = 2.15 x 105, n0 =0.166.
Need:
◦ Smaller resonators.
◦ Higher Q factors.
◦ Different materials.
David McAuslan – QIP-REIDS2011
Smaller V

Single point diamond turning.
◦ Crystalline resonators with R = 40 μm.
◦ Possible to reduce V by 3 orders of magnitude.
[1]
[1] I. S. Grudinin et al., Opt. Commun. 265 (2006)
David McAuslan – QIP-REIDS2011
Higher Q

We have measured Q = 2 x 108 in Y2SiO5 resonators.

Q = 3 x 1011 in CaF2 [1].

Bulk losses in Y2SiO5 measured using Fabry-Perot
cavity [2].
◦ α ≤ 7 x 10-4 cm-1.
◦ Max Q ~ 3 x 108.


At least 2 orders of magnitude improvement
possible.
Bulk losses should be lower in IR.
[1] A. A. Savchenkov et al., Opt Exp. 15 (2007)
[2] H. Goto et al., Opt. Exp. 18 (2010)
David McAuslan – QIP-REIDS2011
Materials

N0<1 for different materials.
David McAuslan – QIP-REIDS2011
Conclusions




Performed an investigation into strong coupling cavity
QED with rare-earth-ion doped WGM resonators.
Direct measurement of cavity QED parameters of a
Pr3+:Y2SiO5 WGM resonator.
◦ g = 2π x 1.73 kHz.
◦ γ = 2π x 0.851 kHz.
◦ γh = 2π x 2.34 kHz.
Observed optical bistability and normal-mode splitting in
resonator.
Achieving the strong coupling regime of cavity QED is
feasible based on existing resonator technology.
David McAuslan – QIP-REIDS2011