D. L. McAuslan, D. Korystov, and J. J. LongdellJack Dodd Centre for Photonics and Ultra-Cold Atoms,

University of Otago, Dunedin, New Zealand.

Coherent Spectroscopy of Coherent Spectroscopy of Rare-Earth-Ion Doped Rare-Earth-Ion Doped

Whispering Gallery Mode Whispering Gallery Mode ResonatorsResonators

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

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

OutlineOutline

David McAuslan – QIP-REIDS2011

Whispering Gallery ModesWhispering Gallery Modes

Electric field confined to equator.

High quality factor.

Small mode volume.

Ideal for strong coupling cavity QED.

[1] S. Arnold et al., Opt. Lett. 28 (2003).

[1]

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

Whispering Gallery ModesWhispering Gallery Modes

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.

[2] [3]

[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).

[1]

[2] [3][4]

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

κ – cavity decay rate:

γ – atomic population decay rate:

γh – atomic phase decay rate:

g – coupling between atoms and cavity:

Strong Coupling RegimeStrong Coupling Regime

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

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.

Strong Coupling RegimeStrong Coupling Regime

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

Reversible State Transfer

Single Atom Detection

Why Strong Coupling?Why Strong Coupling?

D. L. McAuslan et al., Physical Review A 80, 062307 (2009)David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

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.

Aim of ExperimentsAim of Experiments

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

Resonator:◦ 0.05% Pr3+:Y2SiO5.

◦ r = 1.95mm.◦ Q = 2 x 106.

Sample:◦ 0.02% Pr3+:Y2SiO5.

◦ 5x5x5mm cube.

Experimental SetupExperimental Setup

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011

LO

Probe

David McAuslan – QIP-REIDS2011

D. L. McAuslan et al., ArXiv:1104.4150 (2011)

π = 0.32μs for Pin = 700μW

ππ Pulse LengthPulse Length

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

D. L. McAuslan et al., ArXiv:1104.4150 (2011)

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):

Atom-Cavity CouplingAtom-Cavity Coupling

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

D. L. McAuslan et al., ArXiv:1104.4150 (2011)

e-2τ/T2

e-2τ/T2

Through Resonator Coupled into Resonator

Coherence TimeCoherence Time

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

D. L. McAuslan et al., ArXiv:1104.4150 (2011)

e-2τ/T2

e-2τ/T2

Through Resonator Coupled into Resonator

Coherence TimeCoherence Time

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011

T2 = 30.8 μs T2 = 21.0 μs

David McAuslan – QIP-REIDS2011

D. L. McAuslan et al., ArXiv:1104.4150 (2011)

Through Resonator Coupled into Resonator

e-Τ/T1

e-Τ/T1

Population LifetimePopulation Lifetime

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

D. L. McAuslan et al., ArXiv:1104.4150 (2011)

Through Resonator Coupled into Resonator

e-Τ/T1

e-Τ/T1

Population LifetimePopulation Lifetime

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011

T1 = 205μs T1 = 187μs

David McAuslan – QIP-REIDS2011

D. L. McAuslan et al., ArXiv:1104.4150 (2011)

Spectral Hole LifetimeSpectral Hole Lifetime

D. L. McAuslan et al., ArXiv:1104.4150 (2011)David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

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.

Fitting to experimental data gives:◦ g = 2π x 2.2 kHz.

Optical BistabilityOptical Bistability800μW 400μW

200μW 100μW

80μW 40μW

Sweep Sweep

[1] K. Ichimura and H. Goto, PRA 74 (2006)David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

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.

Cavity QED ParametersCavity QED Parameters

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

Smaller VSmaller 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-REIDS2011David McAuslan – QIP-REIDS2011

Higher QHigher 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-REIDS2011David McAuslan – QIP-REIDS2011

N0<1 for different materials.

MaterialsMaterials

David McAuslan – QIP-REIDS2011David McAuslan – QIP-REIDS2011

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.

ConclusionsConclusions

David McAuslan – QIP-REIDS2011