D. L. McAuslan, D. Korystov, and J. J. Longdell Jack Dodd Centre for Photonics and Ultra-Cold Atoms, University of Otago, Dunedin, New Zealand. Coherent Spectroscopy of Rare- Earth-Ion Doped Whispering Gallery Mode Resonators David 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 Outline

Whispering 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-REIDS2011

Whispering Gallery Modes MicrodiskMicrotoroidMicrosphereCrystalline r~ μm. Q=10 7. r~ μm. Q=10 8. r~ μm. Q=10 9. r~ μm. Q= [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-REIDS2011

 κ – cavity decay rate:  γ – atomic population decay rate:  γ h – atomic phase decay rate:  g – coupling between atoms and cavity: Strong Coupling Regime David McAuslan – QIP-REIDS2011

 Critical atom number:  Saturation photon number:  N 0 <1, n 0 <1.  “Good cavity” strong coupling regime: g > κ, γ, γ h.  “Bad cavity” strong coupling regime: κ > g >> γ, γ h. Strong Coupling Regime David McAuslan – QIP-REIDS2011

 Reversible State Transfer  Single Atom Detection Why Strong Coupling? D. L. McAuslan et al., Physical Review A 80, (2009) David McAuslan – QIP-REIDS2011

 Measure the properties of a Pr 3+ :Y 2 SiO 5 resonator. ◦ Atom-cavity coupling. ◦ Coherence time. ◦ Population lifetime. ◦ Spectral hole lifetime.  Calculate cavity QED parameters to determine viability of strong-coupling regime. Aim of Experiments David McAuslan – QIP-REIDS2011

 Resonator: ◦ 0.05% Pr 3+ :Y 2 SiO 5. ◦ r = 1.95mm. ◦ Q = 2 x  Sample: ◦ 0.02% Pr 3+ :Y 2 SiO 5. ◦ 5x5x5mm cube. Experimental Setup D. L. McAuslan et al., ArXiv: (2011) David McAuslan – QIP-REIDS2011 LO Probe David McAuslan – QIP-REIDS2011 D. L. McAuslan et al., ArXiv: (2011)

π = 0.32 μ s for P in = 700 μ W π Pulse Length D. L. McAuslan et al., ArXiv: (2011) David McAuslan – QIP-REIDS2011 D. L. McAuslan et al., ArXiv: (2011)

 Rabi frequency:  Atom-Cavity Coupling:  Compare to g calculated from the theoretical mode volume (V = 5.40 x m 3 for r = 1.95mm): Atom-Cavity Coupling D. L. McAuslan et al., ArXiv: (2011) David McAuslan – QIP-REIDS2011 D. L. McAuslan et al., ArXiv: (2011)

e -2 τ /T 2  Through Resonator  Coupled into Resonator Coherence Time D. L. McAuslan et al., ArXiv: (2011) David McAuslan – QIP-REIDS2011 D. L. McAuslan et al., ArXiv: (2011)

e -2 τ /T 2  Through Resonator  Coupled into Resonator Coherence Time D. L. McAuslan et al., ArXiv: (2011) David McAuslan – QIP-REIDS2011 T 2 = 30.8 μ sT 2 = 21.0 μ s David McAuslan – QIP-REIDS2011 D. L. McAuslan et al., ArXiv: (2011)

 Through Resonator  Coupled into Resonator e - Τ /T 1 Population Lifetime D. L. McAuslan et al., ArXiv: (2011) David McAuslan – QIP-REIDS2011 D. L. McAuslan et al., ArXiv: (2011)

 Through Resonator  Coupled into Resonator e - Τ /T 1 Population Lifetime D. L. McAuslan et al., ArXiv: (2011) David McAuslan – QIP-REIDS2011 T 1 = 205 μ sT 1 = 187 μ s David McAuslan – QIP-REIDS2011 D. L. McAuslan et al., ArXiv: (2011)

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

 Optical bistability and normal-mode splitting studied by Ichimura and Goto in a Pr 3+ :Y 2 SiO 5 Fabry-Perot resonator [1].  Theory modified for a WGM resonator.  Fitting to experimental data gives: ◦ g = 2 π x 2.2 kHz. Optical Bistability 800 μ W400 μ W 200 μ W100 μ W 80 μ W40 μ W Sweep [1] K. Ichimura and H. Goto, PRA 74 (2006) David McAuslan – QIP-REIDS2011

 This resonator: ◦ κ = 2 π x 138 MHz. ◦ γ = 2 π x kHz. ◦ γ h = 2 π x 2.34 kHz. ◦ g = 2 π x 1.73 kHz. ◦ N 0 = 2.15 x 10 5, n 0 =  Need: ◦ Smaller resonators. ◦ Higher Q factors. ◦ Different materials. Cavity QED Parameters 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 10 8 in Y 2 SiO 5 resonators.  Q = 3 x in CaF 2 [1].  Bulk losses in Y 2 SiO 5 measured using Fabry-Perot cavity [2]. ◦ α ≤ 7 x cm -1. ◦ Max Q ~ 3 x  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

 N 0 <1 for different materials. Materials David 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 Pr 3+ :Y 2 SiO 5 WGM resonator. ◦ g = 2 π x 1.73 kHz. ◦ γ = 2 π x kHz. ◦ γ h = 2 π 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. Conclusions David McAuslan – QIP-REIDS2011