1. Ultra-small mode volume, high quality factor photonic crystal microcavities in InP-based lasers and Si membranes Kartik Srinivasan, Paul E. Barclay, Matthew Borselli, and Prof. Oskar Painter California Institute of Technology PECS-V, March 9, 2004

2. PC microcavities for quantum optics  Interested in strong coupling between a single atom (quantum dot) and single photon (cQED)   Coherent coupling rate must exceed decay rates  g > ( ,  ) V eff ~ ( /n) 3  g ~ 10-100 GHz for coupling to Cs atom; compare with ~10-20 MHz in current state-of-the-art cQED with free-space Fabry- Perot cavities (McKeever et al., Nature (2003))  g ~ (1/V eff ) 1/2 ; for PC microcavities, V eff ~ ( /n) 3  g ~ 10-100 GHz for coupling to Cs atom; compare with ~10-20 MHz in current state-of-the-art cQED with free-space Fabry- Perot cavities (McKeever et al., Nature (2003))  g>   Q ~10 4 for PC microcavities (compare with 10 7 -10 8 in Fabry-Perot cavities)  cQED with PC microcavities: low Q, small V eff regime; fast time-scale for coherent interactions  PC microcavities can be designed to have field maximum in either air or dielectric  Interaction with introduced atoms or embedded quantum dots is possible  Next-generation cQED experiments involving integrated atom (qdot)-cavity systems

3. High-Q cavity design Use symmetry and lattice grading to remove Fourier components that radiate FDTD predicted Q~10 5 V eff ~ 1.2( /n) 3 Q relatively robust (remains >10 4 ) to perturbations in lattice grade, hole size. Modal frequency a/ ~0.245 K. Srinivasan and O. Painter, Optics Express 10(15), 670 (July, 2002) K. Srinivasan and O. Painter, PECS-IV

4. PC microcavity lasers – initial demonstration of high-Q Cavities fabricated in InAsP/InGaAsP multi-quantum well material via e-beam lithography, ICP/RIE etching through SiO 2 mask and membrane layers, and HCl/H 2 O undercut wet etch Optically pumped (pulsed) at 830 nm Emission at 1.3  m collected Sub-threshold (near material transparency) emission linewidth gives estimate for cold cavity Q

5. Photonic crystal microcavity lasers  Sub-threshold measurements using a broad pump beam (eliminate thermal heating effects)  Measure linewidth at pump power level ~10% below threshold (best estimate of transparency); Q value of 13,000 measured, near measurement limit due to detector resolution and thermal broadening effects  Optimization of pump beam reduces thresholds to as low as 100  W  Polarization measurements consistent with simulation K. Srinivasan, P.E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, Applied Physics Letters, 83 (15), 1915-1917 (Sept., 2003).

6. Probing PC microcavities with an optical fiber taper  Passive measurement of Q using an external waveguide consisting of a tapered optical fiber with minimum diameter of 1-2  m  Taper interacts with the cavity when aligned laterally and positioned above and in the near-field of the cavity (  z ≤1  m),  Fiber serves as an optical probe of the spectral and spatial properties of the microcavities: can probe both Q and V eff  Fabricate arrays of devices (in Si) with average hole radius (r avg ) varying for a fixed lattice spacing (a)  Mode of interest is lowest frequency resonance for a given a

7. Probing PC cavities with fiber tapers

8. Linewidth Measurements  Cavities fabricated in undercut silicon membranes  Linewidth of cavity mode (  ) examined as a function of taper position above the PC; can back out an unloaded cavity Q factor  FDTD simulations of structure with appropriate hole sizes predict Q~56,000 and V eff ~0.88( /n) 3 K. Srinivasan, P.E. Barclay, M. Borselli, and O. Painter, submitted to Physical Review Letters, Sept. 25, 2003 (available at http://arxiv.org/quant-ph/abs/0309190)

9. Mode localization measurements  Measure depth of coupling (for fixed taper height) as a function of taper displacement from center along the central x and y axes of the cavity  Data reveals envelope of cavity field (relatively broad taper field profile prevents measurement of exact cavity near-field)  Compared with simple coupled mode theory analysis incorporating FDTD simulations of cavity field; consistent with predicted V eff ~0.9( /n) 3  PC microcavity thus simultaneously exhibits high Q and ultra-small V eff

10. Robust high-Q microcavities  Cavity design is robust, both in simulation ( Q>20,000) and experiment (Q>13,000) to significant deviations from the nominal design (both in average r/a and the grade in r/a)  Robustness due primarily to two mechanisms: 1)Use of symmetry to reduce vertical radiation loss – independent of size of lattice holes; ratio of defect hole size to lattice hole size. 2)Grade in hole radius creates a robust way to mode match between defect region and its exterior. Harmonic potential created by modifications to multiple holes; design less sensitive to fluctuations in size and shape of individual holes. K. Srinivasan, P.E. Barclay, and O. Painter, (available at http://arxiv.org/abs/physics/0312060)

11. Recent progress  Cavity Q as high as 56,000 measured  Fiber tapers used to probe other wavelength-scale cavities (microdisks by M. Borselli, et al.)  More efficient means to source cavity  Direct fiber-based excitation limited to 10-20% coupling; such levels also load the resonator (degrade Q)  Currently focused on integrating with suitably designed PC waveguides, which can be sourced by optical fiber tapers with >97% efficiency (P. Barclay et al., Tu-P41)

12. PC microcavities for cQED  Chip-based strong coupling to atomic species (Cs atom)  Similarly, g~100 GHz exceeds  and  for an InAs quantum dot (1 ns lifetime)  Chip-based strong coupling to chip-based atoms (quantum dots)  Single photon sources (Purcell Factor F p ~3,500 estimated) * Collaboration with B. Lev and Prof. H. Mabuchi, Caltech † B. Lev, K. Srinivasan, P.E. Barclay, O. Painter, and H. Mabuchi, http://arxiv.org/quant-ph/abs/0309190, (2004)

13. Acknowledgements Research partially funded by the Powell Foundation Research partially funded by the Powell Foundation K.S. thanks the Hertz Foundation for its graduate fellowship support K.S. thanks the Hertz Foundation for its graduate fellowship support