Ultra-small mode volume, Ultra-small mode volume, high quality factor photonic high quality factor photonic crystal microcavities in InP-crystal microcavities in InP-

based lasers and Si based lasers and Si membranesmembranes

Kartik SrinivasanKartik Srinivasan, Paul E. Barclay, , Paul E. Barclay, Matthew Borselli, and Prof. Oskar Matthew Borselli, and Prof. Oskar

PainterPainter

California Institute of TechnologyCalifornia Institute of Technology

PECS-V, March 9, 2004PECS-V, March 9, 2004

PC microcavities for PC microcavities for quantum opticsquantum optics

Interested in strong coupling between a single atom (quantum dot) and single photon (cQED)

Coherent coupling rate must exceed decay rates g > (,)

g ~ (1/Veff)1/2 ; for PC microcavities, VVeffeff ~ ( ~ (/n)/n)33 g ~ 10-100 GHz for g ~ 10-100 GHz for coupling to Cs atom; compare with ~10-20 MHz in current state-of-coupling to Cs atom; compare with ~10-20 MHz in current state-of-the-art cQED with free-space Fabry-Perot cavities (the-art cQED with free-space Fabry-Perot cavities (McKeever et al., McKeever et al., NatureNature (2003)) (2003))

g>g> Q ~10 Q ~1044 for PC microcavities (compare with 10 for PC microcavities (compare with 1077-10-1088 in Fabry- in Fabry-Perot cavities)Perot cavities)

cQED with PC microcavities: low Q, small VcQED with PC microcavities: low Q, small Veffeff regime; fast time-scale regime; fast time-scale for coherent interactionsfor coherent interactions

PC microcavities can be designed to have field maximum in either air or PC microcavities can be designed to have field maximum in either air or dielectricdielectric

Interaction with introduced atoms or embedded quantum dots is Interaction with introduced atoms or embedded quantum dots is possiblepossible

Next-generation cQED experiments involving integrated atom Next-generation cQED experiments involving integrated atom (qdot)-cavity systems(qdot)-cavity systems

High-Q cavity designHigh-Q cavity design

•Use symmetry and lattice grading to remove Fourier components that radiate

•FDTD predicted Q~105

•Veff ~ 1.2(/n)3

•Q relatively robust (remains >104) 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

PC microcavity lasers – PC microcavity lasers – initial demonstration of initial demonstration of

high-Qhigh-Q•Cavities fabricated in InAsP/InGaAsP multi-quantum well material via e-beam lithography, ICP/RIE etching through SiO2 mask and membrane layers, and HCl/H2O 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

Photonic crystal Photonic crystal microcavity lasersmicrocavity 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 simulationK. Srinivasan, P.E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, Applied Physics Letters, 83 (15), 1915-1917 (Sept., 2003).

Probing PC microcavities Probing PC microcavities with an optical fiber taperwith 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 Veff

Fabricate arrays of devices (in Si) with average hole radius (ravg) varying for a fixed lattice spacing (a)

Mode of interest is lowest frequency resonance for a given a

Probing PC cavities with Probing PC cavities with fiber tapersfiber tapers

Linewidth MeasurementsLinewidth 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 Veff~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)

Mode localization Mode localization measurementsmeasurements

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 Veff~0.9(/n)3

PC microcavity thus simultaneously exhibits high Q and ultra-small Veff

Robust high-Q Robust high-Q microcavitiesmicrocavities

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)

Recent progressRecent progress Cavity Q as high as 56,000 Cavity Q as high as 56,000

measuredmeasured Fiber tapers used to probe Fiber tapers used to probe

other wavelength-scale other wavelength-scale cavities (microdisks by M. cavities (microdisks by M. Borselli, et al.)Borselli, et al.)

More efficient means to More efficient means to source cavity source cavity

Direct fiber-based excitation Direct fiber-based excitation limited to 10-20% coupling; limited to 10-20% coupling; such levels also load the such levels also load the resonator (degrade Q)resonator (degrade Q)

Currently focused on Currently focused on integrating with suitably integrating with suitably designed PC waveguides, designed PC waveguides, which can be sourced by which can be sourced by optical fiber tapers with optical fiber tapers with >97% efficiency (P. Barclay >97% efficiency (P. Barclay et al., Tu-P41)et al., Tu-P41)

PC microcavities for cQEDPC microcavities for cQED Chip-based strong coupling to atomic species (Cs atom)Chip-based strong coupling to atomic species (Cs atom)

Similarly, Similarly, gg~100 GHz exceeds ~100 GHz exceeds and and for an InAs quantum for an InAs quantum dot (1 ns lifetime) dot (1 ns lifetime)

Chip-based strong coupling to chip-based atoms (quantum dots)Chip-based strong coupling to chip-based atoms (quantum dots)Single photon sources (Purcell Factor FSingle photon sources (Purcell Factor Fpp ~3,500 estimated) ~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)

Arriveat : g 16GHz, 4.4GHz, 2.6MHz;

g, strongcouplingcondition#1AlsocalculatecriticalatomnumberN0andsaturationphotonnumberm0;N0

2g2

8.8x105 m0 2

2g21.3x108

N0, m0 1strongcouplingcondition#2Calculations indicateanappreciablechangeinthecavity

transmissionduringasingleatomtransit foradrivestrengthof evenasingle

intracavity photon†

4Q; Q 40000, 852nm, 2.6MHz

g d

. E d

2Veff 3c2

4Veff

Veff 0.9

n3; 0.42re normalizesVeff frompeakof electric

fieldenergy density topeakelectricfield

AcknowledgementsAcknowledgements Research partially funded by the Research partially funded by the

Powell FoundationPowell Foundation K.S. thanks the Hertz Foundation for K.S. thanks the Hertz Foundation for

its graduate fellowship supportits graduate fellowship support