From weak to strong coupling of quantum emitters

From weak to strong coupling of quantum emitters in metallic nano-slit Bragg cavities Ronen Rapaport

Acknowledgments Graduate Students: Nitzan Livneh Moshe Harats Itamar Rosenberg Ilai Schwartz Collaborations: Adiel Zimran, Uri Banin – Chemistry, Hebrew Univ. Ayelet Strauss, Shira Yochelis, Yossi Paltiel – Applied Physics Hebrew Univ. Loren Pfeiffer – EE, Princeton University Gang Chen – Bell Labs Support: -EU FP 7 Marie Currie -ISF (F. I. R. S. T) -Wolfson Family Charitable Trust -Edmond Safra Foundation The nanophotonics and quantum fluids group

Outline • Extraordinary transmission (EOT) in nanoslit arrays • EOT in nanoslit array exposed – Bragg Cavity Model • Two level system in a cavity – the weak and strong coupling limits • 3 Examples of control and manipulations of light-matter coupling: 1. WCL – linear: the Purcell effect and controlled directional emission of quantum dots 2. WCL – nonlinear: enhancement of optical nonlinearities: Two photon absorption induced fluorescence 3. SCL : Strong exciton-Bragg cavity mode coupling: Bragg polaritons The nanophotonics and quantum fluids group

Extraordinary Transmission (EOT) in subwavelength metal Hole/slit arrays Resonant Extraordinary Transmission – output light intensity (at resonant wavelengths) larger than the geometrical ratio of open to opaque areas Iout ( )/Iin( )>(open area)/(total area) Channeling of energy through the subwavelength openings! The nanophotonics and quantum fluids group

EOT in nanoslit arrays: Possible mechanisms TM TM E H EOT of more than 5 EOT Full numerical EM simulations: ◦ No clear physical picture. The nanophotonics and quantum fluids group give full account

EOT in nanoslit arrays: Possible mechanisms TM TM E SPP modes H Surface Plasmon Polaritons (SPPs) Unit cell near field The nanophotonics and quantum fluids group

EOT in nanoslit arrays: Possible mechanisms TM TM E H • Slit-Cavity resonances The nanophotonics and quantum fluids group SPP modes

EOT in nanoslit arrays: Possible mechanisms TE SPP modes E H TE • EOT in TE with a thin dielectric layer • No propagating (or standing) modes in subwavelength slits • No SPP in TE polarization • Waveguide modes The nanophotonics and quantum fluids group

Bragg Cavity Model for EOT • Fabry-Perot Cavity: high resonant transmission with very highly reflective mirrors Standing optical modes constructive forward interference High transmission The nanophotonics and quantum fluids group

Bragg Cavity Model for EOT • Inside the slit array: periodic Bragg (Bloch) modes for g > k, there are modes with m ≠ 0 • Outside the slit array: For g > k, only the mode with m = 0 is propagating We can have Standing m ≠ 0 Bragg waves in the structure! Constructive interference with m=0 mode EOT The nanophotonics and quantum fluids group I. Schwarz et al. , preprint ar. Xiv 1011. 3713

Bragg Cavity Model for EOT Mapping to FP (waveguide) physics: Analytic condition for standing Bragg modes The nanophotonics and quantum fluids group

Bragg Cavity Model for EOT TE TM Very good agreement with full numerical calculations. The nanophotonics and quantum fluids group I. Schwarz et al. , preprint ar. Xiv 1011. 3713

Bragg Cavities • “one mirror” cavities • easily integrated with various active/passive media • small mode volume • easily controllable Q-factor The nanophotonics and quantum fluids group

TLS in a cavity – weak and strong coupling At resonance, the relative strength of the Two Level System (TLS) - cavity interaction is determined by: • the photon decay rate of the cavity κ, • the TLS non-resonant decay rate γ, • the TLS–photon coupling parameter g 0. The nanophotonics and quantum fluids group

TLS in a cavity – weak and strong coupling At resonance, the relative strength of the Two level System (TLS) - cavity interaction is determined by: • the photon decay rate of the cavity κ, • the TLS non-resonant decay rate γ, • the TLS–photon coupling parameter g 0. Weak coupling: g 0<<max(κ, γ) The emission of the photon by the TLS is an irreversible process. Resonant enhancement of spontaneous emission rate into cavity modes. Purcell effect The nanophotonics and quantum fluids group

TLS in a cavity – weak and strong coupling At resonance, the relative strength of the Two level System (TLS) - cavity interaction is determined by: • the photon decay rate of the cavity κ, • the TLS non-resonant decay rate γ, • the TLS–photon coupling parameter g 0. Strong coupling: g 0>>max(κ, γ) The emission of a photon is a reversible process. Vacuum Rabi splitting The nanophotonics and quantum fluids group

TLS in a cavity – weak and strong coupling At resonance, the relative strength of the Two level System (TLS) - cavity interaction is determined by: • the photon decay rate of the cavity κ, • the TLS non-resonant decay rate γ, • the TLS–photon coupling parameter g 0. Strong coupling for excitons in planar microcavities – excitonpolaritons “Dynamical” Exciton – polariton BEC in a microcavity See J. Kasprzak, et al. , Nature, 443 (2006) 409 -414. The nanophotonics and quantum fluids group

1. Weak coupling of Quantum dots to Bragg cavity modes – directional emission Nanocrystal quantum dots - NQDs Nanometric light source: ◦ Essentially a TLS ◦ Tunable emission wavelength ◦ High quantum efficiency Possible applications: ◦ Photodetectors ◦ Solar cells ◦ Lasing medium ◦ Single Photon sources The nanophotonics and quantum fluids group

The nanophotonics and quantum fluids group N. Livneh et al. , Nano Letters(2011)

samples Reference sample – quantum dots on a glass substrate Quantum dots in a polymer layer on the nano-slit array Quantum dot self-assembled monolayer on the nano-slit array The nanophotonics and quantum fluids group N. Livneh et al. , Nano Letters(2011)

Angular emission spectrum - Reference TE No angular dependence – as expected The nanophotonics and quantum fluids group N. Livneh et al. , Nano Letters(2011)

Angular emission spectrum – Nanoslit array TE TE emission Strong angular dependence, directional emission (follow EOT disp. ) The nanophotonics and quantum fluids group N. Livneh et al. , Nano Letters(2011)

p p p Directional emission with divergence of 3. 4 o 20 fold emission enhancement to this angle Photon emission rate: 3. 4 o The interaction with the structure is in the single quantum-dot (photon? ) level p Second order correlation measurements g(2) on the way p The nanophotonics and quantum fluids group N. Livneh et al. , Nano Letters(2011)

Physical explanation – Purcell effect: The emission rate of a dipole in a cavity into a cavity mode is enhanced. Our structure acts as a Bragg cavity with an eigenmode at 0 o → stronger emission to 0 o Near field in 0 o (structure mode) The nanophotonics and quantum fluids group Near field in 15 o

Physical explanation – Purcell effect The dipole emission rate into a cavity mode is given by Experimental values: Numerical model: 3. 4 o Despite a low Q factor, the nanoslit array significantly enhances the emission to 0 o due to a Small modal volume The nanophotonics and quantum fluids group N. Livneh et al. , Nano Letters(2011)

Angular emission spectrum – QD monolayer The nanophotonics and quantum fluids group N. Livneh et al. , Nano Letters(2011)

Towards directional emission of a single QD - The nanophotonics and quantum fluids group

2. enhancement of optical nonlinearities: Two photon absorption induced fluorescence Experimental configuration The nanophotonics and quantum fluids group Excitation and Nanocrystal Quantum Dots Photoluminescence M. Harats et al. , Optics Express (2011) Two photon upconversion process

Two photon absorption induced fluorescence QD absorption: - the intensity enhancement factor in the nanoslit array Using the resonant enhancement of EM fields in the nanoslit array results with The induced upconversion is: Al h d Polymer layer H Al Al a Glass substrate The nanophotonics and quantum fluids group M. Harats et al. , Optics Express (2011)

Two photon absorption induced fluorescence TPA and induced upconverted fluorescence in semiconductor NQDs in TE polarization in metallic nanoslit arrays with a maximal enhancement of ~400 The nanophotonics and quantum fluids group M. Harats et al. , Optics Express (2011)

3. Strong exciton-Bragg cavity mode coupling: Bragg exciton-polaritons in Ga. As QW’s Second order bragg resonance The signature of strong coupling: vacuum Rabi splitting (avoided crossing) The nanophotonics and quantum fluids group

Calculated angular absorption spectrum – no excitons TM The nanophotonics and quantum fluids group

Angular absorption spectrum – with excitons TM Clear vacuum Rabi Splitting (~4 me. V). Clear avoided crossings The nanophotonics and quantum fluids group

Angular absorption spectrum – TE TE TE The nanophotonics and quantum fluids group

Thank you The nanophotonics and quantum fluids group

Experimental results wavelength dependence Using Dynamical Diffraction(1), near-field intensities are What’s happening in the noted is bycalculated the red circles? extracted. An averaged unitwavelengths cell enhancement by: (1) M. M. J. Treacy, Phys. Rev. B, 66(19): 195105, Nov 2002.

Analysis As we used a pulse with a spectral width ( ), the enhancement per wavelength is taken into account: This is good agreement between the experimental and theoretical results