Summary of research activities Gaby Slavcheva Centre for Photonics and Photonic Materials Physics Department, University of Bath, Bath BA2 7AY, United Kingdom BQIT:15, 15-17 April 2015, Colston Hall Bristol, UK

Quantum Well Exciton-Polaritons in planar Microcavities Strongly-coupled cavity-emitter system: e c g e Exciton-polaritons: dressed states of bosonic nature formed by strong coupling of QW excitons to microcavity photons Energy vs. momentum dispersion S. Jiang et al., APL 73, 3031 (1998) C. Weisbuch et al., PRL 69, 3314(1992)

Why exciton-polaritons for QIT applications? Advantages over bare photons and excitons Light effective mass by dressing QW excitons with cavity fields: 𝑚 𝑝 ~ 10 −4 𝑚 𝑒𝑥 Higher critical temperature for BEC : λ T ~ h 2π m p kT Extended wave functions and large coherence lengths reinforced by the photonic component: 𝜆 𝑇 ~ 1-2 μm at 5K  suppress disorder effects Large binding energies and low exciton density by using multiple QWs suppress Auger recombination and exciton ionization Main polariton decay channel – photon leakage from the cavity with energy and momentum conservation – experimental access to energy momentum dispersion Allows build up of many-body quantum coherent effects: BEC, superfluidity Due to excitonic component: weaker diffraction & tighter localisation: smaller λ 𝑝 Polariton waves can be confined into structures with submicron size Strong interparticle interactions: strong nonlinear optical response, lower operational powers ~ fJ/m2 and faster switching speeds ~a few ps Fabrication of Polaritonic Integrated Circuits based on structured microcavities “on a chip” Integrated optical technologies for quantum computing based on linear optics: under active development in the recent decade Nonlinear optical interactions ‘on a chip’: new unexplored field that may play a key role

Nonlinear Polariton Dynamics in Microcavity Wires Particularly promising integration platform for quantum information applications: Large nonlinearity Broad transparency window Mature fabrication technology Possibility of monolithic integration with semiconductor diode lasers and VCSELs By lateral etching of planar semiconductor microcavities: array of 1D MWs Triggered optical parametric oscillator regime Cross-section of a microcavity wire E. Wertz, et al, Nature Physics 6, 860 (2010)

Multi-stability of stationary nonlinear modes and 1D polariton soliton formation 2D scalar mean-field driven-dissipative (Gross-Pitaevskii) polariton model: 𝜕 𝑡 E−𝑖 𝜕 𝑥 2 + 𝜕 𝑦 2 E+ 𝛾 𝑐 −𝑖 𝛿 𝑐 −𝑖−𝑖𝑈 𝑦 =𝑖 Ω 𝑅 𝑦 Ψ +𝐸 𝑝 𝑒 𝑖𝜅𝑥 +𝐸s 𝑒 𝑖𝜅𝑠𝑥 +𝐸s1 𝑒 𝑖𝜅𝑠1𝑥 𝜕 𝑡 Ψ+ 𝛾 𝑒 −𝑖 𝛿 𝑒 −𝑖 Ψ+𝑖 Ψ 2 Ψ=𝑖 Ω 𝑅 𝑦 E G. Slavcheva et al, Optics Letters, 40 1787 (2015)

Soliton propagation in tilted and tapered wires  max=11.5 @ Ep=0.075 ‘polariton soliton amplifier’ repeaters at junctions

Multi-stability and solitons in coupled parallel microcavity wires 𝑖 𝜕 𝐸 1 𝜕𝑡 + Ω 𝑅 Ψ 1 +𝜅 𝐸 2 =0 𝑖 𝜕 𝐸 2 𝜕𝑡 + Ω 𝑅 Ψ 2 +𝜅 𝐸 1 =0 − Ψ 1 2 Ψ 1 + Ω 𝑅 𝐸 1 =0 − Ψ 2 2 Ψ 2 + Ω 𝑅 𝐸 2 =0 𝐸 1 ≠ 𝐸 2 𝐸 1,2 = 𝐴 1,2 𝑒 𝑖𝜔𝑡 Ψ 1,2 = Ψ 1,2 𝑒 𝑖𝜔𝑡 𝐴 1 = 𝐵 1 2 𝐵 1 Ω 𝑅 ; 𝐴 2 = 𝐵 2 2 𝐵 2 Ω 𝑅

Modelling and design of building blocks of polaritonic ICs Simulation of X- and Y- splitters, couplers, routers, amplifiers, logic gates based on soliton logic Simulation of polaritonic Bragg gratings (corrugated microcavity wires) Parametric nonlinearity amplification due to soliton slow down in a periodic potential: low-consumption Polaritonic ICs Soliton percolation in disordered Bragg gratings: Soliton insulator-conductor phase transitions Interplay between nonlinearity and disorder Shklovskii and Efros, ‘Electronic Properties of Doped Semiconductors’, (Springer, 1984)

Many-body effects with polariton solitons in 2D lattices : Quantum simulators Functional operations with discrete solitons in 2D polaritonic lattices Quantum phase transitions with polariton solitons: Mott transition between polariton insulator and superfluid (soliton current) Identify protected gapped phases Exciton polariton lattices in weak confinement potentials: Quantum simulation of Bose-Hubbard and Rabi-Hubbard models Square lattice Triangular d-wave condensation condensation near Dirac points Honeycomb Kagome Kim et al., Nat. Phys. 7, 681 (2011) ; Kim et al. N. J. Phys. (2014);Kusodo et al., PRB (2013); Masumoto et al. New J. Phys. 14, 065002 (2012)

Non-classical light generation using exciton-polaritons: future prospects Strongly-coupled planar microcavity: ~6% squeezing of the internal polariton mode close to the bistability turning point by measuring the noise of the outgoing light (J. Ph. Karr et al. PRA 69, 031802 (R) 2004) 3D polariton confinement: polariton quantum boxes Patterning of a planar cavity with metal: weak optical confinement ~ 200 μeV (S. Utsunomiya et al., Nature Physics 4, 700, 2008) Micropillar etching based on planar microcavity: moderate to strong confinement possible (up to ~20 meV); for deep etching: detrimental surface effects; for shallow etch: strong emission from etched area Patterned mesas (textured microcavities): strong optical confinement on the order of a few meV; no detrimental surface effects 4μm F. Tassone et al. PRA 62, 063809 (2000); El Daif et al. APL 88, 061105 (2006); R. Idrissi Kaitouni et al. PRB 74, 155311 (2006);

Embedding quantum components in the polaritonic ICs: quantum emitters/detectors 1D chains of QDs / polaritonic quantum boxes Polariton soliton formation in the extreme non-linear few-photon regime- few-photon pulses Gap polariton solitons for device applications Artificially engineered periodic structures: 2D coupled-cavity lattices and cavity-emitter lattices (with embedded QDs) Generation of entangled photon pairs in microcavity wires Two-photon Raman scattering (TPRS, hyper-Raman scattering) Biexciton resonant parametric emission(Edamatsu et al. Nature 431, 167 (2004) Incorporate single-photon detectors (e.g. Single-photon transistor)- Kardynal et al. APL 90, 181114 (2007) Generate quantum correlated polariton states designed by quantum interference between integrated polaritonic components

THz photon generation by exciton-polariton condensates BEC proposed as a tool for realisation of a new generation ‘bosonic’ lasers Final state bosonic stimulation triggers emission from excited excitonic states (intra-excitonic transitions) Polariton-triggered THz VCSEL geometry THz VCSEL A. V. Kavokin et al., PRL 108, 197401 (2012) G. Slavcheva et al. PRB 88, 085321 (2013) BCL Bosonic cascade THz laser: cascade between equidistant exciton states confined in a trap (e.g. QW) in a microcavity Waveguide geometry Second-order coherence 𝑔 (2) (0) of THz radiation from each energy level (currently on-going): master Boltzmann eqns.

Exciton Two-Photon Absorption probability Polarisation dependence Polariton-triggered THz VCSEL geometry Changing polarisation from YY to XX one can vary the lasing threshold by a factor of 5 Quantum efficiency polarisation dependence for different polarisation configurations of the two pumping photons at linearly polarised THz emission: maximum 𝜂 found Quantum efficiency polarisation dependence for different polarisation configurations of the two pumping photons at linearly polarised THz emission: maximum 𝜂 found Information and communications technology: terahertz technology for wireless communication, high-speed data processing (opto-chip) and satellite communication

Coherent optical manipulation of a single spin in a charged QD Resonantly-driven ground trion singlet transition: extended spin lifetimes, limited by hyperfine interaction Energy-level diagram of a negatively charged exciton (trion) Selective generation and detection of specific spin states by circularly-polarised optical pulse excitation with predefined helicity 𝜎 − -excitation Initially populated ↑ Initially populated ↓

Master Maxwell’s curl-pseudospin equations for an N-level quantum system Maxwell’s curl equations Density matrix equations Macroscopic polarisation 𝜕𝑯 𝜕𝑡 =− 1 𝜇 𝛻×𝑬 𝜕𝑬 𝜕𝑡 = 1 𝜀 𝛻×𝑯− 1 𝜀 𝜕𝑷 𝜕𝑡 𝜕 𝜌 𝜕𝑡 = 𝑖 ℏ 𝜌 , 𝐻 + 𝜎 − Γ 𝑡 𝜌 𝜎 =𝑑𝑖𝑎𝑔 𝑇𝑟 Γ 𝑖 𝜌 , 𝑖=1,2,…,𝑁 N Lie group algebra N N 𝑁𝑎 - resonant dipole density N-1 ij 3 i ℘= 𝑖 𝑬.𝑒 𝒓 𝑗 3 3 Dipole moment matrix element 2 32 2 2 ij, ij radiative/non-radiative transition rates 21 Master pseudospin equations 1 𝜕 𝑆 𝑗 𝜕𝑡 = 𝑓 𝑗𝑘𝑙 Γ 𝑘 𝑆 𝑙 + 1 2 𝑇𝑟 𝜎 𝜆 𝑗 − 1 𝑇 𝑗 𝑆 𝑗 − 𝑆 𝑗𝑒 , 𝑗=1,2,…,𝑁 𝑁−1 𝑓 𝑗𝑘𝑙 Γ 𝑘 𝑆 𝑙 + 1 2 𝑇𝑟 𝜎 𝜆 𝑗 , 𝑗=𝑁 𝑁−1 +1,…, 𝑁 2 −1 1 E=0 Transverse polarisation relaxation (dephasing) Γ 𝑡 𝑁×𝑁 G. Slavcheva, PRB 77, 115347 (2008)

Single-shot spin initialisation and readout -pulse Tp=1.3 ps E0=3106 Vm-1 -pulse Tp=1.3 ps E0=550 Vm-1 σ − 12-pulse Tp=1.3 ps E0=4107 Vm-1 Model predictions: two ways of reliable initial spin state detection (photon echo and non-monotonic PTRPL trace in time) Sufficiently long time interval ~400 ps exists within which PL traces differ allowing differentiation between the two initial spin states Onset of optical Rabi oscillations regime

Coherent optical spin manipulation through hot trion states in p-doped InAs/GaAs QDs Ey z Ex Hot X+ trion energy-level diagram in a p-doped InAs/GaAs QD Exchange interactions can be revealed in the excited charged excitonic spectra

Discrete-level model of the X+* trion fine structure Longitudinal relaxation Radiative (spontaneous) decay 21 ~1.27 ns 1-hole experiment Estimated spontaneous emission times: 41 ~1.35 ns, 51 ~61 ~1.2 ns; ~9.83 10-29 Cm Non-radiative decay (Theory) Trasverse spin decoherence rates e~ 500 ps; h~ 14 ns; ff~ 125 ps Approach allows predicting optimum pulse parameters (power, duration) for efficient control of spin dynamics Braun et al, PRL 94, 116601 (2005); Eble et al, PRL 102, 146601 (2009)