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

2. 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)

3. 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

4. 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)

5. 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 𝜕 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, (2015)

6. Soliton propagation in tilted and tapered wires
 Ep=0.075
‘polariton soliton amplifier’
repeaters at junctions

7. 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 Ψ 1 + Ω 𝑅 𝐸 1 =0 − Ψ 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 𝐵 1 Ω 𝑅 ; 𝐴 2 = 𝐵 𝐵 2 Ω 𝑅

8. 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)

9. 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, (2012)

10. 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, (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, (2000); El Daif et al. APL 88, (2006);
R. Idrissi Kaitouni et al. PRB 74, (2006);

11. 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, (2007)
Generate quantum correlated polariton states designed by quantum interference between integrated polaritonic components

12. 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, (2012)
G. Slavcheva et al. PRB 88, (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.

13. 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

14. 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 ↓

15. 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 𝑇𝑟 𝜎 𝜆 𝑗 − 1 𝑇 𝑗 𝑆 𝑗 − 𝑆 𝑗𝑒 , 𝑗=1,2,…,𝑁 𝑁−1 𝑓 𝑗𝑘𝑙 Γ 𝑘 𝑆 𝑙 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, (2008)

16. 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

17. Coherent optical spin manipulation through hot trion states in p-doped InAs/GaAs QDsEy 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

18. 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, (2005);
Eble et al, PRL 102, (2009)