Entangled Photon Pairs from Semiconductor Quantum Dots Nikolay

Entangled Photon Pairs from Semiconductor Quantum Dots Nikolay Akopian, Eilon Poem and David Gershoni The Solid State Institute and the Physics Department, Technion, Haifa 32000, Israel Netanel Lindner, Yoav Berlatzky and Joseph Avron The Physics Department, Technion, Haifa 32000, Israel Brian Gerardot and Pierre Petroff Materials Department, UCSB, CA 93106, USA Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Outline n n n Motivation: deterministic sources for entangled photons. Entanglement. Radiative cascades in semiconductor quantum dots. Entanglement by spectral projection. Why does it work in spite of inhomogeneous broadening. Conclusion: semiconductor quantum dots are practical sources for entangled photons on demand. Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Motivation n Entanglement is an essential resource of quantum information processing. Entangled photons are particularly attractive due to their non interacting nature, and the ease with which they can be manipulated. Quantum computing, quantum communication require “Event ready” entangled photon pairs. Therefore, deterministic sources of entangled photons are needed. Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Entanglement n Systems A and B, Hilbert space n The combined state is not entangled (seperable) if Technion – Israel Institute of Technology, Physics Department and Solid State Institute

(not) Entanglement Alice Bob i Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Entanglement n n How can we tell if a general state is entangled? For two qubits, we have the Peres criterion: is entangled iff its partial transposition satisfies A. Peres, Phys. Rev. Lett. 77, 1413, 1996. Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Example n The state gives the density matrix n The partial transpose gives a non –positive matrix Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Strain induced Self assembled Quantum Dots 3 D confinement of charge carriers with discrete spectrum of spin degenerate energy levels. Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Single semiconductor quantum dot Off resonance excitation P S emission due to radiative recombination h S P Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Entangled photon pairs from radiative cascades Right circular polarization S shell 2 e- Left circular polarization S shell 2 h+ Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Bi-exiton radiative casacade Isotropic QD R L Anisotropic QD L R Suggestion: Benson Yamamoto et al PRL 2000 Technion – Israel Institute of Technology, Physics Department and Solid State Institute

The anisotropic e-h exchange interaction H V - + H The photon’s energy indicates the decay path V No entanglement Classical correlations only Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Polarization Momentum wave function HH Environment Reduced Density Matrix For Polarization HV VH VV Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Peres criterion for entanglement: HH HV VH VV Maximal Bell inequality violation: M. Horodecki et. al. , Phys. Lett. A 223, 1 (1996) Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Two photon polarization density matrix: In our case: However, we can still make a measurement on the wave packet: Technion – Israel Institute of Technology, Physics Department and Solid State Institute

The experimental setup Nika Akopian Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Polarization sensitive photoluminescence Spectral diffusion!! Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Polarization density matrix without spectral projection Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Spectral projection – Elimination of the ‘which path’ Information. Photons from both decay paths Technion – Israel Institute of Technology, Physics Department and Solid State Institute

N, γ Spectral filtering Relative Number of photon pairs Off diagonal matrix element Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Density matrix – spectral window of 200 25 μe. V (closed (open slits) Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Density matrix – spectral window of 25 μe. V (closed slits) Bell inequality violation Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Is there any ‘which path’ information left in the degrees of freedom of the QD’s environment ? No remnant ‘which path’ witness in the enviroenment of the QD!! Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Spectral Filtering in the presence of inhomogeneous broadening Energy of X photon (2) Energy conservation Energy of XX photon (1) Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Spectral Filtering in the presence of inhomogeneous broadening Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Conclusions: n First demonstration of entangled photon pairs from the radiative cascade in SCQDs. No other “which path” information in the environment. Deterministic entangled photon pair devices based on SCQD are thus possible provided is increased such that no spectral filtering is needed. Akopian et al, Phys. Rev. Lett. 96, 130501 (2006) n Lindner et al, quant-ph/0601200. n n n Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Intensity Cross--Correlation Function : j D 1 MC i PL Energy Second order Intensity Correlation Function. Ij (t 1) MC D 2 Ii (t 2) correlator I(t) - Intensity conditional probability of detecting photon from line j at time (t+ ) after photon from line i had been detected at time (t) Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Polarization Sensitive Intensity Cross. Correlation Measurements number of correlated radiative cascades Decay time of 0. 8 nsec Γ=1. 6μe. V Time (nsec) Technion – Israel Institute of Technology, Physics Department and Solid State Institute

Polarization Tomography Spectral window 200 μe. V Technion – Israel Institute of Technology, Physics Department and Solid State Institute

no subtraction of events from distinct cascades! 1. 5 ns window Largest negative eigenvalue of the partially transposed matrix:

no subtraction of events from distinct cascades! 0. 6 ns window Largest negative eigenvalue of the partially transposed matrix:

no subtraction of events from distinct cascades! 1. 5 ns temporal window

no subtraction of events from distinct cascades! 0. 6 ns temporal window

Polarization Tomography Spectral window 25 μe. V Technion – Israel Institute of Technology, Physics Department and Solid State Institute