Quantum dots and
entanglement
Tobias Huber
Thanks to…
Uni InnsbruckInstitute for exp. physicsGregor WeihsAna PredojevićMax PrilmüllerStephanie GrabherDaniel FögerHarishankar JayakumarThomas KautenMichael Sehner
Uni InnsbruckInstitute for theo. physicsHelmut RitschLaurin OstermannHashem Zoubi
Uni InnsbruckStaffCarina-Theresa OberhölerArmin SailerChristoph WegscheiderAnton SchönherrJQI @ NIST & UMD
Glenn Solomon
Uni StuttgartMarkus MüllerPeter Michler
Uni WaterlooMilad KoshnegarHamed Majedi
Uni BordeauxPhilippe TamaratBrahim Louis
Uni OlomoucIvo StrakaMiroslav JežekRadim Filip
CNRC CanadaDan DalacuPhilip Poole
Uni WürzburgChristian SchneiderSven Höfling
Why care about quantum light?
www.scienceabc.com www.ligo.caltech.edu/page/ligo-detectors
Communication Interferometry Imaging
www.rp-photonics.com
J. Carolan et al. Science
youtube.com, NIST
Optical quantum computing Metrology Fundamental new physics
sciencealert.com
Outline• Quantum dots (QD)
• (Two photon) entanglement• Polarization entangled photons
• Time-bin entangled photons
• 2 photon resonant excitation
• Hyper-entanglement
Quantum dots
• Semiconductor structure
• confined in all 3 dimensions
©JQI
Bryant and Solomon,
Optics of quantum dots and wires, 2005
Bryant and Solomon, Optics of quantum dots and wires, 2005
Electronic structure:
Confined states:X – ExcitonXX – BiexcitonX+(-) – Charged exciton (trion)XX+(-) – Charged biexciton
Excitation process:
Quantum dot states
Entanglement
• 2-qubit entanglement:
𝜓 𝐴𝐵 ≠ 𝜓 𝐴⨂ 𝜓 𝐵
4 Bell states, e.g. :
𝜙+ = 1
20 𝐴⨂ 0 𝐵 + 1 𝐴⨂ 1 𝐵
= 1
2( 00 + |11⟩)
Polarization entanglement from QDs
𝜙 = 1
2( 𝐻𝐻 + 𝑒𝑖𝑆𝑡/ℏ|𝑉𝑉⟩)
Minimize S by:• Finding a round quantum dot• E-field (Gerardot et al. APL 90, 041101 (2007),
Muller et al. PRL 103, 217402 (2009))
• B-field (Kowalik et al. PRB 75, 195340 (2007)
• Strain (Trotta et al. PRB 88, 155312 (2013)
• Thermal annealing (Ellis et al. APL 90, 011907
(2007))
• Fine-structure splitting S must be small• or fast detection to resolve phase change
H … horizontally polarized photonV … vertically polarized photon
Reconstructed density matrix
Experiment Theory
Fidelity F=0.81(6)Concurrence C=0.71(5)
𝜌 = 𝜓 ⟨𝜓|Polarization entanglement
Time-bin entanglement
𝜓 =1
2𝑒𝑎𝑟𝑙𝑦 𝑋 𝑒𝑎𝑟𝑙𝑦 𝑋𝑋 + 𝑒𝑖𝜙𝑝 𝑙𝑎𝑡𝑒 𝑋 𝑙𝑎𝑡𝑒 𝑋𝑋
Pump interferometer phase 𝜙𝑝
is encoded into the state
Conventional excitation method
is not phase preserving
Resonant excitation necessary
2 photon resonant excitation of the biexciton
biexciton has 𝑀 = 0ground state has M = 0photon has 𝑆 = ±1 ground to biexciton state is (dipole)forbidden
𝐻 = 12Ω(𝑡)(|𝑔⟩⟨𝑥|+|𝑥⟩⟨𝑏|+𝐻.𝑐.+(Δ𝑥−Δ𝑏)|𝑥⟩⟨𝑥|−2Δ𝑏|𝑏⟩⟨𝑏|
Jayakumar et al. Phys. Rev. Lett. 110, 135505 (2013)Huber et al. Phys. Rev. B 93, 201301(R) (2016)
Resonant excitation allowsto create time bin entangledphtons
Reconstructed density matrix
ExperimentTheory
Fidelity F=0.87(4)Concurrence C=0.76(8)
𝜌 = 𝜓 ⟨𝜓|Time-bin entanglement
2 photon resonant excitation• What is it good for?
• deterministic generation of photon pairs Jayakumar et al. Phys. Rev. Lett. 110, 135505 (2013)
• improved indistinguishabilityindistinguishability improves from 0 to 0.39 Huber et al. New J. Phys. 17 123025 (2015)
• coherent controlenables e.g. creation of time bin entangled photons Jayakumar et al. Nature Communications 5, 4251 (2014)
• improved polarization entanglement fidelity improves from 0.72 to 0.81 Müller et al. Nature Photonics 8, 224–228 (2014)
Hyper-entanglement
• Entanglement in two (or more) degrees of freedom
𝜓𝐻𝑦𝑝𝑒𝑟 = 12|𝜓𝑃𝑜𝑙𝑎𝑟𝑖𝑧𝑎𝑡𝑖𝑜𝑛⟩⨂ 𝜓𝑇𝑖𝑚𝑒−𝑏𝑖𝑛
= 12𝐻1𝐻2 + 𝑉1𝑉2 ⊗ ( 𝑒𝑎𝑟𝑙𝑦1𝑒𝑎𝑟𝑙𝑦2 + |𝑙𝑎𝑡𝑒1𝑙𝑎𝑡𝑒2⟩)
• Good for: complete Bell state measurments, superdense coding,
enhanced noise robustness
Hyper-entanglement analysis• Tomographic reconstruction
• For n-qubit tomography:• 4𝑛 parameters are needed
• For a 2x2-qubit hyper-entangled state:• 256 different projections
• Subspaces can be selected:• Neglect projections in the other subspace
• e.g. 𝐻𝐻 = σ𝑖,𝑗∈𝑒𝑎𝑟𝑙𝑦,𝑙𝑎𝑡𝑒 |𝐻𝐻𝑖𝑗⟩
Analysis II and setup
Phase settings:𝜙𝑋(𝑋𝑋) = 0° … +𝑋
𝜙𝑋(𝑋𝑋) = 90° … +𝑌
Full hyper-entangled matrixFull reconstruction
Theory
Fidelity F=0.55(4)
𝜌𝑝𝑜𝑙 ⊗𝜌𝑡𝑖𝑚𝑒−𝑏𝑖𝑛
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