Quantum Dots in Photonic Structures Lecture 13: Entangled photons from QD Jan Suffczyński Wednesdays, 17.00, SDT Projekt Fizyka Plus nr POKL.04.01.02-00-034/11 współfinansowany przez Unię Europejską ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Kapitał Ludzki

3. Entangled photons from a single semiconductor QD Plan for today Reminder 2. Entanglement 3. Entangled photons from a single semiconductor QD

Correlation function represents probability of detection of the second photon at time t + , given that the first one was detected at time t

 = t2 – t1 t1 = 0 t2 = 20 Karta do pomiaru korelacji Od źródła fotonów Karta do pomiaru korelacji  = t2 – t1 Dioda „STOP” Liczba skorelowanych zliczeń n() Dioda „START” t1 = 0 wejście STOP t2 = 20 wejście START

Correlation function Thermal light source: Coherent light source (cw): Thermal light source: time t Coherent light source (cw): time t Single photon source (cw): time t T time t  = t2 – t1 Single photon source (pulsed):

Photon statistics Bose-Einstein distribution LASER Poissonian distribution LASER Sub-poissonian distribution

Pojedyncze fotony z QD na żądanie Autokorelacja emisji z ekscytonu neutralnego (X-X): Od próbki X STOP START Funkcja korelacji drugiego rzędu STOP X START g( 2)(0) = 0.073 = 1/13.6 X Rejestrowane fotony pochodzą z pojedynczej kropki czas 

X-CX cross-corelation

Single carrier capture Three carriers capture Single carrier capture CX after X X after CX Single carrier capture START time CX  >0 ↔ X emission after CX emission: STOP X <0 ↔ CX emission after X emission: START time X STOP CX

XX-X crosscorrelation START (H) STOP (H) START STOP XX X time XX-X cascade

Origin of the emission within the caviy mode Energy PL ~15 meV Cavity mode QD ~1 meV

Why is emission at the mode wavelength observed? Quantum nature of a strongly coupled single quantum dot–cavity system, Hennessy et al., Nature (2007): Time (ns) Autocorrelation M - M Crosscorrelation QD - M „Off-resonant cavity–exciton anticorrelation demonstrates the existence of a new, unidentified mechanism for channelling QD excitations into a non-resonant cavity mode.” „… the cavity is accepting multiple photons at the same time - a surprising result given the observed g(2)(0)≈ 0 in cross-correlation with the exciton.” Strong coupling in a single quantum dot–semiconductor microcavity system, Reithmaier et al., Nature (2004) Strong emission at the mode wavelength even for large QD-mode detunings

Dynamics of the emission of the coupled system Pillar B, diameter = 2.3 mm, gM = 0.45 meV, Q = 3000, Purcell factor Fp= 8 X T = 53 K Energy pillar B M T = 53 K pillar B  X and M decay constants similar

Statistics on different micropillars Strong correlation between exciton and Mode decay constants The same emitter responsible for the emission at both (QD i M) energies QD-M detuning (< 3gM) does not crucial for the QD→M transfer effciency J. Suffczyński, PRL 2009

Contribution from different emission lines  When two lines are detuned similarly from the mode, the contribution from more dephased one to the mode emission is dominant

Phonons - diatomic chain example

Solutions to the Normal Mode Eigenvalue Problem ω(k) for the Diatomic Chain л / a 2 –л k w A B C ω+ = Optic Modes ω- = Acoustic Modes There are two solutions for ω2 for each wavenumber k. That is, there are 2 branches to the “Phonon Dispersion Relation” for each k.

Transverse optic mode for the diatomic chain The amplitude of vibration is strongly exaggerated!

Transverse acoustic mode for the diatomic chain

↔ + = a* c* b* Interpretation of the single photon correlation results Crosscorrelation M - X = (X+CX+XX) - X = X-X + CX-X + XX-X X-X CX-X XX-X 1 + a* b* c* g(2) (t) t ↔ 1 = M-X Hennessy et al., Nature (2007)  g(2)(0) ~ 0  Asymmetry of the M-X correlation histogram g(2) (t) t t (ns)

Quantum Entangled photons from a semiconductor QD

Crystals can produce pairs of photons, heading in different directions Crystals can produce pairs of photons, heading in different directions. These pairs always show the same polarization. ?

These are said to be entangled photons These are said to be entangled photons. If one is measured to be vertically polarized, then its partner kilometers away will also be vertical. ? Entanglement

1) Does a polarizing filter act by a)      selecting light with certain characteristics, like a sieve selects grains larger than the hole size or by       changing the light and rotating its polarization, like crayons and a grid Measurement-Reality

Niels Bohr and Einstein argued for 30 years about how to interpret quantum measurements like these.

Niels Bohr codified what became the standard view of quantum mechanics. The filter is like a grid for crayons - the photon has no polarization until it is measured. It is in a superposition of states.

Einstein felt that the filters were like a sieve Einstein felt that the filters were like a sieve. The photons must contain characteristics that determine what they will do.

The information from the measurement of one can’t possibly fly instantaneously to its partner.

He referred to this as ‘spukhafte Fernwirkungen’ which is usually translated as ‘spooky action-at-a-distance’.

Then in 1964 John Bell devised a test. He looked at what happens if the filters are in different orientations.

2)Four entangled pairs of photons head toward two vertical polarizers.

If four make it through on the left, how many make it through on the right? If four make it through on the left, four will make it through on the right. In this situation, there is 100% agreement between the two photon groups. The amount of agreement is the focus of Bell’s analysis.

Next, we put the filter on the right at 30o. 3) Which of the following would you expect to see if all 4 made it through on the left? a) b) c) d) b) The photon on the left is a vertical photon, so its entangled partner should be one too. The filter is 30 degrees away from vertical, so on average ¾ of the photons will get through.

4) What percentage agreement do you expect on average? 0% 25% 75% 100% b) There will be 75% agreement, therefore 25% disagreement.

5) If the right filter is vertical and the left is placed at –30o, what agreement would you expect? b) 25% c) 75% d) 100% b) This situation is really the same as the previous one if you tilt your head by 30 degrees.

How much agreement is expected? 25% b)50% c)75% d)100% Next we combine the two experiments. The left polarizer is at –30 and the right at +30. How much agreement is expected? 25% b)50% c)75% d)100% c) Each shows 75% passing. In the left case, this results the minimum number of agreements, 50% match. In the right case, none match. Usually we’d get something in between the two possibilities. Agreements could be from 50% to 100%.

7) How much agreement does quantum mechanics predict 7) How much agreement does quantum mechanics predict? Hint: The two filters are at 60 degrees to each other. a) 0% b) 25% c) 50% d) 75% d) They agree ½ x ½ = 25%

7) How much agreement does quantum mechanics predict 7) How much agreement does quantum mechanics predict? Hint: The two filters are at 60 degrees to each other. a) 0% b) 25% c) 50% d) 75% d) They agree ½ x ½ = 25%

The photons have a polarization before measuring - the agreement will be between 100% and 50%. Just apply the rules of quantum mechanics - the agreement should be 25%. The results were conclusively in support of quantum mechanics, not Einstein. The entanglement of photons has been demonstrated with the photons separated by over 20 km. Somehow, measuring one photon, instantly affects its partner 20 km away. Confirmation: Alain Aspect et al. 1983

Turning Interference On and Off Two-slit Interference Pattern No Two-slit Interference Pattern H V

“Ghost” Interference In their 1994 “Ghost Interference” experiment, the Shih Group at the University of Maryland in Baltimore County demonstrated that causing one member of an entangled-photon pair to pass through a double slit produces a double slit interference pattern in the position distribution of the other member of the pair also. If one slit is blocked, however, the two slit interference pattern is replaced by a single-slit diffraction pattern in both detectors. Note that a coincidence was required between the two photon detections.

Enangled photons from a QD The method: biexciton – exciton cascade Obstacle: anisotropy Biexciton Exciton Empty dot The energy carries the information on the polarization of the photon

Entangled photons from a QD The method: biexciton – exciton cascade An obstacle: anisotropy Biexciton Exciton The energy carries the information on the polarization of the photon Empty dot (in circular polarization basis:)

X Xdark X Neutral exciton X Formed by: heavy hole and electron Jz = ±3/2 Jz = ±1/2 4 possible spin states of X Xdark X Jz = -1 Jz = +1 Jz = -2 Jz = +2

Fine structure of neutral exciton ( + )/ 2 X δ1~0.1meV ( – )/ 2 X Anisotropic exchange δ0~1meV Isotropic exchange ( + )/ 2 δ2 ≈0 Xdark ( – )/ 2

(No) entanglement test START (H) STOP (H) START STOP XX X time XX-X cascade

Kaskadowa emisja pary fotonów Energia ~ XX V H AES X V H pusta kropka Brak splątania fotonów w kaskadzie XX-X Dodatnia korelacja zgodnych polaryzacji liniowych fotonów w kaskadzie Czas rozpraszania spinu X: TX ~ 3.4  0.6 ns

(No) entanglement test H V B = 0 XX AES X Conclusion: No entanglement, anisotropy governs the polarization of the emission CdTe/ZnTe QDs Classical polarization correlation of the photons in the XX-X cascade

Obstacle: anisotropy - solutions Find QD with Δ≈0 Tune splitting to zero Erase which‐path information with narrow filter Erase which‐path information by time reordering

Influence of the in-plane electric field on the photoluminescence of individual QDs Kowalik et al., APL’2005 InAs/GaAs Quantum Dots

Evolution of the anisotropy exchange splitting with the applied voltage Kowalik et al., APL’2005

Influence of the in-plane magnetic field on the photoluminescence of individual QDs Magnetic field [T] AES [meV] 2 4 6 0.10 0.14 0.18 1.8904 1.891 Energy [eV] m -PL B=0 experiment model 2 4 6 8 10 Magnetic Field [T] [meV] 0.45 p Angle J-2f [rad] Increase or decrease of the anisotropy splitting, depending on the magnetic field direction K. Kowalik et al., PRB 2007

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

Off diagonal matrix element Spectral filtering N,γ 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 25 μeV (closed slits) Density matrix – spectral window of 200 μeV (open slits) Technion – Israel Institute of Technology, Physics Department and Solid State Institute

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

QD in a pillar molecule: an ultrabright source of entangled photons 10 mm 5 mm

QD as an entangled photons source The idea: obtain polarization entangled photon pairs from biexciton-exciton cascade Main obstacle: anisostropy of the QD  exciton level splitting Hindrance: low collection efficiency (a few %) Energy XX X Ground state The solution: coupling of the X and XX to the modes of the photonic molecule When exciton level homogeneous linewidth larger than exciton anisotropy splitting: polarization entangled photons emitted in XX-X cascade  Increased extraction efficiency due to photon funneling into cavity mode

QD as an entangled photons source Distance R R Radius D = 1 µm Distance CC’= 0.7µm PL Intensity (arb. units) DE E A disk centered on the QD is exposed in the resist. The sample is moved by a distance CC’ and a second disk is defined. The exposure time is adjusted to obtain the desired pillars diameter D. 1.315 1.320 1.325 1.330 1.335 Energy (eV) E - controlled by pillar radius DE – controlled by pillar distance

QD as an entangled photons source Distance R R Radius = 1 µm XX Distance = 0.7 µm DE PL Intensity (arb. units) DE X E E A disk centered on the QD is exposed in the resist. The sample is moved by a distance CC’ and a second disk is defined. The exposure time is adjusted to obtain the desired pillars diameter D. Ground state 1.315 1.320 1.325 1.330 1.335 Energy (eV) E - controlled by pillar Radius DE – controlled by pillar Distance

Pillar molecules Radius R Distance Electronic lithography R = 2 µm 1,315 1,320 1,325 1,330 1,335 PL Intensity (arb. units) Energy (eV) Radius Electronic lithography Radius Distance R = 2 µm

Pillar molecules Radius R Distance Electronic lithography R = 1.75 µm 1,315 1,320 1,325 1,330 1,335 PL Intensity (arb. units) Energy (eV) Radius Electronic lithography Radius R = 1.75 µm Distance R = 2 µm

Pillar molecules Radius R Distance Electronic lithography R = 1.5 µm 1,315 1,320 1,325 1,330 1,335 PL Intensity (arb. units) Energy (eV) Radius Electronic lithography Radius R = 1.5 µm R = 1.75 µm Distance R = 2 µm

Pillar molecules Radius R Distance Electronic lithography R = 1.25 µm 1,315 1,320 1,325 1,330 1,335 PL Intensity (arb. units) Energy (eV) Radius Electronic lithography R = 1.25 µm Radius R = 1.5 µm R = 1.75 µm Distance R = 2 µm

Pillar molecules Photon Energy (meV) R Distance Electronic lithography 1,315 1,320 1,325 1,330 1,335 PL Intensity (arb. units) Energy (eV) Electronic lithography Radius Distance

Experimental realization Purcell effect evidenced on X and XX transitions  The proof of entanglement: polarization resolved second order XX-X crosscorrelations A. Dousse, at al. Nature 2010

Characterization of the source - entanglement Density matrix of the two-photon state  67 % degree of entanglement  Entanglement criteria fullfilled

Characterization of the source - brightness Jaka wydajnosc : 10 MHZ do 80 MHZ  Increased photon collection/extraction efficiency (~30 %)  10 MHz rate of entangled photon pairs collected on the first lens