Entanglement Swapping with Semiconductor-generated Photons
Michael Zopf, Robert Keil, Yan Chen, Jingzhong Yang, Disheng Chen, Fei Ding, Oliver G. Schmidt
EEntanglement Swapping with Semiconductor-generated Photons
Michael Zopf, Robert Keil, Yan Chen, Jingzhong Yang,
1, 2
Disheng Chen, Fei Ding,
1, 2, ∗ and Oliver G. Schmidt
1, 3, † Institute for Integrative Nanosciences, Leibniz IFW Dresden, Helmholtzstraße 20, 01069 Dresden, Germany Institut f¨ur Festk¨orperphysik, Leibniz Universit¨at Hannover, Appelstraße 2, 30167 Hannover, Germany Material Systems for Nanoelectronics, Technische Universit¨at Chemnitz, 09107 Chemnitz, Germany
Transferring entangled states between photon pairs is essential for quantum communication tech-nologies. Semiconductor quantum dots are the most promising candidate for generating polarization-entangled photons deterministically. Recent improvements in photonic quality and brightness nowmake them suited for complex quantum optical purposes in practical devices. Here we demonstratefor the first time swapping of entangled states between two pairs of photons emitted by a singlequantum dot. A joint Bell measurement heralds the successful generation of the Bell state Ψ + witha fidelity of up to 0 . ± .
04. The state’s nonlocal nature is confirmed by violating the CHSH-Bell inequality. Our photon source is compatible with atom-based quantum memories, enablingimplementation of hybrid quantum repeaters. This experiment thus is a major step forward forsemiconductor based quantum communication technologies.
Semiconductor light sources have revolutionized sci-ence and technology since laser diodes [1, 2] andvertical-cavity surface-emitting lasers (VCSELs) [3, 4]arrived in the 1960’s. Quantum mechanics lies at theroots for these devices, yet quantum states of lighthave only in recent decades been studied extensivelyin their own right - sparking the ”second quantum rev-olution”. Semiconductor sources can now emit singlephotons [5] and entangled photons [6] on demand (seeFig. 1a), more reliably and intensely than non-linearcrystals. They hold great potential for a range of ap-plications in quantum communication [7], quantummetrology [8] and quantum computation [9].The next step towards building quantum networks isto transfer entangled states between distinct pairs ofphotons [10–12]. This entails substituting the pairwiseentanglement in two-photon states with entanglementbetween photons from different pairs [13, 14]. The firstexperiment to do this two decades ago [15] used a tech-nique based on spontaneous parametric down conver-sion in a nonlinear optical crystal [16, 17]. Thoughsuch sources are widely used, for example to entanglemultiple photons [18], their brightness and thereforescalability is fundamentally limited owing to Poisso-nian emission statistics [19].Semiconductor quantum dots (QDs), by contrast, areable to generate entangled photon pairs determinis-tically one by one [20]. However, until recently, QDswere too faint and of poor degree of entanglement andindistinguishability to use for advanced quantum ap-plications. Improvements of the past three years haveovercome these limitations. Highly coherent [21] andstrongly entangled photons [22, 23] can now be gener-ated with high brightness [24] and reproducibility [22]from QDs.Here we demonstrate, for the first time, entangle-ment swapping between polarization-entangled pho-tons emitted by a semiconductor QD. The Bell stateΨ + is generated with high fidelity and strong non-local characteristics, proven by violating the CHSH-Bell inequality [25, 26]. Our semiconductor sourcesare compatible with atom-based quantum memories.This opens up their use in devices such as quantumrepeaters (the quantum equivalent of a classical ampli-fier) [27] which are essential for long distance quantumcommunication. Quantum dot ab Alice BobEmission 1 Emission 2BSMBell state 1 Bell state 2Bell state 31962Laser diode
Entangled-photon LED Figure 1. (a)
Historical development of integrated en-tangled photon sources, starting from semiconductor lasersand photonic entanglement based on nonlinear optical ma-terials, to scalable quantum dot sources of entangled pho-tons. (b)
Principle of an entanglement swapping experi-ment using a quantum dot. Two distinct pairs of entan-gled photons are generated (emission 1 and 2). One pho-ton from each pair is directed to a Bell state measurement(BSM). Upon success, the BSM establishes entanglementof the remaining photons sent to Alice and Bob.
ENTANGLED STATE GENERATION
The experimental concept is sketched in Fig. 1b.Two pairs of polarization-entangled photons areconsecutively emitted (emission 1 and 2) by a singlesemiconductor quantum dot. The polarization ofone photon from each pair is measured by separatedetectors, labeled Alice and Bob. Then, a joint Bellstate measurement (BSM) is made on the remainingtwo photons; this swaps the entanglement of theoriginal pairs to the photons that Alice and Bobreceive. The source of entangled photons in ourexperiment are GaAs/AlGaAs QDs grown by localdroplet etching, as they are reliable and reprodu-cable to make with entanglement fidelities close tounity [22] and highly indisitinguishable photons [23]. a r X i v : . [ qu a n t - ph ] J a n bc I n t e n s i t y [ k c p s ] I n t e n s i t y [ k c p s ] Rb D transitionsX XXX XX L a s e r |X|XX|0 Suppressed resonant laserWavelength λ [nm]780 781 782 a Quarter wave plateHalf wave plateLinear polarizer Notch filterDichroic filterLiquid crystal retarder Diffraction gratingSingle-mode fiberSingle photon detector L a s e r QD XX1X1 XX2 X2broadbandoptical antenna V H C o i n c i d e n c e s / s Delay time [ns]-40 000 4020-20 X XX7595
Figure 2.
Experimental setup and quantum dot emission spectra. (a)
Entanglement swapping setup. Twoconsecutive pairs of polarization-entangled photons Xi–XXi (emission i = 1,2) are generated by resonantly exciting aquantum dot (QD) embedded in an optical antenna. The emitted light is cleansed of residual laser signal and thensent to a non-polarizing beam splitter. Two photons XX1 and XX2 from each emission are directed to a Bell statemeasurement (BSM). Coincidence detection heralds the polarization-entanglement of the remaining photons X1 andX2. The latter are guided to two polarization-analyzers Alice and Bob. (b)
QD photoluminescence spectrum underabove-bandgap excitation highlighting the most prominent features, the exciton (X) and bi-exciton (XX) emissions. (c)
Emission spectrum obtained by pulsed resonant two-photon excitation of the bi-exciton state. Decay via the intermediateexciton states results in the emission of spectrally distinct, polarization-entangled photon pairs XX–X. The inset showsthe intensity autocorrelation for each spectral feature, indicating a high single-photon purity of g (2) (0) ≤ . The QDs are embedded in a nanomembrane whichis sandwiched by a silver reflector and a spacinglayer, attached to a gallium phosphide hemsiphericallens [24]. This design provides a broadband opticalantenna, offering photon extraction efficiencies up to65 % while preserving a high single photon purity andentanglement fidelity.The QD antenna’s operating temperature of T = 4 Kis reached using a closed-cycle helium cryostat. A se-lected QD is first triggered by optically pumping thesurrounding host semiconductor material. The emis-sion spectrum in Fig. 2b displays two prominent fea-tures: the exciton (X) emission at 780 . . transitions of ru-bidium, a prominent quantum memory candidate [28].To generate two consecutive polarization-entangledphoton pairs (emission 1 and 2), we exploit the bi-exciton(XX)-exciton(X) radiative cascade [20]. Deter-ministic excitation of the XX state is ensured by reso-nant two-photon excitation [29]. A pair of photons isemitted in the successive decay via the intermediate Xstates to the ground state (left inset of Fig. 2c). Thephotons share the polarization-entangled Bell state | Φ + (cid:105) i in the respective emission i = 1 , | Φ + (cid:105) i = | H X H XX (cid:105) + | V X V XX (cid:105) . (1)with H and V representing horizontal and verticalpolarization of the rectilinear basis.For efficient resonant excitation we use a pulsedTi:sapphire laser operating at a 76MHz repetition rate. Guiding the laser light into a tunable, unbal-anced Mach-Zehnder interferometer yields two con-secutive excitation pulses. The laser’s spectral widthis reduced and the central wavelength adjusted by asuccessive diffraction grating and single-mode fiber.Thus the laser emission wavelength is fixed at the XXtwo-photon resonance between the X and XX emis-sion. Notch filters are used to suppress the scatteredlaser in the QD emission signal. The signal intensityis enhanced further by exciting the QD by a weakcontinuous wave laser emitting at 650nm.Fig. 2c shows the resulting emission spectrum ofthe XX cascade emission and a well-suppressed res-onant laser. The right inset shows the intensity auto-correlation g (2) ( τ ) of the X and XX emissions obtainedin a Hanbury Brown and Twiss measurement [30].Vanishing coincidences at zero delay time bear witnessto a high single photon purity, with values of g (2) X (0) =0 . ± . g (2) XX (0) = 0 . ± . | α (cid:105) is a product ofthe states from emissions 1 and 2. It can be rewritteninto products of Bell states between the X and XXphotons: | α (cid:105) = | Φ + (cid:105) | Φ + (cid:105) = 12 ( | Φ + (cid:105) X | Φ + (cid:105) XX + | Φ − (cid:105) X | Φ − (cid:105) XX + | Ψ + (cid:105) X | Ψ + (cid:105) XX + | Ψ − (cid:105) X | Ψ − (cid:105) XX ) (2)with the four polarization Bell states being | Φ ± (cid:105) = | HH (cid:105) ± | V V (cid:105)| Ψ ± (cid:105) = | HV (cid:105) ± | V H (cid:105) (3)Projecting | α (cid:105) to a Bell state between photons XX1and XX2 will in turn result in a Bell state shared bythe previously uncorrelated X1 and X2. We projectto the state | Ψ + (cid:105) by performing the following BSM:First, photons XX1 and XX2 are sent to interfere ona non-polarizing beam splitter. To ensure successfulquantum interference, the arrival times of XX1 andXX2 have to be matched. Therefore the XX1 photonsare delayed before the BSM, in order to compensatefor the time difference between emission 1 and 2.After interference, the photons pass through an H-or V-oriented polarizer in each beam splitter output,respectively. Single-mode fibers then deliver thephotons to superconducting nanowire single pho-ton detectors (SNSPDs) with time resolutions of 50ps.Successful coincidence detection at the BSM nowleaves the two remaining photons X1 and X2 in theBell state | Φ + (cid:105) AB = | HV (cid:105) + | V H (cid:105) (4)sent to Alice and Bob for measurement. Subsequentarrangement of a quarter-wave plate, half-wave plate,polarizer and SNSPD allows for projection on any de-sired polarization state. In order to compensate foran accumulated phase and retardation in the setupwe employ liquid crystal retarders and tilted quarterwave plates.
INITIAL STATE CHARACTERIZATION
Successful entanglement swapping relies on highentanglement fidelities f i of the initial photon pairs(emission i = 1 ,
2) and on high photon indistin-guishabilities I of the XX photons sent to the BSM.We perform quantum state tomography [31] toreconstruct the full two-photon density matrix ρ i ofemissions i = 1 , | Φ + (cid:105) . Weobtain fidelities of f = 0 . ± . f = 0 . ± . . ± . µ eV, evanescent laserlight background and polarization-dephasing duringthe QD’s emission process are expected to have only c N o r m a li z e d c o i n c i d e n c e s XX2 XX1
CorrelatorHWP || || || polarizationpolarization0 a HVHH HHHVVHVVRe( ρ )0.50.25 VV0 VH HVHH HHHVVHVVIm( ρ )0.50.25 VV0 VH b HH HHHVVHVVIm( ρ )0.50.250Emission 1Emission 2HVHH HHHVVHVVRe( ρ )0.50.25 VV0 VH VHHV VV1 Figure 3.
Degree of entanglement and photon in-distinguishability.
Two-photon density matrices of thephoton pairs Xi–XXi from (a) emission i=1 and (b) emission i=2. Real (left) and imaginary part (right)closely resemble the Bell state | Φ + (cid:105) with fidelities of f = 0 . ± . f = 0 . ± . (c) The indistinguishabil-ity I = 0 . ± .
009 of photons XX1 and XX2 is derivedfrom a Hong-Ou-Mandel measurement. Coincidences aredetected at the output of an unbalanced Mach-Zehnderinterferometer (inset) and binned according to their de-tection delay times. Using a half-wave plate (HWP), co-polarized photons yield reduced coincidences (red) com-pared with crossed polarizations (black). a small effect on the fidelity [22].Fig. 3c shows a coincidence histogram obtained in anindistinguishability measurement [32] based on Hong-Ou-Mandel interference [33]. The two consecutive XXphotons are guided into an unbalanced Mach-Zehnderinterferometer featuring a time delay identical to thatbetween XX1 and XX2. Indistinguishable XX pho-tons will interfere at the second beam splitter andexit it pairwise, observable in the detection of reducedphoton coincidences. Using a half-wave plate (HWP),the photon polarizations at the beam splitter can bemade orthogonal. This renders the photons distin-guishable which in turn gives rise to coincidences. Atzero delay time between the detection events, the co-incidences for parallel polarizations (red) show a sig-nificant reduction in comparison with those for per-pendicular polarizations (black). We extract photonindistinguishabilities of I = 0 . ± . HHHVVHVVRe( ρ AB )0.50.250HH VV a Without BSM (no swapping) b With BSM (entanglement swapping)HHHVVHVVRe( ρ mix )0.50.250 HVHH VVVH HHHVVHVVIm( ρ mix )0.50.250 HVHH VVVH c - f o l d c o i n c i d e n c e s / h D Alice A Bob D Alice D Bob e R b v a p o r t r a n s m i ss i o n LaserQD (X) B e ll p a r a m . S F i d e li t y f A B max S max d ρ AB )0.50.250 HVHH VVVHVHHV Figure 4.
Entanglement swapping with semiconductor-generated photons.
Density matrix of the two-photonstate received by Alice and Bob without (a) and with (b) a heralding Bell state measurement (BSM). The shaded areasrepresent the difference to the ideally obtainable values. Real part (left) and imaginary part (right) of ρ mix show thedistinct signature of a perfect statistical mixture , whereas ρ AB closely resembles the entangled state | ψ + (cid:105) with afidelity of f AB = 0 . ± . (c) Four-fold coincidences as a function of the delay between photons XX1 and XX2 atthe BSM setup. Measurement settings of Alice and Bob in the co-polarized (orange) and cross-polarized (blue) diagonalbases reveal a large difference at zero time delay, as expected in an entanglement swapping experiment. The solid linesdenote the double-sided exponential fit. (d)
Fidelity f and Bell parameter S as a function of gate width of photondetection at the BSM. Large gate widths result in a decreased fidelity of f AB = 0 . ± .
03. At 47 ps gate width, S = 2 . ± .
13 is obtained, violating the CHSH-Bell inequality. The dotted lines are the maximally achievable valuesin case of perfect photon indistinguishability. (e) Rb vapor cell transmission over the frequency detuning at the D transitions for a narrow laser and the X photons from the temperature-tuned QD. Two absorption features are visiblein the QD emission, enabling possible atom-semiconductor based quantum repeater applications. rectly specifies the success probability of the BSM inthe entanglement swapping experiment. The offsetfrom unity arises most likely from internal dephasingprocesses and spectral jittering. Further spectral fil-tering or time-gating of detection events in the BSMcan circumvent these effects at the expense of the BSMcoincidence rate. ENTANGLEMENT SWAPPING
Having ensured high-fidelity emission of entangledphotons we can focus on the execution of theentanglement swapping experiment. As a controlmeasurement, the photon state shared by Alice andBob is first investigated without considering theBSM. The density matrix ρ mix extracted from ourobservations via quantum state tomography is shownin Fig. 4a. The signature of a statistical mixtureof polarization states is evident, with a fidelity of f mix = 0 . ± . . This is expected, since the photons X1 and X2do not stem from the same emission cascade.Now the entanglement shall be swapped from the ini-tial photon pairs to the photons received by Aliceand Bob, as established by coincidences at the BSM.Each SNSPD in the setup detects approx. 0.5 millionQD photons per second. To increase the entangle-ment swapping fidelity we use time gating of BSMdetection events (gate width: 47 ps) at the expenseof the total rate of heralding events. Quantum state tomography is performed using sets of four-fold coin-cidences at different polarization settings for Alice andBob. The determined density matrix shown in Fig. 4closely resembles the Bell state | Ψ + (cid:105) . The fidelity of f AB = 0 . ± .
04 clearly surpasses the classical limitof 0 . f AB is theXX photon indistinguishability. This can also be seenfrom Re ( ρ AB ) in Fig. 4b: The well-fitting diagonalelements are mainly determined by the high initialfidelities f and f . However, the more deviantoff-diagonal elements depend on both the degree ofentanglement and the XX photon indistinguishability.In Fig. 4d the fidelity f AB and the Bell parameter S ,as used in the CHSH-Bell inequality [25, 26], are plot-ted against the temporal gate width. For large gatewidths the fidelity decreases to f AB = 0 . ± . f AB = 0 .
71, given the observed entangle-ment fidelities f i and XX photon indistinguishability I discussed above. The maximum achievable fidelityfor our QD emission is f max = 0 .
89, assuming unityindistinguishability (a gate width approaching zero).In reality this value cannot be approached due tothe limited time resolution of the detectors. TheBell parameter S = 2 . ± .
13 at the 47 ps gateviolates the CHSH-Bell inequality, S ≤
2, by morethan two standard deviations. Assuming perfectindistinguishability it reaches S max = 2 . D transitions at 780 .
04 nm by controlling the QD tem-perature [34]. Fig. 4e displays the Rb vapor celltransmission against the relative frequency detuningof a spectrally narrow laser (black). Two promi-nent absorption features are observed correspondingto the two Rb ground states split by the hyperfineinteraction [35]. Residual Rb in the vapor cell re-sults in the smaller absorption features visible at de-tunings of − ν = (4 . ± .
2) GHz. This opens the door for fur-ther experiments involving the storage of polarization-encoded qubits in atomic quantum memories. In addi-tion, Rb atomic transitions could serve as a commonand global reference at which the QD emission canbe frequency-stabilized [36]. Thus the indistinguisha-bility of photons from distant nodes in a quantumnetwork could be ensured.
DISCUSSION AND OUTLOOK
Demonstrating entanglement swapping between pho-ton pairs emitted from semiconductor QDs marks amilestone for quantum photonics, since these sourcessurpass existing technologies in terms of on-demandphoton emission and scalability. Compatibility withatom-based quantum memories paves the way forhybrid quantum repeater implementations. An effi-cient photon-atom interface requires the linewidthsof both systems to be matched, e.g. by combininglifetime-limited QD emission and Purcell broadeningof atomic lines [37].Further experiments that now become feasible withthese sources are entanglement swapping with photonsfrom distant emitters, multi-photon entanglement orentanglement distillation. The outcome will be dic-tated by the optical quality of these sources. Promis-ing improvements include silicon-integrated strain-tuning platforms, which facilitates the emission ofwavelength-tunable entangled photons [38]. Integrat-ing QDs into micro-cavities can increase their bright-ness and photon indistinguishability [39, 40]. An-other key ingredient towards a scalable quantum pho-tonic network is electrically triggered photon emis- sion [41, 42]. Decoherence due to coupling to the solid-state environment can be controlled by electric fieldsin QD integrated diode structures [43]. Overcomingthe challenge of combinig these techniques in fabri-cated devices will be a next major step in realizingsemiconductor based quantum networks.
ACKNOWLEDGMENTS
We acknowledge funding by the BMBF (Q.com) andthe European Research Council (QD-NOMS). F.D.acknowledges support by IFW Excellence Program.We thank Wenjamin Rosenfeld (LMU M¨unchen),Tobias Macha (Universit¨at Bonn), Matthew Eiles(MPIPKS Dresden), and Franz L¨ochner (FSU Jena)for fruitful discussions.
AUTHOR CONTRIBUTIONS
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