Quantum State Transfer from a Single Photon to a Distant Quantum-Dot Electron Spin
Yu He, Yu-Ming He, Yu-Jia Wei, Xiao Jiang, Kai Chen, Chao-Yang Lu, Jian-Wei Pan, Christian Schneider, Martin Kamp, Sven Hoefling
aa r X i v : . [ qu a n t - ph ] J un Quantum State Transfer from a Single Photon to a Distant Quantum-Dot Electron Spin
Yu He, Yu-Ming He, Yu-Jia Wei, Xiao Jiang, Kai Chen, Chao-Yang Lu, and Jian-Wei Pan
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics,University of Science and Technology of China, Hefei, Anhui 230026, China andCAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics,University of Science and Technology of China, Hefei, Anhui 230026, China
Christian Schneider, Martin Kamp, and Sven H¨ofling
Technische Physik, Physikalisches Instit¨at and Wilhelm Conrad R¨ontgen-Center for Complex Material Systems,Universitat W¨urzburg, Am Hubland, D-97074 W¨uzburg, Germany (Dated: June 27, 2017)Quantum state transfer from flying photons to stationary matter qubits is an important element in the realiza-tion of quantum networks. Self-assembled semiconductor quantum dots provide a promising solid-state platformhosting both single photon and spin, with an inherent light-matter interface. Here, we develop a method to co-herently and actively control the single-photon frequency bins in superposition using electro-optic modulators,and measure the spin-photon entanglement with a fidelity of . ± . . Further, by Greenberger-Horne-Zeilinger-type state projection on the frequency, path and polarization degrees of freedom of a single photon, wedemonstrate quantum state transfer from a single photon to a single electron spin confined in an InGaAs quan-tum dot, separated by 5 meters. The quantum state mapping from the photon’s polarization to the electron’s spinis demonstrated along three different axis on the Bloch sphere, with an average fidelity of . . Self-assembled semiconductor quantum dots (QDs) [1, 2]have received considerable attention for quantum informationprocessing. They can serve as narrow-linewidth single-photonsources with a near-unity quantum efficiency, high photon in-distinguishability, and high extraction efficiency in monolithicmicrocavities [3–7]. Furthermore, QDs have been determin-istically charged with single electrons or holes with long spincoherence time [8]. The confined spin state has been initial-ized by optical cooling [9–11] and coherently controlled usingpicosecond laser pulses [12, 13]. The optical selection rulesin a singly charged QD provides a high-fidelity quantum en-tanglement between the electron spin and the emitted photonsfrequency and polarization. Previous demonstrations of QDspin-photon entanglement [14] relied on fast photon detectorsto resolve the frequency superposition passively [15–18], andthe quantum teleportation from a single photon to a QD spinexploited two-photon interference on a beam splitter whichwas inherently probabilistic [19].In this Letter, we develop a new technique for active mea-surement of single-photon frequency-bin superposition usinga phase-locked electro-optic modulator ( p -EOM). We alsodemonstrate quantum information transfer [20] from a sin-gle photon to a distant electron spin by Greenberger-Horne-Zeilinger (GHZ) state projection on the frequency, path andpolarization degrees of freedom of the single photon. A lay-out of the experiment is depicted in Fig. 1a. Suppose Alicehas a negatively charged single InGaAs QD housed in a 4.2 Kbath cryostat. With an external magnetic field of 2.8 T appliedin Voigt geometry, the spin ground states | ↓i , | ↑i and oneof the trion states | ↓↑⇓i form a Λ system (see left inset ofFig. 1a). Bob, who is separated by 5 meter from Alice, aimsto remotely prepare Alice’s QD spin in an arbitrary superpo-sition state which Alice doesn’t know.Firstly, Alice initializes her QD to | ↓i by optical cool-ing, and then near deterministically excite it to | ↓↑⇓i by a 400 ps π -pulse [11, 21, 22] (see Fig. 1b). The excited state | ↓↑⇓i decays via two possible channels, generating spin-photon entanglement. Two crossed polarizers in the confo-cal microscope are used to extinguish excitation laser leak-age [23], meanwhile projecting the photon polarization to be ( | H i− i | V i ) / √ , where H ( V ) represents horizontal(vertical)polarization. After that, the generated spin-photon entangledstate can be written as (see Supplemental Material [24] fordetails) [15–17]: | Ψ i = 1 √ | ↓i| ω red i − | ↑i| ω blue i ) (1)where | ω red i and | ω blue i are red and blue frequency bins fromthe two decay channels. This spin-photon entangled state canbe directly characterized via active measurement of frequencysuperposition.Alice then sends the photon to Bob through a 5-meter opti-cal fiber. Out of the fiber, Bob prepares the photon polariza-tion to be ( | H i + | V i ) / √ . The photon is then split by a polar-izing beam splitter (PBS) into two paths, i.e., the H is trans-mitted ( T ) whereas the V is reflected ( R ), as shown in Fig. 1b.On the two paths, two etalons are placed, and temperature sta-bilized at the | ω red i and | ω blue i frequency bin for the T and R path, respectively. The bandwidth of the etalons are de-signed to be ∼ ∼ | ω red i and | ω blue i ( ∼ | ω red i → | ω red i| H i| T i and | ω blue i →| ω blue i| V i| R i . Now, the spin-photon entanglement can bewritten in a four-qubit Greenberger-Horne-Zeilinger (GHZ)type state: | Ψ ′ i = 1 √ | ↓i| ω red i| H i| T i − | ↑i| ω blue i| V i| R i ) . (2) a single QD GHZ-statemeasurementfeedback5 meter fiberentanglement a singlephoton > >> > PBS GHZ-state measurementpulsedlaser CW laserCW laser QDB field a -EOM a -EOM 10 ns400 ps6 ps spinreadoutBS QWP BS b crosspolarizers AOM
HWPQWP gratings a Alice Bob AB state encodingspin rotation& spin echospin pumping/readoutpi pulse etalon etalon D S state encoding HWPfiber p -EOM etalon H+V frequency-superpositionmeasurement
FIG. 1. Protocol and experiment setup for photon-to-spin state transfer. a , Alice has a negatively charged QD (see left inset for its energylevel under an in-plane magnetic field). Bob, who is at a distant location, aims to prepare the Alice’s QD spin in arbitrary superposition state.Alice first generates spin-photon entanglement, and then sends the frequency-encoded photon qubit to Bob. Bob uses a specially designedinterferometer (see text for details) to prepare the to-be-teleported state in the photon’s polarization. Finally, the polarization, frequency andpath degrees of freedom of the photon are measured jointly on four GHZ state basis. By implementing appropriate feedback unitary operationsconditioned on the GHZ measurement results, the photon polarization is deterministically transferred to the QD spin. b , Optical arrangementof the experimental setup (see Supplemental Materials for more details). A 10-ns pulse generated by an amplitude electro-optic modulator ( a -EOM) is used for spin initialization/measurement. A 400-ps pulse is used for deterministic spin-photon entanglement generation. The pulsedlaser is modulated by an acousto-optic modulator (AOM) for spin rotation and spin echo pulse sequences. A Sagnac-type interferometer isused to both prepare the to-be-teleported photon polarization state and to perform the GHZ-state measurement. The upper-right inset shows thefrequency qubit measurement module, which consists of a phase-locked electro-optic modulator ( p -EOM) and an etalon. The pink frequency-superposition measurement box contains four frequency qubit measurement modules with one in each optical path. After that, a half-wave plate (HWP) is inserted in the R pathto flip the V polarization to H , disentangling the polarizationfrom | Ψ ′ i . The target state to be transferred is encoded in thephoton’s polarization. Both paths are then placed with a HWPand a quarter-wave plate (QWP) to prepare the polarization inarbitrary superposition: | ψ i p = α | H i + β | V i . The compositequantum system can be written as: | Φ i = 1 √ | ψ i p ⊗ ( | ↓i| ω red i| T i − | ↑i| ω blue i| R i )] . (3)To achieve photon-to-spin state transfer, in a similar spiritto ref. [25] which is a variant of quantum teleportation scheme[26], a crucial step is carrying out joint measurement on thepolarization, frequency and path degrees of freedom of thesingle photon, projecting them onto one of the four GHZ-typestates: | ξ ± i = ( | H i| ω red i| T i ± | V i| ω blue i| R i ) / √ , | χ ± i = ( | H i| ω blue i| R i ± | V i| ω red i| T i ) / √ . (4)It is remarkable to note that the state | Φ i can be written inthe new basis of these four GHZ-type states, | Φ i = 12 [ | ξ + i σ z + | ξ − i − | χ + i iσ y − | χ − i σ x ] ⊗ | ψ i s . (5) This means that, upon measuring the photon with an equalprobability of / at one of the four states | ξ + i , | ξ − i , | χ + i ,and | χ − i , and applying simple Pauli corrections σ z , I , σ y and σ x , respectively, the initial state of the photon is transferred tothe distant spin, which becomes | ψ i s = α | ↓i + β | ↑i .The above scheme requires a spin-photon entanglement asa quantum resource and two classical bits, which can in prin-ciple achieve remote preparation of arbitrary state with 100%efficiency. A simpler protocol would be to measure the photonstate in arbitrary basis and project the spin in a correspondingstate. Such protocol is, however, limited to a maximal successprobability of 50% [25].To project and measure the photon in the GHZ-type states,the two paths are combined on the same PBS with a Sagnac-type interferometer. Out of the PBS, the four GHZ states canbe separated into two groups: | ξ ± i exits through output portA, while | χ ± i exists through port B, as shown in Fig. 1b. Thephoton state in port A and B becomes | ξ ± i A = ( | H i| ω red i ± | V i| ω blue i ) / √ , | χ ± i B = ( | H i| ω blue i ± | V i| ω red i ) / √ . To further differentiate | ξ + i A ( | χ + i B ) with | ξ − i A ( | χ − i B ),one can analyze the polarization and frequency qubit in the su- b ZZ basis ac XX basis d YY basis e p -EOM Etalon C o i n c i den c e C oun t s ( a . u . ) Radio frequency phase (degree)00 01 10 11 00 01 10 11 00 01 10 110.00.20.40.60.81.0 0.00.20.40.60.81.0 0.00.20.40.60.81.0Components Components Components
FIG. 2. Photon frequency qubit measurement and spin-photon en-tanglement. a , Modulated by a p -EOM, the red and blue sidebandsof the frequency qubit are transformed into triple peaks, with theirrelative phase inherited. The overlapped peaks are filtered out withan etalon, where the phase is converted to the field probability am-plitude. b , Measured coincidence counts for spin-photon correla-tion while varying the driving RF field phase delay. c-e, Spin-photon entanglement state normalized coincidence counts on corre-lated measurement basis. The light gray gap shows difference be-tween ideal and experimental values. All the basis are encoded inthe sequence of | spin i| photon i . For the spin qubit, | i ( | i ) of Z,X, Y basis (corresponding to the Pauli matrices σ z , σ x , σ y ) are en-coded as | ↓i ( | ↑i ), ( | ↓i + | ↑i ) / √ ( ( | ↓i − | ↑i ) / √ ), and ( | ↓i + i | ↑i ) / √ ( ( | ↓i − i | ↑i ) / √ ), respectively. While forthe frequency qubit, | i ( | i ) is defined as | ω red i ( | ω blue i ), ( | ω red i + | ω blue i ) / √ ( ( | ω red i − | ω blue i ) / √ ), and ( | ω red i + i | ω blue i ) / √ ( ( | ω red i − i | ω blue i ) / √ ), for Z, X, and Y basis respectively. perposition basis ( | H i± | V i ) / √ and ( | ω red i± | ω blue i ) / √ .Therefore, the four GHZ-type states correspond to the detec-tion events at four single-photon detectors 1, 2, 3, and 4, asshown in Fig. 1b.The photon frequency qubit is coherently measured usinga p -EOM and an etalon. As shown in Fig. 2a, the p -EOM isused to modulate the two frequency bins | ω red i and | ω blue i of the photon, where each bin is transformed into three peaks.When the modulation frequency is set at half of the two bins’separation, the blue side band of | ω red i and the red side bandof | ω blue i overlap with each other, which are then filteredout using an etalon. The intensity of this overlapped bin isproportional to the interference term of | ω red i and | ω blue i ,which thus reflects their relative phase. We control the phaseof the driving RF field applied on the p -EOM to change themeasurement basis of the frequency qubit. The coherent na-ture of this measurement method can be verified by observ-ing a sinusoidal oscillation by measuring the photon intensitywhen the state of the spin and photon’s polarization is fixedat ( | ↓i − | ↑i ) / √ and ( | H i + | V i ) / √ , respectively (seeFig. 2b and Supplemental Materials).We verify the deterministically generated spin-photon en- C oun t s ( a . u . ) Delay (ps) F r i nge v i s i b ili t y ( a . u . ) Delay ( s)
65 ns periodT π π /2 π /2T ab Time offset, (ps) t Time delay, 2T ( s) m t FIG. 3. Ultrafast optical spin echo for prolonging spin coherence ina single QD. a , Control laser pulse sequence. A first π /2 pulse gener-ates a spin coherence, followed by a 19-ns time delay during whichthe spin dephases freely. Next, a π rotation is applied, which effec-tively reserves the direction of spin dephasing. After that, the spinrephases during another 19 ns, at which point another π /2 pulse isapplied to read out the coherence of the spin. b , Measurement of T using spin echo. Ramsey interference fringe amplitude on a semilogplot versus time delay of the whole echo pulse sequence, showing afit to an exponential decay. The inset shows an example of the Ram-sey interference fringe at a time delay of 38 ns. The horizontal axisis the delay time of second π /2 pulse comparing with first π /2 pulse,zero delay shows where the echo pulse sequence is exactly symmet-ric. tanglement state in Eq. (1) before performing the state trans-fer experiment. By replacing the combination of state en-coding and GHZ-state measurement modules in Fig. 1b withthe frequency qubit measurement module in Fig. 2a, correla-tion measurements on the spin and frequency qubits can berealized (see Supplemental Material [24] for setup details).While frequency qubit measurements are achieved by tuningRF field phase as shown in Fig. 2b, spin qubit measurementsare accomplished by utilizing rotation pulse and Ramsey pre-cession to transfer the target spin state population to spin | ↑i . Then read spin | ↑i out with a 10-ns pulse where spin-dependent resonance fluorescence photons [15–18, 29] areregistered by a single-photon detector D s , as shown in Fig. 1b.From the histogram of coincidence counts on ZZ basis givenby Fig. 2c, we get ZZ basis fidelity F ZZ = 0 . ,which is mainly degraded by the imperfection of the spininitialization/measurement pulse. Similarly, from the coin-cidence histograms presented in Fig. 2d and 2e, visibilities V XX = 0 . and V Y Y = 0 . are acquired forcoherent basis XX and YY, respectively. These visibilitiesare mainly limited by a spin dephasing time T ∗ = 1 . ns, where the major dephasing mechanism could be the hy-perfine interaction of the electron with the nuclear spins [27].Except these aforementioned degrading factors, another com-mon factor is QD re-excitation lead by the 400 ps pulse, which a I )
2( )σ z x y b c d I )
2( )σ z x y I )