Quantum Entanglement Between an Optical Photon and a Solid-State Spin Qubit

Vol 466 | 5 August 2010 | doi:10.1038/nature09256 LETTERS

Quantum entanglement between an optical photon and a solid-state spin qubit

E. Togan1*, Y. Chu1*, A. S. Trifonov1, L. Jiang1,2,3, J. Maze1, L. Childress1,4, M. V. G. Dutt1,5, A. S. Sørensen6, P. R. Hemmer7, A. S. Zibrov1 & M. D. Lukin1

Quantum entanglement is among the most fascinating aspects of The key idea of our experiment is illustrated in Fig. 1a. The NV 1 quantum theory . Entangled optical photons are now widely used centre is prepared in a specific excited state (jA2æ in Fig. 1a) that for fundamental tests of quantum mechanics2 and applications decays with equal probability into two different long lived spin states such as quantum cryptography1. Several recent experiments (j61æ) by the emission of orthogonally polarized optical photons at demonstrated entanglement of optical photons with trapped ions3, 637 nm. The entangled state given by equation (1) is created because atoms4,5 and atomic ensembles6–8, which are then used to connect photon polarization is uniquely correlated with the final spin state. remote long-term memory nodes in distributed quantum This entanglement is verified by spin state measurement using a networks9–11. Here we realize quantum entanglement between cycling optical transition following the detection of a 637-nm photon the polarization of a single optical photon and a solid-state qubit of chosen polarization. associated with the single electronic spin of a nitrogen vacancy Understanding and controlling excited state properties is a central centre in diamond. Our experimental entanglement verification challenge for achieving such a coherent interface between spin mem- uses the quantum eraser technique5,12, and demonstrates that a ory and optical photons. In contrast to isolated atoms and ions, solid high degree of control over interactions between a solid-state state systems possess complex excited state properties that depend qubit and the quantum light field can be achieved. The reported sensitively on their local environment23. Non-axial crystal strain is entanglement source can be used in studies of fundamental particularly important to the present realization because it affects the quantum phenomena and provides a key building block for the optical transitions’ selection rules and polarization properties24. solid-state realization of quantum optical networks13,14. In the absence of external strain and electric or magnetic fields, A quantum network13 consists of several nodes, each containing a properties of the six electronic excited states are determined by the long-lived quantum memory and a small quantum processor, that NV centre’s C3v symmetry and spin–orbit and spin–spin interactions are connected via entanglement. Its potential applications include (shown in Fig. 2a)24. Optical transitions between the ground and long-distance quantum communication and distributed quantum excited states are spin preserving, but could change electronic orbital computation15. Several recent experiments demonstrated on-chip angular momentum depending on the photon polarization. Two of the 16 entanglement of solid-state qubits separated by nanometre to mil- excited states, labelled jExæ and jEyæ according to their orbital sym- 17,18 limetre length scales. However, realization of long-distance metry, correspond to the ms 5 0 spin projection. Therefore they couple entanglement based on solid-state systems coupled to single optical only to the j0æ ground state and provide good cycling transitions, photons19 is an outstanding challenge. The nitrogen-vacancy (NV) suitable for readout of the j0æ state population through fluorescence centre, a defect in diamond consisting of a substitutional nitrogen detection. The other four excited states are entangled states of spin and atom and an adjacent vacancy, is a promising candidate for imple- orbital angular momentum. Specifically, the jA2æ state has the form menting a quantum node. The ground state of the negatively charged p1ffiffiffi NV centre is an electronic spin triplet with a 2.88-GHz zero-field jiA2 ~ ðÞðjiE{ jiz1 zjiEz ji{1 2Þ 2 splitting between the magnetic sublevels jms 5 0æ and jms 561æ states (from here on denoted j0æ and j61æ). With long coherence where jE6æ are orbital states with angular momentum projection 61 times20, fast microwave manipulation, and optical preparation and along the NV axis. At the same time, the ground states (j0æ, j61æ)are 21 E æ detection , the NV electronic spin presents a promising qubit can- associated with the orbital state j 0 with zero projection of angular didate. Moreover, it can be coupled to nearby nuclear spins that momentum (for simplicity, the spatial part of the wavefunction is not provide exceptional quantum memories; such coupling allows for explicitly written). Hence, owing to total angular momentum conser- 16,22 A æ 2 æ the robust implementation of few-qubit quantum registers .In vation, the j 2 state decays with equal probability to the j 1 ground this work, we demonstrate the preparation of quantum entangled state through s1 polarized radiation and to j11æ through s2 polarized states between a single photon and the electronic spin of an NV radiation. centre: The inevitable presence of a small strain field, characterized by the D jE æ 1 strain splitting ( s)of x,y , reduces the NV centre’s symmetry and jiY ~ pffiffiffi ðÞðjis{ jiz1 zjisz ji{1 1Þ shifts the energies of the excited state levels according to their orbital 2 wavefunctions. For moderate and high strain, the excited states are 25 where js1æ and js2æ are orthogonal circularly polarized single separated into two branches and there is mixing between levels .In photon states. the upper branch, an energy gap protects jA2æ against low strain and

1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA. 2Department of Physics, California Institute of Technology, Pasadena, California 91125, USA. 3Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA. 4Department of Physics and Astronomy, Bates College, Lewiston, Maine 04240, USA. 5Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA. 6QUANTOP, The Niels Bohr Institute, University of Copenhagen, DK2100 Copenhagen, Denmark. 7Department of Electrical and Computer Engineering, Texas A&M University, College Station, Texas 77843, USA. *These authors contributed equally to this work. 730 ©2010 Macmillan Publishers Limited. All rights reserved NATURE | Vol 466 | 5 August 2010 LETTERS

ab637 nm |A 〉 AOM 2 tunable laser 2 PBS 637 nm Waveguide Waveguide AOM 637.19 nm tunable laser 1 modulator 1 modulator 2 Cryostat V+ Dichroic Dichroic V– BS 1 BS 2 Diamond Waveguide |+1〉 modulator 3 |–1〉 APD PBSHWP BS PSB QWP Microscope ZPL detection objective |0〉 detection Polarization analysis

APD 532 nm AOM laser

Figure 1 | Scheme for spin-photon entanglement. a, Following selective from the NV centre passes through a quarter-wave plate (QWP) and is excitation to the | A2æ state, the L-type three level system decays to two spectrally separated into PSB and ZPL channels, and detected with avalanche different spin states through the emission of orthogonally polarized photodiodes (APDs). The latter channel contains entangled photons and is photons, resulting in spin–photon entanglement. b, Schematic of the optical sent using a beam splitter (BS) through a polarization analysis stage set-up. Individual NV centres are isolated and addressed optically using a consisting of a half-wave plate (HWP) and a polarizing beam splitter (PBS). microscope objective. Two resonant lasers at 637 nm and an off-resonant See text for details. laser at 532 nm address various optical transitions. Fluorescence emitted

magnetic fields, preserving the polarization properties of its optical To ensure that jEyæ is a good cycling transition and jA2æ acts as an transitions. A group theoretical analysis of the excited states and entanglement generation transition as required for the current study, polarization properties of the transitions is given in the Supplemen- we select an NV centre with relatively small strain splitting tary Information. (Ds < 2 3 1.28 GHz). Figure 2b presents its excitation spectrum,

a c

|A 〉 0.0015 10 2

|A 〉 1 5 | 0.0010 Ex〉

0 |E 〉 y 0.0005 PSB fluorescence (a.u.) PSB fluorescence –5 Excited state energies (GHz) Excited state energies |E 〉 1,2 50 100 150 200 250 300 350 –10 QWP angle (degrees) 0246 810 Δ Strain perpendicular to NV axis, s (GHz) b 3,500

| |E Ey〉 x〉 3,000 |A 〉 2 | | 〉 2,500 |E 〉 0〉 0 1,2 |±1〉 |A 〉 2,000 1 |±1〉 1,500 |±1〉

PSB fluorescence (a.u.) PSB fluorescence 1,000

500

2 4 6 8 10 12 14 Frequency (GHz) Figure 2 | Characterization of NV centres. a, Energy levels of the NV centre transition in absorption. The system is initially prepared in | 11æ (blue) or 23 under strain. Solid lines are based on a theoretical model and dots are data | 21æ (red). We then apply a laser pulse of varying polarization to the | A2æ from seven NV centres. The dashed line indicates the NV centre used in this state while collecting fluorescence. Oscillations with visibility 77 6 10% paper. b, Excitation spectrum of the NV centre under continuous wave (c.w.) indicate that the transitions linking | 61æ to | A2æ are circularly polarized and microwave radiation. c, Polarization properties of the | 61æ R | A2æ mutually orthogonal (see Supplementary Information for details). 731 ©2010 Macmillan Publishers Limited. All rights reserved LETTERS NATURE | Vol 466 | 5 August 2010 while Fig. 2c demonstrates the desired polarization properties of the Figure 4a shows the populations in the j61æ states, measured j61æ«jA2æ transitions via resonant excitation. conditionally on the detection of a single circularly polarized ZPL We now turn to the experimental demonstration of spin–photon photon. Excellent correlations between the photon polarization and entanglement. Our experimental set-up is outlined in Fig. 1b and NV spin states are observed. described in the Supplementary Information. To create the entangled To complete the verification of entanglement, we now show that state, we use coherent emission within the narrow-band zero phonon correlations persist when ZPL photons are detected in a rotated line (ZPL), which includes only 4% of the NV centre’s total emission. polarization basis. On detection of a linearly polarized jHæ or jVæ The remaining optical radiation occurs in the frequency shifted pho- photon at time td, the entangled state in equation (1) is projected to ji+ ~ p1ffiffi ðÞjiz1 +ji{1 , respectively. These states subsequently non side band (PSB), which is accompanied by phonon emission that 2 causes deterioration of the spin–photon entanglement26. Isolating evolve in time (t) according to: the weak ZPL emission presents a significant experimental challenge 1 {ivzðÞt{td {iv{ðÞt{td owing to strong reflections of the resonant excitation pulse reaching ji+ t ~ pffiffiffi e jiz1 +e ji{1 ð3Þ the detector. By exciting the NV centre with a circularly polarized 2 2-ns p-pulse that is shorter than the emission timescale, we can use In order to read out the relative phase of superposition states between detection timing to separate reflection from fluorescence photons. A j11æ and j21æ, we use two resonant microwave fields with combination of confocal rejection, modulators and finite transmit- frequenciesv1 and v2 to coherently transfer the state {iv t {iðÞv t{ðÞw {w tivity of our optics suppresses the reflections sufficiently to clearly jiM ~ p1ffiffi e z jiz1 ze { z { ji{1 to j0æ (see detect the NV centre’s ZPL emission in a 20-ns region (Fig. 3). 2 Fig. 3b), where the initial relative phase w1 2 w2 is set to the same For photon state determination, ZPL photons in either the js6æ or value for each round of the experiment. Thus, the conditional prob- jiH ~ p1ffiffi ðÞjisz zjis{ , jiV ~ p1ffiffi ðÞjisz {jis{ basis are selected by 2 2 ability of measuring the state jMæ is a polarization analysis stage and detected after an optical path of + aðÞt ,2 m. Spin readout then occurs after a 0.5-ms spin memory interval 1 cos d pMHj ,V ðÞt ~ ð4Þ following photon detection by transferring population from either d 2 j6 æ the 1 states or from their appropriately chosen superposition into where a(t ) 5 (v1 2 v2)t 1 (w1 2 w2). Equation (4) indicates j æ V d d the 0 state using microwave pulses, 61. The pulses selectively that the two conditional probabilities should oscillate with a p phase j æ«j6 æ v address the 0 1 transitions with resonant frequencies 6 that difference as a function of the photon detection time, td. This can be differ by dv 5 v1 2 v2 5 122 MHz due to an applied magnetic understood as follows. In the presence of Zeeman splitting (dv ? 0), field. For superpositions of j61æ states, an echo sequence is applied the NV centre’s spin state is entangled with both the polarization and before the state transfer to extend the spin coherence time (see frequency of the emitted photon. The photon’s frequency provides Supplementary Information). The transfer is followed by resonant which-path information about its decay. In the spirit of quantum j æ«jE æ excitation of the 0 y transition and collection of the PSB eraser techniques, the detection of jHæ or jVæ at td with high time fluorescence. We carefully calibrate the transferred population mea- resolution (,300 ps = 1/dv) erases the frequency information5,12. j æ sured in the 0 state using the procedure detailed in Methods. When the initial relative phase between the microwave fields V61

a bc |A 〉 |+1〉 |A 〉 2 |–1〉 2 |E 〉 , Ω |E 〉 y V– V+ +1 y |0〉 637.19 nm ZPL V+ V– PSB 637.20 nm H, V | 〉 |+1〉 |+1〉 |–1〉 +1 |–1〉 |–1〉 Ω Ω Ω +1 –1 +1 |0〉 |0〉 |0〉

d Spin Entanglement Spin state polarization generation and readout 104 photon state readout 532 nm 103 excitation 637.19 nm π 102 excitation π Ω 10 +1 Cumulative ZPL counts ZPL detection 0 1020304050 Time of detection (ns) Ω Ω 2ππ +1+ –1 637.20 nm excitation PSB detection Time Figure 3 | Experimental procedure for entanglement generation. a, After text) to | 0æ. c, The population in | 0æ is measured using the 637.20-nm optical spin polarization into | 0æ, population is transferred to | 11æ by a microwave readout transition. d, Pulse sequence for the case where an | Hæ or | Væ ZPL p-pulse (V11). The NV is excited to | A2æ with a 637.19-nm p-pulse and the photon is detected (time axis not to scale). If a s6 photon is detected instead, ZPL emission is collected. b,Ifas1 or s2 photon is detected, the population only a p-pulse on either V11 or V21 is used for spin readout. Inset, detection in | 11æ or | 21æ is transferred to | 0æ.Ifan | Hæ or | Væ photon is detected, a time of ZPL channel photons, showing reflection from diamond surface and t–2p–t echo sequence (see Supplementary Information) is applied with V11 subsequent NV emission (blue) and background counts (purple). and V21, followed by a p-pulse which transfers the population in | Mæ (see 732 ©2010 Macmillan Publishers Limited. All rights reserved NATURE | Vol 466 | 5 August 2010 LETTERS

+ – abV V VH 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2 Conditional probability Conditional probability

–1 +1 –1 +1 +–+ – cd V H V M|H M| 1.0 1.0 p p 0.8 0.8

0.6 0.6

0.4 0.4

0.2 0.2 Conditional probability, Conditional probability, Conditional probability, Conditional probability, 0 0 0 5 10 150 5 10 15 t t d (ns) d (ns) Figure 4 | Measurement of spin-photon correlations in two bases. region is the 68% confidence interval for the fit (solid line) to the time- a, Conditional probability of measuring | 61æ after the detection of a s1 or binned data (Supplementary Information). Errors bars on data points show s2 photon. b, Conditional probability of measuring | 6æ after the detection 61 s.d. Combined with the data shown in a, oscillations with amplitude of an H or V photon, extracted from a fit to data shown in c and d. outside of the yellow regions result in fidelities greater than 0.5. The visibility c, d, Measured conditional probability of finding the electronic spin in the of the measured oscillations are 0.59 6 0.18 (c) and 0.60 6 0.11 (d). state | Mæ after detection of a V (c)orH (d) photon at time td. Blue shaded

is kept constant, the acquired phase difference (v1 2 v2)td gives rise sources include finite signal to noise ratio in the ZPL channel (fidelity to oscillations in the conditional probability and produces an effect decrease 11%), as well as timing jitter (another 4%). The resulting equivalent to varying the relative phase in the measured superposi- expected fidelity (75%) is consistent with our experimental observation; this allows us to verify the coherence of the spin–photon entang- tions. Finally, the entanglement generation succeeds with probability 2 led state. p < 10 6, which is limited by low collection and detection efficiency The detection times of ZPL photons are recorded during the as well as the small probability of ZPL emission. experiment without any time gating, which allows us to study Entanglement of pairs of remote quantum registers is one import- spin–photon correlations without reducing the count rate. The ant potential application of the technique described here11. This can resulting data are analysed in two different ways. First, we time-bin be done by coincidence measurements on a pair of photons emitted the data and use it to evaluate the conditional probabilities of mea- by two remote NV centres. The key figure of merit for such an suring spin state jMæ as a function of jHæ or jVæ photon detection time entanglement operation over a distance L is proportional to (Fig. 4c, d). Off-diagonal elements of the spin–photon density matrix cT p2 , where c < 2p 3 15 MHz is the spontaneous decay rate of are evaluated from a simultaneous fit to the binned data (see 1zct Methods). The time bins are chosen to minimize fit uncertainty, as the NV centre, t 5 L/c is the photon travel time, c is the velocity of described in Supplementary Information. The resulting conditional light, and T is the memory lifetime. A large figure of merit is critical probabilities are used to evaluate a lower bound on the entanglement for applications such as quantum repeaters and entanglement puri- fidelity of F $ 0.69 6 0.068, above the classical limit of 0.5, indicating fication protocols. The 0.5-ms spin memory interval in our experi- the preparation of an entangled state. ments can be extended to several hundred microseconds using spin We further reinforce our analysis using the method of maximum echo techniques. Furthermore, by mapping the electronic spin state likelihood estimate. As described in Supplementary Information, this onto proximal nuclei, T can be extended to hundreds of milli- method is applied to raw, un-binned ZPL photon detection and spin seconds22. The key limitation in attaining a large figure of merit is measurement data and yields a probability distribution of a lower low p. It can be circumvented if optical cavities are used, which bound on the fidelity. Consistent with the time-binned approach, we simultaneously enhances emission into the ZPL and improves col- find that our data are described by a near Gaussian probability lection efficiency through integration with appropriate waveguides. F $ 6 distribution associated with a fidelity of 0.70 0.070 (see For example, by using a photonic crystal nanocavity27–29, the poten- Supplementary Fig. 7). Significantly, the cumulative probability dis- tial rate for spin–spin entanglement generation can be about 1 MHz tribution directly shows that the measured lower bound on the fidel- for t , 1/c and a few hertz for t corresponding to L < 100 km, result- ity is above the classical limit with a probability of 99.7%. cT ing in p2 §1. Beyond this specific application, our ability to Several experimental imperfections reduce the observed entangle- 1zct ment fidelity. First, the measured strain and magnetic field slightly control interactions between NV centres and quantum light fields mixes the jA2æ state with the other excited states. On the basis of demonstrates that quantum optical techniques, such as all-optical 11 30 Fig. 2b, we estimate that the jA2æ state imperfection and photon spin control, non-local entanglement and photon storage , can depolarization in the set-up together reduce the fidelity by 12%, be implemented using long-lived solid-state qubits, paving the way the latter being the dominant effect. Imperfections in readout and for a wide variety of potential applications in quantum optics and echo microwave pulses decrease the fidelity by 3%. Other error quantum information science. 733 ©2010 Macmillan Publishers Limited. All rights reserved LETTERS NATURE | Vol 466 | 5 August 2010

METHODS SUMMARY 9. Cabrillo, C., Cirac, J. I., Garcia-Fernandez, P. & Zoller, P. Creation of entangled Phys. Rev. A Spin readout. We determine the spin of the NV centre by resonantly exciting the states of distant atoms by interference. 59, 1025–1033 (1999). 10. Chou, C. W. et al. Measurement-induced entanglement for excitation stored in j0æ«jEyæ transition and collecting emission on the PSB within a 10-ms window. remote atomic ensembles. Nature 438, 828–832 (2005). To obtain accurate readout levels relevant for calibration of our experimental et al. j æ j6 æ 11. Moehring, D. L. Entanglement of single-atom quantum bits at a distance. data, we effectively project the state of the NV centre into 0 or 1 before spin Nature 449, 68–71 (2007). jE æ jA æ measurement by detecting a PSB photon after exciting to the y or 2 state, 12. Scully, M. O. & Dru¨hl, K. Quantum eraser: a proposed photon correlation respectively. Subsequent readout produces a maximum number of 0.11 6 0.0022 experiment concerning observation and ‘‘delayed choice’’ in quantum mechanics. counts per shot when the NV is initially in the j0æ state and a minimum number Phys. Rev. A 25, 2208–2213 (1982). (consistent with background) when it is in the j61æ states. These levels are then 13. Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008). used to calculate the populations measured for entanglement verification. 14. Childress, L., Taylor, J. M., Sørensen, A. S. & Lukin, M. D. Fault-tolerant quantum Compared to conventional spin measurements in NV centres, this method is less communication based on solid-state photon emitters. Phys. Rev. Lett. 96, 070504 sensitive to effects such as imperfect initial spin polarization, NV photo-ioniza- (2006). tion, and spectral or spatial instabilities. A detailed description of the spin readout 15. Duan, L.-M. & Monroe, C. Robust quantum information processing with atoms, photons, and atomic ensembles. Adv. At. Mol. Opt. Phys. 55, 419–464 (2008). measurement and calibration is given in the Supplementary Information. 16. Neumann, P. et al. Multipartite entanglement among single spins in diamond. Calculation of entanglement fidelity. To estimate the entanglement fidelity, we Science 320, 1326–1329 (2008). first use the conditional measurement shown in Fig. 4a, b to determine diagonal 17. Ansmann, M. et al. Violation of Bell’s inequality in Josephson phase qubits. Nature elements of the spin–photon density matrix in the js6æ, j61æ basis. As s6 photons 461, 504–506 (2009). are emitted with equal probability (see Supplementary Information), we 18. DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting r ~ 1 p ~ 1 ðÞ: + : r ~ 1 ðÞ: + : quantum processor. Nature 460, 240–244 (2009). find sz{ ,sz{ {1jsz 0 96 0 12 , szz ,szz 0 07 0 04 , 1 1 2 2 1 1 2 19. de Riedmatten, H., Afzelius, M., Staudt, M. U., Simon, C. & Gisin, N. A solid-state r ~ 1 ðÞ: + : r ~ 1 ðÞ: + : s{{ ,s{{ 0 10 0 05 ,and s{z ,s{z 0 87 0 14 .Toevaluate light-matter interface at the single-photon level. Nature 456, 773 (2008). 1 1 2 1 1 2 the off-diagonal elements, we rotate the measurement basis by projecting the photon 20. Balasubramanian, G. et al. Ultralong spin coherence time in isotopically Nature Mater. to the jHæ or jVæ states and measuring the conditional probability of being in state engineered diamond. 8, 383–387 (2009). 21. Fuchs, G. D., Dobrovitski, V. V., Toyli, D. M., Heremans, F. J. & Awschalom, D. D. jMæ, which is equal to j6æ for particular choices of a (for example, j1æ 5 jMæja5 ). 0 Gigahertz dynamics of a strongly driven single quantum spin. Science 326, The required diagonal matrix elements in the jHæ, jVæ, j6æ basis are then given by 1 1520–1522 (2009). rVz,Vz~ pMVj ðÞa~0 ,andsimilarlyforrH1,H1,rH2,H2 and rV2,V2.Wemodel 22. Dutt, M. V. G. et al. Quantum register based on individual electronic and nuclear 2 Science the experimentally measured conditional probabilities with the forms spin qubits in diamond. 316, 1312–1316 (2007). 23. Tamarat, P. et al. Spin-flip and spin-conserving optical transitions of the nitrogen- pMjH 5 (bH 1 aHcosa)/2 and pMjV 5 (bV 2 aVcosa)/2, where bH V are the offsets of , vacancy centre in diamond. N. J. Phys. 10, 045004 (2008). the oscillations and aH V are their amplitudes. Using a simultaneous fit to the data , 24. Manson, N., Harrison, J. & Sellars, M. Nitrogen-vacancy center in diamond: model in Fig. 4c, d that constrains the frequency to be the Zeeman splitting, we obtain Phys. Rev. B 1 of the electronic structure and associated dynamics. 74, 104303 the values rVz,Vz{rV{,V{~aV =2~ ðÞ0:53+0:16 , rH{,H{{rHz,Hz~ (2006). 1 2 25. Santori, C. et al. Coherent population trapping of single spins in diamond under aH =2~ ðÞ0:58+0:10 The information obtained is sufficient to provide a lower 2 optical excitation. Phys. Rev. Lett. 97, 247401 (2006). F§ 1 r bound for the entanglement fidelity. Using the analysis in ref. 3 sz{1,sz{1 26. Kaiser, F. et al. Polarization properties of single photons emitted by nitrogen- pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 vacancy defect in diamond at low temperature. Æhttp://arXiv.org/abs/ zrs z ,s z {2 rs z ,s z rs { ,s { zrVz,Vz {rV{,V{zrH{,H{ { 1 { 1 z 1 z 1 { 1 { 1 0906.3426æ (2009). {r Þ, F $ 6 Hz,Hz we find 0.69 0.068. This analysis agrees with the results of an 27. Englund, D., Faraon, A., Fushman, I., Stoltz, N. & Petroff, P. 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Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000). Supplementary Information is linked to the online version of the paper at 2. Aspect, A., Grangier, P. & Roger, G. Experimental realization of Einstein-Podolsky- www.nature.com/nature. Rosen-Bohm Gedankenexperiment: a new violation of Bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982). Acknowledgements We thank F. Jelezko, J. Wrachtrup, V. Jacques, N. Manson, 3. Blinov, B. B., Moehring, D. L., Duan, L. M. & Monroe, C. Observation of J. Taylor and J. MacArthur for discussions and experimental help. This work was entanglement between a single trapped atom and a single photon. Nature 428, supported by the Defense Advanced Research Projects Agency, NSF, Harvard-MIT 153–157 (2004). CUA, the NDSEG Fellowship and the Packard Foundation. The content of the 4. Volz, J. et al. Observation of entanglement of a single photon with a trapped atom. information does not necessarily reflect the position or the policy of the US Phys. Rev. Lett. 96, 030404 (2006). Government, and no official endorsements should be inferred. 5. Wilk, T., Webster, S. C., Kuhn, A. & Rempe, G. Single-atom single-photon Author Contributions All authors contributed extensively to the work presented in Science quantum interface. 317, 488–490 (2007). this paper. 6. Yuan, Z.-S. et al. Experimental demonstration of a BDCZ quantum repeater node. Nature 454, 1098–1101 (2008). Author Information Reprints and permissions information is available at 7. Matsukevich, D. et al. Entanglement of a photon and a collective atomic www.nature.com/reprints. The authors declare no competing financial interests. excitation. Phys. Rev. Lett. 95, 040405 (2005). Readers are welcome to comment on the online version of this article at 8. Sherson, J. F. et al. Quantum teleportation between light and matter. 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METHODS Addressing of the j0æ«j61æ microwave transitions is carried out using a m Experimental set-up. Our experiments are performed using a natural bulk dia- 15- m copper wire attached to the diamond. For simultaneous addressing, mond sample kept below 7 K. A Nikon 0.95 NA microscope objective is used in our two microwave fields (generated by mixing the difference frequency of the confocal set-up to address individual NV centres. Resonant excitation of the read- two transitions with their average frequency) are separated using bandpass out and entanglement generation transitions are done using two external cavity filters, individually attenuated, and recombined to balance their power. Low diode lasers. To overcome the main experimental challenge of ensuring sufficient shot-to-shot noise in the microwave fields’ relative phase is crucial. This is signal to noise of the detected ZPL emission, we eliminate background from laser achieved by triggering all timing-sensitive channels from one output event of light reflected off the diamond surface by creating an isolated excitation p-pulse a controller device that produces the entanglement generation and condi- using two cascaded waveguide modulators. This excitation pulse is sent through a tioned readout sequences. Timing information of both ZPL and PSB photons quarter-wave plate that is fixedduring all experimental runs toproducethe circular are collected by combining them at the input of a time-tagged-single-photon- polarization that most efficiently excites the NV to the jA2æ state. We note that, counting device. because our measurements are conditioned on the detection of an emitted photon, Given an experiment repetition rate of ,100 kHz and an entanglement gen- 2 optical p-pulse imperfections only affect the efficiency of the entanglement generation success probability of p < 10 6, we then detect on average one signal eration and not the measured fidelity. In the collection path, the ZPL is sent to a photon every few seconds. As the microwave p-pulses used for population trans- polarization analysis set-up consisting of an HWP and a PBS for photon state fer to the j0æ state are nearly perfect and about 100 repetitions are required for selection. It then passes through a narrow frequency filter before being detected reliable spin state determination, roughly 24 h of data taking were required for by a low dark count APD. We use a waveguide based electro-optical modulator each of the four photon polarizations measured. Overall, characterization, cal- before the APD to further reduce reflections of the excitation pulse and suppress ibration, and data acquisition for a given NV centre were performed over a detector afterpulsing. Special care is taken to minimize reflections during the roughly two month period. The overall measurement time for each individual measurement window to around the dark count level of the detector. NV centre is limited by the long term mechanical stability of the set-up.