PRL 111, 237403 (2013)
PHYSICAL REVIEW LETTERS
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Indistinguishable Tunable Single Photons Emitted by Spin-Flip Raman Transitions in InGaAs Quantum Dots Yu He (贺煜),1 Yu-Ming He (何玉明),1 Y.-J. Wei,1 X. Jiang,1 M.-C. Chen,1 F.-L. Xiong,1 Y. Zhao,1 Christian Schneider,2 Martin Kamp,2 Sven Ho¨fling,2,1,3 Chao-Yang Lu,1 and Jian-Wei Pan1 1
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2 Technische Physik, Physikalisches Institut and Wilhelm Conrad Ro¨ntgen-Center for Complex Material Systems, Universita¨t Wu¨rzburg, Am Hubland, D-97074 Wu¨zburg, Germany 3 SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom (Received 3 July 2013; published 4 December 2013) This Letter reports all-optically tunable and highly indistinguishable single Raman photons from a driven single quantum dot spin. The frequency, linewidth, and lifetime of the Raman photons are tunable by varying the driving field power and detuning. Under continuous-wave excitation, subnatural linewidth single photons from off-resonant Raman scattering show an indistinguishability of 0.98(3). Under pulse excitation, spin- and time-tagged Raman fluorescence photons show an almost vanishing multiphoton emission probability of 0.01(2) and a two-photon quantum interference visibility of 0.95(3). Lastly, HongOu-Mandel interference is demonstrated between two single photons emitted from remote, independent quantum dots with an unprecedented visibility of 0.87(4). DOI: 10.1103/PhysRevLett.111.237403
PACS numbers: 78.67.Hc, 42.50.Nn, 78.20.Ls, 78.30.j
Optically active self-assembled quantum dots (QDs) are of particular interest for physical realization of quantum information [1]. They promise to serve a dual role as solidstate traps for single electron spins and sources of single photon qubits, as well as provide a quantum interface linking them. The confined electron spin has shown long relaxation time [2] and coherence time [3] and can be optically controlled for high-fidelity spin-state initialization [4], ultrafast rotation [5,6], and readout [7]. The recent demonstrations of QD spin-photon entanglement [8] opened the door for spin-based quantum communication [9] and distributed quantum computing [10] protocols. An outstanding challenge is the realization of entanglement between remote QD spins [11] through quantum interference of two single photons, in a similar way as achieved for trapped ions [12], atomic ensembles [13], and nitrogen vacancy in diamonds [14]. To this end, it is necessary to obtain a high degree of indistinguishability between the coherently scattered, spin-tagged Raman photons. Spontaneous Raman fluorescence from a single QD has been observed [15] and used for spin readout [8]; however, no two-photon Hong-Ou-Mandel (HOM) interference [16] experiment with the Raman photons has been reported. Meanwhile, QD single-photon sources are attractive for applications such as optical quantum computing and quantum metrology [17]. Thus far, most experiments generating single photons from QDs are based on two-level systems, exciting above the band gap [18], from p shell [19], and more recently, resonant s shell [20–23]. Moving to a richer, three-level system is expected to bring practical advantages, for instance, an improved photon indistinguishability, as it is insensitive to excited-state dephasing at large 0031-9007=13=111(23)=237403(5)
detunings [24]. In this direction, an interesting goal would be controlled and deterministic generation of single photons with tailorable waveforms in a coupled QD-cavity system using stimulated Raman adiabatic passage [24,25], as previously realized in trapped atoms [26] and ions [27]. Toward these goals, it is important to perform a detailed investigation on QD Raman-scattered photons. In this Letter, we report the generation of highly indistinguishable and bandwidth-tunable single photons from spin-flip Raman transitions under both cw and pulsed excitations. We have also demonstrated high-visibility quantum interference between two single photons from two coherently driven QDs at a distance. The experiments are carried out at 4.2 K on single selfassembled InGaAs QDs embedded in a planar microcavity [22] and charged with a single excess electron in the conduction band. A magnetic field is applied perpendicular to the optical axis (Voigt geometry), which results in a double system [see Fig. 1(a)]. The magnetic field splits the electron-spin (j"i and j#i) ground states and the trion (consisting of two electrons in a spin singlet and a hole, i.e., j"#*i and j#"+i) excited states according to the in-plane electron and hole g factors (here, ge ¼ 0:483, gh ¼ 0:082). A confocal microscope allows laser excitation of a single QD and collection of emitted Raman photons. In the cw excitation experiment, the bichromatic excitation consists of one laser red detuned from the j#i$j#"+i transition by and the other one blue detuned from the j"i$j"#*i transition by [see Fig. 1(a)]. The two lasers serve for optical pumping and repumping of the electron spin [4], enabling fast spin restoration which is necessary for high repetition rate generations of Raman photons.
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FIG. 1 (color online). All-optically tunable Raman single photons. (a) Energy level diagram. Optical selection rules dictate the polarization of the vertical and diagonal transitions to be vertical (V) and horizontal (H), respectively. (b) Three typical examples of Raman photon spectra. (c) Second-order correlation of the Raman photons for ¼ 1 GHz. Red lines are theoretical fits convolved with the system response (detection time resolution 400 ps) and blue lines are deconvolved fits. (d) Extracted decay time constant shows an increase for larger detunings. The red line is a theoretical fit. (e) Dependence of as a function of pump power. The blue line is a theoretical fit.
Figure 1(b) shows three examples of the Raman spectra measured with a Fabry-Pe´rot scanning cavity for ¼1, 2.5, and 3.5 GHz. The lines 1 and 4 are dominated by the residual laser leakage [28], as verified by second-order correlation measurements that show no antibunching. Here, we focus on spectrally separated lines 2 and 3, as labeled in Fig. 1(b). The center frequencies of the two lines shift accordingly as the excitation lasers are detuned, and the spectral linewidth decreases for increased detunings (see Supplemental Material [28] for more details), in agreement with previous observations [15]. The ability to optically control the spectra of the spin-tagged Raman photons provides an experimental knob—independent of the applied magnetic field—to tune the effective excited state Zeeman splitting or, equivalently, the hole g factor. For example, the hole g factor has been effectively modified from the original gh ¼ 0:082 to gh ¼ 0:154, 0.262, and 0.334 for the laser detunings of ¼ 1, 2.5, and 3.5 GHz, respectively. The Raman line labeled 3 is filtered out using an etalon with a bandwidth of 1 GHz. The single-photon nature is evident from second-order coherence measurements shown in Fig. 1(c), where nearly vanishing multiphoton probabilities are observed at zero delays [g2 ð0Þ ¼ 0:01ð2Þ after deconvolution]. The decay time constant extracted from the intensity-correlation histograms are plotted in Fig. 1(d). For a fixed excitation power, the decay time constants show an increase for large detunings and are fitted (red curve) by the expected dependence of ¼ ð2 þ 2 =2 þ 42 =2 Þ=, where is the spontaneous emission rate and is the Rabi frequency (here, ). The observed prolonged decay time constants in Fig. 1(d) are complementary to the spectral narrowing shown in Fig. S1 of the Supplemental Material [28]. The decay time constant is further investigated as a function of pumping laser power for a fixed detuning ¼ 0. The data are shown in Fig. 1(e), which agree well with the expected dependence (blue curve) of ¼ ð2 þ 2 =2 Þ=. These results demonstrate a wide-range, all-optical tunability of the frequency, bandwidth, and lifetime of the
single Raman photons, which is a useful feature in matching the spectral profile of different QDs [29], between QDs and trapped ions [30], cold-atomic quantum memories [31], or parametric down-conversion [32] for future realization of hybrid quantum networks. In contrast to the previously demonstrated subnatural linewidth single photons in the weak excitation regime [23], the narrow band Raman photon source poses no restriction on the excitation strength; thus, a much higher efficiency can be achieved. Assisted with a high-finesse cavity, a near unity efficiency and arbitrary pulse shaping could be simultaneously achieved [24], as demonstrated in trapped atoms and ions [26,27]. In addition to the single-photon antibunching, applications such as optical quantum computation [17] and quantum networks [12–14] require the consecutive photons to have identical wave packets, i.e., indistinguishable, which can be verified by HOM interference measurement [16]. Two single photons that have identical polarization, frequency, and temporal profiles and are spatially mode matched on a beam splitter will coalesce to a single spatial mode—a pure quantum phenomenon that cannot be explained by classical optics. The HOM interference between two offresonantly ( ¼ 2:5 GHz) scattered Raman photons under cw excitation is carried out with an asymmetric MachZehnder interferometer shown in Fig. 2(a). The time resolution ( 400 ps) of the single-photon detectors is considerably shorter than the lifetime ( 2:7 ns) of the off-resonant ( ¼ 2:5 GHz) Raman photons, thanks to the bandwidth and lifetime tunability. Therefore, the detectors are sufficient to resolve and postselect the events where the two photons arrive simultaneously at the beam splitter. Figures 2(b) and 2(c) depict the time-delay histograms of the two-photon interference measurements for orthogonal and parallel polarization, respectively. The signature of two-photon quantum interference—an almost vanishing coincidence probability [g2k ð0Þ ¼ 0:01ð2Þ]—is observed for the two photons with identical polarization [see Fig. 2(b)]. In contrast, for orthogonally polarized photons, Fig. 2(c) shows a
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FIG. 2 (color online). Quantum interference between two cw Raman photons. (a) Experimental arrangement. The continuous stream of the Raman photons is split into two arms, one of which is delayed by about 10 ns and recombined on a beam splitter (BS). A half-wave plate (HWP) is used to set the polarizations in the two arms to be orthogonal or parallel. APD: Single-photon avalanche diode. (b),(c) Two-photon interference with parallel and orthogonal polarized photons. (d) Interference visibility VðtÞ extracted from (b) and (c).
coincidence count rate dip to 50% [g2? ð0Þ ¼ 0:50ð2Þ] that proves no quantum interference occurs for two distinguishable single photons. A model to quantitatively evaluate the interference visibility is VðtÞ ¼ 1 gð2Þ ðtÞ=gð2Þ ? ðtÞ, where t k is the delay between the arrival time of the two photons. The extracted VðtÞ is plotted in Fig. 2(d). At zero delay, the two-photon visibility gives 0.98(3). This is the first direct observation of near perfect quantum interference between QD single photons in the cw regime [33]. Next, we switch to the pulsed regime of generating Raman fluorescence photons. Figure 3(a) depicts the excitation laser pulse sequence. The first 4-ns-long laser pulse, resonant on the diagonal j#i$j"#*i transition, optically pumps the spin state to j"i [4]. After that, a circularly polarized, 20-ps laser pulse filtered from a mode-locked laser, red detuned from the j#i$j#"+i transition by 120 GHz, coherently rotates the electron spin from j"i to j#i [5]. Together, these two pulses act as deterministic spin (a)
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recycling. Lastly, a 105-ps resonant pulse (see Fig. S2 of the Supplemental Material [28]) deterministically brings the ground state j#i to the excited state j#"+i, followed by spontaneous emission in two possible channels [see the dashed lines in Fig. 3(a)] [8]. A high-resolution spectrum shows predominant Raman fluorescence at lines 1 and 3 [see Fig. 3(a) bottom right-hand panel and caption]. With a pulse repetition rate of 82 MHz, we observed 5000 counts per second on a single-photon detector. After correcting for the detector efficiency, fiber connection loss, grating, and etalon transmission, we estimate about 106 Raman photons per second are coupled into the first lens, which corresponds to an overall source efficiency of 1.2%, limited mainly by the photon extraction efficiency. Figure 3(b) shows the second-order correlation measurement of the pulse-driven Raman photons. At zero delay, it shows an antibunching with a multiphoton probability of g2 ð0Þ ¼ 0:01ð1Þ, which unambiguously proves the single-photon nature of the pulsed Raman photons.
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FIG. 3 (color online). Pulsed indistinguishable Raman photons. (a) Excitation laser pulse sequence. The 4-ns and 105-ps laser pulses are obtained from two cw lasers using electro-optic modulators. The 20-ps laser pulse for spin rotation is filtered from a mode-locked laser. The reference signal of the mode-locked laser is used to synchronize all pulses. Bottom right-hand panel: A typical spectrum of Raman fluorescence under pulsed excitation at a magnetic field of 2.8 T. The appearance of the small peaks at lines 2 and 4 is due to weak, off-resonant driving of the j#i $j"#*i transition by the 105-ps pulse. The imbalance between lines 1 and 3 is due to slight ellipticity of the polarizer in the output arm. The red line is a fit with four Lorentzians. (b) Intensity-correlation histogram of the Raman photons obtained using a Hanbury-Brown–Twiss–type setup. (c) HOM interference between two pulse excited Raman single photons. The dashed box shows a 2.2-ns window in the time interval [ 1:1 ns, 1.1 ns].
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FIG. 4 (color online). High-visibility quantum interference between single photons from two coherently pulsed driven quantum dots at a distance. (a) Energy diagram of the two QDs. QD A is a negatively charged QD [same as Fig. 3(a)]. QD B is a neutral QD excited by a 20-ps resonant laser pulse. (b) Time-resolved two-photon quantum interference. (c) The photon efficiency and interference visibility as a function of time filtering window.
We test the nonpostselective HOM interference experiment between two pulse excited Raman photons. The measurement setup shown in Fig. 2(a) is slightly modified by changing the delay line to 12.4 ns—the time separation of two consecutive single photons emitted from the same QD. A time-delayed histogram of the two-photon coincidence count rate is displayed in Fig. 3(c). We analyze the two-photon events within a coincidence window of 2.2 ns [as labeled by the dashed box in Fig. 3(c)]. In this time interval, the count rate for two incoming photons with parallel polarization is drastically reduced to 5% of that with orthogonal polarization, which corresponds to a raw two-photon interference visibility of 0.95(3). This demonstrates that two pulsed Raman photons from the same QD are highly indistinguishable. Future solid-state quantum networks would require high-visibility quantum interference between single photons emitted from remote, independent QDs. To this end, we further perform HOM quantum interference between the Raman photon and a pulsed resonance fluorescence single photon [22] from a separate QD located in another cryostat with a distance of 1.5 m away [see Fig. 4(a)]. The emission frequencies of the two QDs are tuned into degeneracy using magnetic fields, as confirmed by the spectral overlap shown in Fig. S3 of the Supplemental Material [28]. Furthermore, the pulsed resonance fluorescence emission is filtered to match the linewidth of the Raman photon [28]. The two single photons are then time synchronized and spatially overlapped on a beam splitter, and the two output photons are analyzed in a time-resolved manner. Figure 4(b) displays the coincidence counts for parallel and orthogonal polarized single photons, from which the interference visibility is extracted and plotted in Fig. 4(c). Within a coincidence detection time window of 3 ns (where 96% of the emitted photons fall in), the visibility is 0.77(2). If the time window is narrowed down to 0.75 ns (associated with an efficiency of 46%), the visibility gives
0.87(4). This presents the highest two-photon HOM interference visibility reported so far for two remote QDs [29]. The present experiments are performed on QDs in a low-Q planar microcavity where the overall photon source efficiency is only 1.2%. This figure of merit needs to be improved to meet the threshold of 67% for scalable alloptical quantum computation [34]. To this end, the next step would be to work in the strong coupling regime with tunable, transition-selective cavity-QD coupling [6], where one can use the reversible process of vacuum-stimulated Raman scattering based on adiabatic passage [25] to deterministically generate single photons of arbitrary waveform. We note that, however, despite the loss in the photon collection, detection, and spectral filtering, scalable solid-state quantum repeaters [9] and efficient generation of spin cluster states for measurement-based quantum computation [10] can still be possible. In summary, we have demonstrated the generation of all-optically tunable and highly indistinguishable Raman single photons from single QDs. We have also demonstrated high-visibility quantum interference of two single photons from remote QDs. Combined with the previously established spin-photon entanglement [8], interesting follow-up experiments would be to realize entanglement between distant spins through quantum interference of two spin-tagged single photons from independent QDs. We thank M. Atatu¨re, C. Matthiesen, X.-H. Bao, Y.-A. Chen, B. Zhao, and J.-P. Li for assistance and helpful discussions. This work was supported by the National Natural Science Foundation of China, the Strategic Priority Research Program of the Chinese Academy of Sciences (under Grant No. XDB01000000), and the National Fundamental Research Program (under Grants No. 2011CB921300 and No. 2013CB933300), and the State of Bavaria. S. H. acknowledges the CAS visiting professorship. C.-Y. L. acknowledge the Youth Qianren Program and Churchill College. Y. H. and Y.-M. H. contributed equally to this work.
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[1] R. Hanson and D. D. Awschalom, Nature (London) 453, 1043 (2008); S. Buckley, K. Rivoirem and J. Vucˆkovic´, Rep. Prog. Phys. 75, 126503 (2012); R. J. Warburton, Nat. Mater. 12, 483 (2013). [2] M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, Nature (London) 432, 81 (2004); C.-Y. Lu, Y. Zhao, A. N. Vamivakas, C. Matthiesen, S. Fa¨lt, A. Badolato, and M. Atatu¨re, Phys. Rev. B 81, 035332 (2010). [3] A. Greilich, D. R. Yakovlev, A. Shabaev, Al. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, M. Bayer, Science 313, 341 (2006); X. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, Nature (London) 459, 1105 (2009); D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Ho¨fling, A. Forchel, and Y. Yamamoto, Nat. Photonics 4, 367 (2010). [4] M. Atatu¨re, J. Dreiser, A. Badolato, A. Ho¨gele, K. Karrai, A. Imamoglu, Science 312, 551 (2006); B. D. Gerardot, D. ¨ hberg, S. Seidl, M. Kroner, Brunner, P. A. Dalgarno, P. O K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, Nature (London) 451, 441 (2008). [5] J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, Science 320, 349 (2008); D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, Nature (London) 456, 218 (2008). [6] S. G. Carter, T. M. Sweeney, M. Kim, C. S. Kim, D. Solenov, S. E. Economou, T. L. Reinecke, L. Yang, A. S. Bracker, and D. Gammon, Nat. Photonics 7, 329 (2013). [7] A. N. Vamivakas, C.-Y. Lu, C. Matthiesen, Y. Zhao, S. Fa¨lt, A. Badolato, and M. Atatu¨re, Nature (London) 467, 297 (2010). [8] K. De Greve et al., Nature (London) 491, 421 (2012); W. Gao, P. Fallahi, E. Togan, J. Miguel-Sanchez, and A. Imamoglu, Nature (London) 491, 426 (2012); J. R. Schaibley, A. P. Burgers, G. A. McCracken, L.-M. Duan, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, Phys. Rev. Lett. 110, 167401 (2013). [9] C. Simon, Y.-M. Niquet, X. Caillet, J. Eymery, J.-P. Poizat, and J.-M. Ge´rard, Phys. Rev. B 75, 081302(R) (2007). [10] S. D. Barrett and P. Kok, Phys. Rev. A 71, 060310(R) (2005). [11] See D. Kim, S. G. Carter, A. Greilich, A. S. Bracker, and Daniel Gammon, Nat. Phys. 7, 223 (2011) for entanglement between two tunnel-coupled QD spins in close proximity to one another. [12] D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan, and C. Monroe, Nature (London) 449, 68 (2007). [13] C.-W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature (London) 438, 828 (2005); Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, Nature (London) 454, 1098 (2008). [14] H. Bernien et al., Nature (London) 497, 86 (2013). [15] G. Fernandez, T. Volz, R. Desbuquois, A. Badolato, and A. Imamoglu, Phys. Rev. Lett. 103, 087406 (2009). [16] C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987). [17] P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007); J. L. O’Brien,
[18]
[19]
[20]
[21] [22]
[23]
[24]
[25] [26] [27] [28]
[29]
[30] [31] [32]
[33]
[34]
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week ending 6 DECEMBER 2013
A. Furusawa, and J. Vucˆkovic´, Nat. Photonics 3, 687 (2009); J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z˙ukowski, Rev. Mod. Phys. 84, 777 (2012). P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, A. Imamoglu, Science 290, 2282 (2000). C. Santori, D. Fattal, J. Vucˇkovic´, G. S. Solomon, and Y. Yamamoto, Nature (London) 419, 594 (2002); O. Gazzano, S. M. de Vasconcellos, C. Arnold, A. Nowak, E. Galopin, I. Sagnes, L. Lanco, A. Lemaıˆtre, and P. Senellart, Nat. Commun. 4, 1425 (2013). A. Mu¨ller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, Phys. Rev. Lett. 99, 187402 (2007); A. N. Vamivakas, Y. Zhao, C.-Y. Lu, and M. Atatu¨re, Nat. Phys. 5, 198 (2009); E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, Nat. Phys. 5, 203 (2009). S. Ates, S. Ulrich, S. Reitzenstein, A. Lo¨ffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 103, 167402 (2009). Y.-M. He, Y. He, Y.-J. Wei, D. Wu, M. Atatu¨re, C. Schneider, S. Ho¨fling, M. Kamp, C.-Y. Lu, and J.-W. Pan, Nat. Nanotechnol. 8, 213 (2013). C. Matthiesen, M. Geller, C. H. H. Schulte, C. Le Gall, J. Hansom, Z. Li, M. Hugues, E. Clarke, and M. Atatu¨re, Nat. Commun. 4, 1600 (2013). A. Kiraz, M. Atature, and A. Imamoglu, Phys. Rev. A 69, 032305 (2004); D. Fattal, R. Beausoleil, and Y. Yamamoto, arXiv:quant-ph/0606204; C. Santori, D. Fattal, K.-M. C. Fu, P. E Barclay, and R. G Beausoleil, New J. Phys. 11, 123009 (2009); G. Jaritz and U. Hohenester, Eur. Phys. J. B 82, 29 (2011). A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993). J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, H. J. Kimble, Science 303, 1992 (2004). M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, Nat. Phys. 3, 253 (2007). See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.111.237403 for additional data and for description and analysis of results in this Letter. E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010); R. B. Patel, A. J. Bennett, I. Farrer, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, Nat. Photonics 4, 632 (2010); K. Konthasinghe, M. Peiris, Y. Yu, M. F. Li, J. F. He, L. J. Wang, H. Q. Ni, Z. C. Niu, C. K. Shih, and A. Muller, Phys. Rev. Lett. 109, 267402 (2012). E. Waks and C. Monroe, Phys. Rev. A 80, 062330 (2009). H. Zhang et al., Nat. Photonics 5, 628 (2011). S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 107, 157402 (2011). R. B. Patel, A. Bennett, K. Cooper, P. Atkinson, C. Nicoll, D. Ritchie, and A. Shields, Phys. Rev. Lett. 100, 207405 (2008). M. Varnava, D. E. Browne, and T. Rudolph, Phys. Rev. Lett. 100, 060502 (2008).
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Indistinguishable Tunable Single Photons Emitted by Spin-Flip Raman Transitions in InGaAs Quantum Dots Yu He (贺煜),1 Yu-Ming He (何玉明),1 Y.-J. Wei,1 X. Jiang,1 M.-C. Chen,1 F.-L. Xiong,1 Y. Zhao,1 Christian Schneider,2 Martin Kamp,2 Sven Ho¨fling,2,1,3 Chao-Yang Lu,1 and Jian-Wei Pan1 1
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 2 Technische Physik, Physikalisches Institut and Wilhelm Conrad Ro¨ntgen-Center for Complex Material Systems, Universita¨t Wu¨rzburg, Am Hubland, D-97074 Wu¨zburg, Germany 3 SUPA, School of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom (Received 3 July 2013; published 4 December 2013) This Letter reports all-optically tunable and highly indistinguishable single Raman photons from a driven single quantum dot spin. The frequency, linewidth, and lifetime of the Raman photons are tunable by varying the driving field power and detuning. Under continuous-wave excitation, subnatural linewidth single photons from off-resonant Raman scattering show an indistinguishability of 0.98(3). Under pulse excitation, spin- and time-tagged Raman fluorescence photons show an almost vanishing multiphoton emission probability of 0.01(2) and a two-photon quantum interference visibility of 0.95(3). Lastly, HongOu-Mandel interference is demonstrated between two single photons emitted from remote, independent quantum dots with an unprecedented visibility of 0.87(4). DOI: 10.1103/PhysRevLett.111.237403
PACS numbers: 78.67.Hc, 42.50.Nn, 78.20.Ls, 78.30.j
Optically active self-assembled quantum dots (QDs) are of particular interest for physical realization of quantum information [1]. They promise to serve a dual role as solidstate traps for single electron spins and sources of single photon qubits, as well as provide a quantum interface linking them. The confined electron spin has shown long relaxation time [2] and coherence time [3] and can be optically controlled for high-fidelity spin-state initialization [4], ultrafast rotation [5,6], and readout [7]. The recent demonstrations of QD spin-photon entanglement [8] opened the door for spin-based quantum communication [9] and distributed quantum computing [10] protocols. An outstanding challenge is the realization of entanglement between remote QD spins [11] through quantum interference of two single photons, in a similar way as achieved for trapped ions [12], atomic ensembles [13], and nitrogen vacancy in diamonds [14]. To this end, it is necessary to obtain a high degree of indistinguishability between the coherently scattered, spin-tagged Raman photons. Spontaneous Raman fluorescence from a single QD has been observed [15] and used for spin readout [8]; however, no two-photon Hong-Ou-Mandel (HOM) interference [16] experiment with the Raman photons has been reported. Meanwhile, QD single-photon sources are attractive for applications such as optical quantum computing and quantum metrology [17]. Thus far, most experiments generating single photons from QDs are based on two-level systems, exciting above the band gap [18], from p shell [19], and more recently, resonant s shell [20–23]. Moving to a richer, three-level system is expected to bring practical advantages, for instance, an improved photon indistinguishability, as it is insensitive to excited-state dephasing at large 0031-9007=13=111(23)=237403(5)
detunings [24]. In this direction, an interesting goal would be controlled and deterministic generation of single photons with tailorable waveforms in a coupled QD-cavity system using stimulated Raman adiabatic passage [24,25], as previously realized in trapped atoms [26] and ions [27]. Toward these goals, it is important to perform a detailed investigation on QD Raman-scattered photons. In this Letter, we report the generation of highly indistinguishable and bandwidth-tunable single photons from spin-flip Raman transitions under both cw and pulsed excitations. We have also demonstrated high-visibility quantum interference between two single photons from two coherently driven QDs at a distance. The experiments are carried out at 4.2 K on single selfassembled InGaAs QDs embedded in a planar microcavity [22] and charged with a single excess electron in the conduction band. A magnetic field is applied perpendicular to the optical axis (Voigt geometry), which results in a double system [see Fig. 1(a)]. The magnetic field splits the electron-spin (j"i and j#i) ground states and the trion (consisting of two electrons in a spin singlet and a hole, i.e., j"#*i and j#"+i) excited states according to the in-plane electron and hole g factors (here, ge ¼ 0:483, gh ¼ 0:082). A confocal microscope allows laser excitation of a single QD and collection of emitted Raman photons. In the cw excitation experiment, the bichromatic excitation consists of one laser red detuned from the j#i$j#"+i transition by and the other one blue detuned from the j"i$j"#*i transition by [see Fig. 1(a)]. The two lasers serve for optical pumping and repumping of the electron spin [4], enabling fast spin restoration which is necessary for high repetition rate generations of Raman photons.
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FIG. 1 (color online). All-optically tunable Raman single photons. (a) Energy level diagram. Optical selection rules dictate the polarization of the vertical and diagonal transitions to be vertical (V) and horizontal (H), respectively. (b) Three typical examples of Raman photon spectra. (c) Second-order correlation of the Raman photons for ¼ 1 GHz. Red lines are theoretical fits convolved with the system response (detection time resolution 400 ps) and blue lines are deconvolved fits. (d) Extracted decay time constant shows an increase for larger detunings. The red line is a theoretical fit. (e) Dependence of as a function of pump power. The blue line is a theoretical fit.
Figure 1(b) shows three examples of the Raman spectra measured with a Fabry-Pe´rot scanning cavity for ¼1, 2.5, and 3.5 GHz. The lines 1 and 4 are dominated by the residual laser leakage [28], as verified by second-order correlation measurements that show no antibunching. Here, we focus on spectrally separated lines 2 and 3, as labeled in Fig. 1(b). The center frequencies of the two lines shift accordingly as the excitation lasers are detuned, and the spectral linewidth decreases for increased detunings (see Supplemental Material [28] for more details), in agreement with previous observations [15]. The ability to optically control the spectra of the spin-tagged Raman photons provides an experimental knob—independent of the applied magnetic field—to tune the effective excited state Zeeman splitting or, equivalently, the hole g factor. For example, the hole g factor has been effectively modified from the original gh ¼ 0:082 to gh ¼ 0:154, 0.262, and 0.334 for the laser detunings of ¼ 1, 2.5, and 3.5 GHz, respectively. The Raman line labeled 3 is filtered out using an etalon with a bandwidth of 1 GHz. The single-photon nature is evident from second-order coherence measurements shown in Fig. 1(c), where nearly vanishing multiphoton probabilities are observed at zero delays [g2 ð0Þ ¼ 0:01ð2Þ after deconvolution]. The decay time constant extracted from the intensity-correlation histograms are plotted in Fig. 1(d). For a fixed excitation power, the decay time constants show an increase for large detunings and are fitted (red curve) by the expected dependence of ¼ ð2 þ 2 =2 þ 42 =2 Þ=, where is the spontaneous emission rate and is the Rabi frequency (here, ). The observed prolonged decay time constants in Fig. 1(d) are complementary to the spectral narrowing shown in Fig. S1 of the Supplemental Material [28]. The decay time constant is further investigated as a function of pumping laser power for a fixed detuning ¼ 0. The data are shown in Fig. 1(e), which agree well with the expected dependence (blue curve) of ¼ ð2 þ 2 =2 Þ=. These results demonstrate a wide-range, all-optical tunability of the frequency, bandwidth, and lifetime of the
single Raman photons, which is a useful feature in matching the spectral profile of different QDs [29], between QDs and trapped ions [30], cold-atomic quantum memories [31], or parametric down-conversion [32] for future realization of hybrid quantum networks. In contrast to the previously demonstrated subnatural linewidth single photons in the weak excitation regime [23], the narrow band Raman photon source poses no restriction on the excitation strength; thus, a much higher efficiency can be achieved. Assisted with a high-finesse cavity, a near unity efficiency and arbitrary pulse shaping could be simultaneously achieved [24], as demonstrated in trapped atoms and ions [26,27]. In addition to the single-photon antibunching, applications such as optical quantum computation [17] and quantum networks [12–14] require the consecutive photons to have identical wave packets, i.e., indistinguishable, which can be verified by HOM interference measurement [16]. Two single photons that have identical polarization, frequency, and temporal profiles and are spatially mode matched on a beam splitter will coalesce to a single spatial mode—a pure quantum phenomenon that cannot be explained by classical optics. The HOM interference between two offresonantly ( ¼ 2:5 GHz) scattered Raman photons under cw excitation is carried out with an asymmetric MachZehnder interferometer shown in Fig. 2(a). The time resolution ( 400 ps) of the single-photon detectors is considerably shorter than the lifetime ( 2:7 ns) of the off-resonant ( ¼ 2:5 GHz) Raman photons, thanks to the bandwidth and lifetime tunability. Therefore, the detectors are sufficient to resolve and postselect the events where the two photons arrive simultaneously at the beam splitter. Figures 2(b) and 2(c) depict the time-delay histograms of the two-photon interference measurements for orthogonal and parallel polarization, respectively. The signature of two-photon quantum interference—an almost vanishing coincidence probability [g2k ð0Þ ¼ 0:01ð2Þ]—is observed for the two photons with identical polarization [see Fig. 2(b)]. In contrast, for orthogonally polarized photons, Fig. 2(c) shows a
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FIG. 2 (color online). Quantum interference between two cw Raman photons. (a) Experimental arrangement. The continuous stream of the Raman photons is split into two arms, one of which is delayed by about 10 ns and recombined on a beam splitter (BS). A half-wave plate (HWP) is used to set the polarizations in the two arms to be orthogonal or parallel. APD: Single-photon avalanche diode. (b),(c) Two-photon interference with parallel and orthogonal polarized photons. (d) Interference visibility VðtÞ extracted from (b) and (c).
coincidence count rate dip to 50% [g2? ð0Þ ¼ 0:50ð2Þ] that proves no quantum interference occurs for two distinguishable single photons. A model to quantitatively evaluate the interference visibility is VðtÞ ¼ 1 gð2Þ ðtÞ=gð2Þ ? ðtÞ, where t k is the delay between the arrival time of the two photons. The extracted VðtÞ is plotted in Fig. 2(d). At zero delay, the two-photon visibility gives 0.98(3). This is the first direct observation of near perfect quantum interference between QD single photons in the cw regime [33]. Next, we switch to the pulsed regime of generating Raman fluorescence photons. Figure 3(a) depicts the excitation laser pulse sequence. The first 4-ns-long laser pulse, resonant on the diagonal j#i$j"#*i transition, optically pumps the spin state to j"i [4]. After that, a circularly polarized, 20-ps laser pulse filtered from a mode-locked laser, red detuned from the j#i$j#"+i transition by 120 GHz, coherently rotates the electron spin from j"i to j#i [5]. Together, these two pulses act as deterministic spin (a)
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recycling. Lastly, a 105-ps resonant pulse (see Fig. S2 of the Supplemental Material [28]) deterministically brings the ground state j#i to the excited state j#"+i, followed by spontaneous emission in two possible channels [see the dashed lines in Fig. 3(a)] [8]. A high-resolution spectrum shows predominant Raman fluorescence at lines 1 and 3 [see Fig. 3(a) bottom right-hand panel and caption]. With a pulse repetition rate of 82 MHz, we observed 5000 counts per second on a single-photon detector. After correcting for the detector efficiency, fiber connection loss, grating, and etalon transmission, we estimate about 106 Raman photons per second are coupled into the first lens, which corresponds to an overall source efficiency of 1.2%, limited mainly by the photon extraction efficiency. Figure 3(b) shows the second-order correlation measurement of the pulse-driven Raman photons. At zero delay, it shows an antibunching with a multiphoton probability of g2 ð0Þ ¼ 0:01ð1Þ, which unambiguously proves the single-photon nature of the pulsed Raman photons.
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FIG. 3 (color online). Pulsed indistinguishable Raman photons. (a) Excitation laser pulse sequence. The 4-ns and 105-ps laser pulses are obtained from two cw lasers using electro-optic modulators. The 20-ps laser pulse for spin rotation is filtered from a mode-locked laser. The reference signal of the mode-locked laser is used to synchronize all pulses. Bottom right-hand panel: A typical spectrum of Raman fluorescence under pulsed excitation at a magnetic field of 2.8 T. The appearance of the small peaks at lines 2 and 4 is due to weak, off-resonant driving of the j#i $j"#*i transition by the 105-ps pulse. The imbalance between lines 1 and 3 is due to slight ellipticity of the polarizer in the output arm. The red line is a fit with four Lorentzians. (b) Intensity-correlation histogram of the Raman photons obtained using a Hanbury-Brown–Twiss–type setup. (c) HOM interference between two pulse excited Raman single photons. The dashed box shows a 2.2-ns window in the time interval [ 1:1 ns, 1.1 ns].
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FIG. 4 (color online). High-visibility quantum interference between single photons from two coherently pulsed driven quantum dots at a distance. (a) Energy diagram of the two QDs. QD A is a negatively charged QD [same as Fig. 3(a)]. QD B is a neutral QD excited by a 20-ps resonant laser pulse. (b) Time-resolved two-photon quantum interference. (c) The photon efficiency and interference visibility as a function of time filtering window.
We test the nonpostselective HOM interference experiment between two pulse excited Raman photons. The measurement setup shown in Fig. 2(a) is slightly modified by changing the delay line to 12.4 ns—the time separation of two consecutive single photons emitted from the same QD. A time-delayed histogram of the two-photon coincidence count rate is displayed in Fig. 3(c). We analyze the two-photon events within a coincidence window of 2.2 ns [as labeled by the dashed box in Fig. 3(c)]. In this time interval, the count rate for two incoming photons with parallel polarization is drastically reduced to 5% of that with orthogonal polarization, which corresponds to a raw two-photon interference visibility of 0.95(3). This demonstrates that two pulsed Raman photons from the same QD are highly indistinguishable. Future solid-state quantum networks would require high-visibility quantum interference between single photons emitted from remote, independent QDs. To this end, we further perform HOM quantum interference between the Raman photon and a pulsed resonance fluorescence single photon [22] from a separate QD located in another cryostat with a distance of 1.5 m away [see Fig. 4(a)]. The emission frequencies of the two QDs are tuned into degeneracy using magnetic fields, as confirmed by the spectral overlap shown in Fig. S3 of the Supplemental Material [28]. Furthermore, the pulsed resonance fluorescence emission is filtered to match the linewidth of the Raman photon [28]. The two single photons are then time synchronized and spatially overlapped on a beam splitter, and the two output photons are analyzed in a time-resolved manner. Figure 4(b) displays the coincidence counts for parallel and orthogonal polarized single photons, from which the interference visibility is extracted and plotted in Fig. 4(c). Within a coincidence detection time window of 3 ns (where 96% of the emitted photons fall in), the visibility is 0.77(2). If the time window is narrowed down to 0.75 ns (associated with an efficiency of 46%), the visibility gives
0.87(4). This presents the highest two-photon HOM interference visibility reported so far for two remote QDs [29]. The present experiments are performed on QDs in a low-Q planar microcavity where the overall photon source efficiency is only 1.2%. This figure of merit needs to be improved to meet the threshold of 67% for scalable alloptical quantum computation [34]. To this end, the next step would be to work in the strong coupling regime with tunable, transition-selective cavity-QD coupling [6], where one can use the reversible process of vacuum-stimulated Raman scattering based on adiabatic passage [25] to deterministically generate single photons of arbitrary waveform. We note that, however, despite the loss in the photon collection, detection, and spectral filtering, scalable solid-state quantum repeaters [9] and efficient generation of spin cluster states for measurement-based quantum computation [10] can still be possible. In summary, we have demonstrated the generation of all-optically tunable and highly indistinguishable Raman single photons from single QDs. We have also demonstrated high-visibility quantum interference of two single photons from remote QDs. Combined with the previously established spin-photon entanglement [8], interesting follow-up experiments would be to realize entanglement between distant spins through quantum interference of two spin-tagged single photons from independent QDs. We thank M. Atatu¨re, C. Matthiesen, X.-H. Bao, Y.-A. Chen, B. Zhao, and J.-P. Li for assistance and helpful discussions. This work was supported by the National Natural Science Foundation of China, the Strategic Priority Research Program of the Chinese Academy of Sciences (under Grant No. XDB01000000), and the National Fundamental Research Program (under Grants No. 2011CB921300 and No. 2013CB933300), and the State of Bavaria. S. H. acknowledges the CAS visiting professorship. C.-Y. L. acknowledge the Youth Qianren Program and Churchill College. Y. H. and Y.-M. H. contributed equally to this work.
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[1] R. Hanson and D. D. Awschalom, Nature (London) 453, 1043 (2008); S. Buckley, K. Rivoirem and J. Vucˆkovic´, Rep. Prog. Phys. 75, 126503 (2012); R. J. Warburton, Nat. Mater. 12, 483 (2013). [2] M. Kroutvar, Y. Ducommun, D. Heiss, M. Bichler, D. Schuh, G. Abstreiter, and J. J. Finley, Nature (London) 432, 81 (2004); C.-Y. Lu, Y. Zhao, A. N. Vamivakas, C. Matthiesen, S. Fa¨lt, A. Badolato, and M. Atatu¨re, Phys. Rev. B 81, 035332 (2010). [3] A. Greilich, D. R. Yakovlev, A. Shabaev, Al. L. Efros, I. A. Yugova, R. Oulton, V. Stavarache, D. Reuter, A. Wieck, M. Bayer, Science 313, 341 (2006); X. Xu, W. Yao, B. Sun, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, Nature (London) 459, 1105 (2009); D. Press, K. De Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Ho¨fling, A. Forchel, and Y. Yamamoto, Nat. Photonics 4, 367 (2010). [4] M. Atatu¨re, J. Dreiser, A. Badolato, A. Ho¨gele, K. Karrai, A. Imamoglu, Science 312, 551 (2006); B. D. Gerardot, D. ¨ hberg, S. Seidl, M. Kroner, Brunner, P. A. Dalgarno, P. O K. Karrai, N. G. Stoltz, P. M. Petroff, and R. J. Warburton, Nature (London) 451, 441 (2008). [5] J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, Science 320, 349 (2008); D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, Nature (London) 456, 218 (2008). [6] S. G. Carter, T. M. Sweeney, M. Kim, C. S. Kim, D. Solenov, S. E. Economou, T. L. Reinecke, L. Yang, A. S. Bracker, and D. Gammon, Nat. Photonics 7, 329 (2013). [7] A. N. Vamivakas, C.-Y. Lu, C. Matthiesen, Y. Zhao, S. Fa¨lt, A. Badolato, and M. Atatu¨re, Nature (London) 467, 297 (2010). [8] K. De Greve et al., Nature (London) 491, 421 (2012); W. Gao, P. Fallahi, E. Togan, J. Miguel-Sanchez, and A. Imamoglu, Nature (London) 491, 426 (2012); J. R. Schaibley, A. P. Burgers, G. A. McCracken, L.-M. Duan, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, Phys. Rev. Lett. 110, 167401 (2013). [9] C. Simon, Y.-M. Niquet, X. Caillet, J. Eymery, J.-P. Poizat, and J.-M. Ge´rard, Phys. Rev. B 75, 081302(R) (2007). [10] S. D. Barrett and P. Kok, Phys. Rev. A 71, 060310(R) (2005). [11] See D. Kim, S. G. Carter, A. Greilich, A. S. Bracker, and Daniel Gammon, Nat. Phys. 7, 223 (2011) for entanglement between two tunnel-coupled QD spins in close proximity to one another. [12] D. L. Moehring, P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L.-M. Duan, and C. Monroe, Nature (London) 449, 68 (2007). [13] C.-W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature (London) 438, 828 (2005); Z.-S. Yuan, Y.-A. Chen, B. Zhao, S. Chen, J. Schmiedmayer, and J.-W. Pan, Nature (London) 454, 1098 (2008). [14] H. Bernien et al., Nature (London) 497, 86 (2013). [15] G. Fernandez, T. Volz, R. Desbuquois, A. Badolato, and A. Imamoglu, Phys. Rev. Lett. 103, 087406 (2009). [16] C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987). [17] P. Kok, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Rev. Mod. Phys. 79, 135 (2007); J. L. O’Brien,
[18]
[19]
[20]
[21] [22]
[23]
[24]
[25] [26] [27] [28]
[29]
[30] [31] [32]
[33]
[34]
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A. Furusawa, and J. Vucˆkovic´, Nat. Photonics 3, 687 (2009); J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. Z˙ukowski, Rev. Mod. Phys. 84, 777 (2012). P. Michler, A. Kiraz, C. Becher, W. V. Schoenfeld, P. M. Petroff, L. Zhang, E. Hu, A. Imamoglu, Science 290, 2282 (2000). C. Santori, D. Fattal, J. Vucˇkovic´, G. S. Solomon, and Y. Yamamoto, Nature (London) 419, 594 (2002); O. Gazzano, S. M. de Vasconcellos, C. Arnold, A. Nowak, E. Galopin, I. Sagnes, L. Lanco, A. Lemaıˆtre, and P. Senellart, Nat. Commun. 4, 1425 (2013). A. Mu¨ller, E. B. Flagg, P. Bianucci, X. Y. Wang, D. G. Deppe, W. Ma, J. Zhang, G. J. Salamo, M. Xiao, and C. K. Shih, Phys. Rev. Lett. 99, 187402 (2007); A. N. Vamivakas, Y. Zhao, C.-Y. Lu, and M. Atatu¨re, Nat. Phys. 5, 198 (2009); E. B. Flagg, A. Muller, J. W. Robertson, S. Founta, D. G. Deppe, M. Xiao, W. Ma, G. J. Salamo, and C. K. Shih, Nat. Phys. 5, 203 (2009). S. Ates, S. Ulrich, S. Reitzenstein, A. Lo¨ffler, A. Forchel, and P. Michler, Phys. Rev. Lett. 103, 167402 (2009). Y.-M. He, Y. He, Y.-J. Wei, D. Wu, M. Atatu¨re, C. Schneider, S. Ho¨fling, M. Kamp, C.-Y. Lu, and J.-W. Pan, Nat. Nanotechnol. 8, 213 (2013). C. Matthiesen, M. Geller, C. H. H. Schulte, C. Le Gall, J. Hansom, Z. Li, M. Hugues, E. Clarke, and M. Atatu¨re, Nat. Commun. 4, 1600 (2013). A. Kiraz, M. Atature, and A. Imamoglu, Phys. Rev. A 69, 032305 (2004); D. Fattal, R. Beausoleil, and Y. Yamamoto, arXiv:quant-ph/0606204; C. Santori, D. Fattal, K.-M. C. Fu, P. E Barclay, and R. G Beausoleil, New J. Phys. 11, 123009 (2009); G. Jaritz and U. Hohenester, Eur. Phys. J. B 82, 29 (2011). A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993). J. McKeever, A. Boca, A. D. Boozer, R. Miller, J. R. Buck, A. Kuzmich, H. J. Kimble, Science 303, 1992 (2004). M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, Nat. Phys. 3, 253 (2007). See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevLett.111.237403 for additional data and for description and analysis of results in this Letter. E. B. Flagg, A. Muller, S. V. Polyakov, A. Ling, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 104, 137401 (2010); R. B. Patel, A. J. Bennett, I. Farrer, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, Nat. Photonics 4, 632 (2010); K. Konthasinghe, M. Peiris, Y. Yu, M. F. Li, J. F. He, L. J. Wang, H. Q. Ni, Z. C. Niu, C. K. Shih, and A. Muller, Phys. Rev. Lett. 109, 267402 (2012). E. Waks and C. Monroe, Phys. Rev. A 80, 062330 (2009). H. Zhang et al., Nat. Photonics 5, 628 (2011). S. V. Polyakov, A. Muller, E. B. Flagg, A. Ling, N. Borjemscaia, E. Van Keuren, A. Migdall, and G. S. Solomon, Phys. Rev. Lett. 107, 157402 (2011). R. B. Patel, A. Bennett, K. Cooper, P. Atkinson, C. Nicoll, D. Ritchie, and A. Shields, Phys. Rev. Lett. 100, 207405 (2008). M. Varnava, D. E. Browne, and T. Rudolph, Phys. Rev. Lett. 100, 060502 (2008).
