Letter pubs.acs.org/NanoLett
Entangling Single Photons from Independently Tuned Semiconductor Nanoemitters Kaoru Sanaka,*,†,‡ Alexander Pawlis,†,§ Thaddeus D. Ladd,†,‡ Darin J. Sleiter,† Klaus Lischka,§ and Yoshihisa Yamamoto†,‡ †
E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, United States National Institute of Informatics, Hitotsubashi 2-1-2, Chiyodaku, Tokyo 101-8403, Japan § Department of Physics, University of Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany ‡
ABSTRACT: Quantum communication systems based on nanoscale semiconductor devices is challenged by inhomogeneities from device to device. We address this challenge using ZnMgSe/ZnSe quantum-well nanostructures with local laserbased heating to tune the emission of single impurity-bound exciton emitters in two separate devices. The matched emission in combination with photon bunching enables quantum interference from the devices and allows the postselection of polarization-entangled single photons. The ability to entangle single photons emitted from nanometer-sized sources separated by macroscopic distances provides an essential step for a solid-state realization of a large-scale quantum optical network. This paves the way toward measurement-based entanglement generation between remote electron spins localized at macroscopically separated fluorine impurities. KEYWORDS: Quantum repeater, single-photon source, quantum interference, indistinguishability, entanglement
Q
emitters. Isolated impurity-bound excitons in semiconductors are also promising to bridge the atomic regime to solid-state systems, since the impurity-bound-exciton-related transitions can provide higher recombination rates than in QDs and NVcenters. Furthermore, the emission has a small inhomogeneous linewidth, allowing for strong quantum interference.13 Moreover, the single electron spin of the neutral donor in its orbital ground state, and possibly the nuclear spin of the donor, can be used as a long-lived matter qubit.14 Fluorine donors in ZnSe (ZnSe:F) are particularly well-suited for such applications, since they exhibit bright emission, the nuclear decoherence of the electron spin may be suppressed by isotopic purification, and the spin-1/2 19F nucleus has 100% natural abundance.15−17 However, the use of nanostructures to isolate individual impurity-bound emitters in ZnSe introduces inhomogeneous broadening of more than 100 GHz, leaving a low probability to find a pair spectrally matched within the ∼1 GHz lifetimelimited line width. Therefore, engineered spectral alignment is necessary to achieve quantum interference between multiple sources. In this report, we demonstrate a technique for independent control of the emission wavelength of photonic emitters in the ZnSe/F system, and we use this technique to form polarization-entangled photons from remote semiconductor emitters. Figure 1a shows the material composition of the photon emitter made from a ZnMgSe/ZnSe single-photon device
uantum networks based on quantum teleportation may enable future secure communication over macroscopic distances or distributed quantum computation. In a common model of a quantum network, nodes contain long-lived quantum memories and small quantum processors which are connected by entangled photons.1−4 The nodes are manifested by nanostructures or nanoresonators that contain matter qubits interfaced with a photonic quantum communication channel (i.e., waveguides). Such nanodevices are required to form a photon-matter quantum entangled state in a solid-state material. The interactions at two nodes result in the emission of a pair of indistinguishable single photons. The subsequent entanglement procedure of these “flying qubits” entangles the matter qubits while destroying the photons. Only the photons interact, leaving behind entangled qubits at long distances.5,6 This form of quantum repeater protocol requires photonic sources with a high level of homogeneity, allowing independently generated single photons to interfere and become entangled via conditional single-photon detection. Independent emitters of identical single photons are available from laser-cooled atoms and trapped ions.7,8 However, the emission efficiency of these sources is limited and the trapping time can adversely impact the speed of a large-scale network. Single-photon emitters from solid-state systems such as semiconductor quantum dots (QDs)9−11 or nitrogen-vacancy (NV) centers in diamond12 may allow scalability to on-chip devices with greater speed of operation. Although these emitters are rarely identical, recently reported experimental results10,12 demonstrate several methods of local tuning applied to QDs as well as NV centers in diamond to match individual © 2012 American Chemical Society
Received: May 21, 2012 Published: July 27, 2012 4611
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with electron-beam writing and wet-chemical etching. The 100nm-diameter postnanostructures contain only 2 or 3 fluorine donor atoms on average, which may be separately observed due to strain-induced inhomogeneous broadening. Figure 1b shows the band diagram of the device, resulting from calculations including the strain-induced shifts of the band structure in the ZnSe and (Zn,Mg)Se layers. Figure 1c shows a schematic of the experiment. The emitters were maintained at a temperature of 6 K in a continuous flow liquid helium cryostat. We have chosen two nanodevices for this study, emitters 1 and 2, with distinct and nearly frequency matched emission lines related to individual fluorine donors. The two nanodevices are located on different semiconductor chips in the same cryostat separated by about 5 cm. A 3-ps pulsed laser (λ ∼ 410 nm) is applied to pump both emitters simultaneously. The photoluminescence from the two separate emitters is combined into a single polarization beam splitter (PBS). The output mode is then connected to one of two detection setups, shown in parts d and e of Figure 1. The measurement of the photon indistinguishability is performed by using the setup drawn in Figure 1d, constructed with a half-wave plate (HWP), which rotates the polarization state by 45°, and a second PBS. The quantum interference is detected by single-photon counting modules (SPCMs). The combination of two PBSs and HWP works as a 50/50 beam splitter. If the photons are identical, they will bunch at a single detector, reducing the probability of a coincidence photon-count at the output. This reduction of coincidence probability is called the Hong-Ou-Mandel (HOM) effect and is the signature of two-photon quantum interference.18 The theoretical expectation for the measurement of the HOM effect is described in terms of annihilation operators âj for mode j.19,20 In this notation, the first- and second-order correlation function of photons from emitter 1 and 2 are given † (2) † † as g(1) j (τ) = ⟨âj (t)âj(t + τ)⟩/⟨nj⟩ and gj (τ) = ⟨âj (t)âj (t + τ) 2 † aj(t + τ)aj(t)⟩/⟨nj⟩ , (j = 1, 2) where nj = âj âj. The detected modes, labeled 3 and 4, are in general some superposition of modes 1 and 2, depending on the measurement setup. The coincidence detection probability for modes 3 and 4 at the output of the beam splitter is quantified by the crosscorrelation function
Figure 1. (a) The material composition of the nanoscale semiconductor single-photon emitter. Fluorine atoms are doped in the 2 nm narrow ZnSe layer sandwiched by (Zn,Mg)Se buffer layers; these provide the shallow donor potential for the generated excitons in the device. Samples are grown on a GaAs substrate by molecular beam epitaxy and structured by e-beam lithography and chemical wetetching. (b) Calculated energy band structure given by the composition of the device. The smaller band gap ZnSe layer is sandwiched by the larger band gap (Zn,Mg)Se buffer layer to form the quantum-well structure. The potential given by donor atoms are expected to be about 5−15 meV below the conduction band. (c) Schematic of experimental setup. The semiconductor emitters on two separated semiconductor chips (shown as the emitter 1 and 2) are placed on remote stages separated by 5 cm in a 6 K cooled cryostat close to the windows. A 3-ps pump pulse beam is applied to both semiconductor chips and a temperature control laser is applied simultaneously only to emitter 1 on upper semiconductor chip. The emitted photons are combined into a single optical mode at the first PBS but with orthogonal polarizations. Optical delay with a prism is used to adjust the photon arrival time, and a monochromatic filter constructed with a holographic grating is used to select a desired narrow band region of about 2 nm. (d) The detection part of the setup used to measure the coincidence difference under the degenerate and nondegenerate condition of photons from emitters 1 and 2. The HWP is set to rotate the polarization by 45°. The two orthogonal incident polarizations are equally mixed in each output of the second PBS, in which case the whole setup works as a 50/50 beam splitter. The outputs from the second PBS are collected by SPCM. (e) The detection part of the setup to entangle the independently generated photons from emitters 1 and 2. The input optical mode is separated with a NPBS and is collected by SPCMs followed by QWP and POL.
(2) g34 (τ ) = [|x31x41|2 g1(2)(τ ) + |x32x42|2 g2(2)(τ )
* x41x32x42 * I (τ )}] + |x31x42|2 + |x32x41|2 − 2Re{x31 /[(|x31|2 + |x32|2 )(|x41|2 + |x42|2 )]
(1)
where the quantities xjk are given by x j1 = ⟨n1⟩1/2 [sin(2ϕj − θj) + i sin θj]
(2)
x j2 = ⟨n2⟩1/2 [cos(2ϕj − θj) + i cos θj]
(3)
For the setup in Figure 1d, in which the photons in input optical modes 1 and 2 leading from the sources combine in a 50/50 beam splitter, ϕ3 = ϕ4 = 0, and θ3 = θ4 = π/4. The average photon fluxes from each source, ⟨nj⟩ for j = 1, 2, are adjusted via their respective optical pumps to be nearly equal, at a level resulting in about 104 counts per second. For this setup, then, the term including I(τ) appears as a “dip” as τ is changed, subtracting from the other terms. The complex value I(τ) combines the wavepacket overlap of the two sources and the (1) product of single-photon coherence factors, g(1) 1 (τ){g2 (τ)}*.
structure. The total multilayer structure shown in Figure 1a was grown on a (100)-GaAs substrate and a 20-nm buffer layer of ZnSe, to guarantee optimal interface properties. The ZnSe quantum well (QW) has a thickness of 2 nm and is sandwiched between two 28-nm-thick ZnMgSe barrier layers with a magnesium concentration of about 13%. Fluorine was δdoped in the central region of the ZnSe QW. The nanofabrication of posts with 100-nm-diameter was performed 4612
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Figure 2. (a) Emission spectra of photons from a selected emitter 1 on the upper semiconductor chip. The left inset shows the level structure of the transition. D0 referents the F-bound electron manifold, while D0X refers to the F-bound exciton manifold. The ground-state bound-exciton transition D0X to D0 occurs at wavelength 437.29 nm. This spectrum results from above-bandgap (∼410 nm) pulsing followed by fast nonradiative relaxation into the bound-exciton ground states. Free exciton recombination in the quantum well with heavy hole (Fx-hh) and light hole (Fx-lh) is observed in the shorter wavelength region. The right insets show the normalized photon correlation histogram of the main emission line. (b) Zoomed emission spectra of the main emission line corresponding to D0X to D0 with temperature control laser input. The main emission line from emitter 2 on the lower semiconductor chip is shown at a dashed line with 437.32 nm. The right inset shows the dependence of the modified wavelength on the control laser power. (c) Normalized photon cross-correlation histogram of the time delays of arrival of two photons on the photodetectors in the start−stop configuration. Blue bars show the histogram when no control laser is applied. Red bars show the histogram when the control laser is applied. The intrinsic coincidence background level and two-photon coincidence mixture level given by measured second-order photon correlation functions are shown with gray bars. The inset shows the smoothed coincidence counts before integration for the control laser both off and on. The arrow shows the 1.6 ns time window used for the integration of counts.
In order to tune the emission wavelength of the emitters, a heating control with an infrared laser diode (λ ∼ 780 nm) is applied to emitter 1. With the laser heating, the bandgap of the ZnSe and ZnMgSe layers shifts to lower energy, so that the D0X transition is also red-shifted with increasing laser power. The wavelength modification with heating control laser input is believed to be due to the temperature dependence of the crystal lattice constant, which in turn modifies the bandgap.21 The emission shifts by more than 100 GHz for a heating power of 82 mW. Figure 2b shows the emission spectrum of emitter 1 zoomed to the vicinity of the D0X → D0 transition as the heating laser power is varied. The D0X → D0 line shifts to lower energy as the applied control laser power is increased. The degenerate condition between two emitters is achieved at a control laser power of 25 mW. The right inset shows the dependence of the modified D0X → D0 wavelength depending on the control laser power. Figure 2c shows the experimentally observed crosscorrelation function g(2) 34 (τ), found by integration of coincidence counts in each delay bin and normalizing by the average intensity. The figure shows g(2) 34 (τ) both when the tuning laser is on, in which case |I(0)| is increased, and when it is off, in which (2) case |I(0)| is reduced. The value of g(2) 34 (τ) at zero delay, g34 (0) should be compared to the sum of the coincidence rate for distinguishable photons (0.5, corresponding to I(0) ≃ 0), and the independently measured coincidence background {g(2) 1 (0) + (0)}/4 = 0.12 ± 0.01. This sum is the “mixture level” g(2) 2 indicated in Figure 2c. With the tuning laser off, the coincidence detection probability is found to be g(2) 34 (0) =
The latter provides a term oscillating with the angular frequency mismatch between the two sources while damped by dephasing processes. Bringing this term close to unity requires matching the wavelengths of the emitters to within their lifetimes. The resulting absolute value of I(τ) at τ = 0 is termed “indistinguishability”, measured as the visibility of the HOM dip. Note that due to background coincidences from individual sources, the coincidence detection probability g(2) 34 (τ) does not reach zero at τ = 0 even for perfect indistinguishability. Figure 2a shows the spectrum of emitter 1. The sharp transition from fluorine donor-bound exciton D0X to neutral donor D0 is evident at a wavelength of 437.29 nm. The left inset schematically illustrates this transition. The right inset shows the second-order correlation function of the D0X → D0 spectral line, observed while blocking emission from the other semiconductor chip in the cryostat. This second-order correlation histogram features a series of peaks separated by 13 ns, the repetition period of the pulsed laser. The residual two-photon probability at zero delay is measured to be g(2) 1 (0) = 0.28 ± 0.04, well below the nonclassical single-photon condition of 0.5. This measurement verifies that the photon is coming from the recombination of a single fluorine-donorbound exciton. Emitter 2 from a second chip features a similarly shaped spectrum as emitter 1, however the D0X → D0 transition occurs at a longer wavelength of 437.32 nm and the second-order correlation function at zero delay is g(2) 2 (0) = 0.19 ± 0.03. 4613
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0.70 ± 0.09, a value coincident within one standard deviation from the expected result for distinguishable photons. In contrast, when the wavelengths are brought to degeneracy by the tuning laser, the two-photon coincidence detection probability reaches a minimum of g(2) 34 (0) = 0.45 ± 0.09, nearly two standard deviations below the mixture level. From the measurement results, we find that the tuning laser allows an indistinguishability at zero delay of I(0) = 0.45 ± 0.18. The indistinguishability is reduced from the ideal limit of 1.0 mainly due the imperfect overlap of the spatial modes of the two photons. The indistinguishability is also deteriorated by dipole dephasing times, leading to photon wavepackets with random phase jitter. Noisy relaxation from higher-energy states to the lowest bound-exciton state and phonon broadening from tuning-laser heating also contribute to reduced indistinguishability. The interference of indistinguishable photons allows entanglement generation.22 To attempt this, the detection part of the setup is altered to that shown in Figure 1e. The PBS polarizes the photons from emitters 1 and 2, respectively, as vertical (V) and horizontal (H). These photons are combined into the same spatial optical mode with orthogonal polarization states. The input photons are then split with a 50/50 nonpolarizing beam splitter (NPBS) to the output modes 3 and 4, which lead to SPCMs for photon-counting. If indistinguishability were perfect and two-photon background events negligible, and if we discard events where two photons bunch in the same mode and record only the coincidence events between modes 3 and 4, then this setup postselects the polarization-entangled state |Ψ−⟩34 = (|H⟩3|V⟩4 −|V⟩3|H⟩4)/√2 with probability of 1/2 per input photon pair. To evaluate the result, quarter-wave plates (QWP) and polarizers (POL) are inserted prior to the SPCMs. By rotating these elements, we can choose any polarization basis for measurement, including the PBS polarization outputs of H and V, as well as the diagonal (D) and antidiagonal (A) states, respectively |D⟩ = (|H⟩ + |V⟩)/√2 and |A⟩ = (|H⟩ − |V⟩)/ √2, and also right- and left-circular states, respectively |R⟩ = (|H⟩ + i|V⟩)/√2 and |L⟩ = (|H⟩ − i|V⟩)/√2. As a result, we are able to vary each term in eq 1, using the angle of each QWP fast axis φj and the angle of each polarizer θj. For example, the VV configuration sets ϕ3 = ϕ4 = 0 and θ3 = θ4 = π/2, and only the g(2) 1 (0) background contributes to the coincidence counting. If θ4 = 0, VH coincidences are sought, and eq 1 gives unity corresponding to distinguishable photon counting. Figure 3a shows the measured cross correlation function at zero delay of combinations of VV and VH polarization bases. When the DD polarization basis is selected by shifting to ϕ3 = ϕ4 = 0 and putting θ3 = θ4 = π/4, the indistinguishability term contributes, and the two photons destructively interfere. This setup is fully equivalent, up to attenuation, to the measurement of the HOM dip. The (2) coincidences from g(2) 1 (0) and g2 (0) continue to give constant intrinsic coincidence backgrounds, as in the results of Figure 2c. In contrast, when the DA basis is selected by putting θ4 = −π/4, the indistinguishability term becomes positive and the two photons constructively interfere. The coincidence detection probability becomes higher than the mixture level. Circular polarization bases RR and RL give similar correlation, as shown in the same figure. The larger DA and RL components may also be understood by noting that the |Ψ−⟩34 Bell state is anticorrelated in all bases.
Figure 3. (a) Coincidence detection ratio with parallel and orthogonal settings of polarizers. Combinations are horizontal (H), vertical (V), diagonal (D), antidiagonal (A), right-circular (R), and left circular (L) polarization bases. The intrinsic coincidence backgrounds and detection mixture levels evaluated from measured second-order correlation functions are displayed with shadow. (b) Reconstructed two-photon density matrix with real and imaginary parts. They are obtained by the coincidence detection measurements with 16 combinations of polarization bases by means of quantum state tomography.
Entanglement is measured using the polarization correlation data shown in Figure 3a. We begin with reconstruction of the complete density matrix by means of quantum state tomography, which requires coincidence measurements for 16 combinations of polarization bases.23,24 Reconstructed real and imaginary parts of the two-photon polarization density matrix ρE are shown in Figure 3b. The expected density matrix values correspond to the model ρM = {[ 2|Ψ−⟩⟨Ψ−| + [1 − I(0)](|HV ⟩⟨VH | + |VH ⟩⟨HV |) + g1(2)(0)|VV ⟩⟨VV | + g2(2)(0)|HH ⟩⟨HH |}/[2 + g1(2)(0) + g2(2)(0)] 4614
(4)
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The fidelity of this model density matrix to the tomographically measured result ρE is F = (Tr[((ρ M ) 1/2 ρ E (ρ M ) 1/2) 1/2 ]) 2 . Strong similarity between model and experiment indicates that the deviations of the measured photon correlations from the ideal results corresponding to a pure |Ψ−⟩34 state are dominated by the known, independently measured nonidealities of imperfect indistinguishability I(0) and spurious multiphoton event probability g(2) j (0). The results, as well as the fidelity of this density matrix to the desired |Ψ−⟩, its linear entropy, and its entanglement concurrence, are summarized in Table 1. In this table, the mean
measures. Our technique naturally produces one entangled pair per cycle, unlike spontaneous processes for entanglement generation. This technology therefore presents strong promise for a wide variety of potential applications in large-scale quantum optical networks, such as quantum repeater protocols.
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Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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Table 1. The Various Parameters to Characterize the Entanglement of the Two-Photon Polarization States Numerically Estimated from Measurement Results Parameter Fidelity to Model Fidelity to Ψ− (ref 23) Fidelity to Ψ− (ref 24) Linear Entropy (ref 24) Concurrence (ref 24)
Model − 0.60 0.59 0.77 0.19
± ± ± ±
0.08 0.08 0.08 0.14
ACKNOWLEDGMENTS These research results have been supported by “Quantum key distribution” project, NTT Basic Research Laboratories, the Commissioned Research “Quantum Repeater project” of National Institute of Information and Communications Technology (NICT), “Project for developing innovation system” of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), “Deutsche Forschungsgemeinschaft” (DFG), and through “Quantum information processing project”, its Funding Program for World-leading Innovative Research and development on Science and Technology (FIRST).
Experiment 0.95 0.58 0.53 0.82 0.11
± ± ± ± ±
AUTHOR INFORMATION
0.03 0.05 0.03 0.03 0.06
values result from an analysis using averaged experimental results in both the parameters contained in ρM and the determination of ρE, while the uncertainties result from Monte Carlo simulations of the same analysis procedure using input statistics derived from measured statistical variation of count rates. Our observation of entanglement concurrence is a direct measure of entanglement of formation24 and the obtained value of C = 0.11 ± 0.06 indicates 97% confidence that our experiment generates some entanglement. Although the measured values are still not enough for practical uses in optical quantum networks, the entanglement of photons from macroscopically separated semiconductor emitters shown here is statistically significant. For future practical applications, it is necessary to improve several factors that deteriorate the indistinguishability such as spatial mode mismatch, non-negligible background coincidences, and dipole dephasing in the emitters. Fortunately, there are many practical methods available for improving these factors in future devices. Microcavity structures in the emitters can enhance the emission ratio and are known to improve indistinguishability. Furthermore, connection to waveguide structures and single-mode fibers would enable nearly ideal spatial mode matches between the independently generated photons. These methods have all been demonstrated using self-assembled quantum dots.9−11,25,26 The F/ZnSe system has similar abilities as selfassembled dots for future device engineering, but with improved homogeneity. Fluorine ion-implantation technologies are also under development that will allow the placement of single fluorine impurities into a designated position (for example in the center of the nanodevice) to improve the single photon statistics of each emitter.27 We assume that these techniques will enable polarization entangled states with high indistinguishability and far less corruption from coincidence backgrounds. In conclusion, we have experimentally generated polarization-entangled photons emitted from semiconductor nanodevices placed at distant positions. The indistinguishability of the single photons was achieved by local laser heating to control the spectral emission of one emitter. The formation of entanglement was indicated by nonzero concurrence and other
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