Abstract

Light emission from solid-state quantum emitters is inherently prone to environmental decoherence, which results in a line broadening and in the deterioration of photon indistinguishability. Here we employ photon correlation Fourier spectroscopy (PCFS) to study the temporal evolution of such a broadening in two prominent systems: GaAs and In(Ga)As quantum dots. Differently from previous experiments, the emitters are driven with short laser pulses as required for the generation of high-purity single photons, the time scales we probe range from a few nanoseconds to milliseconds and, simultaneously, the spectral resolution we achieve can be as small as ∼ 2µeV. We find pronounced differences in the temporal evolution of different optical transition lines, which we attribute to differences in their homogeneous linewidth and sensitivity to charge noise. We analyze the effect of irradiation with additional white light, which reduces blinking at the cost of enhanced charge noise. Due to its robustness against experimental imperfections and its high temporal resolution and bandwidth, PCFS outperforms established spectroscopy techniques, such as Michelson interferometry. We discuss its practical implementation and the possibility to use it to estimate the indistinguishability of consecutively emitted single photons for applications in quantum communication and photonic-based quantum information processing.

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2019 (5)

M. Gurioli, Z. Wang, A. Rastelli, T. Kuroda, and S. Sanguinetti, “Droplet epitaxy of semiconductor nanostructures for quantum photonic devices,” Nat. Mater. 18(8), 799–810 (2019).
[Crossref]

M. Reindl, J. H. Weber, D. Huber, C. Schimpf, S. F. C. da Silva, S. L. Portalupi, R. Trotta, P. Michler, and A. Rastelli, “Highly indistinguishable single photons from incoherently and coherently excited GaAs quantum dots,” Phys. Rev. B 100(15), 155420 (2019).
[Crossref]

F. B. Basset, M. B. Rota, C. Schimpf, D. Tedeschi, K. D. Zeuner, S. F. C. da Silva, M. Reindl, V. Zwiller, K. D. Jöns, A. Rastelli, and R. Trotta, “Entanglement swapping with photons generated on-demand by a quantum dot,” Phys. Rev. Lett. 123(16), 160501 (2019).
[Crossref]

J. Liu, R. Su, Y. Wei, B. Yao, S. F. C. da Silva, Y. Yu, J. Iles-Smith, K. Srinivasan, A. Rastelli, J. Li, and X. Wang, “A solid-state source of strongly entangled photon pairs with high brightness and indistinguishability,” Nat. Nanotechnol. 14(6), 586–593 (2019).
[Crossref]

J. H. Weber, B. Kambs, J. Kettler, S. Kern, J. Maisch, H. Vural, M. Jetter, S. L. Portalupi, C. Becher, and P. Michler, “Two-photon interference in the telecom C-band after frequency conversion of photons from remote quantum emitters,” Nat. Nanotechnol. 14(1), 23–26 (2019).
[Crossref]

2018 (10)

J. H. Weber, J. Kettler, H. Vural, M. Müller, J. Maisch, M. Jetter, S. L. Portalupi, and P. Michler, “Overcoming correlation fluctuations in two-photon interference experiments with differently bright and independently blinking remote quantum emitters,” Phys. Rev. B 97(19), 195414 (2018).
[Crossref]

Y. Chen, M. Zopf, R. Keil, F. Ding, and O. G. Schmidt, “Highly-efficient extraction of entangled photons from quantum dots using a broadband optical antenna,” Nat. Commun. 9(1), 2994 (2018).
[Crossref]

P. Klenovský, P. Steindl, J. Aberl, E. Zallo, R. Trotta, A. Rastelli, and T. Fromherz, “Effect of second-order piezoelectricity on the excitonic structure of stress-tuned In(Ga)As/GaAs quantum dots,” Phys. Rev. B 97(24), 245314 (2018).
[Crossref]

O. Gazzano, T. Huber, V. Loo, S. Polyakov, E. B. Flagg, and G. S. Solomon, “Effects of resonant-laser excitation on the emission properties in a single quantum dot,” Optica 5(4), 354–359 (2018).
[Crossref]

D. Huber, M. Reindl, S. F. Covre da Silva, C. Schimpf, J. Martín-Sánchez, H. Huang, G. Piredda, J. Edlinger, A. Rastelli, and R. Trotta, “Strain-Tunable GaAs Quantum Dot: A Nearly Dephasing-Free Source of Entangled Photon Pairs on Demand,” Phys. Rev. Lett. 121(3), 033902 (2018).
[Crossref]

S. Gerhardt, J. Iles-Smith, D. P. S. McCutcheon, Y.-M. He, S. Unsleber, S. Betzold, N. Gregersen, J. Mørk, S. Höfling, and C. Schneider, “Intrinsic and environmental effects on the interference properties of a high-performance quantum dot single-photon source,” Phys. Rev. B 97(19), 195432 (2018).
[Crossref]

L. Schweickert, K. D. Jöns, K. D. Zeuner, S. F. Covre Da Silva, H. Huang, T. Lettner, M. Reindl, J. Zichi, R. Trotta, A. Rastelli, and V. Zwiller, “On-demand generation of background-free single photons from a solid-state source,” Appl. Phys. Lett. 112(9), 093106 (2018).
[Crossref]

M. Reindl, D. Huber, C. Schimpf, S. F. Covre, M. B. Rota, H. Huang, V. Zwiller, K. D. Jöns, A. Rastelli, and R. Trotta, “All-photonic quantum teleportation using on-demand solid-state quantum emitters,” Sci. Adv. 4(12), eaau1255 (2018).
[Crossref]

H. Wang, W. Li, X. Jiang, Y.-M. He, Y.-H. Li, X. Ding, M.-C. Chen, J. Qin, C.-Z. Peng, C. Schneider, M. Kamp, W.-J. Zhang, H. Li, L.-X. You, Z. Wang, J. P. Dowling, S. Höfling, C.-Y. Lu, and J.-W. Pan, “Toward scalable boson sampling with photon loss,” Phys. Rev. Lett. 120(23), 230502 (2018).
[Crossref]

B. Kambs and C. Becher, “Limitations on the indistinguishability of photons from remote solid state sources,” New J. Phys. 20(11), 115003 (2018).
[Crossref]

2017 (8)

F. Lenzini, B. Haylock, J. C. Loredo, R. A. Abrahão, N. A. Zakaria, S. Kasture, I. Sagnes, A. Lemaitre, H. Phan, D. V. Dao, P. Senellart, M. P. Almeida, A. G. White, and M. Lobino, “Active demultiplexing of single photons from a solid-state source,” Laser Photonics Rev. 11(3), 1600297 (2017).
[Crossref]

P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12(11), 1026–1039 (2017).
[Crossref]

A. Reigue, J. Iles-Smith, F. Lux, L. Monniello, M. Bernard, F. Margaillan, A. Lemaitre, A. Martinez, D. P. McCutcheon, J. Mørk, R. Hostein, and V. Voliotis, “Probing Electron-Phonon Interaction through Two-Photon Interference in Resonantly Driven Semiconductor Quantum Dots,” Phys. Rev. Lett. 118(23), 233602 (2017).
[Crossref]

D. Huber, M. Reindl, Y. Huo, H. Huang, J. S. Wildmann, O. G. Schmidt, A. Rastelli, and R. Trotta, “Highly indistinguishable and strongly entangled photons from symmetric GaAs quantum dots,” Nat. Commun. 8(1), 15506 (2017).
[Crossref]

M. Reindl, K. Joens, D. Huber, C. Schimpf, Y. Huo, V. Zwiller, A. Rastelli, and R. Trotta, “Phonon-assisted two-photon interference from remote quantum emitters,” Nano Lett. 17(7), 4090–4095 (2017).
[Crossref]

J. Iles-Smith, D. P. McCutcheon, A. Nazir, and J. Mørk, “Phonon scattering inhibits simultaneous near-unity efficiency and indistinguishability in semiconductor single-photon sources,” Nat. Photonics 11(8), 521–526 (2017).
[Crossref]

J. Aberl, P. Klenovský, J. S. Wildmann, J. Martín-Sánchez, T. Fromherz, E. Zallo, J. Humlíček, A. Rastelli, and R. Trotta, “Inversion of the exciton built-in dipole moment in In(Ga)As quantum dots via nonlinear piezoelectric effect,” Phys. Rev. B 96(4), 045414 (2017).
[Crossref]

H. Huang, R. Trotta, Y. Huo, T. Lettner, J. S. Wildmann, J. Martín-Sánchez, D. Huber, M. Reindl, J. Zhang, E. Zallo, O. G. Schmidt, and A. Rastelli, “Electrically-Pumped Wavelength-Tunable GaAs Quantum Dots Interfaced with Rubidium Atoms,” ACS Photonics 4(4), 868–872 (2017).
[Crossref]

2016 (4)

T. H. Chung, G. Juska, S. T. Moroni, A. Pescaglini, A. Gocalinska, and E. Pelucchi, “Selective carrier injection into patterned arrays of pyramidal quantum dots for entangled photon light-emitting diodes,” Nat. Photonics 10(12), 782–787 (2016).
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2015 (3)

A. V. Kuhlmann, J. H. Prechtel, J. Houel, A. Ludwig, D. Reuter, A. D. Wieck, and R. J. Warburton, “Transform-limited single photons from a single quantum dot,” Nat. Commun. 6(1), 8204 (2015).
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2014 (3)

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2013 (6)

Y. M. He, Y. He, Y. J. Wei, D. Wu, M. Atatüre, C. Schneider, S. Höfling, M. Kamp, C. Y. Lu, and J. W. Pan, “On-demand semiconductor single-photon source with near-unity indistinguishability,” Nat. Nanotechnol. 8(3), 213–217 (2013).
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2010 (3)

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2008 (1)

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2006 (4)

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2005 (1)

C. Simon and J. P. Poizat, “Creating single time-bin-entangled photon pairs,” Phys. Rev. Lett. 94(3), 030502 (2005).
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2003 (1)

T. Legero, T. Wilk, A. Kuhn, and G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B: Lasers Opt. 77(8), 797–802 (2003).
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2002 (4)

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2000 (1)

P. Michler, A. Imamoǧlu, M. Mason, P. Carson, G. Strouse, and S. Buratto, “Quantum correlation among photons from a single quantum dot at room temperature,” Nature 406(6799), 968–970 (2000).
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ACS Photonics (1)

H. Huang, R. Trotta, Y. Huo, T. Lettner, J. S. Wildmann, J. Martín-Sánchez, D. Huber, M. Reindl, J. Zhang, E. Zallo, O. G. Schmidt, and A. Rastelli, “Electrically-Pumped Wavelength-Tunable GaAs Quantum Dots Interfaced with Rubidium Atoms,” ACS Photonics 4(4), 868–872 (2017).
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Adv. At. Mol. Opt. Phys. (1)

T. Legero, T. Wilk, A. Kuhn, and G. Rempe, “Characterization of Single Photons Using Two-Photon Interference,” Adv. At. Mol. Opt. Phys. 53, 253–289 (2006).
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Appl. Phys. B: Lasers Opt. (1)

T. Legero, T. Wilk, A. Kuhn, and G. Rempe, “Time-resolved two-photon quantum interference,” Appl. Phys. B: Lasers Opt. 77(8), 797–802 (2003).
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Appl. Phys. Lett. (4)

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Laser Photonics Rev. (1)

F. Lenzini, B. Haylock, J. C. Loredo, R. A. Abrahão, N. A. Zakaria, S. Kasture, I. Sagnes, A. Lemaitre, H. Phan, D. V. Dao, P. Senellart, M. P. Almeida, A. G. White, and M. Lobino, “Active demultiplexing of single photons from a solid-state source,” Laser Photonics Rev. 11(3), 1600297 (2017).
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Nano Lett. (1)

M. Reindl, K. Joens, D. Huber, C. Schimpf, Y. Huo, V. Zwiller, A. Rastelli, and R. Trotta, “Phonon-assisted two-photon interference from remote quantum emitters,” Nano Lett. 17(7), 4090–4095 (2017).
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Nanoscale Res. Lett. (1)

C. Heyn, M. Klingbeil, C. Strelow, A. Stemmann, S. Mendach, and W. Hansen, “Single-dot Spectroscopy of GaAs Quantum Dots Fabricated by Filling of Self-assembled Nanoholes,” Nanoscale Res. Lett. 5(10), 1633–1636 (2010).
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Nat. Commun. (4)

Y. Chen, M. Zopf, R. Keil, F. Ding, and O. G. Schmidt, “Highly-efficient extraction of entangled photons from quantum dots using a broadband optical antenna,” Nat. Commun. 9(1), 2994 (2018).
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D. Huber, M. Reindl, Y. Huo, H. Huang, J. S. Wildmann, O. G. Schmidt, A. Rastelli, and R. Trotta, “Highly indistinguishable and strongly entangled photons from symmetric GaAs quantum dots,” Nat. Commun. 8(1), 15506 (2017).
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A. V. Kuhlmann, J. H. Prechtel, J. Houel, A. Ludwig, D. Reuter, A. D. Wieck, and R. J. Warburton, “Transform-limited single photons from a single quantum dot,” Nat. Commun. 6(1), 8204 (2015).
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J. Zhang, J. S. Wildmann, F. Ding, R. Trotta, Y. Huo, E. Zallo, D. Huber, A. Rastelli, and O. G. Schmidt, “High yield and ultrafast sources of electrically triggered entangled-photon pairs based on strain-tunable quantum dots,” Nat. Commun. 6(1), 10067 (2015).
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Nat. Mater. (1)

M. Gurioli, Z. Wang, A. Rastelli, T. Kuroda, and S. Sanguinetti, “Droplet epitaxy of semiconductor nanostructures for quantum photonic devices,” Nat. Mater. 18(8), 799–810 (2019).
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Nat. Nanotechnol. (4)

J. Liu, R. Su, Y. Wei, B. Yao, S. F. C. da Silva, Y. Yu, J. Iles-Smith, K. Srinivasan, A. Rastelli, J. Li, and X. Wang, “A solid-state source of strongly entangled photon pairs with high brightness and indistinguishability,” Nat. Nanotechnol. 14(6), 586–593 (2019).
[Crossref]

Y. M. He, Y. He, Y. J. Wei, D. Wu, M. Atatüre, C. Schneider, S. Höfling, M. Kamp, C. Y. Lu, and J. W. Pan, “On-demand semiconductor single-photon source with near-unity indistinguishability,” Nat. Nanotechnol. 8(3), 213–217 (2013).
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P. Senellart, G. Solomon, and A. White, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12(11), 1026–1039 (2017).
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J. H. Weber, B. Kambs, J. Kettler, S. Kern, J. Maisch, H. Vural, M. Jetter, S. L. Portalupi, C. Becher, and P. Michler, “Two-photon interference in the telecom C-band after frequency conversion of photons from remote quantum emitters,” Nat. Nanotechnol. 14(1), 23–26 (2019).
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Nat. Photonics (4)

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Figures (10)

Fig. 1.
Fig. 1. Sketch of the experimental setup. The quantum dots (QDs) are placed in a cryostat and excited by a pulsed TiSa laser with a pulse duration of about 5 ps and a separation of 12.5 ns. Each pulse is doubled by an unbalanced Mach-Zehnder interferometer (MZ) with a time delay of 2 ns. Additional white light provided by an LED can be coupled into the excitation path. The emitted photons (XX and X) from the QD’s decay cascade can be filtered in polarization by a half-wave-plate (HWP) and a polariser (Pol), so that only one fine structure component is selected. Variable notch filters (NF) with a bandwidth of 0.4 nm reject the stray light from the laser. The signal is guided to a Michelson interferometer, consisting of two retroreflectors (RR), one of them on a motorized linear stage with 300 mm travel range. The reflected beams interfere at a beam splitter (BS). Both beams are spectrally filtered by monochromators (M) to select either the X or XX emission line and finally measured by avalanche photodiodes (APDs) - connected to correlation hardware.
Fig. 2.
Fig. 2. (a) Emission spectra of a GaAs quantum dot (QD) under resonant two-photon excitation (TPE) - measured by micro photoluminescence ($\mu PL$) spectroscopy. XX and X mark the emission lines of the biexcition to exciton- and the excition to groundstate radiative transitions, respectively. (b) Time traces of the X and XX emission from the GaAs QD. Convoluted fits, considering the instrument response function, yield lifetimes of $T_{1_,\textrm {XX}}=115(4)$ ps and $T_{1_,\textrm {X}}=267(14)$ ps. (c) Emission spectra of an In(Ga)As QD under TPE. (d) Time traces from the In(Ga)As QD. The fitted lifetimes are $T_{1_,\textrm {XX}}=186(6)$ ps and $T_{1_,\textrm {X}}=351(15)$ ps.
Fig. 3.
Fig. 3. (a) Recorded coincidence histogram (corresponding to the unnormalized $g^{(2)}(\tau )$) of the X emission of a GaAs QD for a time delay $\tau$ at the nanosecond timescale and fixed optical path delay of $\delta =0$. The absence of a peak at $\tau =0$ reflects the single photon emission characteristics of the QD. (b) Normalized second order correlation function $g^{(2)}$ of the X photons as a function of $\delta$ and $\tau$. The value (ideally) drops to $0.5$ at $\delta =0$ and converges to $1$ at sufficiently large values of $\delta$, with a functional behaviour depending on the dephasing mechanisms at different $\tau$.
Fig. 4.
Fig. 4. (a) Distribution of the spectral shifts $p(\epsilon )$ at $\tau =2$ ns, for both fine structure components (FSCs) of the X signal of a GaAs QD. The doublet appears as a triplet in $p(\epsilon )$. The fitted sidepeaks are located at the energy corresponding to the fine structure splitting $S=8.3(1)$ µeV and show a FWHM of 6.81(11) µeV. (b) One FSC of the same signal evaluated at $\tau =2$ ns with a fitted FWHM of $6.48(8)$ µeV. (c, d) Distribution for the X emission at $\tau =100$ µs, for both and one FSC, respectively. The distinct peaks from the FSCs are obscured, the FWHM of the inhomogeneously broadened lines are 39.2(2) µeV and 38.4(3) µeV, respectively.
Fig. 5.
Fig. 5. (a-c) Distribution of spectral shifts $p(\epsilon )$ of the X and XX emission of an GaAs QD at time delays $\tau$. One FSC was selected by a polarizer. (d) Full width at half maximum (FWHM) of $p(\epsilon )$ as a function of $\tau$ in the range from 2 ns to 1 ms. The dashed lines in the inset correspond to the X and XX Fourier limits of $2\Gamma _{\textrm {X}}=4.93(25)$ µeV and $2\Gamma _{\textrm {XX}}=11.45(40)$ µeV, respectively.
Fig. 6.
Fig. 6. (a-c) Distribution of spectral shifts $p(\epsilon )$ of the X and XX emission of an In(Ga)As QD at time delays $\tau$. One FSC was selected by a polarizer. (d) Full width at half maximum (FWHM) of $p(\epsilon )$ as a function of $\tau$ in the range from 2 ns to 1 ms. The dashed lines correspond to the X and XX Fourier limits of $2\Gamma _{\textrm {X}}=3.75(6)$ µeV and $2\Gamma _{\textrm {XX}}=7.09(20)$ µeV, respectively.
Fig. 7.
Fig. 7. (a-c) Distribution of spectral shifts $p(\epsilon )$ of the X signal of a GaAs QD without (blue) and with (magenta) additional white light illumination at different $\tau$. (d) FWHM of $p(\epsilon )$ as a function of $\tau$ in a range from 2 ns to 1 ms. The dashed line indicates the X Fourier limit of $2\Gamma _{\textrm {X}}=4.93(25)$ µeV. (e) Second order correlation function $g^{(2)}(\tau )$ at $\delta =600$ mm. The bunching, indicating the blinking of the QD emission, is reduced by white light illumination.
Fig. 8.
Fig. 8. (a-c) Distribution of the spectral shifts $p(\zeta )$ for different $\tau$. (d) FWHM of $p(\zeta )$ for all evaluated time bins. (e) Michelson measurement of the HeNe Laser, yielding a FWHM of 1.89(11) µeV.
Fig. 9.
Fig. 9. (a) HOM interference measurement of the X signal of a GaAs QD with a photon time delay of $\tau =2$ ns, introduced by an unbalanced Mach-Zehnder (MZ). The quintuplet, arising from the MZ, was fitted with the sum of five Pseudo-Voigt functions with equal FWHM and shape factor. Comparing the peak areas at $\tau =0$ with the "classical" peaks at $\tau =\pm 2$ ns yields a visibility of $V_{\textrm {HOM}}^{\textrm {X}}=63(2)\% $. (b) HOM measurement of a different dot and a photon delay of $\tau =12.5$ ns. The area of each side peak at ±25 ns correspond to the double of the expected peak area at $\tau =0$ in the cross-polarized configuration. This allows to deduce the visibility to $43(3)\% $.
Fig. 10.
Fig. 10. HOM interference measurements of the X (a) and XX (b) signals of a In(Ga)As QD with a photon delay of $1.5$ ns. The HOM visibility values after correcting for the BS imperfections are $V_{\textrm {HOM}}^{\textrm {X}}=57(4)\% $ and $V_{\textrm {HOM}}^{\textrm {XX}}=67(5)\% $.

Equations (10)

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I A ( t , δ i ) 1 + cos [ ( 2 v t + δ i ) ω ( t ) / c ] , I B ( t , δ i ) 1 cos [ ( 2 v t + δ i ) ω ( t ) / c ] .
g ( 2 ) ( τ , δ i ) = I A ( t , δ i ) I B ( t + τ , δ i ) t I A ( t , δ i ) t I B ( t + τ , δ i ) t ,
g ( 2 ) ( τ , δ i ) = 1 1 2 T 0 T cos ( ζ τ ( t ) δ i / c ) d t ,
g ( 2 ) ( τ , δ i ) = 1 1 2 cos ( ζ δ i / c ) p τ ( ζ ) d ζ ,
p τ ( ζ j ) = 2 | k = 0 N 1 [ 1 g τ ( 2 ) ( δ k ) ] e 2 π i N k j | 2 ,
p τ ( ζ ) = s t ( ω ) s t + τ ( ω + ζ ) d ω .
g ( 2 ) ( τ ) = 1 T 0 T i A , i B δ ( t t i A ) δ ( t t i B + τ ) d t 1 T ( 0 T i A δ ( t t i A ) d t ) 1 T ( 0 T i B δ ( t t i B + τ ) d t ) ,
g ( 2 ) ( τ ) = n ( τ ) T S 1 S 2
g Δ τ ( 2 ) = T S 1 S 2 1 Δ τ τ A τ B n ( τ ) d τ =: N Δ τ n Δ τ ,
V HOM real = 1 ( 1 ϵ ) 2 T 2 + R 2 2 T R V HOM meas ,

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