Letter pubs.acs.org/JPCL
Entangled Photon Excited Fluorescence in Organic Materials: An Ultrafast Coincidence Detector Oleg Varnavski, Brian Pinsky, and Theodore Goodson, III* Department of Chemistry, Department of Applied Physics, Department of Macromolecular Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States ABSTRACT: We report the fluorescence emission from organic systems selectively excited by entangled pairs of photons. We have demonstrated a linear dependence of this two-photon excited fluorescence on the excitation intensity which is a unique nonclassical feature of two-photon interactions induced by entangled photons. The entangled photon (ETPA) excited fluorescence has been detected in several organic molecules possessing a high entangled photon absorption cross section. The ETPA fluorescence showed a nonmonotonic dependence on the delay between signal and idler beams. The fluorescence signal was detectable within the signal−idler relative delay time interval of ∼100 fs. This time is comparable with the estimated entanglement time, TE, making the ETPA-excited fluorescence in organic materials an ideal ultrafast coincidence detector. These results have widespread impact in applications ranging from spectroscopy to chemical and biological sensing, imaging, and microscopy.
efficient ETPA absorber with strong fluorescence was a persistent challenge in the realization of such a detector. We have previously experimentally demonstrated that the ETPA cross section can be very large in organic chromophores.15,18−20 Utilizing a porphyrin chromophore we showed that the entangled two-photon absorption could be observed with off-resonant photons at a flux about 10 orders of magnitude smaller than what is needed to do the classical two-photon experiment.18 Some of the efficient ETPA organic materials possessed a decent fluorescence quantum yield which allowed us to detect the ETPA excited fluorescence in a proofof-concept experiment.15 In this contribution we focus on the properties of the ETPAexcited fluorescence in different organic materials as a function of the excitation flux. We also probe the spatiotemporal characteristics of the excitation biphotons generated by a spontaneous parametric downconversion process at different phase-matching and component delay conditions. In particular, we demonstrate the linear excitation intensity dependence of the two-photon excited fluorescence. The linear dependence on the input intensity is unique to the entangled photon absorption,11,12,16,21 clearly indicating the entangled photon absorption as a selective excitation mechanism for the observed emission. We also report a nonmonotonic variation of the ETPA fluorescence as a function of the delay between the signal and idler components of the biphoton generated in spontaneous parametric down-conversion (SPDC) which is characteristic for the ETPA process.14,15
he use of nonclassical fields of light may provide spectroscopists with an enhanced tool set to study light−matter interactions.1−3 The entangled-state illumination is also at the heart of several quantum imaging implementations4−6 as well as background-free quantum ghost imaging techniques.7 These nonclassical approaches often provide important performance advantages over their conventional optical counterparts that employ coherent light sources, which have been ascribed to the inherent quantum mechanical correlations between photons that constitute an entangled pair.1−3,8−10 The phenomenon of entangled two-photon absorption (ETPA) has been theoretically predicted to exhibit interesting nonclassical effects such as linear rather than quadratic dependence of absorption rate on the excitation intensity which is dominant at low excitation density regimes.11,12 It was also shown that the ETPA process was a nonmonotonic effect which oscillates at a frequency depending on the parameters such as entanglement time and area as well as coupling of the states of the system (detuning).9,13−15 ETPA has been experimentally demonstrated in both atomic16,17 and molecular systems.15,18−20 The ETPA experiments in organic macromolecules showed remarkably high efficiency of twophoton absorption in this case allowing for obtaining measurable absorption at excitation flux below 106photons/ s.15,18−20 The best way to observe the simultaneous arrival of two photons is to detect a nonlinear photon−photon interaction between them. Because of extremely low efficiencies of typical nonlinear interactions with entangled photons, the detection of their inherent nonclassical correlations has been limited mostly to photoelectric coincidence counters with relatively slow response. Biphoton excited fluorescence is an ideal tool to detect fast nonclassical correlations. However, the lack of an
T
© 2016 American Chemical Society
Received: October 13, 2016 Accepted: December 28, 2016 Published: December 28, 2016 388
DOI: 10.1021/acs.jpclett.6b02378 J. Phys. Chem. Lett. 2017, 8, 388−393
Letter
The Journal of Physical Chemistry Letters
Figure 1. Schematic experimental setup for biphoton excited fluorescence measurements. Interference filters (IFB, IFR) and dichroic mirrors (DM) separate second harmonic (SG) light from fundamental and entangled photons from SG. Power references are provided by the photodetector (PD). Biphoton excited fluorescence is collected by the fluorescence collection unit (see text for details). Spatial profile images are obtained with an ICCD camera. A 50/50 nonpolarizing beam splitter (NPBS) polarizers, and APD detectors are used for polarization visibility measurements. Delay between the photons of the downconverted pair is provided by a set of crystal quartz plates of different thicknesses.
Biphoton absorbing materials used in this work were chosen based on the chromophore, architecture, one-photon absorption wavelength, fluorescence quantum yield, and previous ETPA results. Biphoton fluorescence measurements have been carried out using a fluorescence collection unit (FCU, Figure 1). This unit was specifically designed for high-efficiency collection of the fluorescent light from a sample which was located at the assembly center. The FCU consists of a hemispherical mirror and a spherical cap mirror whose optical apertures are matched such that the assembly forms a spherically enclosed reflecting surface with two ports to allow entry and exit of the biphoton excitation light and a port to the output fluorescence light that is collected within the FCU. The hemispherical surface is centered on the sample of interest such that all light that is emitted within the FCU will originate from or near the center of the curvature of this mirror. The radius of the spherical cap mirror has been chosen to direct the light originating from the center of the hemispherical mirror toward the output port. The reflective surfaces of the assembly have a protected Ag coating to maximize the reflectivity in the visible range. The fluorescence light collected by the FCU was detected by the photomultiplier tube (R7518P, Hamamatsu, Inc.) in a photon-counting mode. The photomultiplier (PMT) has dark count rate ∼10 counts/s and is not sensitive to 800 nm light. Long pass filter with the cutoff wavelength 435 nm has been installed in front of the PMT to cut any spurious blue light near 400 nm. By removing the interference filter, detuning the BBO II, and proper attenuation of the blue beam, we were able to obtain and calibrate the blue excitation beam with the flux of 1.27 × 107 photons/s. Using this beam for classical onephoton excitation of the chromophore fluorescence with known quantum yield we have estimated the fluorescence collection efficiency of the FCU under weak light conditions similar to those used in biphoton experiment. Our estimation showed the collection efficiency of 17% for the fluorescence centered at 450
The most widely used method for the generation of entangled photon pairs (biphotons) is SPDC where two lower-frequency photons are generated when a strong pump interacts with a nonlinear crystal.22−25 In our experiments we use β-barium borate (BBO II) crystal designed for type II SPDC as a nonclassical light source. The experimental setup (Figure 1) is pumped by a mode-locked Ti:Sapphire laser (Spectra-Physics MaiTai, pulsewidth ≤ 100 fs, 80 MHz repetition rate) with emission centered at 800 nm with 12 nm spectral bandwidth). The 800 nm output is frequency doubled in 1 mm thick β-barium borate crystal (BBO I) to produce a SHG beam at 400 nm. This SHG beam is then focused onto a 0.5 mm thickness β-barium borate (BBO II) crystal. Within type II SPDC phase-matching conditions, the signal (o-ray) and idler (e-ray) photons are generated at orthogonal polarizations. A dichroic mirror (DM) and the interference filter (IF) with bandwidth 12 nm centered at 800 nm are used to remove the remaining 400 nm light and select the near-degenerate biphotons. Downconverted photons are detected by silicon avalanche photodiode (APD) single-photon counting modules (PerkinElmer SPCM-AQR-13) or by an intensified charge-coupled device (ICCD) camera (PIMAX2:1003). To vary the input flux, the fundamental beam is attenuated using a continuously variable neutral density filter wheel, with photodetector (PD) serving as references for the input power. Net input photon rate (NIPR) has been calibrated with APD versus photodetector in the fundamental beam using the cell filled with pure solvent, thus taking into account quartz surface reflections and scattering losses. Using the cell filled with pure solvent (typically different solvents for different materials) as a reference provides the means for an accurate background calibration in ETPA absorption measurements. All necessary corrections specified by the manufacturer have been made for the counting rate obtained with single-photon counting modules (quantum yield and dead time corrections). 389
DOI: 10.1021/acs.jpclett.6b02378 J. Phys. Chem. Lett. 2017, 8, 388−393
Letter
The Journal of Physical Chemistry Letters nm (which corresponds to the fluorescence peak of bis[18]annulene). This efficiency includes the geometrical efficiency of the FCU, attenuations by filters, and PMT photocathode shape mismatch. After proper integration and background subtraction, the fluorescence detection system was able to reliably detect the fluorescence signal as small as a few photons per second. Experimenting with different ETPA-active organic materials we found that the probe bis[18]annulene (bowtie, BT, Figure 2) showed the most intense and reliable ETPA-excited
Figure 3. Entangled photon excited fluorescence of bis[18]annulene (BT) in dichloromethane as a function of the phase-matching condition in SPDC unit. The SPDC output field spatial distributions collected with the CCD camera at different BBO angle are shown in the top panels.
Figure 2. Absorption and fluorescence spectra of bis[18]annulene in dichloromethane. Excitation wavelength for fluorescence is 400 nm.
fluorescence. Similar molecule was used in our earlier experiments on spatial control of the ETPA process in organic molecule.20 This chromophore demonstrated a strong classical (random) TPA absorption and a decent fluorescence quantum yield of 0.45.26 The excitation processes and related exciton models for the annulenes and bis-annulenes have been also studied.27 We have investigated the effect of the light-focusing conditions on the efficient excitation of the fluorescence excited by entangled photons in order to provide the best indepth resolution for the entangled two-photon excited fluorescence (ETPA-excited fluorescence) (Figure 3). We have detected and compared the BT ETPA-excited fluorescence for different phase-matching conditions of the spontaneous parametric down conversion entangled photon pair generator. In our experiments we have simultaneously observed the excitation spatial beam structure and the ETPA fluorescence intensity on a few-photon-per-second level. We have investigated noncollinear two-beam excitation conditions and compared the resulting fluorescence with the collinear excitation of the ETPA fluorescence. Special attention was given to the greatest possible signal-to-noise ratio and background suppression in all regimes. The excitation route with no overlap of the signal and idler beams (“separated” phase-matching conditions) showed much lower signal as compared to two-beam excitation (Figure 4). After the background subtraction we found that the separated beams excitation in noncollinear geometry actually provides negligible ETPA fluorescence intensity, thus paving the way to the very selective in-depth ETPA fluorescence detection. This result correlates well with the previously reported entangled photon absorption measurements in the same organic molecule.20 We have also compared the ETPA fluorescence produced by
Figure 4. Biphoton excited fluorescence as a function of the excitation flux from SPDC generator for different organic molecules. The detected signal from pure solvent is also shown.
different ETPA-active organic molecules. The fluorescence intensity roughly followed the product of the previously measured ETPA cross section and the fluorescence quantum yield. It is important to note the linear dependence of the fluorescence signal on the input photon flux. The excitation process is an off-resonance two-photon process, and the linear intensity dependence stems exclusively from nonclassical properties of the signal and idler photons.13,16,17,21 The entangled photon excited fluorescence is the result of many orders of magnitude more efficient biphoton absorption as compared to the random classical two-photon absorption 390
DOI: 10.1021/acs.jpclett.6b02378 J. Phys. Chem. Lett. 2017, 8, 388−393
Letter
The Journal of Physical Chemistry Letters process.15,17,19 The entangled two-photon absorption rate, RE, can be derived from time-dependent second-order perturbation theory in terms of the second-order correlation function.12 In theory, the ETPA effect is accompanied by nonentangled photons or random TPA effect.11 The overall TPA rate, RE, can be thus expressed13,18,19 as the summation of the linear ETPA rate and the quadratic TPA rate, RE = σEϕ + δRϕ2, where σE is the ETPA cross section, δR the random TPA cross section, and ϕ the input photon flux density of photon pairs. The ETPA cross section, σE, has been theoretically calculated for the biphoton generated by a type II down-conversion process.13,14 For the monochromatic pump at frequency ωp, degenerate signal and idler photons (ω1 = ω2 = ωp/2), and negligible intermediate state line widths, the σE can be expressed as14 σe(Te , τ ) =
πωp2 16AETE
Figure 5. Nonmonotonic variation of the biphoton−excited fluorescence of bis[18]annulene (BT) as a function of the delay time between biphoton components introduced by birefringent crystals. The spatial distribution of the SPDC output field (SPDC phase-matching condition) used in this experiment is shown in the inset.
δ(εf − εg − ωp) 2
×
∑ Ai{2 − exp[−iΔi(TE − τ)] − exp[−iΔi(TE + τ)]} i
(1)
suggested the asymmetrical rectangular shape of the biphoton wavepacket associated with the type II SPDC22,28 modified with the 12 nm width interference filter installed in the SPDC output beam in front of the fluorescence detection unit. In this case, the envelope corresponding to the time domain amplitude of the biphoton wave function can be expressed in terms of the error function:22
where AE and TE are entanglement area and entanglement time, respectively; εg and εf are the energy of the ground and excited state, respectively; Δi = εi − εg − ωp/2 is the detuning energy with i ranging over intermediate energy levels; τ is the variable delay between signal and idler photons; Ai = Di/Δi with the transition matrix element the dipole moment operator Di.14 It is assumed that the photon pair absorption can take place only within a rectangular time window, TE, defined by the nonlinear crystal length, and that eq 1 holds for −TE < τ < TE.14 It is also suggested that the signal was externally delayed with respect to the idler to compensate the mean transit time delay in the SPDC type II crystal.22,28 In general, the arrival times of the signal and idler photons were shown to be correlated within a time interval which is inversely proportional to their spectral width.17,21,29,30 For the case of degenerate type II SPDC, it translates to the above condition −TE < τ < TE as the biphoton wavepacket spectral width is defined by 1/TE if no spectral filtering is applied to the SPDC output beam.9,22,31 It was also shown that the dependence of σE on τ within the ±TE interval (eq 1) could be observed for a particular spectral shape of the photons, sine cardinal shape, which corresponds to the rectangular pulse in the time domain.31 For the Gaussian spectral shape, no nonmonotonic τ-dependence has been theoretically predicted.31 We have measured the dependence of ETPA-excited fluorescence as a function of the signal−idler mutual delay (Figure 5). A set of crystal quartz plates of different thicknesess was used to change the optical delay between the signal and idler components of the biphoton. The fast axes of the quartz plates were aligned along the o-ray polarization plane of the BBO, thus causing the relative delay of the signal component with respect to the idler one. By variation of the amount of quartz material into the SPDC output beam, we were able to change the optical delay between the signal and idler components of the biphoton at the rate of ∼28 fs/mm of quartz at 800 nm. The ETPA fluorescence intensity showed a nonmonotonic dependence on the delay similar to that earlier observed for the entangled photon absorption rate.14−17 We modeled this dependence for the ETPA fluorescence using eq 1 within the delay time interval −TE < τ < TE assuming a single intermediate level. To account for a broader range of τ, we
⎧ ⎡ Δω τ ⎤ ⎡ Δωf (τ − 2TE) ⎤⎫ Π*(τ , TE) = F0⎨erf⎢ f ⎥ − erf⎢ ⎥⎬ ⎣ ⎦⎭ 2 ⎩ ⎣ 2 ⎦ (2)
where Δωf is the bandwidth of the filter and F0 is the filter’s transmission at its peak. To simulate the ETPA experimental data for the ETPA fluorescence, we used the combination of the equation for the ETPA cross section (eq 1) for one intermediate level with the envelope (eq 2) associated with the finite entanglement time and the spectral filtering: ΦETPA (Te , τ ) = Φ0 × |{2 − exp[−iΔ(TE − τ )] − exp[−iΔ(TE + τ )]}|2 ⎧ ⎡ Δω τ ⎤ ⎡ Δωf (τ − 2TE) ⎤⎫ × ⎨erf⎢ f ⎥ − erf⎢ ⎥⎬ ⎣ ⎦⎭ 2 ⎩ ⎣ 2 ⎦ (3)
where ΦETPA(Te,τ) is ETPA fluorescence intensity and Δ is a detuning from the intermediate level. The entanglement time, TE = 63 fs, was estimated from the mean group velocity delay of the idler beam with respect to the signal beam in the BBO crystal and the detuning Δ as a variable parameter. Initially we also made the shift of the mean τ position a variable parameter. The best fit to the experimental data showed this shift to be ∼54 fs, which is quite close to the entanglement time, TE. While the number of time delay points in this initial experiment was limited, we were able to estimate the smallest detuning Δ ≅ 0.78 × 1014 s−1 within the single virtual level model. The experiment utilizing the birefringent crystal wedges for finetuning the idler−signal delay to obtain more detailed information about the contribution of the intermediate state to the entangled photon fluorescence process is in progress. Strong selective biphoton absorption makes the organic system described above a perfect coincidence detector when 391
DOI: 10.1021/acs.jpclett.6b02378 J. Phys. Chem. Lett. 2017, 8, 388−393
Letter
The Journal of Physical Chemistry Letters the ETPA-excited fluorescence is used as a coincidence reporter. As opposite to the electronic coincidence circuit with the time window in the range of nanoseconds, the ETPAfluorescence coincidence counter is extremely fast, having the time window of the order of entanglement time, TE, which is 63 fs in our case. The majority of protocols of quantum information and image processing include heralding or coincidence measurements.32,33 The system fidelity in this case can be often quantified in terms of the ratio of true coincidences, T, to false (accidental) coincidences, F. For example, for single-photon image identification experiments, the ratio T/(F + T) defines the confidence level of the discrimination of the object A from object B.34 Maximum possible T/F ratio is proportional to the reciprocal product of the photon rate, Φ, and the duration of the coincidence window, Δτ:34
T /F ∝ 1/ΦΔτ
(5) Ono, T.; Okamoto, R.; Takeuchi, S. An entanglement-enhanced microscope. Nat. Commun. 2013, 4, 2426. (6) Shapiro, J.; Lloyd, S. Quantum illumination versus coherent-state target detection. New J. Phys. 2009, 11, 063045. (7) Chirkin, A. S. Ghost images without the background based on Bell states. JETP Lett. 2016, 103, 282−285. (8) Shih, Y. Quantum imaging, quantum lithography and the uncertainty principle. Eur. Phys. J. D 2003, 22, 485−493. (9) Lissandrin, F.; Saleh, B. E. A.; Sergienko, A. V.; Teich, M. C. Quantum theory of entangled-photon photoemission. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 165317. (10) Boto, A. N.; Kok, P.; Abrams, D. S.; Braunstein, S. L.; Williams, C. P.; Dowling, J. P. Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit. Phys. Rev. Lett. 2000, 85, 2733−2736. (11) Javanainen, J.; Gould, P. L. Linear intensity dependence of a two-photon transition rate. Phys. Rev. A: At., Mol., Opt. Phys. 1990, 41, 5088−5091. (12) Gea-Banacloche, I. Two-photon absorption of nonclassical light. Phys. Rev. Lett. 1989, 62, 1603−1606. (13) Fei, H. B.; Jost, B. M.; Popescu, S.; Saleh, B. E. A.; Teich, M. C. Entanglement-induced two-photon transparency. Phys. Rev. Lett. 1997, 78, 1679−1682. (14) Saleh, B. E. A.; Jost, B. M.; Fei, H.-B.; Teich, M. C. EntangledPhoton Virtual-State Spectroscopy. Phys. Rev. Lett. 1998, 80, 3483− 3486. (15) Upton, L.; Harpham, M.; Suzer, O.; Richter, M.; Mukamel, S.; Goodson, T. Optically Excited Entangled States in Organic Molecules Illuminate the Dark. J. Phys. Chem. Lett. 2013, 4, 2046−2052. (16) Georgiades, N.Ph.; Polzik, E. S.; Edamatsu, K.; Kimble, H. J.; Parkins, A. S. Nonclassical Excitation for Atoms in a Squeezed Vacuum. Phys. Rev. Lett. 1995, 75, 3426−3429. (17) Dayan, B.; Pe’er, A.; Friesem, A. A.; Silberberg, Y. Two Photon Absorption and Coherent Control with Broadband Down-Converted Light. Phys. Rev. Lett. 2004, 93, 023005. (18) Lee, D. I.; Goodson, T. Entangled photon absorption in an organic porphyrin dendrimer. J. Phys. Chem. B 2006, 110, 25582− 25585. (19) Harpham, M. R.; Süzer, Ö .; Ma, C.-Q.; Bäuerle, P.; Goodson, T., III Thiophene Dendrimers as Entangled Photon Sensor Materials. J. Am. Chem. Soc. 2009, 131, 973−979. (20) Guzman, A. R.; Harpham, M. R.; Süzer, Ö .; Haley, M. M.; Goodson, T. G., III Spatial Control of Entangled Two-Photon Absorption with Organic Chromophores. J. Am. Chem. Soc. 2010, 132, 7840−7841. (21) Dayan, B.; Pe’er, A.; Friesem, A. A.; Silberberg, Y. Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons. Phys. Rev. Lett. 2005, 94, 043602. (22) Rubin, M. H.; Klyshko, D. N.; Shih, Y. H.; Sergienko, A. V. Theory of Two-Photon Entanglement in Type-II Optical Parametric Down-Conversion. Phys. Rev. A: At., Mol., Opt. Phys. 1994, 50, 5122− 5133. (23) Kurtsiefer, C.; Oberparleiter, M.; Weinfurter, H. Generation of Correlated Photon Pairs in Type-II Parametric Down Conversion − Revisited. J. Mod. Opt. 2001, 48, 1997−2007. (24) Bennink, R. S.; Liu, Y.; Earl, D.; Grice, W. P. Spatial Distinguishability of Photons Produced by Spontaneous Parametric Down-Conversion with a Focused Pump. Phys. Rev. A: At., Mol., Opt. Phys. 2006, 74, 023802. (25) Süzer, Ö .; Goodson, T. Does pump beam intensity affect the efficiency of spontaneous parametric down conversion? Opt. Express 2008, 16, 20166−20175. (26) Bhaskar, A.; Guda, R.; Haley, M. M.; Goodson, T. Building symmetric two-dimensional two-photon materials. J. Am. Chem. Soc. 2006, 128, 13972−13973. (27) Anand, S.; Varnavski, O.; Marsden, J. A.; Haley, M. M.; Schlegel, H. B.; Goodson, T. Optical Excitations in Carbon Architectures Based on Dodecadehydrotribenzo [18] annulene. J. Phys. Chem. A 2006, 110, 1305−1318.
(4)
The ETPA-fluorescence based coincidence device has a ∼4 orders of magnitude shorter coincidence time window, which translates to similar increase in T/F and to dramatic improvement in a confidence level of the image discrimination. Shorter coincidence windows and related high confidence levels in coincidence experiments will allow for shorter collection times and better fidelity in performing other quantum optics protocols as well.33 In summary, we have investigated the main features of the entangled photon excited fluorescence in a set of organic molecules. For several ETPA-active chromophores we demonstrated the linear dependence of the fluorescence on the excitation intensity following a two-photon absorption process. This is a characteristic of nonclassical correlations in the twophoton process. A nonmonotonic signal−idler delay dependence of the ETPA-excited fluorescence has been detected and assigned to the intermediate level contribution. These unique features of the ETPA-excited fluorescence may allow the design of new types of spectroscopic tools, sensors, and novel lowintensity microscopy approaches.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Theodore Goodson III: 0000-0003-2453-2290 Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was based on work supported by the National Science Foundation through Grant CHE 1607949
■
REFERENCES
(1) Schlawin, F.; Dorfman, K. E.; Fingerhut, B. P.; Mukamel, S. Suppression of population transport and control of exciton distributions by entangled photons. Nat. Commun. 2013, 4, 1782. (2) Schlawin, F.; Mukamel, S. Two-photon Spectroscopy of Excitons with Entangled Photons. J. Chem. Phys. 2013, 139, 244110. (3) Roslyak, O.; Marx, C. A.; Mukamel, S. Nonlinear spectroscopy with entangled photons: Manipulating quantum pathways of matter. Phys. Rev. A: At., Mol., Opt. Phys. 2009, 79, 033832. (4) Shih, Y. H. Quantum Imaging. IEEE J. Sel. Top. Quantum Electron. 2007, 13, 1016−1030. 392
DOI: 10.1021/acs.jpclett.6b02378 J. Phys. Chem. Lett. 2017, 8, 388−393
Letter
The Journal of Physical Chemistry Letters (28) Shih, Y. Entangled biphoton source − property and preparation. Rep. Prog. Phys. 2003, 66, 1009−1044. (29) Dayan, B. Theory of two-photon interactions with broadband down-converted light and entangled photons. Phys. Rev. A: At., Mol., Opt. Phys. 2007, 76, 043813. (30) Hong, C. K.; Ou, Z. Y.; Mandel, L. Measurement of Subpicosecond Time Intervals between Two Photons by Interference. Phys. Rev. Lett. 1987, 59, 2044−2046. (31) Leon-Montiel, R. de J.; Svozilik, J.; Salazar-Serrano, L. J.; Torres, J. P. Role of the Spectral Shape of Quantum Correlations in TwoPhoton Virtual-State Spectroscopy. New J. Phys. 2013, 15, 053023. (32) Zoller, P.; Beth, Th.; Binosi, D.; Blatt, R.; Briegel, H.; Bruss, D.; Calarco, T.; Cirac, J. I.; Deutsch, D.; Eisert, J.; Ekert, A.; Fabre, C.; Gisin, N.; Grangiere, P.; Grassl, M.; Haroche, S.; Imamoglu, A.; Karlson, A.; Kempe, J.; Kouwenhoven, L.; Kröll, S.; Leuchs, G.; Lewenstein, M.; Loss, D.; Lütkenhaus, N.; Massar, S.; Mooij, J. E.; Plenio, M. B.; Polzik, E.; Popescu, S.; Rempe, G.; Sergienko, A.; Suter, D.; Twamley, J.; Wendin, G.; Werner, R.; Winter, A.; Wrachtrup, J.; Zeilinger, A. Quantum information Processing and Communication. Eur. Phys. J. D 2005, 36, 203−228. (33) Takeuchi, S. Recent Progress in Single-Photon and EntangledPhoton Generation and Applications. Jpn. J. Appl. Phys. 2014, 53, 030101. (34) Malik, M.; Shin, H.; O’Sullivan, M.; Zerom, P.; Boyd, R. W. Quantum Ghost Image Identification with Correlated Photon Pairs. Phys. Rev. Lett. 2010, 104, 163602.
393
DOI: 10.1021/acs.jpclett.6b02378 J. Phys. Chem. Lett. 2017, 8, 388−393
