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Optical Absorption Measurements with Parametric Down-Converted Photons Zhi Zhao, Kent A. Meyer, William B. Whitten,* and Robert W. Shaw Chemical Sciences Division, Oak Ridge National Laboratory P.O. Box 2008, Oak Ridge, Tennessee 37831-6142 It has been known for some time that correlated detection of pairs of photons generated by parametric down-conversion can eliminate several sources of error that occur in single-beam measurements. In the correlated photon measurements, the down-converted photons are separated into two beams with one photon of a pair in each beam. The absolute detection efficiency of a detector in one beam can be determined from the count rate of a detector in the other beam and the coincidence rate for the two detectors. These ideas can be used to measure the optical absorbance of a sample placed in front of one of the detectors. Errors due to stray light and dark counts are substantially reduced and fluctuations in pump intensity largely eliminated. The purpose of this note is to describe the use of coincidence detection of pairs of photons generated by spontaneous parametric down-conversion for measurements of optical absorbance. With certain geometries, it is possible to separate the down-converted pairs into two beams such that each beam contains one of the two photons. Under such conditions, it is possible to use one stream of photons as a reference beam to monitor the intensity of photons in the other beam to compensate for noise on the pump beam generating the down-converted light (quantum noise eater). It is possible to discount many of the stray counts, whether dark counts from detectors or unpaired down-converted photons by counting only detected coincidences. Burnham and Weinberg1 showed that absolute detector efficiencies could be calculated from the coincidence count rate together with the rates from detectors in the two beams. Since an absorber in one of the beams can be folded into the detection efficiency of the absorber-detector combination, it should be possible to use a setup similar to theirs for absorbance determinations with improved performance relative to conventional classical methods. In addition to the work of Burnham and Weinberg, there have been a number of other reports describing the use of downconverted photon pairs for absolute detector efficiency determinations.2–6 The general thrust of these articles was improved detector metrology. While absorbance determination was not mentioned * Corresponding author. Phone: (865) 574-4921. Fax: (865) 574-8363. E-mail:
[email protected]. (1) Burnham, D. C.; Weinberg, D. L. Phys. Rev. Lett. 1970, 25, 84–87. (2) Klyshko, D. N. Sov. J. Quantum Electron. 1980, 10, 1112–1116. (3) Rarity, J. G.; Ridley, K. D.; Tapster, P. R. Appl. Opt. 1987, 26, 4616–4619. (4) Kwiat, P. G.; Steinberg, A. M.; Chiao, R. Y.; Eberhard, P. H.; Petroff, M. D. Appl. Opt. 1994, 33, 1844–1853. (5) Lindenthal, M.; Kofler, J. Appl. Opt. 2006, 45, 6059–6064. (6) Polyakov, S. V.; Migdall, A. L. Opt. Express 2007, 15, 1390–1407. 10.1021/ac800911t CCC: $40.75 2008 American Chemical Society Published on Web 08/26/2008
explicitly, the treatment of various sources of error and time response in these articles obviously is relevant to the present investigation as well. The measurement is based on the simultaneous generation of pairs of photons in the down-conversion process.7,8 Because of the angular generation of the down-converted pairs, it is possible to separate the pairs into two beams, one photon in each beam. If the beams are directed onto detectors capable of detecting individual photons, the detection of a photon in one beam assures the presence of the conjugate photon in the other beam. The detection efficiency of the second detector including any losses in the beam path is the ratio of the photons assured to be present in that beam that it detects to the total number of photons assured to be present. To be reasonably certain that the photons detected by the two detectors are from the same pair, their arrival time must be within a certain coincidence gate time, usually several nanoseconds, determined primarily by the time response of the detectors and electronics. If N1 is the arrival rate of photons at detector D1 and R1 ) η1N1 is the rate of detection, at least R1 photons per second will be present in beam 2 and a fraction η2 of these will be detected. Thus the coincidence rate for the two detectors will be Rc ) η2R1. The extra photons detected by detector D2 are mostly those from photons conjugated to those missed by detector D1. Thus, from a measurement of R1 and Rc, we can determine the efficiency of D2 including any losses in the beam path. Similarly, we can determine η1 from Rc and R2. If, as in the present case, we want to measure the component of the loss, li, due to an absorber placed in beam i, we can express the absolute propagation/detection efficiency, ηi, as ηi ) liζi, where ζi includes detector efficiency and propagation losses excluding the absorber. The most important point is that the results are completely independent of the pump laser intensity or its fluctuations. The three count rates, R1, R2, and Rc are measured concurrently. For an absorbance determination of a solution in a cuvette, a blank determination is usually made in addition to the sample absorbance and the results subtracted. Both determinations are absolute using this method, but any errors in cuvette alignment or the like would still be present. The method would be most useful for flow cell measurements where the sample cell need not be moved. Before starting the absorbance experiments, we set up single and two-photon interferometry experiments to verify that we could generate correlated pairs of down-converted photons.8 The experimental arrangement for these interferometry experiments (7) Hong, C. K.; Mandel, L. Phys. Rev. A. 1985, 31, 2409–2418. (8) Kwiat, P. G.; Mattle, K.; Weinfurter, H.; Zeilinger, A. Phys. Rev. Lett. 1995, 75, 4337–4341.
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Figure 1. Diagram of the experiment for single- and two-photon interferometry of down-converted photon pairs. For single-photon interferometry, beamsplitter BS2 was removed. For two-photon interferometry, the beam to mirror M2 was blocked and the half-wave plate, HWP, used to ensure that photons entering BS2 had the same polarization. Coincidences at D1 and D2 were recorded for both experiments.
is shown in Figure 1. The beams shown in the figure lie in a horizontal plane parallel to the optical table. The pump source for the down-converted photons was a beam of 351-nm photons from a Coherent Inova-90 argon ion laser. A 60° quartz prism was used to turn the beam and separate the 364-nm line from the pump beam. The vertically polarized pump beam was then focused onto a 0.5-cm × 0.5-cm × 0.2-cm β barium borate (BBO) crystal with the optic axis 49.2° from the face normal in the vertical plane. This configuration assured type II noncolinear phase matching whereby the extraordinary ray produced by the pump beam generated ordinary and extraordinary photon pairs of 702-nm wavelength. The focal length of the lens in the pump beam was chosen to optimize the intensity of the collected conjugate photon pairs, as described by Kurtsiefer et al.9 As shown by Kwiat et al.,8 the ordinary photons were emitted in a cone whose axis was in the vertical plane below the horizontal. The extraordinary photons were emitted in a cone with an axis above the horizontal. For the crystal cut selected, the two cones intersected along two directions in the horizontal plane. (The inset in Figure 1 represents the intersection of the two cones with a plane normal to the pump beam. The solid circle represents the cone of extraordinary rays while the dashed circle represents the ordinary rays. The two dots where the circles intersect indicate the two beams of photons selected by spatial filtering for these experiments.) Energy and momentum conservation in the down-conversion process requires the two photons to be coplanar with the pump beam and on different cones. A photon emitted along one of these directions could be either horizontally or vertically polarized since it could have been from the ordinary or extraordinary cone. Because of the type II phase matching, however, with simultaneous generation of an ordinary and extraordinary photon, the photon emitted in the other direction must have had the opposite polarization. Frequency-degenerate pairs of photons produced in this way are said to be polarization-entangled. While this behavior is not a necessary condition for the present investigation, the experimental arrangement which was set up for other experiments provided a convenient way to separate the two beams of conjugate photons for these measurements. The divergence of the two down-converted beams was limited by spatial filtering. Optical path difference compensation was used (9) Kurtsiefer, C.; Oberparleiter, M.; Weinfurter, H. Phys. Rev. A 2001, 64, 023802-1–4.
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Figure 2. Single-photon interference pattern. The envelope is an indication of the coherence length of the down-converted photons. The data points are connected by black lines to guide the eye. The red curve is an envelope function fit to the interference fringes.
in some of the experiments. A BBO crystal of half the thickness of the down-conversion crystal together with a 90° half-wave polarization rotator was placed in each beam to give first order correction for the velocity difference for ordinary and extraordinary photons in the primary crystal.8 One of the beams was passed through a Michelson interferometer that was used to measure the coherence length of the individual photons in that beam (with single-photon detection of only that beam) or as a means to introduce a variable path delay for two-photon interferometry. In the latter measurements, the path to M2 was blocked and the two beams were crossed at a beamsplitter, BS2, before coincidence detection. This measurement, described by Hong, Ou, and Mandel,10 permits a determination of the degree of simultaneity of the down-converted photons as well as a measure of the accidental coincidences. The method for collection and detection of the down-converted photons has been described by Kurtsiefer et al.9 The two beams were focused by 10× microscope objective lenses into single-mode optical fibers factory-coupled to single-photon avalanche diode (SPAD) detectors (SPCM-AQR-13-FC, EG&G). The 35-ns TTLlevel output pulses from the SPADs were inverted using pulse transformers and further narrowed by constant-fraction discriminators (CFD935, ORTEC). Coincidence measurements were performed with a coincidence logic gate (CO4020, ORTEC) with a ∼5-ns window. With this window value, the accidental count rate was smaller than 0.5 s-1, 3 orders of magnitude lower than the coincidence count rate. With 3-nm bandpass filters in each beam, the overall collection and detection efficiency was approximately 20%. The results of a single beam interference scan are shown in Figure 2. For this measurement, the beamsplitter BS2 in Figure 1 was removed. Coincidence detection was used to ensure that the single photons at D1 were entangled with photons striking D2. Coincidence detection also improves visibility by reducing effects of dark counts and stray light. The intensity of the downconverted beam was such that there was little chance of two photons being within the interferometer at the same time. Thus, (10) Hong, C. K.; Ou, Z. Y.; Mandel, L. Phys. Rev. Lett. 1987, 59, 2044–2046.
Figure 4. Experimental setup for absorbance measurements.
Figure 3. Two-photon interference pattern. The data points are connected by black lines to guide the eye. The fluctuations here are random noise.
the trace is a single photon interference pattern. The points for delays from roughly -100 to +100 µm depict the interference fringes. The delay interval between points was 600 nm. Thus, the interference fringes that should have a periodicity of λ/2, or 351 nm, were under sampled. The intensity of the interference (red envelope curve) as a function of path difference is an indication of the coherence length of the down-converted photons and hence their frequency bandwidth (or time duration). The width of the envelope at half-maximum path delay for this measurement was 120 ± 10 µm. For two-photon interferometry, the beam to mirror M2 was blocked, and beamsplitter BS2 was replaced at the point where the two down-converted beams crossed in front of their detectors (Figure 1).10 A half-wave plate, HWP, was used to rotate the polarization of one beam by 90° so that both photons of a correlated pair would have the same polarization. The variable path of the Michelson interferometer was used to alter the path difference of the two down-converted beams while their photons were detected in coincidence. (The time width of the coincidence window, 5 ns, served only to correlate the photon pairs, since the window could accommodate a path difference of more than 1 m). A two-photon interference pattern measured under the same conditions as for Figure 2 is shown in Figure 3. The pronounced dip is a quantum-mechanical phenomenon. When two indistinguishable photons (in polarization and arrival time) enter a beam splitter, their wave function must be symmetrical with respect to interchange of the photons. This causes both photons to arrive at the same detector, resulting in a zero coincidence rate when they arrive within a coherence length.10 The round-trip path delay corresponding to the width at half-maximum, 60 ± 4 µm, was approximately 0.5 that of Figure 2, as predicted theoretically. The half-width also gives an upper limit to the difference in generation time of the two down-converted photons, 200 fs in this case. From an experimental standpoint, the depth of the two-photon interference pattern showed that the level of accidental coincidences was very low. Optical absorbance measurements were made by placing a 1-cm path-length quartz cuvette containing the sample solution in one of the two down-conversion beams between the BBO crystal
and the collection optics, as shown in Figure 4. For optical absorption measurements, the compensation optical elements and optical delay line components were not necessary because the 5-ns coincidence window could accommodate a large difference in optical path. The samples were solutions of IR 144 laser dye in ethanol. The IR 144 dye, obtained from Lambda Physik GmbH, has an absorbance maximum at 750 nm with an extinction coefficient of 9.0 × 104 L mole-1 cm-1 at 704 nm. Solutions with a range of absorbance values were prepared by diluting a 0.43 g L-1 stock solution in ethanol with 95% spectrophotometric-grade ethanol. The photon count rate from the detector in the sample beam and the coincidence rate from the two detectors were measured for a series of absorbance values ranging from 0 to greater than 3. The results of these measurements are plotted in Figure 5 as measured absorbance versus values calculated from the sample concentrations. The plot in Figure 5a is a single-beam determination using only the counts recorded in the sample beam by detector D2 in Figure 4. The absorbance deviated from the expected value for values of 2.0 or greater because of stray light or thermal detector noise. The absorbance values in Figure 5b were calculated from both the reference beam and coincidence counts, as described above. The accuracy of the determination using coincidence detection of the down-converted pairs is clearly superior to the single-beam determinations. Correction for stray light and dark counts was not necessary in the two-beam measurement because the probability of an accidental coincidence was low.1 Furthermore, the intensity of the pump beam does not enter explicitly into the calculations, the absorbance calculated from the coincidence measurements is independent of the source intensity or fluctuations. Because errors due to the fluctuations of the pump laser could be minimized by the simultaneous detection of the reference beam and coincidences, the major sources of error in this experiment were mechanical misalignment when the sample cuvette was replaced and statistical errors in counting the coincidences. The former errors can be reduced considerably by using a flow cell to contain the analyte. The counting errors are assumed to obey Poissonian statistics and therefore should be equal to the square root of the number of coincidences, thus becoming less important at higher beam intensity and low sample absorbance. For the pump intensity in the present experiment, the counting error became appreciable for absorbance greater than 3. A dark count in the reference channel is indistinguishable from an absorbed photon in the sample channel since in either case there is a missing coincidence. This source of error will decrease faster with reference beam intensity than the counting errors. It can be shown that the errors in R1 due to counting statistics Analytical Chemistry, Vol. 80, No. 19, October 1, 2008
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single-beam photons, Alteper et al.11 have recently shown that a two-crystal generation scheme based on type-I phase matching with compensation for aberations previously encountered can yield high correlated pair intensities. They achieved an intensity of 2 × 106 detected photon pairs s-1 at detector saturation. Their geometry still maintained the ability to spatially separate the residual pump beam from the down-converted photons. A drawback of degenerate parametric down-conversion for analyte detection in separations methods is that the frequency of the down-converted photons is not in a very useful spectral region for detection of many analytes. Wavelength degeneracy of the two beams is not a necessary requirement for the measurement. There have been recent studies of nondegenerate parametric downconversion for other applications in which one photon, usually of long wavelength, is used as a trigger to indicate the presence of a conjugate photon.12 This process, sometimes known as heralded single photon generation has the potential of producing a pair of down-converted beams, one of which has a frequency approaching that of the pump beam. Recently, an approach to heralded single photon generation based on four-wave parametric conversion has been reported by Fulconis et al.13 They were able to generate 0.1 pair of photons per pump pulse with an average pump power of ∼3 mW. In future work, we plan to explore the use of correlated photon pairs for absorption detection of analytes in flowing fluidic systems. We will attempt to shorten the wavelength of the sample beam photons for a better match with the absorption spectrum of typical analytes using nondegenerate parametric processes, both with CW and pulsed pump laser sources.
Figure 5. (a) Absorbance calculated from counts at D2 versus values from concentration. (b) Absorbance calculated from R1, R2, and Rc versus values from concentration.
determine a lower limit to detectable absorbance that is proportional to (R1)-1/2. One significant improvement for absorbance measurements with correlated photons would be to increase the rate of generation of the photon pairs. While the type-II noncolinear generation has been shown to give an exceptional ratio of correlated pairs to
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ACKNOWLEDGMENT This research was sponsored by the Division of Chemical Sciences, Biosciences, and Geosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC0500OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC.
Received for review May 2, 2008. Accepted June 23, 2008. AC800911T (11) Altepeter, J. B.; Jeffrey, E. R.; Kwiat, P. G. Opt. Express 2005, 13, 8951– 8959. (12) Alibart, O.; Ostrowsky, D. B.; Baldi, P.; Tanzilli, S. Opt. Lett. 2005, 30, 1539–1541. (13) Fulconis, J.; Alibart, O.; O’Brian, J. L.; Wadsworth, W. J.; Rarity, J. G. Phys. Rev. Lett. 2007, 99, 120501.
