Entangled Two Photon Absorption Cross Section on the 808 nm

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Entangled Two-Photon Absorption Cross Section on the 808 nm Region for the Common Dyes Zinc Tetraphenylporphyrin and Rhodamine B Juan Pablo Villabona-Monsalve, Omar Calderón-Losada, Mayerlin Nunez Portela, and Alejandra Valencia J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b06450 • Publication Date (Web): 21 Sep 2017 Downloaded from http://pubs.acs.org on September 27, 2017

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The Journal of Physical Chemistry

Entangled Two Photon Absorption Cross Section on the 808 nm Region for the Common Dyes Zinc Tetraphenylporphyrin and Rhodamine B Juan P. Villabona-Monsalve,

∗, †, ‡

Omar Calderón-Losada,

and Alejandra Valencia

†Laboratorio

†

M. Nuñez Portela,

∗, †

†

de Óptica Cuántica, Universidad de los Andes, A.A. 4976, Bogotá D.C., Colombia

‡Currently

at: Escuela de Química, Universidad Industrial de Santander. Bucaramanga, Santander 680002, Colombia

E-mail: [email protected]; [email protected]

1

ACS Paragon Plus Environment


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Abstract We report the measurement of the entangled two photon absorption (ETPA) cross section, σE , at 808 nm on organic chromophores in solution in a low photon ux regime. We performed measurements on Zinc tetraphenylporphyrin (ZnTPP) in Toluene and Rhodamine B (RhB) in Methanol. This is, to the best of our knowledge, the rst time that σE is measured for RhB. Additionally, we report a study of the dependence of σE on the molecular concentration for both molecular systems. In contrast to previous

experiments, our measurements are based on detecting the pairs of photons that are transmitted by the molecular system. By using a coincidence count circuit it was possible to improve the signal to noise ratio. This type of work is important for the development of spectroscopic and microscopic techniques using entangled photons.

Introduction Two photon absorption (TPA) is a non-linear process in which, by absorbing two photons, a specic electronic excited state of a system can be accessed 1 . In this process, energy conservation is satised given that the sum of the energy of the individual photons should be equal to the energy of the transition that is addresed. The TPA phenomena was theoretically proposed by Maria Goeppert Mayer on 1931 2 and it was experimentally demonstrated after the invention of the laser 3 . TPA has been studied using high intensity pulsed lasers on the femtosecond 46 and picosecond 7 regime and it has been extensively used for spectroscopic and microscopic techniques 8 as well as in photoinduced phenomena on a wide variety of materials 9,10 . In recent years, an interest to study TPA induced by sources with dierent statistical properties than lasers, such as thermal, 11 squeezed 12 and entangled light 5,6,13,14 , has appeared. Particularly, entangled light has been experimentally tested as a convenient source to induce two-photon transitions on molecules due to its non-classical properties. One of the motivations for this type of work is the possibility to induce TPA with a low photon ux. 2


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This capability may have important implications reducing photodestruction probability and photo-bleaching of the sample, allowing to develop less invasive methods to study TPA in biological samples 15,16 . Entangled light has also been used to induce TPA in semiconductors to study temporal correlations of twin beams 17 . From a theoretical perspective, TPA induced by entangled light with dierent type of frequency correlations has been studied as a tool to learn about the spectral properties of a sample 1824 . In this paper, we study TPA induced in molecules by entangled light, generated by the process of Spontaneous Parametric Down Conversion (SPDC) 25 pumped by a cw laser, at a low photon ux. The probability of entangled TPA (ETPA) in a sample is quantied by means of the entangled TPA cross section, σE . We infer the value of σE for the commercially available compounds Zinc tetraphenylporphyrin (ZnTPP) and Rhodamine B (RhB) by measuring the absorption signal. Measurements of σE for ZnTTP have been previously reported 5 ; however, this is, to the best of our knowledge, the rst time that σE is measured for RhB. Additionally, we report, for these two molecules, a study of the dependence of σE on the molecular concentration. In contrast to previous experiments 5,6,13 , our measurements are based on detecting, by means of a coincidence count circuit, the pairs of photons that are transmitted by the molecular system, improving the signal to noise ratio for the cases in which the studied samples do not present one-photon absorption at the wavelength of the entangled light.

Operational Model In this section, we present the operational approach we used to obtain σE from experiments based on coincidence counts. In general, TPA can be induced by using entangled light and random light sources such as lasers. Considering a molecular system, the TPA rate per molecule, rTPA , can be written as 2628 :

rTPA = σE φ + δR φ2 , 3


(1)


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where φ is the incident photon ux density (photons s −1 cm−2 ) impinging on the molecule and δR is the random TPA cross section, where random refers to light sources that present a Poisson distribution in the photon number. The quadratic term in Eq. (1) represents the contribution of random sources to rTPA . Typically, δR is on the order of 102 GM (1 GM= 10−50 cm4 s photon−1 molecule−1 ) and therefore, a high photon ux density ( 1018 photons s−1 cm−2 ) is required to induce TPA. A signicant dierence between random and entangled TPA rates is clearly seen by the dependence of rT P A on the incident photon ux. The linear dependence with φ for entangled light, the term σE φ in Eq. (1), and the fact that

σE can be on the order of 10−18 cm2 molecule−1 , allows to observe TPA with a photon ux density on the order of 1012 photons s−1 cm−2 as reported in Ref. 6. These values for photon ux density are signicantly lower than the one for random sources. It is important to notice that σE and δr depend on the energy of the transition being induced in the sample and on the characteristics of the light source that is used to drive the two photon transition 5 . Let us consider the case where TPA in a molecule is induced by a source of entangled light with a rate rETPA . In this case, the quadratic dependence on the photon ux in Eq. (1) can be neglected and rTPA = rETPA . Considering a source of entangled light that produces pairs of photons, φ = 2φ0 , with φ0 denoting the incident entangled photon pair ux density impinging on the molecule. In this case,

rETPA = 2σE φ0 .

(2)

From the experimental point of view, the quantity rETPA can be estimated by measuring the rate of photon pairs absorbed by a molecular system, Rabs . For a sample containing N molecules on a volume V ,

rETPA =

2Rabs . N

(3)

Comparing the theoretical expression for rETPA , Eq. (2), with the experimental version in Eq. (3), and taking into account that N = cV NA , with c the concentration of molecules 4


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in the sample and NA Avogadro's number,

Rabs = cV NA σE φ0 .

(4)

In particular, in a conguration where the detection system is based on measuring the coincidence rate of photon pairs, the incident entangled photon pair ux density becomes

φ0 = R/A, where R is the detected rate of photon pairs produced by the light source that interacts with the molecules in an area A. Under these considerations,

Rabs =

cV NA σE R. A

(5)

For molecules studied in liquid solution, it is important to account for the signal scattered by the solvent. In order to do this, it is necessary to measure the rate of photon pairs transmitted through the solvent, Rsolvent , that becomes the incident entangled photon pair ux impinging on the molecules ( R → Rsolvent ); therefore, Eq. (5) becomes

Rabs =

cV NA σE Rsolvent . A

(6)

Equation (6) allows to estimate σE for a molecule from variables that can be experimentally controlled. By measuring Rabs as a function of Rsolvent and performing a linear t, it is possible to estimate σE for a given molecule at a particular concentration. The experimental procedure to infer σE will be described in detail in the following sections.

Experiment In this section, we describe the experiment to obtain σE for two dierent molecular systems. The experimental setup is shown in Figure 1. Entangled photon pairs are produced by SPDC, send into a sample that can be ZnTPP or RhB, and nally detected by single photon

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counters that are connected to a FPGA (Field Programmable Gate Array) to measure single and coincidence count rates. In the following, a detailed description of the entangled light source and the molecular systems will be presented. SPC2 xyz MP

SM-OF-BS

SPC1

L4

FPGA

CW Diode Laser 404 nm

LPF

L2 L3

Control and acquisition

M4 M2

VNDF L1

BBO

DM LPF Sample M3

PD

M1

ZnTPP

RhB

Figure 1: Experimental setup to measure ETPA for dierent molecules. The entangled light source is based on SPDC produced at a BBO crystal pumped by a cw laser. Dierent lenses, L, are used to control the spatial shape of the light. Mirrors, M, are used to guide the light in the experiment. SPDC photons are couple to a ber beam splitter, SM-OF-BS, and then detected by single photon counters, SPC1 and SPC2. The molecules at the bottom are the ones studied in this work.

Entangled Light Source The entangled light to induce ETPA in molecules was generated by the process of SPDC on a non-linear crystal. Roughly speaking, SPDC is a process in which a photon from a pump beam with a wavelength λp impinges on a non-linear crystal and occasionally, pairs of photons, known as signal and idler, are produced with wavelengths λs and λi , respectively. In our setup, Figure 1, a cw laser at 404 nm pumps a 1 mm BBO ( β -Barium Borate) type I crystal to produce SPDC photons on a degenerate and collinear conguration center at

λ0s = λ0i = 808 nm. The pump is focused into the crystal by L1 ( f1 = 50 mm). The pump power is monitored by a photodiode (PD) and it is tuned from 0.05 mW to 17 mW by means of a motorized variable neutral density lter (VNDF) Thorlabs NDC-50C-4M. After 6


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the BBO, the SPDC light is collected by L2 ( f2 = 50 mm) and then focused by L3 ( f3 = 300 mm) to produce a beam waist w0 = 61 µm on the position of the sample. Following L3, a dichroic mirror (DM) and a long pass lter (LPF), with cuto wavelength at 750 nm, are used to remove the residual pump beam. After passing through the sample, the SPDC photons are coupled by using L4 ( f4 = 11 mm) into a single mode optical ber-beamsplitter (SM-OFBS) from OZ-optics. L4 is mounted on a three axis micrometric positioner ( xyz MP) that has an extra LPF to reduce the detection of the residual pump beam. The photons from the SM-OF-BS outputs are detected by SPC1 and SPC2, single-photon counters (PerkinElmer, SPCM-AQR-13). The output from the detectors is electronically analyzed by the FPGA to obtain the rate of single and coincidence counts in a 9 ns time window. The single photon count rate from our source at the maximum pump power is on the order of

5 × 105 photons s−1 . The photon ux density estimated from the coincidence count rate and the focusing area of the entangled photons is on the order of 2 × 109 photons cm−2 s−1 . In order to study ETPA, it is relevant to discuss the frequency correlations between the photon pairs produced in the SPDC source. These frequency correlations are often described by a joint spectrum 29,30 . The joint spectrum can be studied by looking at its behavior in the variables ωs + ωi and ωs − ωi , where ωs = 2πc/λs is the frequency of the signal photon and ωi = 2πc/λi is the frequency of the idler photon. The bandwidth in the variable ωs + ωi is dened by the spectral width of the light pumping the SPDC crystal. Therefore, for a cw pump, as the one in our experiment, the width of ωs +ωi presents a very narrow feature. This leads to an excitation of a two photon transition with a well dene energy that corresponds to the pump frequency ωp = ωs +ωi . Therefore, it is valid to apply a wavelength independent model for Rabs as the one presented in Eq. (6). In the joint spectrum, the variable ωs − ωi denes the entanglement time, TE , of the photon pairs. Specically, they are Fourier transform conjugate variables. In the absence of a dispersive medium, a small TE implies a broad joint spectral width in the variable

ωs − ωi . For the parameters of the crystal and the wavelength of the pump, the bandwidth 7



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of this variable at full width half maximum was calculated to be around 130 nm, leading to a TE ≈ 17 fs 25 .

Molecular Systems The measurement of σE was performed on the commercially available compounds Zinc tetraphenylporphyrin (ZnTPP) and Rhodamine B (RhB). ZnTPP was obtained from mesoTetraphenylporphhyrin ( ≥95 % purity, Sigma-Aldrich) by the method reported on Ref. 31 and dissolved on high performance liquid chromatography (HPLC) grade Toluene. RhB ( ≥95 % purity, Sigma-Aldrich) was used as received and dissolved on HPLC grade Methanol. The sample was placed in our setup as indicated in Figure 1 using a quartz cuvette of 10 mm pathlength. Taking into account that the waist of the SPDC photons in the sample leads to a Rayleigh range of 14 mm, the interaction volume can be considered as a cylinder with transverse area and volume on the order of 2 × 10−4 cm2 and 2 × 10−4 cm3 , respectively. We prepared dierent concentrations for the molecules in the corresponding solvent. The concentration values were obtained by considering the reported values for the extinction coecients 32,33 and by measuring the one-photon absorption spectra using a Specord 50 Plus spectrophotometer (Analytik Jena). The measured one-photon spectra for RhB and ZnTPP are shown in Figure 2a and Figure 2b, respectively. The energy levels excited by the entangled photons are depicted in Figure 2c and Figure 2d for both molecules. The corresponding energy diagram for RhB is shown in Figure 2c. Based on the two photon spectroscopic information available in the literature for RhB 33 , there is TPA for two photons at 800 nm that is represented by the vertical dashed arrow in the gure. This transition is not associated to a pure electronic transition but can be excited due to the coupling of an electronic and vibrational state. For ZnTPP, to the best of our knowledge, there is no information regarding the TPA spectrum. However, due to the centrosymetric properties of the molecule, the behavior of the TPA can be qualitatively estimated from the linear spectroscopic information 3436 . The energy 8


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a) RhB

A)

c) RhB S2 (355 nm AB) 400 nm AB

final state

S1 (545 nm AB) Virtual states

S0

One-photon absorption (a.u)

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One-photon absorption (a.u)

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B)

initial state

d) Zn TPP

b) Zn TPP

0 S 2

S2 (423 nm AB)

final state (S2´)

S1 (549 nm AB) Virtual states

S2´

S0

S0

initial state

Figure 2: a) and b) One-photon spectra for RhB and ZnTPP, respectively. c) and d) Energy levels for the molecules studied in our setup. levels for ZnTPP in Figure 2d are inferred from Ref. 3436, where the TPA corresponds to the transition S0 → S20 . In both cases, for RhB and ZnTPP, the TPA is addressed by intermediate virtual states indicated by the shadow region in the gures. In previous reports, the value of σE and δr have been determined for ZnTPP 5 . In these measurements entangled light was produced by SPDC generated by a pulsed laser and, before interacting with the sample, it was ltered using a 20 nm bandpass lter around 800 nm. The detection system in their case was based only on single counts. On the other hand, values of

δr for RhB have been reported for wavelengths around 800 nm 33,37 ; however, the value of σE has never been reported. In our experimental setup, the molecular system was illuminated with the whole spectrum of the SPDC photons centered at 808 nm with a bandwidth of 130 nm full width half maximum since we did not use band pass lters. Besides their importance for spectroscopic and microscopic techniques, the selected molecules for this study have shown relevance for dierent applications such as optical sensors 6 . This versatility is based on their photophysics, characterized by high uorescence quantum yields and long lifetimes for the rst electronic excited state 33,34,38,39 .

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Results and Discussion

Figure 3: Experimental data for Rsolvent and Rsample as a function of Ppump . Panel (a) corresponds to Toluene and panel (b) corresponds to Methanol. Panel (c) shows the behavior of Rsample for ZnTPP in Toluene with a concentration of c = 63 µM and panel (c) shows this behavior for RhB in Methanol with a concentration of c = 4.5 mM. In order to get a value of σE , it is necessary to measure the rate of photon pairs absorbed by a molecular system, Rabs , as a function of Rsolvent , as stated in Eq. (6). For molecules in a solvent, Rabs = (Rsolvent − Rsample ), where Rsample is the detected rate of photon pairs that passes through the sample, i.e., through solvent plus molecular system. For a xed concentration, volume and area, it is possible to measure Rsolvent and Rsample as a function of the power of the pump beam, Ppump , that generates the entangled photon pairs. These results are presented in Figure 3a and Figure 3b for Toluene and Methanol and in Figure 3c and Figure 3d for ZnTPP and RhB for a given concentration in their corresponding solvents. Each point on Figure 3 corresponds to an average of 60 measurements of one second each. Error bars represent the standard deviation for each measurement. A linear dependence is observed in these graphs. In particular, Figure 3a and Figure 3b allow to nd the correspondence between Ppump and Rsolvent . For a particular sample, Rabs as a function of Rsolvent is obtained by using the correspondence between Ppump and Rsolvent and subtracting Rsample from Rsolvent . Figure 4 shows the curves Rabs as a function of Rsolvent for dierent concentrations of the studied molecules. Figure 4a depicts the results for ZnTPP and Figure 4b for RhB. The data reported corresponds 10


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Rabs [Photon pairs/s]

1500 a) ZnTPP 17 M 63 M 12 M 120 230 0 M 1400 00 M

1000

500

0 0

500

1000

1500

R solvent

2000

2500

3000

3500

[Photon pairs/s]

abs

[Photon pairs/s]

3000 b) Rh B 0.038 mM 0.19 mM 4.5 mM 58 mM 110 mM

2000

1000

R

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 0

1500

3000

R solvent

4500

6000

7500

[Photon pairs/s]

Figure 4: Experimental data for Rabs as a function of Rsolvent for dierent concentrations of the studied molecules. Panel (a) corresponds to ZnTPP in Toluene and panel (b) corresponds to RhB in Methanol. The solid lines are linear ts to the data. The tting parameters are used to calculate σe for each concentration.

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to the ETPA signal since the one-photon absorption for RhB and ZnTPP are ruled out as demonstrated in the linear spectra in Figure 2a and Figure 2b. For the low concentrations in the samples, scattering eects are mainly due to the solvent. By subtracting Rsample from

Rsolvent , the eects of the scattering are removed. Absorption signals on the order of 1000 photon pairs s−1 can be observed for dierent concentrations at dierent values of Rsolvent . At low values of Rsolvent (50 photon pairs s−1 ), the measured values for Rabs are less than 20 photon pairs s−1 , indicating a good signal to noise ratio. The solid lines in Figure 4 correspond to linear ts to the data. The ts were forced to pass through the origin since the background noise was minimized due to the characteristics of the entangled light source and the coincidence detection system. According to Eq. (6), the slope of the t is related to the product σE c. Therefore, there are dierent values of σE and c that can turn into the same slope. This is the case for the concentrations 120 µM and 1400 µM of ZnTPP in Figure 4a and for the concentrations of

0.038 mM and 0.19 mM of RhB in Figure 4b. The results of σE for dierent concentrations are summarized in Table 1 and plotted in Figure 5a for ZnTPP and in Figure 5b for RhB. The measured value of σE for ZnTPP is approximately one order of magnitude bigger that the value obtained for RhB. This dierence is expected since the two photon absorption in ZnTPP correspond to an electronic transition while for RhB is due to the coupling of an electronic and a vibration state. A strong decay is observed for σE when the concentration increases in Figure 5. This behavior can be understood by an analogy with previous reports on the dependence of δr and σE with the concentration 6,40 . The decreasing of σE for high concentrations can be interpreted by considering aggregation of the molecules that lead to screening eects. As an additional argument to rule out scattering as the physical eect that leads to our experimental results, we compared the values measured for σE with values reported for the Rayleigh scattering. For RhB in methanol, the Rayleigh scattering cross section at 694 nm has been reported to be 2.1 × 10−22 cm2 /molecule 41 . The scattering cross section scales as

12


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Table 1: Values of σE for dierent concentrations obtained from the tting parameters in Figure 4. c (µM ) 17 63 120 230 1400 c (mM) 0.038 0.19 4.5 58 110

ZnTPP σE × 10−18 (cm2 molecule−1 ) 42 ± 5.2 5.1 ± 0.46 3.2 ± 0.20 1.1 ± 0.07 0.27 ± 0.026 RhB σE × 10−18 (cm2 molecule−1 ) 4.2 ± 0.34 0.80 ± 0.068 0.063 ± 0.0039 0.011 ± 0.00084 0.017 ± 0.0018

λ−4 , therefore, it is expected, that at 808 nm, the value of the Rayleigh cross section is on the same order of magnitude. Our measured values for σE are four orders of magnitude larger than this value.

Conclusions We reported on the measurement of the entangled two photon absorption cross section, σE , for ZnTPP and RhB. The value of σE for ZnTPP agrees with previously reported results. For RhB, this is the rst time that a measurement for σE has been performed. Additionally, we showed that sample concentration has important eects on σE . The data we reported was taken in an experimental setup with two main features that are dierent from previous setups to measure σE . First, our entangled light source was based on SPDC pumped by a cw laser instead of a pulsed laser. Second, the detection system we used was based on counting the rate of photon pairs absorbed by the molecules instead of the number of single photons absorbed. This last feature, allowed us to show that regardless the low photon ux density of entangled photons ( 109 photons cm−2 s−1 ), the ETPA processes can be induced

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Figure 5: Dependence of σE with the concentration of molecules in a solvent. Panel (a) corresponds to ZnTPP in Toluene and panel (b) corresponds to RhB in Methanol. and the number of absorbed photon pairs can be measured for samples that do not present one-photon absorption at the wavelength of the entangled light. By comparing the measured

σE values with the typical Rayleigh scattering we conclude that our results are due to the process of ETPA in the molecules and not to scattering. The obtained experimental results provide support for the implementation of spectroscopic and microscopic techniques based on the process of entangled two-photon absorption on molecules. Additionally, this type of work is benecial for studying biological samples and the implementation of detection systems operating at low photon uxes.

Acknowledgement This work was nancially supported by Facultad de Ciencias, Universidad de los Andes, Bogotá, Colombia. M.N.P. acknowledges the nancial support of FAPA project of Facultad de Ciencias, Universidad de los Andes, Bogotá, Colombia. The authors thank Dr. Yenny 14


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Hernández at Universidad de los Andes for fruitful discussions and Dr. Gilma Granados at Universidad Nacional de Colombia for the synthesis and purication of Zinc tetraphenylporphyrin.

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Graphical TOC Entry Sample holder

Frequency Entangled Photon Source

Coincidence Detection

Ph

Ph

N

N

N

Zn N

O

N

N

Ph O HO

Ph

RhB

ZnTPP

20


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Entangled Two Photon Absorption Cross Section on the 808 nm

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