Squeezed light induced two-photon absorption fluorescence of fluorescein biomarkers

Two-photon absorption (TPA) microscopy (with near-infrared illumination) is the method of choice for in vivo imaging of tissues down to millimeter depths.¹ It bears several advantages including intrinsic high 3D resolution due to significant TPA occurring only in close vicinity to the focal volume, reduced out-of focus bleaching, highly reduced autofluorescence, and the capability of nearly aberration-free deep-tissue focusing along with reduced absorption.^2–5 Unfortunately, classical TPA is an extremely inefficient process with absorption cross sections δ_r on the order of $10−48 cm4·s/photon$⁠.⁶ Therefore, TPA sensing and imaging generally require the use of high-intensity pulsed lasers, to ensure the near-simultaneous presence of two photons to induce the process.^7,8 However, since the excitation pulse peak power is typically 10⁵ times the average power, samples are prone to endure significant photo- and thermal damage.^9,10

In parallel, using the unique quantum energy-time entanglement characteristics of photon pairs generated by spontaneous parametric downconversion (SPDC), the entangled TPA (ETPA) rate can be vastly enhanced,^6,11–14 with the absorption cross section σ_e for ETPA in the range of $10−18−10−22 cm2$⁠. Most notably, the linear dependence of ETPA on the input photon-pair flux, which was first predicted by Gea-Banacloche¹⁵ and Javanainen and Gould,¹⁶ was also verified experimentally.^{6,11,13,14,17,18} It is a major advantage over the quadratic dependence of classical TPA as the need for high intensity excitation becomes obsolete. However, most current ETPA implementations with biological specimens are limited by a low flux of $∼107$ photon pairs $/s$⁠,^6,11,13,14 equivalent to only $∼10$ pW for near-infrared wavelengths. This is mostly due to loss of correlation and difficulty of tuning biphoton wavelength in the nonlinear crystals. It is also worth mentioning that a much more efficient photon pair flux generation has been demonstrated by Jechow et al. using a type-0 quasi-phase-matched periodically poled-lithium-niobate waveguide crystal.¹⁹ Their photon-pair flux can be as high as $∼1011$ photon pairs/s.

In this work, we utilize a different quantum light source that is based on the four-wave mixing (FWM) process in an atomic ⁸⁵Rb vapor cell.^20–26 The setup and the respective atomic level structure are shown in Figs. 1(a) and 1(b). The medium possesses a large third-order electric susceptibility $χ(3)$ and is pumped by a strong narrow-band continuous-wave (CW) laser at frequency ν₁ (λ = 795 nm) with a typical linewidth $Δν1∼100$ kHz. Applying an additional coherent CW seed beam at frequency $νp=ν1−(νHF+δ)$⁠, where ν_HF and δ are the hyperfine splitting in the electronic ground state of ⁸⁵Rb and the two-photon detuning in Fig. 1(b) (see the supplementary material for further experimental details), respectively, two pump photons are converted into a pair of twin photons, namely, “probe ν_p” and “conjugate ν_c” photons, adhering to the energy conservation $2ν1=νp+νc$ [see the level structure in Fig. 1(b)]. The resulting “twin beams” are strongly quantum-correlated and are also referred to as (seeded) two-mode squeezed light.²⁷ Major advantages are narrow-band probe and conjugate beams (⁠$∼20$ MHz)^26,28 along with a freely adjustable photon-pair flux between 10¹³ and 10¹⁶ photons/s,^{20,21,23–26} which is a few orders of magnitude higher than that for SPDC. Also, since FWM in atomic vapors is an nonlinear parametric process based on ground-state coherences,²⁹ in which the main advantage arises from small two-photon detuning from real states, whereas in nonlinear crystals, there is no real state to which the signal or idler photon is close, the generation of quantum correlations with FWM in atomic vapors can be, therefore, very efficient. As can be seen from Fig. 1(c), the twin beams exhibit an intensity-difference squeezing of 6.5 dB, which is indicative of strong quantum correlations²⁷ (see the supplementary material for further details of the squeezing measurement).

In this study, we analyze and compare classical TPA and squeezed-light induced TPA (SL-TPA) fluorescence rates in fluorescein and in he laser dye 4-dicyanomethylene-2-methyl-6-(p(dimethylamino)styryl)-4H-pyran (DCM) (see the supplementary material for sample preparation). Fluorescein is one of the most frequently used biomarkers for bioimaging and biosensing.³⁰ Its small size is very convenient for in vivo imaging applications although its relatively small classical TPA cross section generates low amounts of fluorescence.^7,8 The SL-TPA setup is depicted in Fig. 1(a). A 10× objective (Thorlabs RMS10X) focuses the near-infrared excitation light onto a solution of fluorophores. Following TPA, fluorescence is collected by a second 10× objective (Thorlabs RMS10X) at an angle of $90°$ and guided to a photo-multiplier tube (PMT) (Thorlabs PMTSS in conjugation with a PMT transimpedance amplifier Thorlabs TIA60). Two optical low-pass filters (Thorlabs FESH0750) exclude stray pump photons. The measured PMT voltage outputs (see the inset in Fig. 2) are converted into fluorescence rates of arbitrary units (since the PMT's response to an input photon is an inverse voltage pulse, adding all the inverse voltages in a given time window can, therefore, give us a quantity that is proportional to the input photon flux up to a conversion factor, see the supplementary material for further data acquisition details). For classical TPA measurements, only the coherent pump beam is focused into the microscope objective, with the same focus spot size at the sample. Utilized powers for the twin beams were ranging from $30 μ$W to the maximum of 8 mW.

Measured classical TPA fluorescence rates for fluorescein, as a function of the input power, are shown by the red diamonds in Fig. 2, with error bars denoting one standard deviation. The observed quadratic power law relationship agrees well with the established literature for classical TPA, where the fluorescence signal is proportional to the square of excitation light intensity.³¹ Fluorescence rates induced by SL-TPA with an optical power of 8 mW (3.5 mW + 1.0 mW probe and seed; 3.5 mW conjugate) and an optical power of 4 mW (1.75 mW + 0.5 mW probe and seed; 1.75 mW conjugate) together with an optical power of 6 mW (2.6 mW + 0.8 mW probe and seed; 2.6 mW conjugate) and an optical power of 3 mW (1.3 mW + 0.4 mW probe and seed; 1.3 mW conjugate) are depicted by the green stars (although the 3 mW and 6 mW data points were taken on a different day, the trend is similar). Due to experimental constraints, 8 mW is the maximal power we are able to acquire for the squeezed light. The measured coherent rates are fitted by the quadratic function $R(I)=I2×1.5 mW−2$ (dashed-dotted red line), which represents the benchmark of the true fluorescence rate as a function of the input power. It can be observed from the figure that the signal for 8 mW of coherent excitation deviates the strongest from the fit. This fact can be attributed to background noise (e.g., electronic dark counts and spurious counts from stray ambient light) and the overall low signal to noise ratio (SNR) of the measurement (characterized by a standard deviation encompassing negative values). Following the fitted curve, the fluorescence rate for 8 mW coherent excitation is, thus, merely $9.6×101$ (a.u.). For SL-TPA of 8 mW excitation power, the fluorescence rate is $∼4.46×103$ (a.u.). This value corresponds to a striking $∼46.5$-fold enhancement over the coherent excitation. Vice versa, increasing the coherent excitation power sevenfold to $∼55$ mW, and thus the classical TPA rate by $∼47.3$-fold, the measured rates for 8 mW SL-TPA and 55 mW classical TPA match, thus confirming the previous statement. Subtracting the contribution from the 1 mW coherent seed beam power, it can be argued that the measured SL-TPA enhancement is around $∼60$-fold over 7 mW coherent excitation. Note that the seed is uncorrelated to the quantum correlated photon pairs and that 1 mW of coherent seed excitation itself will induce negligible classical TPA rates. More importantly, the measured fluorescence rate for 4 mW SL-TPA is $∼2.02×103$ (a.u.). Subtracting the respective optical power of the seed beam, we end up with the input flux ratio of $7/3.5=2.00$⁠, which matches the measured ratio $4.46/2.02=2.21$ well (within the calculated uncertainties). This is also true for the SL-TPA of 6 mW and 3 mW, which is indicative of the linear dependence on the input photon-pair flux that is expected for fluorescein in this regime. Quadratic terms, thus, do not seem to contribute here.

TPA is highly sensitive to the near-instantaneous arrival of two photons at the sample, in particular, with respect to the virtual state lifetime of the intermediate states used for the electronic transition from the ground to the final state.^13,18 In ETPA, this is quantified by the entanglement time T_e.^6,13,32 Adjusting T_e should change the measured SL-TPA enhancement. Hence, an investigation of the effect of relative temporal delay between the entangled photon pairs is conducted. The ETPA cross section σ_e is inversely proportional to T_e and, thus, the mean group velocity delay between the entangled photon pairs. In the FWM process of the atomic ⁸⁵Rb vapor, the group delay between the entangled pairs can be adjusted by changing the two-photon detuning δ of the double-Λ configuration in Fig. 1(b).²⁸ The red, green, and blue bars in Fig. 3 show the fluorescence rates induced by 8 mW SL-TPA for the values δ = –10 MHz, –5 MHz, and 0 MHz, respectively. For each δ value, the same relative intensity-difference squeezing of 6.5 dB [see Fig. 1(c)] is maintained, such that the results are not affected by different entanglement levels. For $δ=−5$ MHz, a relatively small delay is achieved.²⁸ Degraded fluorescence rates for $δ=−10$ MHz and δ = 0 MHz confirm that the SL-TPA enhancement is degraded when the relative delay between the photon pairs is tuned away from its optimal value. Further experimental details on how to change the two-photon detuning δ can be found in the supplementary material.

In general, the ETPA rate R_e as a function of the input photon-pair flux density $ϕ$ is expected to follow the functional behavior $Re(ϕ)=σeϕ+δrϕ2$⁠, where σ_e and δ_r are the cross sections for ETPA and classical TPA, respectively, and are determined by the electronic level structure of the system undergoing TPA.^12,17,18,33 Both values can be determined experimentally or calculated theoretically via second-order perturbation theory for a sufficiently simple system.¹⁸ As previously established, the coincident arrival and absorption of an entangled photon pair lead to the linear dependence $Re(ϕ)=σeϕ$⁠, provided that $ϕ$ is sufficiently small.^6,13,14 For sufficiently high photon-pair fluxes, TPA can be induced by uncorrelated photons from different pairs as well. The respective rate is equivalent to the classical TPA rate $δrϕ2$⁠. Parity between both contributions is reached at the critical flux $ϕc=σe/δr$⁠. Most previous ETPA experiments with biomarkers and low photon-pair fluxes observed only the linear dependence.^6,13,14

With means of investigating SL-TPA with high and freely adjustable optical powers, we investigated its functional behavior in DCM laser dye (see the supplementary material for its preparation). DCM dyes are known for strong TPA around an excitation wavelength of 800 nm, and along with a milli molar suspension, optical powers in the μW regime are sufficient to induce enough TPA fluorescence.^34,35 The measured coherent TPA rates shown as red squares in Fig. 4 agree well with a quadratic behavior, represented by the fit function $R(I)=I2×0.304 μW−2$⁠. For SL-TPA in DCM, on the other hand, we observed a non-linear behavior of the functional form $R(I)=I×7.9 μW−1+I2×0.59 μW−2$⁠. The polynomial behavior of SL-TPA in Fig. 4 implies that the photon-pair flux is already high enough to observe both linear and quadratic contributions. In fact, given the fit values, parity is already reached at $Ic=7.9 μW−1/0.304 μW−2=26.0 μW$ for the DCM solution.

It is worth pointing out that the DCM laser dye solution requires much lower excitation powers than the fluorescein solution to produce appreciable TPA fluorescence rates, most probably due to a larger classical TPA cross section δ_r. In Fig. 4, the DCM signal at 130 μW coherent excitation (⁠$∼0.45×104$ a.u.) roughly equals the fluorescein signal at 55 mW coherent excitation (⁠$∼4.43×103$ a.u.). Taking into account the concentration of the two solutions (see the supplementary material for the details of sample preparation),³⁶ we estimate that the classical TPA cross section δ_r of DCM is roughly 1800 times larger than that of fluorescein. However, the ETPA cross section σ_e of DCM is actually smaller than that of fluorescein, as demonstrated by the relatively small SL-TPA enhancements. The difference can be attributed to different electronic level structures of these two organic molecules.⁶ 

In conclusion, this work investigates two-photon absorption fluorescence rates in fluorescein biomarkers and in DCM laser dye, induced by a coherent CW excitation light and by the bright two-mode squeezed light. For the coherent CW excitation, both fluorophores show the well-expected quadratic dependence on the input photon flux. The experimental results for fluorescein with SL-TPA, however, demonstrate a linear dependence on the input optical power, along with an ∼47-fold TPA fluorescence enhancement for 8 mW squeezed light compared to 8 mW coherent light. This can be attributed to the predominant occurrence of entangled two-photon absorption of quantum-correlated photon pairs. In addition and different from previous works using quantum states of light for TPA in fluorophores, we report that SL-TPA in DCM laser dye is governed by a polynomial behavior, which can be entirely attributed to its far greater entangled photon-pair flux, as compared to using SPDC sources. Thus, this work demonstrates that our FWM based bright two-mode squeezed light source can achieve ultra-low intensity TPA for biosensing and bioimaging and, thus, bear the potential to open up unconventional avenues for in vivo deep tissue studies of biological specimens via TPA.

See the supplementary material for complete experimental details, squeezing measurements, data acquisition, and sample preparation.

This work was supported by the Air Force Office of Scientific Research (Award No. FA-9550-18-1-0141) and the Robert A. Welch Foundation (Award No. A-1943-20180324).

We thank V. Yakovlev for discussions on spectroscopy with entangled photon pairs and for the suggestion of fluorescein biomarkers. We also thank A. Sokolov and A. Zheltikov for informative comments. A.C. acknowledges support from the Alexander von Humboldt Foundation in the framework of a Feodor Lynen Research Fellowship. F. L. acknowledges support from the Herman F. Heep and Minnie Belle Heep Texas A\&M University Endowed Fund held/administered by the Texas A\&M Foundation.