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We present the first demonstration of fluorescence correlation spectroscopy (FCS) using superconducting nanowire single-photon detectors (SSPDs) which are free of afterpulses unlike the avalanche photodiode (APD). Multimode-fiber-coupled SSPDs with high system detection efficiency for visible wavelengths were developed and implemented in the FCS system. We performed FCS measurements for Rhodamine B and 6G as fluorescent samples, and found that autocorrelation functions obtained by the SSPDs showed a noise-free curve in the short correlation time region of sub microseconds where the afterpulse effect was dominant using the APD. The obtained results clearly indicate the advantage of SSPDs for the FCS system.
© 2014 Optical Society of America
1. Introduction
Nowadays, the importance of single-photon detection techniques is growing in various research fields such as quantum information, quantum optics, and life sciences [1]. In the field of life science, various techniques exist to extract information on the physical and chemical dynamics in biological samples by detecting the fluorescence emitted from molecules e.g., fluorescence recovery after photobleaching (FRAP), fluorescence loss in photobleaching (FLIP), and fluorescence resonance energy transfer (FRET) [2]. Among the various methods, fluorescence correlation spectroscopy (FCS) is known as a powerful tool for investigating the molecular motion of fluorescent materials in living cells as well as in aqueous solutions in vivo [3,4]. FCS can determine the size and number of molecules by measuring the temporal autocorrelation of fluorescence from the fluorescently labeled molecules. Conventionally, silicon avalanche photodiodes (APDs) have been used as the single-photon detector in the FCS system since APDs have a high detection efficiency of 60 – 70% for photons with the visible wavelengths [1,5]. However, APDs have an undesired pulse noise after a photon detection, called “afterpulse”. The afterpulsing phenomenon is considered to be caused by charge carriers trapped in the energy states in the band gap during an avalanche event. Afterpulses typically appear within several hundred nanoseconds after detecting a photon, and generate a fake autocorrelation component, making it impossible to determine autocorrelation functions in the sub-microsecond regime. Owing to this afterpulse problem in the sub-microsecond regime, short-time-scale phenomena such as rotational diffusion of molecules have not been observed in the FCS measurements. Besides APDs, the photomultiplier tube (PMT) has been also used in the FCS system, but its detection efficiency is generally lower than that of the APDs [1]. Although the effect of afterpulsing in the autocorrelation function can be reduced by a cross-correlation measurement, the system becomes complex and costly because two single-photon detectors are required for the two split fluorescent optical paths. Consequently, an afterpulse-free single-photon detector has been in demand for investigating fast physical/chemical dynamics in molecules within the sub-microsecond time scale.
Among the various single-photon detectors, superconducting nanowire single-photon detectors (SSPDs or SNSPDs) have been developed very actively, and their performance has improved over the last few years [6–10]. So far, the target wavelength of the SSPD has mainly been telecommunication wavelengths (1.3−1.55 μm), and the SSPDs have been developed for and applied to the research fields in which telecommunication wavelengths are used, such as quantum information and quantum optics [11,12]. On the other hand, recently the SSPD optimized for shorter wavelengths has been developed and its system detection efficiency reached as high as 70% for the visible wavelength of 635 nm with multimode fiber coupling [13]. In addition, the SSPD is free from the afterpulse effect because the photon detection mechanism of the SSPD is based on the temporal transition to the normal state from the superconducting state caused by an incident photon. After detecting the photon, the SSPD simply recovers to the superconducting state again; therefore, no afterpulse is generated, unlike the APD. Thus, it is expected that visible-wavelength SSPDs will provide significant advantage in determining autocorrelation functions at a sub-microsecond level. In this paper, we demonstrate a first FCS experiment by using visible-wavelength SSPDs and present the advantages of the SSPD for incorporation into the FCS system.
2. FCS system with visible wavelength SSPD
2.1 Fabrication and multimode fiber packaging of SSPD
In the FCS experiment, the fluorescent photons are emitted from the target molecules as the result of an energy excitation. The wavelength of the emitted photons is generally in the visible range, e.g., ~570 nm for Rhodamine B and ~510 nm for Green Fluorescent Protein (GFP). In order to detect a single photon within this wavelength region efficiently, we have developed a visible wavelength SSPD (VW-SSPD) with a front-side illumination structure [13]. For the present study, we fabricated the devices on two types of substrates: thermally oxidized silicon (Si) substrate (VW-SSPD-1) and Si substrate with a dielectric mirror (VW-SSPD-2) [13]. For the VW-SSPD-1, a niobium nitride (NbN) film was deposited on a silicon dioxide (SiO2) layer on the Si substrate by dc reactive sputtering, and then, it was patterned to a nanowire by electron beam lithography and reactive ion etching. For the VW-SSPD-2, first a SiO2 film was deposited on the dielectric mirror layer by rf sputtering, and then the NbN film was deposited and patterned. For both devices, the thickness of the NbN nanowire was 10.5 nm and that of SiO2 layer was 100 nm. The SiO2 layer works as an optical cavity to enhance the optical absorptance in NbN, and the SiO2 thickness was therefore chosen to be 100 nm, corresponding to λ/4n, where λ is the target wavelength of ~600 nm and n is the refractive index of the SiO2 layer. In the VW-SSPD-2, owing to the dielectric mirror with reflectance higher than 99% for wavelengths from 400 nm to 1000 nm, the optical absorptance in NbN can be enhanced further [13,14]. The line width and spacing of the NbN nanowire are 150 nm and 150 nm for the VW-SSPD-1, and 150 nm and 100 nm for the VW-SSPD-2, respectively. The superconducting critical temperature was 7.7 K for both devices and the critical currents were 32.3 μA and 22.8 μA for VW-SSPD-1 and VW-SSPD-2, respectively.
In the FCS system, the photons emitted from the fluorescence molecules are collected into the multimode fiber of 50 μm diameter, and then transmitted to the detector. In order to couple the photons to the VW-SSPDs efficiently, we designed the circular active area to have a diameter of 35-μm, and mounted the device onto a multimode-fiber-coupled package [13]. In the package, the diameter of the incident light is focused to 28 μm at the active area by graded index (GRIN) lenses spliced to the tip of the multimode fiber. Since the focused spot size is sufficiently small compared to the device active area, we can expect almost perfect optical coupling between the incident photons and the VW-SSPDs. The packaged VW-SSPDs were mounted on a Gifford–McMahon cryocooler system with an operating temperature of 2.3 K [10]. The cryocooler system has multimode fiber input ports, and thus it is compatible with the FCS system equipped with a multimode fiber output for the emitted fluorescence.
2.2 FCS setup with VW-SSPD
Figure 1(a) shows the schematics of the FCS setup with the VW-SSPD. The optics were integrated into the fluorescence microscope (Axioplan2, Carl Zeiss) with a C-Apochromat 40x/1.2 (Carl Zeiss) objective lens. The excitation light is radiated onto the sample by an excitation laser, elevating the energy state of the sample to an excited state from the ground state. Then, the energy state transits to a lower excited state and finally relaxes to the ground state. During the relaxation process to the ground state, the sample emits fluorescent photons of a wavelength corresponding to the energy gap between the lower excited state and ground state. The emitted fluorescent photons are collected into the multimode fiber by the confocal lenses and finally enter the VW-SSPD. When the VW-SSPD detects a photon, the output pulses are transmitted to the digital correlator (ALV-5000/FAST, ALV-GmbH) via low noise amplifiers and a comparator that perform the transformation from the VW-SSPD signal to the transistor-transistor-logic (TTL) signal. In the digital correlator, the autocorrelation function is calculated from the input signals in real time with a temporal resolution of 12.5 ns. The autocorrelation function is defined as
where I(t) is the fluorescence intensity at time t, and the notation <...> indicates the temporal average. The obtained autocorrelation function contains information on the size and number of the fluorescent molecules existing in the confocal region, e.g., the molecule number N can be derived from the autocorrelation function at τ = 0 using for the Poisson distribution [3]. In this study, we used Rhodamine B and Rhodamine 6G as fluorescent specimens in order to confirm the advantages of the FCS system with the VW-SSPD. Figure 1(b) shows an intensity spectrum of the excitation and the emission of the fluorescence for Rhodamine B (solid line) and Rhodamine 6G (dashed line). The center wavelengths of Rhodamine B (Rhodamine 6G) for the excitation and fluorescence are 558 nm (525 nm) and 571 nm (547 nm), respectively. A HeNe laser of wavelength 543 nm (Uniphase 1676) and an Ar laser of wavelength 488 nm (Melles Griot) were used as the excitation lasers for Rhodamine B and Rhodamine 6G, respectively.
Fig. 1 (a) Schematics of the FCS system with VW-SSPD. (b) Intensity spectrum of excitation and fluorescence for Rhodamine B (solid line) and Rhodamine 6G (dashed line).
3. Results and discussion
3.1 Performance of VW-SSPDs
Prior to the FCS experiment, we evaluated the performances of the developed VW-SSPDs. In the measurement, we used a continuous wave laser of wavelength 635 nm as a photon source, and controlled the input optical power using optical attenuators [13]. Figure 2(a) shows the bias current dependencies of the system detection efficiency (SDE) and the dark count rate (DCR). For the VW-SSPD-1 (black circle), the maximum SDE reached 44% at a bias current of 30 μA with the relatively high DCR of 2.4 kcps. Owing to a trend towards saturation of the SDE, the SDE maintained a high value even at a lower bias current and a lower DCR, e.g., 43% with 1-kcps DCR and 41% with 100-cps DCR. For the VW-SSPD-2 (red square), a SDE of 61% with 100-cps DCR, higher than that of the VW-SSPD1, was obtained because a higher optical absorptance was realized by the dielectric mirror. Figure 2(b) shows the response count rate dependence of the normalized SDE. The normalized SDE decreases for higher response count rates because counting loss takes place when a photon arrives within the recovery time after a photon detection event. The VW-SSPD-1 and VW-SSPD-2 showed the response count rate of 9.7 MHz and 5.1 MHz, respectively, when the normalized SDE becomes 0.5 (3 dB cutoff). The difference in the count rates of the two devices originates fromthe different kinetic inductances of the different nanowire lengths [15]. The obtained count rate for both devices reached several MHz, and thus the developed VW-SSPDs are promising for applying to sub-microsecond level FCS measurements.
Fig. 2 (a) Bias current dependences of the system detection efficiency (filled symbol) and dark count rate (open symbol) for the VW-SSPDs. (b) Normalized system detection efficiency vs. response count rate for the VW-SSPD-1 (black circle) and VW-SSPD-2 (red square).
3.2 Autocorrelation curves of Rhodamine B and Rhodamine 6G
As the first experiment to demonstrate the advantage of the VW-SSPDs for FCS, we measured the autocorrelation function of 1.0-μM Rhodamine B. Figure 3(a) shows the obtained autocorrelation curves using a commercial APD (black line, SPCM-AQR-15-FC, Perkin Elmer) with a detection efficiency of ~70%, and our VW-SSPD-1 (red line). The photons emitted by the fluorescent sample were detected using the fluorescence filter set for red fluorescence (BP540, FT580, LP590, Carl Zeiss) of the microscope. The excitation laser power was 1.55 mW just behind the output shutter of the laser. The 10-s measurement was repeated three times, and the averaged autocorrelation function was obtained. As shown in the figure, a peak structure clearly appeared in the sub microsecond region for the autocorrelation obtained by using the APD. As mentioned above, this peak is due to the afterpulsing of the APD; the error pulses are triggered by the photon detection event and thus the fake autocorrelation between the true output pulse and error pulse appears below the microsecond region. This afterpulsing effect makes it impossible to determine autocorrelation functions correctly and to analyze the biological phenomenon in the sub-microsecond regime.
Fig. 3 (a) Autocorrelation functions vs. correlation time of Rhodamine B. Black and red lines indicate the data obtained by using APD and VW-SSPD-1, respectively. (b) Autocorrelation functions of Rhodamine 6G (black and red symbols) and fitted curves (green lines) by using Eq. (2). Inset: overall view around 1 μs of the autocorrelation function for Rhodamine 6G.
The red line in Fig. 3(a) shows the autocorrelation function by the VW-SSPD-1 at a bias current of 29.0 μA. Although the detection efficiency of 43% was smaller than that of the APD, a clear autocorrelation curve was obtained. Furthermore, in contrast to the autocorrelation function obtained by the APD, a flat structure without a peak was obtained in the sub-microsecond region. This result exactly indicates the advantage of the FCS system with the VW-SSPD; the short temporal correlation below 1 μs can be observed and analyzed without disturbance by any noise. In the VW-SSPD-1, the autocorrelation function rose at ~60 ns, and thus the temporal region in which the autocorrelation was observed was not very wide below 1 μs. However, since the minimum correlation time is determined by the count rate of the detector, the autocorrelation function in the wider temporal range can be observed by improving the counting rate. The counting rate can be improved without a decrease of theSDE by adopting a multi-element structure [9,16]. By incorporating the VW-SSPDs with higher count rates in the FCS system, the unexplored autocorrelation function in the nanosecond regime can be obtained.
Figure 3(b) shows the measured autocorrelation function of 0.1-μM Rhodamine 6G by using the APD (black symbols) and VW-SSPD-2 (red symbols) and their fitted curves of the theoretical autocorrelation function (green lines). The inset of Fig. 3(b) shows the overall view around 1 μs of the autocorrelation function. The excitation laser power was 8.10 mW just behind the output shutter of the laser. Fluorescence was detected using the fluorescence filter set for green fluorescence (BP470/20, FT493, BP505-530, Carl Zeiss) of the microscope. The 30-s measurement was repeated three times, and the averaged autocorrelation function was obtained. The bias current for VW-SSPD-2 was fixed at 18.0 μA, at which the SDE was 60%. As shown in Fig. 3(b), the minimum correlation time for the VW-SSPD-2 is approximately 0.4 μs, larger than that of VW-SSPD-1 because of the lower count rate, and thus the measurable sub microsecond region is small. Meanwhile, the obtained autocorrelation curve without the afterpulse component enabled clear analysis of the data: from the fitting of the data to the theoretical curve [3,17], we found that the triplet component appeared in the Rhodamine 6G, indicating that there is an energy relaxation process to the ground state from the excited triplet state. Table 1 summarizes the fitting results of the theoretical autocorrelation function for the single-component diffusion sample considering the existence of a triplet component given by
where N is the average number of molecules inside the measurement volume, τD is the diffusion time, s is the ratio between the axial width and the lateral width of the detection volume, T is the fraction of molecules in the triplet state, and τT is the relaxation time for singlet–triplet relaxation. The time range of the autocorrelation function to be fitted was from 2 μs to 131 ms. τT was estimated to be 10.3 μs by fitting to the autocorrelation curve obtained by using VW-SSPD-2. On the other hand, in the autocorrelation curve obtained by the APD, the obtained data could not be analyzed correctly because the large contribution from afterpulsing obscured the intrinsic autocorrelation curve of Rhodamine 6G, although some fitted values could be obtained. As shown in this result, the afterpulse-free VW-SSPD has an advantage for FCS measurements not only for the short-time phenomena in the sub-microsecond region, but also for the longer dynamics such as the relaxation process from the triplet state.
Table 1. Fitted results of the FCS measurements of 0.1-μM Rhodamine 6G
4. Conclusion
In summary, we demonstrated FCS measurements using SSPDs optimized for visible wavelengths for the first time. By implementing afterpulse-free SSPDs in the FCS system, we found that the sub-microsecond region in the autocorrelation function could be observed, in contrast to the APD-FCS system where the afterpulse of the APD dominated and hid the intrinsic autocorrelation function. Furthermore, for the longer correlation time region over microseconds, the SSPD revealed the existence of the triplet component at approximately 10 μs for Rhodamine 6G, which could not be observed using the APD. In future, the autocorrelation function in very small time regimes of nanoseconds can be observed by improving the counting rate of the SSPD. Our results presented in this work will open new possibilities for revealing the hitherto unexplored ultrafast dynamics of biological molecules in living cells.
Acknowledgments
This work was supported by a grant from the Japan Science and Technology Agency (to YH and HT). The authors thank Saburo Imamura and Makoto Soutome for their technical support.
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