High speed photon number resolving detector with titanium transition edge sensor

Journal of Low Temperature Physics manuscript No. (will be inserted by the editor) D. Fukuda G. Fujii A. Yoshizawa H. Tsuchida R.M.T. Damayanthi H. Takahashi S. Inoue M. Ohkubo High speed photon number resolving detector with titanium transition edge sensor Received July 23, 27, Accepted September 15, 27 Keywords Quantum efficiency, counting rate, energy resolution Abstract We have developed new photon number resolving detectors with titanium transition edge sensors (Ti-TESs) for a high counting rate operation in quantum information. The titanium superconducting films were fabricated by ultrahigh vacuum electron beam evaporation, and showed a sharp superconducting transition at 359 mk. The device was coupled to a single mode optical fiber, and cooled down to 1 mk. Some of optical responses of the devices were measured by illuminating heavily attenuated laser pulses at wavelengths of 45 nm and 155 nm. As a result, the device showed a fast decay time constant of 3 ns, which enables the operation at the counting rate of 4 kcps. The energy resolution was.76 ev at 45 nm and.68 ev at 1.5 µm, that make it possible to clearly resolve the number of photons of incident laser pulses. These features of the high counting rate operation and the reasonable energy resolution are very promising for quantum information field. PACS numbers: 3.67.Hk, 74.25.Fy, 3.67.Dd 1 Introduction In an optical quantum field, there are increasing strong demands to generate, operate and evaluate very weak light pulses which include a few number of photons. D. Fukuda, G. Fujii, A. Yoshizawa, H. Tsuchida, M. Ohkubo National Institute of Advanced Industrial Science and Technology 1-1-1 Umezono, Tsukuba, Ibaraki, 35-8563, Japan E-mail: d.fukuda@aist.go.jp R.M.T. Damayanthi, H. Takahashi The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan S. Inoue Nihon University, 1-8-14 Kanda-Surugadai, Chiyoda-ku, Tokyo, 11-833, Japan

2 Modulation TES bias I Lstray SQUID bias I Amp. V out LD Attenuater Optical fiber Rs Linp SQUID TES cold stage at 1 mk Fig. 1 Experimental setup for highly attenuated laser pulse measurement with Ti-TES. Main applications of these weak light pulses are a quantum key distribution(qkd) and the realization of quantum optical gates. In order to ensure the security of the QKD, or as a key component of the optical gate, the high performance photon detectors are required, which can not only detect the arrival of the light pulses, but also discriminate the number of photons. Recently, a transition edge sensor based on a tungsten superconductor(w-tes) showed very high performances such as a high energy resolution.2 ev and a high quantum efficiency 88 % with the response time of 4 µs 1,2. In the optical quantum information field, however, much faster response is required. To improve the timing property of the TES, we have been developing the titanium-based TESs operated at 36 mk. In this paper, we will show the first results of the photon number discrimination property with the 3 ns response time. 2 Device preparation The response time of the TES in an electron-photon decoupling limit is inversely proportional to the cubic of the operating temperature, and independent of the sensor volume. Thus we have used a titanium superconductor as the TES, which has the transition temperature at 39 mk in bulk. The superconducting titanium films were fabricated by ultra-high vacuum electron beam evaporation. The detail fabrication process of the Ti-TESs is described in the reference 3. The device size used in the experiment is 1 µm 1 µm square and the thickness is 46 nm. The Ti-TES showed the superconductivity at the temperature 359 mk. The normal resistance R n of the TES is 4.81 Ω. The device was connected to an single mode optical fiber with the distance of approximately 1 µm. The laser spot on the device is overfilled, thus the optical coupling loss is not negligible. As shown in Fig. 1, the Ti-TES is electrically connected in series to a shunt resistance (R s = 88 mω) and an input coil (L input 1 nh) of the SQUID amplifier with a twisted NbTi superconducting wire of a 15 cm length, which has the stray inductance L stay = 14 nh. The measured maximum cut-off frequency in the read out circuit is 5.1 MHz. This wide bandwidth is very effective to achieve a stable electrothermal feed back operation.

3 5.x1-7 Averaged pulse TES current change (A) 4.x1-7 3.x1-7 2.x1-7 1.x1-7 n=3 n=2 n=1 (exp(-x/ fall )-exp(-x/ rise )) rise time 6 ns fall time 3 ns. 1 s 1.x1-6 1.5x1-6 2.x1-6 2.5x1-6 3.x1-6 time (s) Fig. 2 (Color online) Example of observed signals for the absorbed photon number n (averaged). The device was biased at the TES resistance R of.5 R n. The 1 µm size Ti-TES was cooled down to 1 mk in a adiabatic demagnetization refrigerator. We have used pulsed laser light sources at 45 nm and 155 nm wavelengths. The typical pulse widths of both wavelengths are tens of pico seconds. The averaged laser power was strongly attenuated to the level of a few photons in each light pulse. The repetition frequency of the pulsed laser was changeable from 1 khz to 1 MHz. The observed signals were accumulated with an 8-bit digital oscilloscope in a 1 GHz bandwidth. 3 Results Figure 2 shows the observed averaged signals by illumination of the laser pulses at 45 nm. In order to obtain the time constant of the signals, we have fitted the time-dependent signal shapes with the following formula 4 : f(t) = A [ exp ( t t τ fall ) exp ( t t τ rise )], (1) where A, t, τ fall, and τ rise are the pulse height, the laser incident time, the fall time, and the rise time, respectively. The best fitting values of these time constants are τ rise = 6 ns and τ fall = 3 ns. The fall time constant is more than ten times faster than the value previously reported 5. From the power flow of the Ti-TES Joule heating, we have obtained the thermal conductance G = 3.3 1 1 W/K. The heat capacity of our TES is calculated to 1.5 1 15 J/K. From these values of τ fall, C and G, we obtained the thermal sensitivity α = 8 and the saturation energy E sat = 42 ev. Thus, the theoretical energy resolution limit, which is derived from the Johnson noise and the phonon fluctuation noise, is E FWHM =.22 ev, that indicates the high energy resolution comparable to the W-TES can be possible even at a high speed operation.

4 The detection efficiency of the incident energy, which is defined as the ratio of the detected energy to the incident energy, is k =.85 for the Ti-TES from the fitting results of (1). The previously reported value of the W-TES, which was fabricated on a silicon substrate, was k =.4 6. The energy loss would become an additional noise source such as a down conversion phonon noise 1. In our device, the titanium film is fabricated on the SiN films with the thickness of 5 nm. These di-electric layer may play a role to reduce the phonon loss to the silicon substrate. Figure 3 shows the pulse hight spectrum for laser pulses at 45 nm (left) and 155 nm (right). We can clearly observe the several peaks, which represent the number of photons absorbed in the TES film. The number of absorbed photons is obeyed by a Poisson distribution, so the shape of the spectrum N(x) can be described with considering the dispersion of the TES energy resolution as follows 11 : N(x) = 1 max P n (l)exp{ (x l) 2 /2σ 2 }, (2) 2πσ l where P n (l) is the Poisson distribution with an average photon number of n absorbed in the TES, and σ is the standard deviation of the detected energy fluctuations for each pulse event. By fitting the measured spectrum with (2), we obtained the energy resolution E FWHM and the quantum efficiency (QE) of the Ti-TES, which are summarized in Table 1. Because of a surface reflectance of the titanium film, the values of the QE in the table is lower than the valules of the W-TES, which is embedded with an optical absorption cavity 5,7. The baseline noise E NEP is.63 ev at the bias point R bias of 2. Ω in the series of the measurements. The observed energy resolutions E FWHM in table 1 are slightly worse than E NEP, which may be concerned with a position-dependent response in the TES. If the TES has the relatively higher resistance of a few Ω, the temperature profile inside the TES is not uniform, and hence the TES would be separated into two regions of a superconducting and normal states 8. These features are characterized with a thermal healing length η = κd/h 9, where k, d and h are the thermal conductivity of the TES, the film thickness, and the thermal conductance per area. If we assume the h value is described as G/A, where A is the TES area, we obtain the thermal healing length for the W-TES and the Ti-TES as 36 µm and 26 µm, respectively. The η for the Ti-TES is comparable to the device size of 1 µm, hence the Ti-TES will be much dominated by the position dependent response. However, the η can be much longer by using a bilayer structure to enhance the thermal diffusion in the TES. The dependence of the energy resolution on the counting rate was investigated by changing the repetition frequency of the laser pluses. Figure 4 show the results of the dependence in the repetition frequency from 1 khz to 7 khz. Up to the frequency of 4 khz, the pulse height spectrum does not affected by the laser repetition frequency and the energy resolution is a constant value. Over 5 khz, the energy resolution and the quality of the spectrum are rapidly degraded. However, the operation of the TES at the counting rate of 4 khz is the fastest record ever reported, as far as we know.

5 4 2 35 3 n=1 E =.31 ev( =45 nm) 15 n=1 n=2 E =.8 ev( =155 nm) counts/bin 25 2 15 counts/bin 1 n=3 n=4 1 5 n=2 n=3 n=4 2 4 6 8 1 12 14 channel 5 n=5 n=6 2 4 6 8 1 12 14 channel Fig. 3 (Color online) The measurement results of the pulse height spectrum for light pulses at 45 nm(left) and 155 nm(right). E γ is the energy of one photon at the measurement wavelengths. 3 4 Counts/bin 3 2 1 1 khz 5 khz 7 khz Energy resolution (ev) 2 1 4 khz 2 4 6 8 1 12 Channel 1 4 1 5 1 6 Counting rate (Hz) Fig. 4 (Color online) The high counting rate capability measurement results. (left) The energy resolution at the counting rate from 1 khz to 7 khz. (right) The energy resolution dependency on the counting rate. 4 Conclusions In order to realize the high speed photon number resolving detector with a MHz counting rate, we have fabricated titanium-based transition edge sensors operated at 359 mk. The Ti-TES device successfully showed the photon number discrimination at 45 nm and 155 nm wavelengths with the counting rate over sub MHz. The measured energy resolution was.7 ev (FWHM) and the value was not degraded up to.4 MHz counting rate. Table 1 The energy resolution( E FWHM ) and the Quantum efficiency(qe) of the Ti-TES wavelength Incident photon number Fitting result of n E FWHM QE 45 nm 8.6/pulse.48.76 ev 5.6 % 155 nm 25.2/pulse 2.27.68 ev 9. %

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