Current Status of Josephson Arbitrary Waveform Synthesis at NMIJ/AIST

INVITED PAPER

Current Status of Josephson Arbitrary Waveform Synthesis at

NMIJ

/AIST

Nobu-hisa KANEKO†a), Michitaka MARUYAMA†, and Chiharu URANO†∗, Nonmembers

SUMMARY AC-waveform synthesis with quantum-mechanical accu-racy has been attracting many researchers, especially metrologists in na-tional metrology institutes, not only for its scientific interest but its poten-tial benefit to industries. We describe the current status at National Metrol-ogy Institute of Japan of development of a Josephson arbitrary waveform synthesizer based on programmable and pulse-driven Josephson junction arrays.

key words: voltage standard, Josephson junction array, programmable Josephson voltage standard, pulse driven Josephson voltage standard, Josephson arbitrary waveform synthesizer

1. Introduction

“Measurement standards” scientifically guarantee consis-tency in measurements. DC voltage standards in indus-try have been calibrated by Josephson voltage standards (JVS), which have been utilized since the 1990 Recommen-dation 2 (CI-1988) [1] of the CIPM (International Com-mittee for Weights and Measures) under the Metre Con-vention. Nowadays conventional JVS’ are commercially available and JVS’ calibration services in developed coun-tries actually provide Zener diode voltage standards and high precision voltmeters with extremely small uncertain-ties and one stop testing capabiliuncertain-ties. A conventional JVS consists of an under-damped superconductor (S)-Insulator (I)-Superconductor (S) (SIS) type Josephson junction ar-ray (JJA), and microwave source and bias current source. The array contains over ten thousand serially connected Josephson junctions and is radiated with microwave around 100 GHz. When n-th voltage step is used and the number of junctions is n(n= n×n), and the frequency of the mi-crowave, f , the quantized voltage, V, is theoretically given by the following Josephson equation,

V = n f · h

2e. (1)

Here, h stands for the Planck constant, and e is the ele-mentary charge. This equation is experimentally proved with various superconductors and experimental conditions

Manuscript received July 14, 2010. Manuscript revised October 7, 2010.

†_{The authors are with the Institute of Advanced Industrial} Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), Tsukuba-shi, 305-8563 Japan.

∗_{Presently (March, 2010 to February, 2012), with the National} Institute on Standard and Technology (NIST, USA) as a guest re-searcher.

a) E-mail: [email protected] DOI: 10.1587/transele.E94.C.273

Fig. 1 I− V characteristics of a SIS type (a) and a SNS or SINIS type (b) junctions (or Josephson junction arrays) with irradiation of microwave. (a) A under-dumped SIS junction shows multi-valued function which has a possibilities of selection of an undesired voltage step. (b) A over-dumped SNS or SINIS junction shows a single-valued function which allows us to quick ON/OFF setting of the bias current.

to have one of the most accurately substantiated universality in materials science. Then the quantized voltage is deter-mined by the values of n, f , and the magnetic flux quantum Φ0= h/(2e) = 1/KJ(KJ: the Josephson constant).

An important issue here is that the profile of a current-voltage (I− V) curve of a SIS junction is not a single-valued function but a multi-valued function. Typical I− V charac-teristic is shown in Fig. 1(a). To obtain the desired quantized voltage, first, an appropriate bias current applied so that the bias load I− V line crosses the desired quantized voltage step. Then the bias current turns off. The desired quantized voltage is then acquired without bias current, though there is a non-negligible possibility of settling to the neighboring quantized steps. And this procedure requires finite time.

“AC” JVS has also been studied by national metrol-ogy institutes (NMIs) not only for scientific interests but for potential application to industries. Here AC JVS is often also called the “Josephson arbitrary waveform synthesizer (JAWS)” for general purpose (not only for standards). Once quantized AC voltage standard is established, it has clear benefits to power industry, smart grids, medical industry, and calibration of arbitrary waveforms, calibration of A/D converters and so on. Many researchers in the field of volt-age standards and mains power direct their attention to this subject for this reason. But the SIS junction requires time to settle to the desired quantized voltage step as mentioned above, and an over-damped SNS (or SINIS, “N” stands for Normal metal) junction, which has a I− V curve of single-valued function is necessary (see Fig. 1(b)). Since the 1980s, several ideas to utilize JAWS based on SNS junctions have been proposed mainly by researchers at the National Insti-tute of Standards and Technology (NIST) in USA [2], [3]. Copyright c 2011 The Institute of Electronics, Information and Communication Engineers

All the ideas are summarized in two methods: “modula-tion” of “n” or “ f ” in Eq. (1). In other words, either is con-trolled as a time-dependent parameter. Such methods are partly symbolically explained in the following equations:

V = n(t) · f · h

2e, (2)

V = n · f (t) · h

2e. (3)

To realize the JAWS explained by Eq. (2), the Josephson junction array is binary or ternary segmented, and each seg-ment is connected to an independent bias current source. The bias sources control segments of the array, with the bias current of+I, 0, and −I, here, I represents the current at the center of the quantized voltage step. This is schematically shown in Fig. 2. As a result, the output analog voltage signal is the stepwise approximation of the desired waveform, in which each voltage step has quantum-mechanical accuracy. A voltage standard with this method is often called an (AC) Programmable Josephson Voltage Standard ((AC-)PJVS). This is considered a binary type A/D converter. PJVS have been widely studied in many NMIs aiming for both DC and AC metrological applications [4]–[6].

As for the JAWS corresponding to Eq. (3), the array is not segmented, but is irradiated with a stream of current pulses. The stream of current pulses was beforehand modu-lated according to theΔ-Σ converted digital data of the de-sired waveform. Each current pulse is quantized by the JJA to multiples of the magnetic flux quantum,Φ0 = h/(2e), in other words, the time integral of this signal is a quantized voltage. Through the well-defined low pass filters (LPFs), the generated stream of the quantized voltage “pulses” is converted to a well-defined desired analog waveform which has quantum-mechanical accuracy. This JAWS is called a Pulse-driven Josephson Voltage Standard (PD-JVS), which is regarded as a serial type A/D converter. This PD-JVS is schematically shown in Fig. 3.

A benefit of the AC-PJVS is that the output voltage is relatively large (as large as 10 V and recently up to 20 V), so that it can substitute for DC JVS (which is currently re-alized with SIS junctions). But the stepwise-approximated AC waveform contains transients (e.g. jitter, dither) between steps and results in significant errors for frequencies above 1 kHz. Thus the AC-PJVS is suitable for low frequency waveform synthesis e.g. for mains frequency.

In the case of PD-JVS, the generated waveform is

ex-Fig. 3 Schematic of PD-JVS. The JJA is irradiated by the modulated cur-rent pulse. Output analog signal is well defined by the JJA, “voltage quan-tizer,” and calibrated LPFs.

tremely pure with low noise or negligibly small distortion (down to 140 dB). But the voltage level is relatively small, currently less than 300 mV. The pulse patterns that are used to generate waveforms are programmed in a memory in a pulse pattern generator (PPG). The lowest frequency of the generated waveform, flowest = fclk/M, is determined by the PPG clock frequency (the pulse repetition frequency), fclk, and the maximum memory length of the PPG, M. In our system the PPG is equipped with a memory as large as 134 217 728 bit/Channel, then the lowest frequency of the generated waveform is as low as 74.5 Hz when the PPG is operated with the clock frequency of 10 GHz. To generate waveforms with lower frequencies, e.g. mains frequency, therefore the required memory length becomes extremely large. In general PD-JVS is often applied to generation of waveform with higher frequency than that by AC-PJVS. In addition, JAWS based on PD-JVS can work as a calculable pseudo-random noise source, which is a key component in redefinition of the Boltzmann constant [7]–[9].

In this paper, we summarize activities on AC-PJVS and PD-JVS developments at NMIJ/AIST.

2. Programmable Josephson Voltage Standard

At NMIJ, AIST, a 10-V DC PJVS system has been devel-oped using a compact 10-K two-stage Gifford-McMahon (GM) cryocooler [10]. The system operates with JJA chips based on a NbN/TiNx/NbN over-damped junction technol-ogy [11]. Excellent agreement between the system and a conventional Josephson voltage standard of 3 parts in 109 was reported [10]. Our next subject is to upgrade the DC PJVS system for synthesizing AC waveforms. In this sec-tion, we report our first step in the development of an AC-PJVS system. Synthesis of sinusoidal waveforms with a fre-quency range of up to 2 kHz and preliminary experiments for a sampling measurement have been demonstrated. 2.1 Experimental Setup

Fig. 4 Photograph of the AC-PJVS system with a compact 10-K cooler and a customized bias source.

Fig. 5 1-kHz sine waveform synthesized with our AC-PJVS system. The inset enlarges the area indicated with the circle.

voltage [10] except for the bias source that is customized for AC waveform synthesis. The system is composed of a NbN-based over-damped JJA chip mounted in a vacuum chamber, a compact two-stage GM cryocooler (0.1 [email protected] K), a mi-crowave source and a bias source (Fig. 4). The 10-bit AC-PJVS chip includes two 65 536 junction arrays, enabling maximum peak amplitude in the output voltage of about 4 V at the microwave frequency of 16 GHz. The bias source has 12-bit digital-to-analog converters, which are controlled via an optically-coupled digital circuit to eliminate electri-cal noise. Each channel of the bias source has two ports for supplying/returning current to/from each segment.

2.2 Results

To ensure correct operation of the AC-PJVS chip on a quan-tized voltage step, the microwave responses of the junc-tions in each channel (segment) were measured. As a re-sult, we obtained bias margins greater than 0.69 mA for op-erating on the 1st-order Shapiro step at a microwave fre-quency of 16 GHz for all segments. Figure 5 shows a 1-kHz sine waveform synthesized using the AC-PJVS system op-erated within the bias margins. The waveform is stepwise-approximated with 64 steps for one cycle. We have

suc-Fig. 6 Maximum standard deviations vs. sampling timing measured for a synthesized sine waveform at a frequency of 0.976 562 5 kHz, with peak voltage amplitude of about 2 V and with 64 steps per cycle. The aperture time of the sampling was 2μs.

ceeded, at present, in generating AC waveforms with peak amplitude of up to about 4 V in the frequency range from 0.1 Hz to 2 kHz. One of the important factors limiting the performance of the AC-PJVS is the error occurring during transitions between the steps. In the transient, the values of output voltage are not quantized, which produces a measure-ment uncertainty. To evaluate the time duration of the tran-sient, we carried out a measurement for synthesized wave-forms using a sampling digital voltmeter (DVM), as follows. In this measurement, a sine waveform at a frequency of 0.976 562 5 kHz and with peak voltage amplitude of about 2 V approximated with 64 steps for one cycle (i.e., the step width of 16μs) was used. The sampling frequency of the DVM was 61.25 kHz (equal to the step interval), and the aperture time was 2μs. Measurement of one set of the sam-pled data was carried out for one cycle of the waveform, and the same measurement was repeated 10 times to obtain the standard deviations. The above measurement was then re-peated with different sampling delays, that is, relative phase between the sampling and the waveform. Figure 6 shows the maximum value of the standard deviations in one cy-cle for each sampling delay. As the sampling timing just overlaps the transients, the values of standard deviation in-creased drastically. On the other hand, the values obtained between the transients stay below the uncertainty level due to the DVM. From this result, the duration time of the tran-sient is roughly estimated to be less than 5μs taking the aperture time into account. We then made direct observa-tions of the waveforms using a digitizer to reveal detailed structures of the transient. As a result, we found that the transient is composed of the main transition followed by ringing. The obtained values of the time duration for the main transition are 0.3μs–2.0 μs, whereas the values for the time duration including the ringing are 0.5μs–3.8 μs. The maximum value for the time duration including the ring-ing, 3.8μs, is consistent with the value obtained in the above measurement using a DVM. For the RMS measurement, fur-ther improvement and understanding are needed to suppress the systematic errors related to the transients and so forth [12], [13]. We consider, on the other hand, that our system is valid for the measurements using the “sampling techniques”

in waveform synthesis by PD-JVS with an over-damped JJA based on SINIS junctions with modulated current pulse trains at 49.7 MHz, which are generated by a mode-locked fiber laser [15]–[17]. Currently NMIJ is working on PD-JVS with NbN-based SNS junctions, and some preliminary results will be reported in this section.

3.1 Experimental Setup

We employed SNS Josephson junctions fabricated using the AIST NbN process. 480 and 1600 junctions are arranged in the center line of 50−Ω coplanar waveguides in JJAs [18]. The temperature of the chip was controlled by a heater on the chip to suppress hysteresis in the I− V curve due to self-heating of Josephson junctions. A 5 mm× 5 mm JJA chip is flip-chip-bonded on a 16 mm× 16 mm chip carrier which is mounted on a 32-port broadband probe module (cryoprobe) on the 2nd stage (4 K) of a GM cryocooler (1 [email protected] K). A photo diode (PD, UTC-PD), which operates up to 40 GHz, is also installed on the 2nd stage of the cryocooler. The PD is connected to one of the ports of the cryoprobe and it can supply a JJA with current pulses. Optical pulse trains gen-erated by a multiplexer with an electrical/optical converter (MUX with E/O) are transmitted to the PD through an op-tical fiber. The other 31 ports are connected to the interface on the jacket of the cryocooler with broadband coaxial ca-bles. These cables can be used for readout of the output voltage and for injecting RF signals generated by a pulse pattern generator (PPG), for example. Our PPG operates up to 12.5 Gbps and has 4 channels. Each channel has a memory of 134 Mbits. This allows us to generate a wave-form of 74.5 Hz when clocked at 10 GHz. One period of the waveform is encoded in a binary bit stream using 2nd order Δ − Σ modulation and stored in the memory of the PPG. The picture and the block diagram of the system are shown in Figs. 7, and 8 respectively.

Our system has several advantages over the predeces-sors. First, the JJA is electrically separated by the optical fiber from the room-temperature electrical equipment. Then the JJA is completely free from the electrical noise from the pulse pattern generator, etc. Second, the optical fiber has a very wide bandwidth, so the shape of the pulse keeps its form well at the JJA. Third, the GM cryocooler enable invariable temperature distribution of the output cable and makes the length of the cable roughly half or shorter in com-parison with an usual liquid 4He Dewar insert. Then the transmission characteristics of the cable can be well-defined and does not change with time. In the case of a usual4He

Fig. 7 Picture of the NMIJ’s PD-JVS which is equipped with the pulse pattern generator, the LN modulator, the GM cryocooler with optical input, the broadband cryoprobe, and the JJA.

Fig. 8 Block diagram of the NMIJ’s PD-JVS. The generated voltage pulse train by PPG is converted to a modulated optical pulse train by a LN modulator. The optical pulse train is input to the photo detector (UTC-PD) and converted to a current pulse train. Then finally the current pulse train is injected to the JJA. The JJA is mounted on the broadband cryoprobe, which allows us to replace the devices easily.

Dewar insert, however, as the liquid level drops, the charac-teristics of the cable change with time.

We tried two modes of operation of JJAs with the above-mentioned equipment. The first method is to drive a JJA with current pulses generated by optical pulses. The second way is the so-called AC-coupling method [19]. In this report, the first method and the result are shown. A two stage inductive voltage divider (IVD) was used to character-ize the low pass filters (LPF) on a JJA chip.

3.2 Results

Figure 9 shows a spectrum of a unipolar sine wave gener-ated with the optical method. The frequency of the funda-mental at 74.5 Hz agrees well with the value determined by the clock frequency (= 10.0 GHz) and the memory length (= 134 Mbit/Channel) of the PPG. The background spurious noise of harmonics of the 50 Hz power line signal were ob-served with the maximum intensity of−70 dBc. These har-monics are due to a grounding problem of our chip holder, in which all the outer conductors of the coaxial cables shares the same ground at the body of the chip holder. The noise

Fig. 9 Spectrum of a waveform of 74.5 Hz, generated with a NMIJ’s PD-JVS of the SNS junction array.

Fig. 10 A Spectrum of a sinusoidal waveforms: (a) 76 kHz, generated by NMIJ’s PD-JVS of the SNS junction array. Background is also shown with a gray line. The inset is the time-domain waveform. (b)74 kHz, generated by a commercial waveform synthesizer (displayed for comparison with the PD-JVS).

floor except the harmonics of 50 Hz power line is as low as−86 dBc. The amplitude of the waveform was 0.878 mV (rms). The output voltage of the JJA was mainly limited by the small output current of the PD due to a reduction of its responsivity at low temperature. A spectrum of a sinusoidal waveform of 76 kHz is shown in Fig. 10(a). For comparison and to demonstrate the performance of the PD-JVS, a wave-form, which was generated by a commercial semiconductor-based waveform synthesizer, is also shown. The waveform

generated by the PD-JVS is clearly purer than that by the semiconductor-based synthesizer (see Fig. 10(b)).

4. Summary and Future Plan

We have demonstrated AC waveform synthesis using an AC programmable Josephson voltage standard (AC-PJVS) system with a 10-K Gifford-McMahon (GM) cryocooler. Stepwise-approximated waveforms with peak amplitudes of up to 4 V and at frequencies below 2 kHz were generated. The transient time in the obtained waveforms seems short enough at least for the measurements using the sampling method. We are now attempting more precise experiments and evaluation of the uncertainty in the sampling measure-ments. As a next step, we plan to measure an AC/DC difference standard using a calibrator in a frequency range around/below mains frequency (50 Hz or 60 Hz). It is nec-essary to minimize the effect of transients, and characterize its behavior more precisely for this purpose.

The performance of the pulse driven Josephson voltage standard (PD-JVS) system was also verified through arbi-trary waveform synthesis from tens of kHz down to close to mains frequency. The unique characteristics of our system are the large memory size of the pulse pattern generator to synthesize low frequency waveforms, and the optical input which is connected to the photo detector (PD) and installed on the cold head close to the Josephson junction array (JJA). The optical input allows us to keep the wide bandwidth, and reduce electrical noise from the electrical equipment, e.g. a pulse pattern generator. And the GM cryocooler enables invariable temperature distribution of the output cable and makes the length of the cable roughly half or shorter in com-parison with a conventional liquid4He Dewar insert. This can not be easily realized with an usual4_{He Dewar insert,} because the level of the liquid drops with time. Then the transmission characteristics of the cable can be well-defined and do not change with time.

We have recently developed a new broadband probe module (cryoprobe) in which all the outer conductors of the coaxial cables are insulated from the chip holder and the cry-ocooler in order to avoid the grounding problem. In addition to the 32-port cryoprobe, we have developed a 20-port ver-sion for 1 cm× 1 cm chips that are free from the grounding problem. These new chip holders will be installed in a new pulse tube type cryocooler with much smaller mechanical vibration than a GM cryocooler. The new cryocooler will be equipped with double PDs so that it is possible to syn-thesize bipolar waveforms. The memory length of the PPG, which we have lately developed, is 8 times as large as that of the current device, enabling us to generate a waveform with lower frequency down to around 20 Hz.

AC-PJVS has an advantage over PD-JVS in the point of view of its high output voltage level up to 20 V. But the gen-erated stepwise-approximated waveform is contaminated by harmonics due to the transition between quantized voltage steps. Then the effective value of the voltage has rather high uncertainty at higher frequency range (i.e., kHz-range in this

thus power. In a “Smart Grid” system, an AC-PJVS may provide a standard with the necessary accuracy and instant measurements to make effective utilization of various power sources, which may be a combination of stable and unstable sources.

On the other hand, the waveform generated by the PD-JVS has neither of the stepwise profile nor in-band har-monic content like that of AC-PJVS. The PD-JVS has an advantage from the point of view of the purity and intrin-sic accuracy of the waveform. Then when one needs to synthesize a pure and quantum-mechanical quality wave-form, the PD-JVS is the best method for the application. But the voltage level is rather lower (∼ 300 mV and up to 1 V in near future) than that of AC-PJVS, so the application of this technique is various kinds of waveform (sinusoidal, pulse, triangle, saw tooth, etc.) standards, and as a stan-dard signal for signal generators. The calculable pseudo ran-dom noise (white noise) synthesized by the PD-JVS, with a voltage level well defined by quantum mechanics can cal-ibrate a white noise measurement system (cross correla-tion measurement system) for Johnson noise thermometry (JNT). In the process of the redefinition of the Boltzmann constant, a JNT based on quantum statistical mechanics and the fluctuation-dissipation theorem is playing an important roll. And once the Boltzmann constant is redefined, a JNT will be utilized in measurements of thermodynamics tem-peratures in temperature standards. This “calibrated” cross correlation measurement system will be also useful for ba-sic phyba-sics, verification of fluctuation-dissipation theorem in various materials and in the vicinity of phase transitions, verification of nonequilibrium fluctuation relations and so on.

Acknowledgements

Authors thank S. Kiryu with Tokyo City University for use-ful discussion. M. Maezawa with AIST and S. Nagasawa, T. Sato, and M. Hidaka with ISTEC provided us with SI-NIS type Josephson junction arrays. H. Yamamori and T. Yamada with AIST also provided us NbN based SNS Josephson junction arrays and helped us with AC-PJVS measurements. Authors greatly appreciate their contribu-tions.

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Nobu-hisa Kaneko received Ph.D. in To-hoku University, Japan, in 1997. He joined the National Research Institute in Inorganic Mate-rials, Japan in 1996. He had belonged to Ap-plied Physics and Stanford Leaner Accelerator Center, Stanford University, USA, from 1999 to 2003. He has been a member of the Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), since 2003. He has been the section chief of Electricity Standards Section 2 (quan-tum electrical metrology), Electricity and Magnetism Division since 2008.

Michitaka Maruyama received the B.S., M.S. and Ph.D. degrees in electronic engineer-ing from Nagoya University, Nagoya, Japan, in 1996, 1998 and 2001, respectively. In 2001, he joined the development of HTS sampler sys-tems at the Fundamental Research Laboratories of NEC Corporation, Tsukuba, Japan. From 2003, he worked with the Superconductivity Re-search Laboratory, International Superconduc-tivity Technology Center (SRL-ISTEC), Tokyo, Japan, where he continued the development of the sampler systems. From 2006 to 2008, he was engaged in the devel-opment of superconducting analogue to digital converters at SRL-ISTEC, Tsukuba, Japan. In October 2008, he joined the National Metrology In-stitute of Japan (NMIJ), National InIn-stitute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan, where he has worked on the de-velopment of AC and DC Josephson voltage standards.

Chiharu Urano received B.E., M.E. and Ph.D. degree from the University of Tokyo, Japan, in 1995, 1997 and 2000, respectively. He was a Postdoctoral fellow at the University of Tokyo (2000–2001) and the Japan Science and Technology Organization (2001–2002). He joined the National Institute of Advanced Indus-trial Science and Technology (AIST), Tsukuba, Japan, in 2002. He was involved in develop-ment of the Quantized Hall Resistance standard (2002–2003). He has been in charge of the Josephson voltage standard since 2003. He participated in the develop-ment of watt balance at BIPM from September 2007 to March 2008. He is staying at NIST since March 2010. Dr. Urano is a member of The Physical Society of Japan and The Japan Society of Applied Physics.