JP2018194518A - Frequency multiplexing read-out device and design method of the same - Google Patents

Abstract

To provide a frequency multiplexing read-out device that has a common shape, structure and dimension with respect to many pixels different in a resonance frequency f, and has a SQUID small in an error relative to a design value, over a wide range of division parameter a, and to provide a design method of the frequency multiplexing read-out device.SOLUTION: A plurality of pixels having a read-out unit to which a SQUID, a resonator, and capacitor are parallely connected, and a detection unit changing a resonance frequency of the read-out unit in accordance with a detection signal, and a read-out line to be connected to the pixel are wired. The SQUID has an input coil, an annular electrode in which a Josephson junction is formed, a ground electrode, and a ground contact electrically connecting between the annular electrode and the ground electrode, and respective SQUIDs in the plurality of pixels are formed by making the input coil, the annular electrode, and the ground electrode common, and are formed so that a formation position of the ground contact with respect to the annular electrode is different.SELECTED DRAWING: Figure 4

Description

  The present invention relates to frequency multiplex readout devices, and more particularly to microwave band frequency multiplex readout devices for large scale superconducting detector arrays.

Superconducting detectors have a low noise property that surpasses existing detectors such as semiconductors against electromagnetic waves and energetic particles in the wavelength range of nine digits from millimeter waves to gamma rays. Astronomical observation, basic science, materials Used in fields such as analysis, biometrics, and quantum cryptography.
On the other hand, the light receiving area and the number of pixels in the realized superconducting detector system are several orders of magnitude smaller than those of an existing detector array such as a CCD. Since the small light receiving area requires a small signal amount and the low pixel number requires scanning at the time of imaging, both present a serious problem of a long measurement time.

In order to avoid the fundamental limitation of the superconducting detector that increases the light receiving area per single pixel, the performance is lowered. Therefore, a method for increasing the light receiving area by constructing a large number of pixels having a small light receiving area is desired.
On the other hand, when the signal readout line of a multi-pixel superconducting detector in a cryogenic environment is connected in parallel to the room temperature signal processing system, the number of signal lines between the cryogenic temperature and room temperature increases almost in proportion to the number of pixels. This leads to an increase in heat inflow to the cryogenic temperature. That is, the increase in the number of pixels necessitates an increase in the cooling capacity, volume, and price of the cryogenic cooling system that controls the volume and power consumption of the superconducting detector system.
In order to solve this problem, research has been made on a multiple readout device that collects the outputs of a plurality of pixels into a small number of readout lines at a very low temperature. Among a plurality of multiplexing schemes proposed so far, the signal-to-noise ratio does not decrease in principle with the increase in the number of pixels, and the number of multiplexed pixels per readout line becomes the maximum in principle. The microwave band frequency multiplexing method is particularly effective (see Non-Patent Documents 1 and 2).

FIG. 1 shows a configuration of a conventional microwave band frequency division multiplex reading apparatus. A superconducting detector (hereinafter referred to as a detector; 531, 532, 533,... In FIG. 1) is supplied with a bias current from a detector bias current source 65, and has a variable resistance whose resistance changes with photon incidence. .
Further, in the microwave frequency division multiplexing readout device, the same number N of superconducting thin film resonators (hereinafter referred to as resonators; 581, 582, 583,...) In FIG. And the length of each resonator, that is, the resonance frequency f _R is a value for each pixel so as to be distributed on the frequency axis. have.
The detection chip 51 and the readout chip 52 are connected by wiring inductance (541, 542, 543,... In FIG. 1), and an incident signal of a photon detected by the detection chip 51 is transmitted to the readout chip 52 through a coil. It is supposed to be shaped.
The resonance frequency f _R of a certain resonator changes with the output of the detector coupled with the resonator.
The output current of each detector includes a Josephson junction element (571, 572, 573,... In FIG. 1), a SQUID ring inductance (561, 562, 563,... In FIG. 1), and a SQUID ring inductance. Flows into a SQUID (superconducting quantum interference device) consisting of SQUID input coils (551, 552, 553,... Let
Based on this principle, the resonant frequency f _R is a function of the incident photon energy to each detector.
Thus, by measuring the difference between the resonance frequency f _R in the case of there is an input to the resonance frequency f _R in the case of the input signal is no input to the detector (= 0) relates to all pixels, the incident photons to each pixel Energy can be identified. The other ends of the N resonators are connected to one microwave readout line (610, 611, 612, 613,... In FIG. 1) via a coupling capacitor C _C (591, 592, 593,. ).

The microwave readout line is drawn to room temperature at both the input and output terminals, a microwave signal source 64 at the input terminal, a spectrum analyzer at the output terminal, and the like for measuring the microwave power as a function of the frequency f _MW ( (Not shown) are connected via a cryogenic low noise amplifier 62 and a coaxial line 63.
Further, the multiplexing chip and the cryogenic low noise amplifier which are the core of the microwave band frequency multiplexing readout device are arranged in a cryogenic cooling device 60 such as a cryostat, so that the multiplexing chip 50 can perform superconducting operation. .

In this system, the resonance frequency f _R changes depending on the termination impedance Z _L of the resonator, and the termination impedance Z _L is a function of the internal state of the SQUID, that is, the detector output current.
Sufficiency distant frequency of the read signal from the resonant frequency f _R, and sufficiently high design than the series impedance of the coupling being connected to the microwave read line capacitor C _C and the resonator 50Ω microwave read line putting, it is possible to ignore the microwave current branch to the resonator side of the microwave read line in the coupling capacitor C _C.
That is, the microwave power injected from the input end does not flow out to the resonator side and is almost entirely consumed by the measuring instrument connected to the output end. On the other hand, in the resonance frequency f _R, the series impedance of the coupling capacitor C _C and the resonators connected to the microwave read line is almost zero, most of the microwave current, microwave read line in the coupling capacitor C _C Flows out to the resonator side, the current flowing through the readout line to the output terminal at room temperature is drastically reduced. That is, the microwave power injected from the input end is reflected by the resonator in the resonance state, and consumption at the output end resistance is drastically reduced.

Since the above resonance phenomenon occurs with respect to N resonance frequencies f _R , the frequency dependence of the microwave transmittance of the chip is as shown in FIG. Furthermore, as shown in FIG. 2B, each resonance frequency f _R is modulated by the intensity of light incident on each pixel via an input current to a superconducting quantum interference device (SQUID) coupled to the resonator. Receive. 2 shows the frequency-to-transmittance characteristics ((a) in the figure) of the frequency multiplexed signal output from the multiplexing chip 50 and the frequency pair obtained by enlarging the part indicated by a circle in (a) in the figure. It is a figure which shows the transmittance | permeability characteristic ((b) in a figure). The change in the resonance frequency is a period of Φ ₀ with respect to the magnetic flux Φ _{A applied} to the SQUID, but in (b) in the figure, representative three values (Φ _A / Φ ₀ = _0, 0.25, Only 0.5) is shown.
If such information is read at once by a measuring instrument on the output end side of the microwave readout line, simultaneous readout of multiple pixel outputs by a small number of readout lines can be realized.

In this microwave band frequency multiplex readout device, since the resonance frequency f _R is a function of the incident light intensity to the detector, the resonator and the SQUID (ring self-inductance L _S , critical current I _{0 of the} Josephson junction element) ) Coupling mechanism is required.
As a coupling method, there are two types, a magnetic coupling type (see Non-Patent Documents 1 to 3) shown in FIG. 3A and a direct coupling type (Non-Patent Documents 1, 2, and 4) shown in FIG. 3B. Broadly divided. 3A is a diagram showing an equivalent circuit of a resonator-SQUID coupling by a magnetic coupling type, and FIG. 3B is a diagram showing an equivalent circuit of a resonator-SQUID coupling by a direct coupling type. is there.

In the magnetic coupling type, a coil (self-inductance L _MW ) having a mutual inductance M _MW with the SQUID terminates the resonator. On the other hand, in the direct coupling type, the SQUID terminates the resonator.
Both the magnetic coupling type and the direct coupling type are common in that the termination inductance L _{L of the} resonator is modulated by the internal state of the SQUID. The difference is in the size of the termination inductance L _L.
In the direct coupling type, the termination inductance L _L of the resonator can be greatly reduced as compared with the magnetic coupling type. A supplementary explanation will be given below.
In the case of the magnetic coupling type, the termination inductance L _L is expressed by the following equation (1).

However, the formula (1), wherein η _M ≡M _MW / _{L S} indicates the index representing the coupling strength between the resonator and the _{SQUID, L J ≡L J0 × sec} (2πΦ / Φ 0) is The equivalent inductance of the Josephson junction element as a function of the flux quantum Φ ₀ period with respect to the flux linkage Φ to the SQUID ring is shown, and L _J0 ≡Φ ₀ / (2πI ₀ ), and Φ ₀ ≡h / ( 2e). Here, h is a Planck constant, and e is a unit charge.

On the other hand, in the case of the direct coupling type, the termination inductance L _L is expressed by the following equation (2).

However, in said Formula (2), (eta) _D = 1-a shows the index | exponent showing the intensity | strength of the direct coupling | bonding of a resonator and SQUID, and a (0 <a <1) is shown in FIG.3 (b). The left and right division indexes of the SQUID ring inductance with the signal injection line from the resonator as an axis are shown (see Non-Patent Document 4). Note that 0 <η _D <1 from 0 <a <1.

Assuming the case where the coupling degree between the resonator and the SQUID is equal in the equations (1) and (2) (η _M = η _D ≡η), the difference in termination inductance L _L between the magnetic coupling type and the direct coupling type is It is expressed as the following formula (3).

Considering the weak coupling condition between _{L MW} and SQUID which is eta ≦ 1 and commonly employed _L S << _{L MW} and _{L LMC} ≒ _{L MW,} from the equation _{(3), L LDI ≒ L LMC -L MW} <<L _LMC is derived.
In fact, in the three examples listed in Tables 7.1, 7.2, and 7.3 in Non-Patent Document 2, L _MW = 77.6 pH, 145 pH, 186 pH, η L _S = M _MW = 1.65 pH, respectively. 9.42 pH, 5.46 pH, (L _LMC -L _LDI ) / L _MW = 0.978, 0.938, 0.973, and L _LDI << L _LMC .
Therefore, as described above, the direct coupling type can significantly reduce the termination inductance L _L of the resonator as compared with the magnetic coupling type.

Next, an advantage when the termination inductance L _L is reduced will be described. The resonance frequency f _R is given by the following equation (4) based on the parameters for each pixel (see Non-Patent Document 2).

However, In the formula _(4), f Rλ _/ 4 indicates the frequency at which the resonator length is 1/4 wavelength, Z ₀ represents the characteristic impedance of the distributed constant lines constituting a resonator.
In this equation (4), the resonance frequency f _R deviates from the quarter-wave resonance frequency f _{Rλ / 4} due to the coupling capacitor C _C and the termination inductance L _L , and 4f _{Rλ / 4} C _C Z ₀ << 1 when the _{4f Rλ / 4 L L / Z} 0 << 1, the ratio of each shift, respectively, about _{400f Rλ / 4 C C Z 0} %, given by about _{400f Rλ / 4 L L / Z} 0% Is shown.

Than the operating principle of a microwave band frequency multiplexed reading device, it is important to obtain a resonant frequency f _R as designed. Deviation from a design value of the actual values of the unavoidable coupling capacitor C _C and the terminating inductance L _L in the device manufacturing process, it is highly desirable to reduce the degree of contribution to f _R variation.
Coupling capacitor C _C are the same in the magnetic coupling type and the direct coupling type, the difference between them do not typically cause.
On the other hand, when the terminating inductance L _L relative magnitude [delta] L L _/ L _L of the variation [delta] L _L of assuming a situation that is not dependent on end inductance L _L, as described above, the direct coupling type, terminating inductance compared with magnetically coupled Since L _L can be reduced by orders of magnitude, the direct coupling type is advantageous.
Actually, under the conditions of the typical value f _{Rλ / 4} ≈6 GHz, C _C ≈10 fF, L _L ≈0.1 nH, and Z ₀ ≈50 Ω in the magnetic coupling system described in Non-Patent Document 2, ₄₀₀ f _{Rλ / 4} C _C Z ₀ ≒ 1.2%, estimated to _{400f Rλ / 4 L L / Z} 0 ≒ 4.8%, the contribution of end inductance _{L L} exceeds the contribution of the coupling capacitor _{C C.}
That is, the deviation of each pixel from the design value of the resonance frequency f _R is strongly dependent on the realization precision of the end inductance L _L than achieved precision of the coupling capacitor C _C.

In the magnetic coupling type, a value sufficiently larger than the mutual inductance (M _{MW in} FIG. 3A) that controls the coupling between the resonator and the SQUID is set to a mutual inductance that controls the coupling between the detector and the SQUID (FIG. 3A). Therefore, a coupling coil for the detector (L _{I in} FIG. 3A) is placed just outside the SQUID ring, and further, a coupling coil for the resonator (FIG. 3) is placed outside the coupling coil. It is common to arrange (L _MW ) of (a) (see Non-Patent Documents 1 to 3).
In such an arrangement, the shape and dimensions of the coil _{L MW} responsible for between resonators -SQUID binding, the shape of the detector -SQUID linkages coil _{L I,} can not be designed independently of the dimensions.
Therefore, on multiple readout circuit chip corresponding to the detector array having different specifications for each pixel, not only the coupling coil L _I and the detector, different shapes for each pixel with respect to the resonator, the size, inductance Coupling coil L _MW is required (see Non-Patent Document 5).
Therefore, it becomes difficult to suppress the realization accuracy of the termination inductance L _L and the mutual inductance M _{MW to} a certain value or less in all pixels as compared with a chip to which a single resonator-SQUID coupling coil is applied.

Above, in the microwave band frequency multiplexing readout device, the selection of the direct coupling type capable of reducing end inductance L _L, conditions that achieve the accuracy of the terminating inductance L _L does not dominate the realization precision of the resonance frequency f _R, i.e., L _L / The condition of Z ₀ << C _C Z ₀ can be realized.

The range of change in the resonance frequency f _R in the case where the detector output current corresponding to [Phi _0/2 in SQUID input magnetic flux conversion is changed to Delta] f _R. Note that Φ ₀ ≡h / (2e) is a magnetic flux quantum, h is a Plank constant, e is a unit charge, and the response of the SQUID to the magnetic flux is known to be a Φ ₀ period. Yes. In the magnetic coupling type, a relational expression between Δf _R and f _R is given by the following expression (5) (see Non-Patent Document 2).

However, in the above equation (5), λ≡L _S / L _J0 , and in order to ensure a one-to-one correspondence from input magnetic flux (current) required for detector reading to output frequency, λ <1 Is known to be required. Further, according to the calculation by the present inventors, λ ≦ 0.6 is desirable in order to increase the conversion efficiency from input to output.
The equation (5) means that Δf _R can be set to a constant value between pixels having different f _R by assigning a η _M ² L _S value unique to each pixel to each SQUID.

On the other hand, in direct coupling type conventional research (see Non-Patent Documents 1 and 2), the inductance involved in coupling with the resonator is only the self-inductance L _S , and two inductances (self-inductance L _{S as} in the magnetic coupling type). Since there is no degree of freedom due to mutual inductance M _MW ), Δf _R cannot be made to be a constant value between pixels having different resonance frequencies f _R as shown in Equation (5).
As shown in FIG. 3B, the present inventors pay attention to the fact that the self-inductance L _S of the SQUID ring can be divided into left and right with the signal injection line from the resonator as an axis, and the Josephson junction element side inductance is expressed as aL. Introduce a division parameter a ( _S -ID of the self-inductance L _S of the SQUID ring with the signal injection line from the resonator as an axis; 0 <a <1) where _{S is} the opposite side (1-a) L _S It was proposed to do (refer nonpatent literature 4).
Further, the present inventors subsequently discovered that the direct coupling type can have the same degree of freedom between Δf _{R and} f _R as in the magnetic coupling type by using the division parameter a. That is, the relational expression between Δf _R and resonance frequency f _R in this system is the following expression (6).

However, an η _D ≡1-a, replacing the equation eta _M the eta _D (a or ^{_{M MW 2 / L S (1}} -a) 2 L S) in (5), the equation (6) can get.

By the way, in this proposal, a microstrip type (vertical type) SQUID ring is adopted for a SQUID having a planar structure ring that is widely used in microwave band frequency division readout devices.
The planar structure ring is composed of only a superconductor electrode in the same vertical layer, and does not have a superconductor ground electrode under the electrode. The planar structure ring is widely used as a SQUID for magnetometers, but there are few experimental reports on the error between the actual value of the inductance and the design value, and high-precision Δf _R and difficult applicability to say that sufficient to apparatus realizing the resonant frequency f _R is required.
Also, in contrast to the ring of L _S ≈70 pH used in the SQUID for magnetometers, the SQUID ring of L _S ≈10 pH is desired in the microwave frequency division multiplexing readout device, but the planar structure ring has such a small value of self If the inductance L _{S is} to be realized, there is a disadvantage that the coupling efficiency with the detector is lowered.
On the other hand, in the microstrip type (vertical type) SQUID ring, a superconductor ground electrode is present in the lowermost layer, and a superconductor strip electrode is laminated thereon with an interlayer insulating layer interposed therebetween ( Non-patent document 4).
In the microstrip type (vertical type) SQUID ring, an analytical expression that is easy to be associated with a physical image is given that the inductance value is proportional to the ratio of the length and width of the inductance (see Non-Patent Document 6). In addition, the high-precision feasibility of designing with this analytical expression has been verified by many experiments so far.
Explain the reason for the former. When a current I _{1 is} passed in one direction of the strip electrode, a mirror image current −I ₁ having the same magnitude and opposite direction flows in a region immediately below the strip electrode in the ground electrode. The vertical reciprocating current (I ₁ , −I ₁ ) flows at a position that is so close (typically about 10 ⁻⁷ m) that it is difficult to distinguish from a location sufficiently away from these electrodes. The generated magnetic fields cancel each other at a distance, and the horizontal direction is almost confined in a narrow area with a rectangular cross section defined by the width of the strip electrode and the vertical direction by the thickness of the interlayer insulation layer plus the thickness of the upper and lower electrodes. You can think of it. Moreover, since it is known from electromagnetism that the magnetic field in the rectangular cross section is almost constant regardless of location, by simply multiplying the uniform magnetic field by the rectangular cross section and the vacuum permeability. The flux linkage to the reciprocating current (I ₁ , −I ₁ ) is obtained with high accuracy.
Since the inductance is a physical quantity obtained by dividing the flux linkage by the reciprocating current, there is no ground electrode and no mirror image current is generated. Therefore, the inductance is opposed to about 10 ⁻⁵ m in the horizontal direction, not in the vertical direction. In the microstrip SQUID ring, the amount of flux linkage to the SQUID ring is reduced compared to a planar structure ring in which a reciprocating current flowing through two electrodes generates a flux linkage.
Therefore, the microstrip type SQUID ring is suitable for realizing a small inductance of L _S ≈10 pH.
From the above, it is advantageous to apply the microstrip type SQUID ring to a direct coupling type microwave band frequency division multiplex reading apparatus.

However, the above proposal (Non-Patent Document 4) merely shows that the self-inductance L _S and the ring inductance length are in a linear relationship when a = 0.5 is fixed, and the following points are not clarified. .
(1) Device structure, shape, and dimensions suitable for realizing a wide range of division parameters a.
(2) aL _S and (1-a) the difference between the design value and the actual values of _{L S.}

Regarding (1), when different SQUIDs having different shapes, structures, and dimensions have different division parameters a (see Non-Patent Document 5), many kinds of SQUIDs are required on the chip as the number of pixels increases, and f There is concern that the accuracy of realization of _R may be impaired.
In order to solve this problem, a device structure, size, and shape that can easily suppress the realization accuracy of all pixels within a certain value is desired.
That is, over the division parameter a wide range, for many pixels having different resonant frequencies f _R, application of the SQUID is required to have a common shape, structure and size.
Regarding (2), realization of Δf _R and f _R as designed is an important key for the normal functioning of the frequency-multiplexed readout circuit.

J. A. B Mates et al .: “Demonstration of a multiplexer of dissipationless superconducting quantum interference devices,” Appl. Phys. Lett. 92 (2008) 023514 (DOI: 10.1063 / 1.2803852). J. A. B Mates: “The microwave SQUID multiplexer,” Ph.D thesis, Univ. Colorado (2011). S. Kempf et al .: “Demonstration of a scalable frequency-domain readout of metallic magnetic calorimeters by means of a SQUID multiplexers,” AIP advances, 7 (2017) 015007 (DOI: 10.1063 / 1.4973872). F. Hirayama et al .: “Microwave SQUID Multiplexer for TES Readout,” IEEE Trans. Appl. Supercond., 23 (2013) 2500405 (DOI. 10.1109 / TASC.2012.2237474). D. Swetz, et al .: “First x-ray scattering observations by the NIST-Illinois soft x-ray microcalorimeter spectrometer at the Advanced Photon Source,” 2EOr2D-04, Appl. Supercond. Conf. 2014, Charlotte, USA, 10 -15 August, 2014. W. H. Chang: “The inductance of a superconducting strip transmission line,” J. Appl. Phys., 50 (1979) 8129 (DOI: 10.1063 / 1.325953).

The present invention solves the above-mentioned problems in the prior art, and has a common shape, structure, and dimensions for many pixels having different resonance frequencies f _R over a wide range of division parameters a, It is an object of the present invention to provide a frequency multiplex readout apparatus having a SQUID with a small error and a design method thereof.

Means for solving the problems are as follows. That is,
<1> A SQUID, a resonator, and a capacitor are connected in series in this order, and a readout unit formed as a resonant circuit having a specific resonance frequency, and connected to the SQUID, and the resonance of the readout unit according to a detection signal A plurality of pixels each having a different resonance frequency, connected to the pixel on the capacitor side, and a signal having the same frequency as the resonance frequency for each pixel from the input end. A single readout line to which a frequency dispersion multiplexed signal distributed and multiplexed on the axis is supplied and a modulation signal of the frequency dispersion multiplexed signal before and after the change of the resonance frequency can be output from the output end The SQUID is electrically connected to the input coil connected to the detection unit and the resonator, and a Josephson junction is formed. An annular electrode; a ground electrode disposed opposite to the annular electrode; and a ground contact that electrically connects the annular electrode to the ground electrode, wherein the annular electrode is connected to the resonator and the ground contact. The SQUIDs of the plurality of pixels are formed in common with the input coil, the annular electrode, and the ground electrode, and the formation position of the ground contact with respect to the annular electrode is A frequency multiplex readout device, wherein the frequency multiplex readout device is formed differently.
<2> of the annular electrode self-inductance as L _S, resonators constitutes a parallel connection of the annular electrode - two self-inductance in the connections between the ground contacts, respectively and aL _S and (1-a) L _S The frequency multiplex readout apparatus according to <1>, wherein the division parameter a satisfies the following expression: 0.02 ≦ a ≦ 0.98.
<3> The frequency multiplex reading apparatus according to <2>, wherein the division parameter a satisfies the following expression: 0.29 ≦ a ≦ 0.77.
<4> The frequency multiple readout device according to any one of <1> to <3>, wherein the self-inductance of the annular electrode is 5 pH or more.
<5> The frequency multiplex readout device according to <4>, wherein the resonance frequency in each pixel is 4 GHz or more.
<6> A SQUID, a resonator, and a capacitor are connected in series in this order, and a readout unit formed as a resonance circuit having a specific resonance frequency, and the resonance of the readout unit connected to the SQUID and in accordance with a detection signal A plurality of pixels having different resonance frequencies, connected to the pixels on the capacitor side, and a signal having the same frequency as the resonance frequency for each pixel from the input end. The frequency dispersion multiplexed signal distributed and multiplexed above is supplied, and a single readout line from which the modulation signal of the frequency dispersion multiplexed signal before and after the change of the resonance frequency is output from the output end is arranged. The SQUID is connected to the detection unit, and an annular electrode that is electrically connected to the resonator and forms a Josephson junction. A ground electrode disposed opposite to the annular electrode, and a ground contact for electrically connecting the annular electrode to the ground electrode, wherein the annular electrode parallels the resonator and the ground contact. For the frequency multiplex readout device configured to be connected, each SQUID in a plurality of the pixels is designed so that the input coil, the annular electrode, and the ground electrode are in common, and the ground contact to the annular electrode A design method for a frequency multiplex readout apparatus, wherein the design is made so that the formation positions of the two are different.
<7> of the annular electrode the self-inductance as L _S, resonators constitutes a parallel connection of the annular electrode - two self-inductance in the connections between the ground contacts, respectively and aL _S and (1-a) L _S The design method of the frequency multiplex readout device according to <6>, wherein the formation position of the ground contact with respect to the annular electrode is designed so that the division parameter a satisfies the following expression: 0.02 ≦ a ≦ 0.98.
<8> The method for designing a frequency multiplex readout apparatus according to <7>, wherein the formation position of the ground contact with respect to the annular electrode is designed so that the division parameter a satisfies the following expression: 0.29 ≦ a ≦ 0.77.

According to the present invention, the above-mentioned problems in the prior art can be solved, and a common shape, structure, and dimensions are provided for many pixels having different resonance frequencies f _R over a wide range of division parameters a. In addition, it is possible to provide a frequency multiplex readout apparatus having a SQUID with a small error from a design value and a design method thereof.

It is a figure which shows the structure of the conventional microwave band frequency multiplex reading apparatus. Frequency vs. transmittance characteristics ((a) in the figure) of the frequency multiplexed signal output from the multiplexing chip, and frequency vs. transmittance characteristics ((a) in the figure) in which the portion indicated by a circle is enlarged It is a figure which shows (b)). It is a figure which shows the equivalent circuit of the resonator-SQUID coupling | bonding by a magnetic coupling type. It is a figure which shows the equivalent circuit of the resonator-SQUID coupling | bonding by a direct coupling type. It is a figure which shows the structure of the frequency multiplexing read-out apparatus which concerns on one Embodiment of this invention. It is a figure which shows the optical microscope photograph which shows an example of the resonator-SQUID coupling | bonding in this invention. FIG. 6 is a diagram schematically showing a cross section taken along line A′-A ″ in FIG. It is a figure which shows the equivalent circuit of the resonator-SQUID coupling | bonding in this invention. each measured value of aL _S and (1-a) _{L S,} is a view showing the relationship between the self-inductance _{L S} of the SQUID ring electrodes which has been determined from the sum of both. It is a figure which shows the electrode length _lJJ dependence of the division parameter a of both a design value and an actual measurement value. It is a diagram showing the relationship between the resonant frequency f _R for the SQUID input magnetic flux change between the maximum amount of change Delta] f _R.

(Frequency multiplex readout device and design method thereof)
A frequency multiplex readout apparatus and a design method thereof according to the present invention will be described with reference to the drawings.
As shown in FIG. 4, the frequency multiplex readout apparatus according to an embodiment of the present invention includes a multiplexed chip 10 in which a plurality of pixels are arranged as a main member. The multiplexing chip 10 includes a detection chip 11, a readout chip 12, and microwave readout lines 210, 211, 212, and 213. FIG. 4 is a diagram showing a configuration of a frequency multiplex reading apparatus according to an embodiment of the present invention.

In the reading chip 12, a resonator 181 including a SQUID (SQUID input coil 151, a SQUID ring inductance 161, etc.), a superconducting thin film resonator, and the like, and a coupling capacitor 191 are connected in series in this order, and a specific resonance frequency f _R One readout section formed as a resonance circuit having other readout section groups (SQUID (SQUID input coils 152, 153, SQUID ring inductances 162, 163, etc.), resonator 182 configured similarly to the readout section) , 183 and coupling capacitors 192, 193). Different resonance frequencies f _R are set in the plurality of reading units according to the lengths of the resonators (181, 182 and 183), respectively.
The details of the SQUID that is the core of the technology in the present invention will be described later with reference to the drawings.

In the detection chip 11, a superconducting detector 131 composed of a superconducting transition edge detector (TES) or the like is connected to a SQUID SQUID input coil 151 via a wiring inductance 141, and according to a detection signal. One detection unit that changes the resonance frequency f _R of the reading unit and another detection unit group (SQUID (superconducting detectors 132 and 133, wiring inductances 142 and 143) configured similarly to the detection unit) Each detection unit is connected to the readout unit in a one-to-one relationship, and one pixel is configured by one detection unit and the readout unit.
The physical quantity to be detected in the detection unit can be variously set according to the configuration of the superconducting detector, and generally includes the energy of photons and particles, the amplitude of electromagnetic waves, and the like.

One readout line formed by the microwave readout lines 210, 211, 212, 213,... Is read out from each pixel at an inter-line connection point (for example, a connection point between the microwave readout lines 210 and 211). It is connected by a capacitor side parts, frequency dispersion multiplexed signal obtained by multiplexing distributed on the frequency axis signal of the resonance frequency f _R of the same frequency for each pixel from the microwave signal source 24 of the input end is supplied At the same time, the modulation signal of the frequency dispersion multiplexed signal before and after the change of the resonance frequency can be output from the output end.
The output signal is amplified by a cryogenic low noise amplifier 22 configured by, for example, a high electron mobility transistor (HEMT) or the like, and is connected to an external measuring instrument (not shown) via a coaxial line 23. Is analyzed.
Further, the multiplexing chip 10 and the cryogenic low noise amplifier 22 are accommodated in a cryogenic cooling device 20 composed of a cryostat or the like for superconducting operation.

A general operation of the frequency multiplex readout apparatus configured as described above will be described.
The same number N of resonators as the number of pixels N (an integer equal to or greater than 1) has a value for each pixel so that the resonance frequencies f _R are dispersed on the frequency axis.
The resonance frequency f _R of a resonator, varies with the output of the detection unit. The output current of the detector flows through the SQUID, and changes the internal inductance of the SQUID, that is, the termination condition of the resonator.
Based on this principle, the resonance frequency f _R is a function of the detection signal detected by each detection unit.
Therefore, the detection signal of the difference between the resonance frequency f _R in the case of there is an input to the resonance frequency f _R in the case of the input signal is no input to the detection section (= 0) is measured relates all the pixels, to each of the pixels Can be identified. The other end of the N resonators are connected to one microwave read lines via a coupling capacitor C _C.

In this system, with respect to the read signal sufficiently distant frequency from the resonant frequency f _R, thoroughly than a coupling capacitor C _C connected to the microwave read line and the series impedance of each resonator to 50Ω microwave read line If you leave high design, it is possible to ignore the microwave current branch to the resonator side of the microwave read line in the coupling capacitor C _C.
That is, the microwave power injected from the input end does not flow out to the resonator side and is almost entirely consumed by the measuring instrument connected to the output end. On the other hand, in the resonance frequency f _R, and the series impedance of the coupling capacitor C _C and the resonators connected to the microwave read line, almost zero, most of the microwave current, microwave read in the coupling capacitor C _C As a result, the current flowing out from the line to the resonator side and flowing through the readout line to the output terminal at room temperature is drastically reduced. That is, the microwave power injected from the input end is reflected by the resonator in the resonance state, and consumption at the output end resistance is drastically reduced.

Since occur to the resonance frequency f _R of the resonance phenomenon are N or more, the frequency dependence of the microwave transmittance of the chip, the form shown above in FIG. 2 in (a). Further, as shown in FIG. 2 (b), each resonance frequency f _R is the intensity of incident light to each pixel via an input current to the superconducting quantum interference element (SQUID) coupled to the resonator. Received modulation by
If such information is read at once by a measuring instrument on the output end side of the microwave readout line, simultaneous readout of multiple pixel outputs by a small number of readout lines can be realized.

The SQUID in the frequency multiplex readout apparatus according to the present invention is arranged to face the annular electrode, the input coil connected to the detector, the annular electrode that is electrically connected to the resonator and that forms the Josephson junction. A ground electrode and a ground contact that electrically connects the annular electrode and the ground electrode are provided, and the annular electrode connects the resonator and the ground contact in parallel.
That is, by using a direct coupling type resonator-SQUID coupling that electrically connects the annular electrode and the resonator, the termination impedance L _L of the resonator described above (see FIG. 3B; _LLDI ) It is set as the structure which reduces.
In addition, the annular electrode is formed on the ground electrode, and by providing a microstrip type (vertical type) SQUID ring structure in which an interlinkage magnetic flux is generated by a current flowing through the annular electrode and a mirror image current flowing through the ground electrode, Analytical formula that makes the electrode self-inductance (SQUID ring inductance) L _S relatively low, and that the self-inductance L _S is proportional to the ratio of the length and width of the inductance, which is easy to associate with a simple physical image (non-patented) The design guideline based on the literature 6) and the high feasibility of the design can be obtained.

  One configuration example of the SQUID in the present invention will be specifically described with reference to FIGS. This SQUID has a microstrip type (vertical type) SQUID ring structure. FIG. 5A is an optical micrograph showing an example of the resonator-SQUID coupling in the present invention. FIG. 5B is a diagram schematically showing a cross section taken along line A′-A ″ in FIG. FIG. 5C is a diagram showing an equivalent circuit of the resonator-SQUID coupling in the present invention.

The SQUID is composed of an input coil (not shown) connected to the detector and an SQUID ring structure 16 (microstrip (vertical) type) that is inductively coupled to the input coil.
As shown in FIGS. 5A and 5B, the SQUID ring structure 16 includes a layered superconductor ground electrode (GP, 16a), an annular electrode disposed opposite to the ground electrode, and a ground It has a ground contact (GNP (LL to GP)) formed by a through hole that short-circuits between the electrode and the annular electrode.
The annular electrode is formed of a superconductor, and is formed of a superconductor with a layered strip electrode (Lower-Layer (LL), 16c) disposed opposite to the ground electrode via an interlayer insulating layer (16b). A layered upper electrode (Upper-Layer (UL), FIG. 5) is arranged above the strip electrode through an interlayer insulating layer (not shown) so as to bridge between two separated portions of the strip electrode. (A) A round mark indicating JJ (UL to LL) in the lower end side is a rectangular portion extending in the vertical direction in the figure) and the strip electrode and the upper electrode are electrically connected to each other. The Josephson junction element (JJ (UL to LL)) to be formed and the Josephson junction element are arranged opposite to each other across the connection point between the resonator in the upper electrode (Resonator), and the strip electrode It is formed with vias (Via (UL to LL)) formed by through holes made of superconductor that electrically connect the partial electrodes. That is, the connection between the resonator and the annular electrode is made at the upper electrode portion between the Josephson junction element and the via.
In the SQUID configured as described above, two lines that are branched from the connection point with the resonator to the ground contact are formed in the annular electrode, and the annular electrode is connected to the resonator and the ground contact by the two lines. Are configured to be connected in parallel. In these two lines, the inductance of aL _S is distributed to the side passing through the Josephson junction element, and (1-a) L _S is distributed to the side passing through the via (see FIG. 5C).
Here, the division parameter a (0 <a <1) is set according to the formation position of the ground contact (see FIG. 5A) with respect to the strip electrode in the annular electrode.

The strip electrode constituting most of the annular electrode has a microstrip structure having a constant thickness and width, and has a shape in which convex bent portions are formed on the upper and lower sides in FIG. However, the bent portion is formed for setting the self-inductance L _S depending on the line length of the annular electrode, and may be more or less formed. Furthermore, the shape of the annular electrode may be a rectangular shape or an annular shape, and is not limited to the shape shown in FIG. In this example, the annular electrode is formed with a two-layer structure of a strip electrode and an upper electrode. However, the annular electrode may be formed of a single layer electrode in which a Josephson junction is formed in the line. Moreover, as SQUID, it can manufacture by well-known lithography processing etc.

(1-a) L _S and aL _{S obtained} by dividing the self-inductance L _S of the annular electrode in the equivalent circuit shown in FIG. 5C by the left and right parallel connection are Josephson from the junction point with the resonator of the annular electrode. Self-inductance at a portion from the junction element to the ground contact (approximately the portion indicated by the electrode length l _JJ from the Josephson junction element to the ground contact in the strip electrode (see FIG. 5A)) (AL _S ) and the self-inductance ((1-a) L _S ) in the remaining electrode length via the via obtained by subtracting the electrode length l _JJ from the total length lT of the annular electrode.

By adopting such a microstrip type (vertical type) SQUID ring structure, the ring electrode self-inductance (SQUID ring inductance) L _S is divided into aL _S and (1-a) L _S. This results in allocating both microstrip lines having a ratio of length to width that realizes both inductance values while keeping the dimensions constant.
This means that if the annular electrode formed of a microstrip line of a single width, the total length lT annular electrodes, merely a: By internally divides (1-a), and aL _S (1- a) It means that partitioning into L _S can be realized.
Also, the division of this aL _S and (1-a) L _S may be set at a forming position of the ground contact, the formation positions of the ground contact to the annular electrode is clear of the Josephson device and via It is possible to make it close to a distance that ensures separation. The closest distance δ between the ground contact and the Josephson junction element or the via is suppressed by the processing accuracy at the time of element fabrication such as an alignment error of the lithography exposure apparatus, and is typically about 1 μm.
The minimum value of the division parameter a (δ + r _GC + r _JV ) / l _T , which is determined by a value obtained by adding the ground contact radius r _GC and the radius r _{JV of} the via and Josephson junction element to this processing accuracy, is obtained from the division parameter a. The ground contact can be arranged at an arbitrary position of the annular electrode corresponding to the range of the maximum value 1− (δ + r _GC + r _JV ) / l _T.
That is, in the direct coupling method between the resonator and the SQUID shown in FIGS. 5A to 5C, the division parameter is maintained while the shape, structure, and dimensions of the coupling portion are kept constant between a plurality of pixels having different resonance frequencies. It is theoretically predicted that a can be set to a wide range of values of (δ + r _GC + r _JV ) / l _T ≦ a ≦ 1− (δ + r _GC + r _JV ) / l _T. For example, under the typical values of δ≈1 μm, r _GC ≈5 μm, r _JV ≈1 μm, and l _T ≈500 μm, the division parameter a is varied in the range of 0.02 ≦ a ≦ 0.98. Can do.

This selectivity of the division parameter a contributes to making the values of Δf _R uniform for many pixels having different resonance frequencies f _R , and further, the division parameter a is a ground for the annular electrode between the SQUIDs in each pixel. Since only the contact formation position is changed and the shape, structure, and dimensions of the SQUID are obtained in common, the value of Δf _R can be designed with higher accuracy, and the SQUID that is actually manufactured is a known lithography process. Therefore, the error from the design value can be small.
That is, in the frequency multiplex readout apparatus according to the present invention, each SQUID in a plurality of pixels is formed so as to share the input coil, the annular electrode, and the ground electrode, and the formation positions of the ground contacts with respect to the annular electrode are different. To be an important core of technology.
In the frequency multiplex reading apparatus according to the present invention, configurations other than the SQUID can be applied to configurations known in the known frequency multiplex reading apparatus as long as the effects of the present invention are not hindered.

In order to verify the effect of the present invention, a pixel for a microwave multiple readout circuit device having a SQUID having the structure shown in FIGS. 5A to 5C is designed and prototyped. while the overall length l _T of the strip electrodes of a portion to a constant, the strip electrodes one end internally dividing points from (Josephson device JJ vicinity) (ground contact forming position) to the electrode length l _{JJ (FIGS.} 5 (a) changing the reference) was measured each value of aL _S and (1-a) L _S is the self-inductance of the left and right of the strip electrodes. The measurement was performed according to the method described in Non-Patent Document 4.

To electrode length _{l JJ,} showing the respective measured values of aL _S and (1-a) _{L S,} the relationship between the self-inductance _{L S} of the annular electrodes which has been determined from the sum of the two in FIG.
As shown in FIG. 6, with respect to the electrode length _{l JJ} is the distance from the Josephson device JJ to ground contacts GND (LLtoGP), with aL _S and (1-a) _{L S} is varied almost linearly, self It can be seen that the inductance L _S is a substantially constant value. The fact that the self-inductance L _S becomes a substantially constant value is consistent with the theory that the self-inductance L _S depends not on the electrode length l _JJ but on the total length l _T.

Further, the design value and the actual measurement value for the division parameter a were compared, and good matching shown in FIG. 7 was obtained in the range of 0.29 ≦ a ≦ 0.77. FIG. 7 is a diagram showing the dependency of the design parameter (solid line) and the measured value (circle) on the electrode length l _JJ of the division parameter a.
Here, in the design equation which gives the self-inductance L _S, by assuming the thickness of the interlayer insulator, the sum of the magnetic field penetration depth of the upper and lower superconducting electrodes is a strip electrode and the ground electrode and 380 nm, the self-inductance L _S As a result, the design value and the actual measurement value in the relational expression between and the inductance length almost coincide with each other.
Note that the assumed value of 380 nm is likely to make the actually measured value closer to the design value by improving the film thickness controllability of the insulating insulator.
From these results, it is considered that the division parameter a can be made variable in the range of 0.02 ≦ a ≦ 0.98, which is theoretically supported, by changing the electrode length l _JJ in a wider range.

FIG. 8 shows the application to the detection target signal of the frequency multiplex readout apparatus of the present invention. Figure 8 is a graph showing the relationship between the resonance frequency f _R for the SQUID input magnetic flux change between the maximum amount of change Delta] f _R.
The four curves shown in FIG. 8 indicate that in the equations (5) and (6), η _M = 1 at the time of magnetic coupling with respect to the self-inductance (SQUID ring inductance) L _S values of the four SQUID annular electrodes, A combination of the resonance frequency f _R and the maximum change amount Δf _R with respect to the change in the input magnetic flux of the SQUID under the condition satisfying η _D = 1 (hereinafter, both parameters are represented by “η” as a common value) at the time of coupling. Represents.
Also, the three dotted lines parallel to the horizontal axis indicate the readout in the frequency multiplex readout apparatus of the present invention for multiplex readout using a superconducting transition edge detector array optimized for the following measurement object as a detection unit. In the case of using the unit, the relationship between the resonance frequency f _R and the signal band per pixel to be set in the reading unit (assuming that Δf _R is realized because of the optimal condition) is shown.

Application A. Millimeter wave amplitude measurement bolometer (Reference 1 below), gamma-ray photon counting detector (Reference 2 below), etc. (signal band (≈Δf _R ) = about 300 kHz (see Reference 2 below))
Application B. X-ray photon counting detector for astronomical observation (reference 3 below) and basic scientific measurement (reference 4 below) (signal band (≈Δf _R ) = about 3 MHz (see reference 5 below))
Application C. X-ray photon counting detector for elemental analysis for industrial use, such as material development (reference document 3 below) (signal band (≈Δf _R ) = about 25 MHz (see reference document 5 below))
Reference 1: D. Schwan et al .: “Invited Article: Millimeter-wave bolometer array receiver for the Atacama pathfinder experiment Sunyaev-Zel'dovich (APEX-SZ) instrument,” Rev. Sci. Instrum., 82 (2011) 091301 (DOI: 10.1063 / 1.3637460).
Reference 2: BL Zink, et al .: “Array-compatible transition-edge sensor microcalorimeter g-ray detector with 42 eV energy resolution at 103 keV,” Appl. Phys. Lett., 89 (2006) 124101 (DOI: 10.1063 /1.2352712).
Reference 3: K. Mitsuda et al .: “TES X-ray microcalorimeters for X-ray astronomy and material analysis,” Physica C: Superconductivity and its applications 530 (2016) 93 (DOI: 10.1016 / j.physc.2016.03. 018).
Reference 4: A. Giachero, et al ,: “Development of multiplexed rf-SQUID based microcalorimeter detectors for the HOLMS experiment,” 1EOr2C-06, Applied Superconductivity Conference, Denver, USA, 04-09 September, 2016.
A. Nucciotti et al .: “Status of the HOLMS detector development,” Nucl. Instrum. Meth. Phy. Res. A 824 (2016) 182.
Reference 5: KD Irwin, GC Hilton, DA Wollman, JM Martinis, “Thermal-response time of superconducting transition-edge microcalorimeters,” J. Appl. Phys. 83 (1998) 3978 (DOI: 10.1063 / 1.367153).

The region below the curve in FIG. 8 is realized by η ≦ 1, that is, by both coupling methods regardless of the magnetic coupling type or the direct coupling type. The region above the curve is η ≧ 1, which is theoretically possible with the magnetic coupling type, but cannot be realized with the direct coupling type. Being limited to the region of η ≦ 1 seems to be a direct coupling type defect at first glance, but in practice it is not so for many applications.
Formula (5), (6) than Obviously, to increase the resonance frequency _{f R,} Delta] f _R, together with proportional to the square of the resonant frequency _{f R,} is η bond strength between the resonator and SQUID Under a constant value condition, Δf _R is proportional to the self-inductance L _S.
The resonance frequency f _R is set to the operating frequency band of a measuring instrument such as a cryogenic low noise amplifier arranged on the output side of the frequency multiplexing device. By setting the coupling strength η between the resonator and the SQUID to be large and setting the coupling strength η between the resonator and the SQUID to be small in high-frequency signal reading, Δf _R is set to a constant value regardless of f _R.

In FIG. 8, in the region of η ≦ 1, for all of the four types of self-inductance L _S values (5 pH, 10 pH, 20 pH, 40 pH), in the region of 4 GHz or more, which is a typical band of a cryogenic low noise amplifier, Application A. And the application B. It shows that it covers the application of.
_Further, with respect to L S = 40pH, the application C. in _{f R} ≧ 4 GHz With _covering, even for L S = 5 pH, in _{f R} ≧ 10 GHz, the application C. You can see that it covers.
HEMT amplifiers exhibiting extremely low noise temperature (absolute temperature number K) in the microwave band have recently been increased in frequency, and models that cover the 4 GHz to 16 GHz band and the 6 GHz to 20 GHz band (see Reference 6 below). Are on the market. In the future, if the utilization of these broadband (high frequency) HEMT amplifiers is considered, in applications that cannot be supported in the current 4 GHz to 8 GHz band, for example, applications that require a region of 10 GHz or more, self of L _S = 5 pH The application using the SQUID having an inductance (SQUID ring inductance) value C.I. Is also envisaged.
Reference 6: Low Noise Factory: http://www.lownoisefactory.com/

The frequency multiplex reading apparatus of the present invention described above can simultaneously satisfy the following items that have been difficult to realize in the past.
1) The inductance that controls the coupling between the superconducting detector and the SQUID and the inductance that controls the coupling between the resonator and the SQUID can be designed independently. It is possible to easily cope with a use in which the degree of coupling between the detector and the SQUID is different for each pixel, and the deviation from the design value between the pixels can be suppressed uniformly.
2) The design value of each inductance is given as an analytical expression associated with a physical image, and the quantitative feasibility of the design value is verified over a wide range of parameters included in the design expression. Therefore, it is possible to improve the accuracy of realizing the resonance frequency and the device performance.
3) The contribution of the termination inductance of the resonator, which is one factor of deviation from the design value of the resonance frequency, can be ignored. This improves the realization accuracy of the resonant frequency.

The frequency multiplexing readout apparatus of the present invention is expected to be used for a plurality of types of superconducting detector arrays as described below.
・ X-ray element analyzer for electron microscope ・ Spectroscopic microscope for faint light (visible and near infrared) ・ Non-destructive & remote sensing element (isotope) analyzer for nuclear control ・ Secret weapon ・ Remote sensing device for drugs In addition to the superconducting detector, the frequency multiplexing readout device of the present invention can be applied to readout of a large number of superconducting qubits as hardware basic elements for realizing artificial intelligence.

10, 50 Multiplexing chip 11, 51 Detection chip 12, 52 Reading chip 131, 132, 133, 531, 532, 533 Superconducting detector 141, 142, 143, 541, 542, 543 Wiring inductance 151, 152, 153 551,552,553 SQUID input coil 161,162,163,561,562,563 SQUID ring inductance 571,572,573 Josephson junction element 181,182,183,581,582,583 resonator 191,192,193 591, 592, 593 Coupling capacitor 20, 60 Cryogenic cooling device 210, 211, 212, 213, 610, 611, 612, 613 Microwave readout line 22, 62 Cryogenic low noise amplifier 23, 63 Coaxial line 24, 64 micro wave Issue source 25,65 detector bias current source 16 microstrip (vertical) type SQUID ring structure 16a ground electrode 16b interlayer insulating layer 16c strip electrodes

Claims (8)

A SQUID, a resonator, and a capacitor are connected in series in this order, and a readout unit formed as a resonance circuit having a specific resonance frequency, and connected to the SQUID, and changes the resonance frequency of the readout unit according to a detection signal A plurality of pixels each having a resonance frequency different from each other,
A frequency dispersion multiplexed signal obtained by dispersing and multiplexing a signal having the same frequency as the resonance frequency for each pixel on the frequency axis is connected from the input side to the pixel on the capacitor side, and from the output end. A single readout line capable of outputting a modulation signal of the frequency dispersion multiplexed signal before and after the change of the resonance frequency is arranged;
The SQUID is connected to the detection unit, an annular electrode that is electrically connected to the resonator and forms a Josephson junction, and a ground electrode that is disposed to face the annular electrode. The annular electrode and a ground contact that electrically connects the ground electrode, and the annular electrode is configured to connect the resonator and the ground contact in parallel.
Each of the SQUIDs in the plurality of pixels is formed by sharing the input coil, the annular electrode, and the ground electrode, and is formed so that the formation position of the ground contact with respect to the annular electrode is different. A frequency multiplex reading apparatus. The self-inductance of the annular electrode as L _S, resonators constitutes a parallel connection of the annular electrode - dividing parameter a to the self-inductance of the two connections between the ground contacts, respectively aL _S and (1-a) L _S The frequency multiplex readout apparatus according to claim 1, wherein: satisfies the following expression: 0.02 ≦ a ≦ 0.98.   The frequency division multiplex reading apparatus according to claim 2, wherein the division parameter a satisfies the following expression: 0.29≤a≤0.77.   4. The frequency multiplex readout apparatus according to claim 1, wherein the self-inductance of the annular electrode is 5 pH or more.   5. The frequency multiplex readout apparatus according to claim 4, wherein the resonance frequency in each pixel is 4 GHz or more. A SQUID, a resonator, and a capacitor are connected in series in this order, and a readout unit formed as a resonance circuit having a specific resonance frequency, and connected to the SQUID, and changes the resonance frequency of the readout unit according to a detection signal A plurality of pixels having different resonance frequencies;
A frequency dispersion multiplexed signal obtained by dispersing and multiplexing a signal having the same frequency as the resonance frequency for each pixel on the frequency axis is connected from the input side to the pixel on the capacitor side, and from the output end. A single readout line from which a modulation signal of the frequency dispersion multiplexed signal before and after the change of the resonance frequency is output is arranged;
The SQUID is connected to the detection unit, an annular electrode that is electrically connected to the resonator and forms a Josephson junction, and a ground electrode that is disposed to face the annular electrode. A frequency multiplex readout device having a ground contact that electrically connects the annular electrode to the ground electrode, and the annular electrode is configured to connect the resonator and the ground contact in parallel.
Each of the SQUIDs in the plurality of pixels is designed so that the input coil, the annular electrode, and the ground electrode are common, and is designed so that the formation position of the ground contact with respect to the annular electrode is different. Design method for frequency multiplex readout apparatus. The self-inductance of the annular electrode as L _S, resonators constitutes a parallel connection of the annular electrode - dividing parameter a to the self-inductance of the two connections between the ground contacts, respectively aL _S and (1-a) L _S 7. The design method of the frequency multiplex readout apparatus according to claim 6, wherein the formation position of the ground contact with respect to the annular electrode is designed so as to satisfy the following expression: 0.02 ≦ a ≦ 0.98. 8. The design method of a frequency multiplex readout apparatus according to claim 7, wherein the formation position of the ground contact with respect to the annular electrode is designed so that the division parameter a satisfies the following expression: 0.29 ≦ a ≦ 0.77.