Superconducting interferometer

Abstract

Superconducting interferometer (20) comprising two SQUIPTs (100, 200), each comprising a superconducting loops (24a, 24b), placed in parallel between a first terminal (22) arranged to be connected to a ground voltage and two metal tunnel probes (26a, 26b), the interferometer (20) being arranged to be placed into a magnetic flux (Φ) and a first current (I1) and a second current (I2) flowing through a first Josephson junction (28a) and a second Josephson junction (28b) placed into a respective loops (24a, 24b), thus producing a respective voltage drop (V1, V2) at each tunnel probe (26a, 26b), wherein the interferometer (20) is arranged to generate an output voltage (Vout) as a function of said voltage drops (V1, V2), said output voltage (Vout) being a linear function of the magnetic flux (Φ) given a predetermined additional component (Δφ) of the magnetic flux (Φ) introduced into one of the two loops (24a, 24b).

Description

[0001] DESCRIPTION SUPERCONDUCTING INTERFEROMETER

[0002] The present invention relates to a superconducting interferometer.

[0003] Superconducting direct current quantum interference devices (DC- SQUIDs) are widely used as highly sensitive magnetometers and amplifiers. However, their voltage response has typically a poor linearity.

[0004] SQUIDs are the reference standard for measuring variations of magnetic fluxes and all the physical quantities that can be converted into a current and / or into a magnetic field (see for example J. Clarke and A. I. Braginski, “The SQUID Handbook’, edited by J. Clarke and A. I. Braginski, Vol. 1 (Wiley, 2004), A. Barone and G. Paternb, “Physics and Applications of the Josephson Effect’, John Wiley & Sons Inc, New York, (1982), R. Kleiner, D. Koelle, F. Ludwig, and J. Clarke, Proc. IEEE 92,1534-1548 (2004), M. J. Martinez-Perez and D. Koelle, NanoSQUIDs: “Basics & recent advances in Supercond. Nanoscale” (De Gruyter, 2017) Chap. 11 , pp. 339-382, C. Granata and A. Vettoliere, Phys. Rep. 614, 1-69 (2016), and R. L. Fagaly, H.-J. Krause, M. Muck, S. Tanaka, H. Nowak, R. Stolz, J. Kirtley, T. Schurig, J. Beyer, R. McDermott, W. Vodel, R. Geithner and P. Seidel, “Superconducting Quantum Interference (SQUIDs)” in Appl. Supercond. (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2015) pp. 949-1110).

[0005] Furthermore, SQUIDs can be integrated into larger systems and used for signal processing applications (see V. K. Kornev, N. V. Kolotinskiy, and O. A. Mukhanov, Supercond. Sci. Technol. 33, 113001 (2020)).

[0006] The conventional implementation of direct current SQUIDs (DC- SQUIDs) includes a pair of Josephson junctions (JJ) closed on a superconducting ring, whose critical current is modulated by the magnetic flux with a periodicity equal to the quantum of magnetic flux cpO = h / 2e.

[0007] However, DC-SQUIDs are characterized by poor performance in terms of linearity and dynamic range: these problems are generally circumvented by means of a specific optimization which, at the cost of a drastic reduction in bandwidth, is implemented through the introduction of external feedback loops or through the construction of arrays of interferometers. This leads to a reduction of the operating bandwidth, an increase in design complexity and a drastic worsening of integrability of the device.

[0008] At high frequency, on the other hand, open-loop SQUID amplifiers have been shown to be effective for applications up to the gigahertz frequency range, showing however severe limitations due to a significant non-linear distortion (see Prokopenko, S. Shitov, I. Lapitskaya, V. Koshelets, and J. Mygind, IEEE Trans. Applied Supercond. 13, 1042- 1045 (2003), G. Prokopenko, S. Shitov, D. Balashov, P. Dmitriev, V. Koshelets, and J. Mygind, IEEE Trans. Applied Supercond. 11 , 1239- 1242 (2001 ), M. Muck and J. Clarke, Appl. Phys. Lett. 78, 3666-3668 (2001 ), G. Prokopenko, D. Balashov, S. Shitov, V. Koshelets, and J. Mygind, IEEE Trans. Applied Supercond. 9,2902-2905 (1999), G. Prokopenko, S. Shitov, V. Koshelets, D. Balashov, and J. Mygind, IEEE Trans. Applied Supercond. 7, 3496-3499 (1997), M. Huber, P. Neil, R. Benson, D. Burns, A. Corey, C. Flynn, Y. Kitaygorodskaya, O. Massihzadeh, J. Martinis, and G. Hilton, IEEE Trans. Applied Supercond. 11 , 1251-1256 (2001 ), M. Muck and J. Clarke, Appl. Phys. Lett. 78, 3666- 3668 (2001 ), M. Muck and J. Clarke, Rev. Sci. Instrum. 72, 3691-3693 (2001 ), M. Muck, M.-O. Andre, J. Clarke, J. Gail, and C. Heiden, Appl. Phys. Lett. 75, 3545-3547 (1999), M. O. Andre, M. Muck, J. Clarke, J. Gail, and C. Heiden, Appl. Phys. Lett. 75, 698-700 (1999), M. Muck, M. O. Andre, J. Clarke, J. Gail, and C. Heiden, Appl. Phys. Lett. 72, 2885-2887 (1998)).

[0009] A solution to these restrictions has arisen from the introduction of a class of superconducting interferometers based on the parallel of two or more superconducting interferometers. The main types of these interferometers are bi-SQUIDs and D-SQUIDs. In the bi-SQUIDs, a third Josephson junction, closed on a main superconducting ring, is placed in parallel to a DC-SQUID to compensate for its non-linear response. This results in a highly linear voltage response. Although such promising premises, due to the large area of the Josephson junctions and the high value of their inductance, bi-SQUID in Nb showed a non-ideal voltage response and bad linearity performances making it necessary to realize bi-SQUID matrices containing from tens to hundreds of unit cells.

[0010] The D-SQUIDs consist in the parallel of two identical DC-SQUIDs whose voltage drop is measured differentially and in which a constant additional magnetic flux component is added to in one of the two rings. Such devices provide an effective linearization of the voltage response and allow to obtain a high common-mode rejection ratio, however, it does not appear that D-SQUIDs have yet found space in real-world applications.

[0011] There is therefore the need to have an innovative superconducting interferometer which has a simple design, which can be used as amplifier and which can be easily integrated with existing devices in a wide range of applications, thus overcoming the problems of the prior art.

[0012] These and other objects are fully achieved by virtue of a superconducting interferometer having the characteristics defined in independent claim 1 .

[0013] Preferred embodiments of the invention are specified in the dependent claims, whose subject-matter is to be understood as forming integral or integrating part of the present description.

[0014] Further characteristic and advantages of the present invention will become apparent from the following description, provided merely by way of non-limiting example, with reference to the attached drawings, in which:

[0015] - Figure 1 shows a superconducting quantum interference proximity transistor (SQUIPT) according to the prior art;

[0016] - Figure 2 shows a schematic circuit of a double-loop three-terminal superconducting interferometer according to the present invention. - Figure 3 shows the output voltage signal of a double-loop three- terminal superconducting interferometer according to the present invention.

[0017] The proposed superconducting interferometer covers the same applications of the DC-SQUIDs, in terms of operating temperatures and inductive coupling operation, but has the advantage of having an intrinsically highly linear voltage response.

[0018] The present invention relates to a double-loop three-terminal superconducting interferometer which exploits as elementary cell a superconducting quantum interference proximity transistor (SQUIPT) as disclosed for example in F. Giazotto, J. T. Peltonen, M. Meschke, J. P. Pekola, Nature Phys. 6, 254 (2010), F. Giazotto, F. Taddei, Phys. Rev. B 84, 214502 (2011 ), A. Ronzani, C. Altimiras, F. Giazotto, Phys. Rev Appl. 2, 024005 (2014), S. D’Ambrosio, M. Meissner, C. Blanc, A. Ronzani, F. Giazotto, Appl. Phys. Lett. 107, 113110 (2015) and P. Virtanen, A. Ronzani, F. Giazotto, Phys. Rev. Appl. 6, 054002 (2016).

[0019] A known superconducting quantum interference proximity transistor (SQUIPT) 2 is schematically represented in Figure 1 .

[0020] The SQUIPT 2 is an interferometer composed of a superconducting ring or loop 4 closed on a Josephson junction 6 comprising a metal constriction (weak-link) or, alternatively, a constriction based on a superconducting wire. In case of metal constriction, the metal is a non- superconducting metal.

[0021] A tunnel probe 8, made of a superconductor or of a non- superconducting metal, is coupled to the Josephson junction 6 through an insulating barrier layer 10 through which a current can flow thanks to the quantum tunnel effect. The superconducting tunnel probe 8 is preferably placed in the center of the Josephson junction 6.

[0022] On the opposite side of the tunnel probe 8 a current injection electrode 9, such as an electric contact, is connected to the superconducting loop 4, said electric contact being preferably made up of the same material of the superconducting loop 4.

[0023] Although a vast majority of Josephson junctions exploit a conventional superconducting I insulating I superconducting (SIS) scheme, the Josephson effect can also be observed in weak-links based on a superconductor (SS'S), on a semiconductor, on a metal (N) enclosed between a pair of superconducting contacts (SNS) or on 2-dimensional materials such as, e.g., graphene. The SNS junctions support a non- dissipative current thanks to the superconducting proximity effect which originates from the formation of the Andreev bound states in the region of the Josephson junction 6 and which provides the correlations of the Cooper condensate to the electron gas in clean electrical contact with the superconducting contacts.

[0024] One of the most relevant consequences of this mechanism is the modification of the density of the states (DOS) of the metal of the Josephson junction 6, in which a gap opens with an amplitude that is a function of a phase difference cp of a superconducting order parameter at the ends of the junction. The phase difference cp is a function of a magnetic flux into which the superconducting loop 4 is threaded and, for a closed superconducting circuit (i.e., the superconducting loop 4 itself), it holds the quantization law of the magnetic flux , which requires that an accumulated phase cp along a closed superconducting path is equal to an integer multiple of 2TT0O, where 0o is the magnetic flux quantum.

[0025] A circuit 12 comprises a current generator 14 arranged to inject a current into the circuit 12 and an amplifier 16 arranged to record a voltage drop between the tunnel probe 8 and the current injection electrode 9. Such voltage drop is function of the magnetic flux 0 into which the superconducting loop 4 is threaded, following from the mechanism explained below. A current flowing through the Josephson tunnel junction 6 (tunnel current IT) is a function of the density of the states in the weak-link using the conventional equation: where is the energy, / the spatial extension of the tunnel junction, ] / the potential drop across the junction, T the temperature, DOSN and DOSs the densities of states of the weak-link and probe electrode, respectively, and / the Fermi-Dirac distribution.

[0026] It follows that the voltage-current characteristic of the SQUIPT 2 depends on the magnetic flux threading the superconducting loop 4 and that, in other words, by operating the SQUIPT 2 at constant current, a measurement of the potential drop across the SQUIPT 2 provides a measure of the variation of the magnetic flux .

[0027] It is worth to emphasize that the physical mechanism underlying the reading of the magnetic flux 0 is fundamentally different from that of the SQUIDs, in which the dependence of the voltage drop on the magnetic flux 0 derives from a quantum interference between supercurrents circulating in the two arms of the SQUID. In the SQUIPT 2, however, the variation originates from the modification of the density of the states in the weak-link.

[0028] Figure 2 shows a schematic circuit of a double-loop three-terminal superconducting interferometer 20 according to the present invention.

[0029] The double-loop three-terminal superconducting interferometer 20 comprises two SQUIPTs 100, 200, each comprising a superconducting loops or rings 24a, 24b.

[0030] In the following of the description the double-loop three-terminal superconducting interferometer will be referred as “bi-SQUIPT’. The two SQUIPTs 100, 200 are placed in parallel between a first terminal 22, arranged to be connected to a ground voltage and representing a ground contact common to the two superconducting loops or rings 24a, 24b of the bi-SQUIPT 20, and two metal tunnel probes 26a, 26b representing other two terminals of the bi-SQUIPT 20.

[0031] A first current h and a second current I2 (having a same positive sign) are arranged to flow through a first Josephson junction 28a and a second Josephson junction 28b placed into a respective superconducting loop 24a, 24b, respectively, thus producing a respective voltage drop Vi, V2 at each tunnel probe 26a, 26b.

[0032] As in the case of the single SQUIPT 2, the DOS in the regions of the Josephson junctions 28a, 28b is a function of the magnetic flux concatenated to the respective loop 24a, 24b.

[0033] In a perfectly symmetrical bi-SQUIPT 20, the following applies:

[0034] Vout = Vi -V2 =0 for each value of .

[0035] Vout represents an output voltage signal of the SQUIPT 2.

[0036] In the SQUIPT 2 of Figure 2, the output voltage signal Vout is obtained by performing a difference between the two voltage drops Vi, V2 through an amplifier 30. Other known techniques can be applied to obtain such output voltage signal Vout starting from the voltage drops Vi, V2.

[0037] However, by introducing an additional flux component Acp into one of the two rings 24a, 24b, the output voltage signal Vout is again a function of the magnetic flux 0, thus allowing the generation of an output voltage signal. In this configuration, the output voltage signal Vout is determined not only by the parameters that determine the response of each single SQUIPT 100, 200, but also by the amplitude of the additional flux component Acp. The output voltage signal Vout of the bi-SQUIPT 20 operated in the above-described configuration is shown in Fig. 3, which is a graph of the voltage as a function of the ratio cp / cpo where cpo represents the magnetic flux quantum. The output voltage signal Vout is represented by a first curve 500 while two other curves 502, 504 represent the voltage drops Vi, -V2 at each probe 26a, 26b, respectively.

[0038] Alternatively, the first current I1 and the second current I2 have opposite sign and the output voltage signal Vout is calculated as the sum of the voltage drops Vi, V2.

[0039] The most relevant characteristic of the bi-SQUIPT 20 is the linearity of its voltage response for limited variations of the magnetic flux <1>. In particular, with an appropriate choice of operation parameters, it is possible to obtain a spurious free dynamic range (SFDR, defined as the ratio between the amplitudes of the fundamental harmonic and the maximum amplitude spectral component of the output signal obtained in response to a sinusoidal modulation of magnetic flux) of about 60 dB.

[0040] Clearly, the principle of the invention remaining the same, the embodiments and the details of production can be varied considerably from what has been described and illustrated purely by way of non-limiting example, without departing from the scope of protection of the present as defined in the attached claims.

Claims

CLAIMS1. Superconducting interferometer (20) comprising two SQUIPTs (100, 200), each SQLIIPT (100, 200) comprising a superconducting loop (24a, 24b), placed in parallel between a first terminal (22) arranged to be connected to a ground voltage and two metal tunnel probes (26a, 26b), the superconducting interferometer (20) being arranged to be placed into a magnetic flux (0) and a first current (h) and a second current (I2) flowing respectively through a first Josephson junction (28a) and a second Josephson junction (28b) each placed into a respective superconducting loop (24a, 24b), thus producing a respective voltage drop (Vi, V2) at each tunnel probe (26a, 26b), wherein the superconducting interferometer (20) is arranged to generate an output voltage signal (Vout) as a function of said voltage drops (Vi, V2), said output voltage signal (Vout) being a linear function of the magnetic flux ( ) given a predetermined additional flux component (Acp) of the magnetic flux (0) introduced into one of the two superconducting loops (24a, 24b).

2. Superconducting interferometer according to claim 1 , wherein the first current (I1) and the second current (I2) have a same positive sign and the output voltage signal (Vout) is obtained as difference between the respective voltage drops (Vi, V2).

3. Superconducting interferometer according to claim 1 , wherein the first current (h) and the second current (I2) have opposite sign and the output voltage signal (Vout) is obtained as sum between the respective voltage drops (Vi, V2).

4. Superconducting interferometer according to any of the preceding claims, wherein the output voltage signal (Vout) is function of the amplitude of the additional flux component (Acp).

5. Superconducting interferometer according to any of the preceding claims, wherein the output voltage signal (Vout) has a spurious free dynamic range of about 60 dB.

Images