Microwave signal amplifier with isolation

Abstract

The invention relates to a microwave signal amplifier comprising a chain of nonlinear inductive dipole elements, each forming a superconducting asymmetric loop with Josephson junctions, said chain being arranged between an input of the chain for applying a signal to be amplified and an output of the chain at which an output signal is developed, the amplifier further comprising a controllable magnetic flux generation system for circulating a current in said loops, the amplifier further comprising a first microwave pump and a coupling means for connecting said input of the chain to the first pump, the first pump generating, through the first coupling means, a wave in the chain in the direction from the input to the output at a set frequency to transfer power at the frequency of the signal to be amplified.The device further comprises a second microwave pump and a second coupling means for connecting the output of the chain to said second pump. The second pump generates, through the second coupling means, a wave in the chain in the direction from the output to the input, at a frequency different from that of the first pump, and thus attenuates, in said direction from the output to the input, the microwaves propagating at the frequency of the signal to be amplified. Figure for the abbreviation: Fig. 1.

Description

Title of the invention: Microwave signal amplifier with isolation Technical field - technological background

[0001] The invention falls within the field of amplifiers for very weak electromagnetic signals, particularly but not exclusively for quantum computing.

[0002] In particular, the invention relates to the field of circuits transmitting microwaves. It involves designing and operating these circuits, ensuring that the signals of interest are amplified, that no spurious signals are generated, and that ambient noise and noise from the components used are kept away from the amplification chain or filtered within it, both in the direction of amplification and in the opposite direction. This is because it is necessary to avoid exposing the signal source to waves that would reach it through the playback chain—traversed in the opposite direction—and disrupt it. Avoiding the transfer of waves in the opposite direction is referred to as isolating the source, and this constitutes a task in itself.

[0003] The circuits considered may be highly integrated circuits. They are based on components with superconducting properties, called superconducting components, which are placed in cryogenic chambers to benefit from a temperature of at most a few K (a few Kelvins).

[0004] Typically, the superconducting circuit under consideration is an amplification circuit designed to amplify a microwave wave emanating from a qubit or quantum bit, whose state is to be determined. Alternatively, it can be used to read spin magnetic resonance information (in other words, electronic paramagnetic resonance), or to amplify a radio wave of astronomical origin. In all these situations, a very low-power microwave is to be amplified.

[0005] In this context, parametric amplifiers are known, based on a medium with non-linear behavior, which allows for wave mixing, namely the transfer of energy from one frequency to another. The non-linear behavior is modified by regulating the medium in order to obtain the phase-matching phenomenon at the basis of wave mixing.

[0006] In a parametric amplifier performing four-wave mixing (by Kerr effect), two waves are incident: a pump wave with pulsation cop and the wave to be amplified, or signal wave, with pulsation cos. The amplifier transfers energy from the pump wave to the signal wave, which is thus amplified, and also creates a complementary wave with a pulsation coc to keep the energy unchanged.

[0007] Superconducting elements such as Josephson junctions constitute the material support in which the non-linearity that underlies the parametric amplification of the waves passing through them occurs. This is then referred to as a Josephson parametric amplifier (JPA). These JPA amplifiers are effective in the microwave range.

[0008] To obtain significant gains, standing wave amplifiers built around a resonant cavity have been proposed, as in Planat, 2018, Phys. Rev. Applied 11, 034014-2019. The bandwidth is on the order of 45 MHz. It can be multiplied by 10 by impedance matching.

[0009] Traveling wave parametric amplifiers (TWPAs) have also been proposed, for example, the US8878626B2. In these structures, numerous nonlinear elements connected in a chain form a transmission line for signal propagation. Phase matching can be achieved by the presence of resonators on the line, as in Macklin, Science, 2015, 350, 6258, 307, or by modulating the dimension of the line, as in the US8878626B2.

[0010] In US2018 / 0034425A1, the chain-connected elements are assemblies of Josephson junctions arranged in loops. The loops are coupled asymmetrically, each by four poles. Regulation is achieved by adjusting the intensity of a magnetic flux that is arranged to pass through the loops.

[0011] Amplification in TWPAs is achieved through a wave-mixing process resulting from the coupling between propagation modes in the nonlinear medium: the medium is excited with a strong pump wave at the frequency cop, causing the amplification of a weaker signal at the frequency cos, and the creation of a complementary wave at the frequency coc. The bandwidth of a TWPA can be several GHz. In practice, distortion in the dispersion relation is generated by opening a photon gap in the dispersion relation by periodically modulating the transmission line or by creating a band gap by introducing resonant elements into the transmission line. Nevertheless, significant ripples are observed in the gain profile. And the amplification bandwidth is fixed by design.

[0012] Known traveling wave or TWPA microwave amplifiers allow the signal to pass from the amplifier input to the amplifier output, but also the noise present from the output to the input. They are therefore said to be reciprocal.

[0013] Such reciprocal traveling-wave microwave amplifiers, due to their reciprocal nature, require use in conjunction with an additional microwave component called an isolator, which enables the isolation mentioned in the introduction. This component, placed between the source and the microwave, provides the isolation mentioned in the introduction. Low-power microwaves that we wish to amplify, and the traveling wave amplifier (and therefore generally housed in a very low-temperature enclosure) allows us to filter, in the direction from the playback devices and towards the source, the parasitic signals generated by the traveling wave amplifier itself or by components or the environment on the other side of the amplifier, such as, for example, an additional amplifier using HEMT (high electron mobility transistor) technology. However, these microwave isolators have a significant physical footprint (and use magnetic fields: they are components containing permanent magnets, whose magnetic fields can affect qubits and superconducting amplifiers) and cannot be directly integrated onto a chip.It is therefore difficult or inefficient to place such an amplifier in a very low-temperature enclosure, especially one that requires multiplexing numerous signals. Alternatively, or in conjunction with isolators, circulators have been used, but these components also have a significant footprint.

[0014] Lecoq et al., Phys. Rev. Applied 7, 024028 2017 and Lecoq et al., Phys. Rev Lett. 126, 020502, 2020, describe the use of a Josephson junction parametric amplifier with a loop in the frequency space. These authors suggest that this amplifier protects the readout cavity and the qubit on which it is implemented. The system is a standing wave system requiring four microwave sources, and its bandwidth—approximately 10 MHz—is narrow.

[0015] Ranzani et al., Physs Rev. Applied 8, 054035, 2017, presented a transmission line based on Josephson junctions, in groups of five with a total of 740 junctions, inserted between 50 Q transmission line segments. A tone (or wave) from a cop pump modulates the line inductance and enables the frequency conversion of a signal propagating jointly with the pump.

[0016] Frattini et al., Appl. Phys. Lett. 110, 222603, 2017, presented a dipole called the SNAIL, a nonlinear superconducting asymmetric inductive element, consisting of four Josephson junctions distributed across two branches, with three large junctions (tunnel energy Ej) on one branch and one small junction (tunnel energy aEj) on the other branch. This element enables three-wave mixing. Frattini et al., Phys. Rev. Applied 10, 054020, 2018, then disclosed a chain of 20 SNAIL dipole elements (consisting of three large junctions Lj and one small junction Lj / a) in series subjected to an identical magnetic flux for all elements, varied from 0 to 0.5 flux quantums. The authors discuss the optimization of three-wave mixing amplification and the minimization of four-wave mixing.

[0017] Perelshtein et al. 2022, Physical Review Applied 18, 024063 uses SNAILs, numbering 1632, comprising only three Josephson junctions: a small junction, aEJ, on one branch and two large junctions, EJ, on the other branch with the same dipole orientation throughout the entire chain. For a flux quantum of zero, the line impedance is less than 50Q and there is no 3-wave mixing. At a flux quantum of 0.4, these authors observed 3-wave mixing and some 4-wave mixing.

[0018] Ranadive et al., Nature Communications, 2022, 13, 1737, proposed placing the SNAILs in an inverted orientation relative to each other with respect to the field, in an alternating manner, to suppress three-wave mixing processes (the SNAILs are placed with alternating magnetic flux polarity, i.e., they are physically oriented so that the magnetic flux polarization between two adjacent SNAIL cells is reversed, taking advantage of the fact that the second-order nonlinearity factor g3, which quantifies the three-wave mixing phenomenon, is an odd function of the external flux). The system comprises, at 20 mK, 700 cells extending over 6 mm, each cell containing a superconducting loop with three large Josephson junctions (critical current 10) and one small one (low critical current, rIO) in two arms.The ratio between the critical current of the small and large Josephson junctions (r) is chosen such that the amplitudes of the second-order nonlinearity (g3) and the third-order nonlinearity (g4) are anticorrelated. These authors observed a significant amplification for a flux quantum of 0.5, relative to the unit magnetic flux quantum ¢0. They thus present a broadband transmission line with a strong third-order nonlinearity—which therefore allows for four-wave mixing—the g4 factor, which can be adjusted to positive or negative values. The reported phenomenon is called inverted Kerr phase matching. The combined bandwidth is reported to be 3 GHz, with no gaps in the transmission. Summary of the invention

[0019] In addition to being reciprocal, TWPAs suffer from reflections at the junction with transmission lines, and from back-emission.

[0020] The present invention solves the isolation problem, because the proposed principles break the reciprocity of existing amplifiers and therefore do not allow the propagation of signals or noise from the output of the amplifier to its input and therefore to the device under test.

[0021] For this purpose, a microwave signal amplifier is proposed comprising a chain of nonlinear inductive dipole elements, each forming a superconducting asymmetric loop with Josephson junctions, said chain being arranged between an input of the chain for applying a signal to be amplified of known frequency and an output of the chain at which an output signal develops, the amplifier including further a controllable magnetic flux generation system to circulate a current in said loops, the amplifier further comprising a first microwave pump and a coupling means of said input of the chain to the first pump, the first pump generating through the first coupling means a wave in the chain in the direction from the input to the output of a frequency set to transfer power to microwaves propagating in a band around the frequency of the signal to be amplified.

[0022] The amplifier further comprises a second microwave pump and a second coupling means for connecting said output of the chain to said second pump. The second pump generates, through the second coupling means, a wave in the chain in the direction from the output to the input, at a frequency different from that of the first pump, and such as to attenuate, in said direction from the output to the input, the microwaves propagating in a band (generally different from the previously mentioned band for amplification) around the frequency of the signal to be amplified. This attenuation can be achieved by a frequency conversion mechanism.

[0023] The principles thus stated make it possible to obtain a parametric traveling-wave amplifier that is also a powerful reverse-direction isolator, over a bandwidth of several hundred MHz (typically 800 MHz) and which can be tuned over several GHz, with a typical center frequency of 6 GHz. With such a device, bulky and magnetic additional microwave isolators or circulators are avoided: it is possible to have a direct connection without an intermediate isolator between the microwave source to be amplified and the parametric amplifier. The footprint of the components to be installed in the cryogenic chamber is therefore controlled. Amplification can be achieved with a gain of 20 dB while obtaining 30 dB of isolation in the other direction.

[0024] Remarkably, these principles require only two microwave pumps, not three or four as with some prior art devices. This is noteworthy from a scaling perspective.

[0025] With these principles, moreover, the gain profile is regular, without abrupt ripples as in devices in which phase tuning is obtained by modulation of the line width based on simple Josephson junctions, which exhibit impedance mismatches.

[0026] According to advantageous and optional features:

[0027] - the dipole elements of the chain can be identical, and that the flux ma genetic is, relative to the flux quantum of the loops, set to be non-zero modulo 0.5, and preferably between 0.05 and 0.35, and preferably between 0.1 and 0.3.

[0028] - nonlinear asymmetric inductive elements of the chain may include between their two poles a first and a second branch connected in parallel one of the other, the first branch being made up of a network of at least two Josephson junctions in series, the second branch being made up of a single Josephson junction or a second network of Josephson junctions in series, a number of Josephson junctions in the second network being less than a number of Josephson junctions in the first network;

[0029] - the dipole elements and the magnetic flux generation system can be configured in such a way that the asymmetric loops of successive dipole elements along the chain are subjected to a magnetic flux of similar intensity but in the opposite direction from one asymmetric loop to a next loop in the chain, and preferably from one asymmetric loop to the immediately next loop in the chain;

[0030] - the nonlinear asymmetric inductive elements may include between their two poles one branch comprising one or more identical small Josephson junctions and one branch comprising one or more identical large Josephson junctions, a critical current ratio r between small junction and large junction being between 0.01 and 0.25, and preferably between 0.05 and 0.20.

[0031] - nonlinear superconducting asymmetric inductive elements can between their two poles a branch comprising a single Josephson junction called a small junction and a branch comprising three identical Josephson junctions called large junctions, in series.

[0032] - the nonlinear asymmetric inductive elements may include small and large Josephson junctions, small Josephson junctions having an inductance between 1300 and 2500 pH, preferably between 1600 and 2200 pH or large Josephson junctions having an inductance between 100 and 300 pH, preferably between 140 and 260 pH.

[0033] - the magnetic flux generation system may consist of an electromagnet unique, developing a uniform magnetic field across the entire chain.

[0034] - the chain may comprise between 500 and 1300 non-inductive dipole elements linear, and preferably between 600 and 850.

[0035] - the first pump can emit a microwave at a frequency between 5.2 and 10.5 GHz, preferably between 6.0 and 10 GHz.

[0036] - the second pump can emit a microwave at a frequency between 8.4 and 13.5 GHz, preferably between 9.7 and 13.5 GHz.

[0037] - a difference in frequencies between the microwaves emitted by the first pump and the second pump can be between 2 and 6 GHz, the second pump emitting at a higher or lower frequency than the first.

[0038] - the signal to be amplified may be present at a frequency of the order between 5.0 and 7.8 GHz, preferably between 6.0 and 6.4 GHz. Typically, this is a signal derived from a qubit.

[0039] - the first coupling means can be a diplexer applying a high-pass filter to the microwaves of the first pump and directing them to the chain, and applying a low-pass filter to the microwaves of the signal to be amplified and also directing them to the chain.

[0040] - the second coupling means can be a diplexer applying a pass- filter high to the microwaves of the second pump and directing them to the chain, and applying a low-pass filter to the microwaves coming from the chain and directing them to a playback chain. List of figures

[0041] Figures 1 and 2 show a circuit according to an embodiment of the invention.

[0042] Figure 3 is a graph of the numerical values ​​of the attenuation obtained.

[0043] Figure 4 is a view of the evolution of the gain values ​​as a function of the flux and the frequency.

[0044] The [Fig.5] is a view of the numerical gain values ​​in one direction and in the opposite direction. Detailed description

[0045] [Fig.1] As shown in [Fig.1], a chain of nonlinear asymmetric inductive superconducting elements (SNAIL) is inserted at the center of a transmission line section, indicated in the figure as a 50 Q transmission line - an impedance value used in a standard way, for example coaxial, and advantageously differential between two conducting lines.

[0046] The device consists of several hundred dipole cells connected in series, extending over a total length of a few millimeters, each cell containing a superconducting loop with three large Josephson junctions (high critical current 10 or inductance L) and one small one (low critical current rIO with r <l ou inductance L / a avec a<l) dans respectivement un bras et l’autre bras de la boucle.

[0047] The SNAIL chain—typically 700 SNAILs, but other values ​​are possible—is fabricated on a silicon substrate using evaporation and deposition techniques. It connects a conductive line upstream of the chain to a conductive line downstream. The second conductive lines upstream and downstream are directly connected by a conductor. A dielectric layer, for example alumina, placed between the SNAIL chain and the copper line provides the required ground capacitance to match the impedance of the transmission line to a standard 50 Ω environment.

[0048] Within each SNAIL, the junctions are all coplanar, and the SNAILs in the chain are all coplanar. A current-carrying coil of a few centimeters in diameter to polarize the device, with low field asymmetry across the SNAIL loop chain.

[0049] In one embodiment, the SNAILs are constructed with an alternating pattern such that, moving from one end of the chain to the other, for every other SNAIL, the branch with large Josephson junctions is on the left and the branch with small Josephson junctions is on the right, and then for the next SNAIL, the branch with large Josephson junctions is on the right and the branch with small Josephson junctions is on the left. This has already been presented in Ranadive et al., Nature Communications, 2022, 13, 1737. The SNAILs are thus placed with alternating magnetic flux polarity, being physically oriented so as to reverse the magnetic flux polarization for any two adjacent SNAIL cells. In another embodiment, the alternation does not occur at every SNAIL, but at every other SNAIL, or at every N SNAIL, where N is an integer.

[0050] From left to right in the figure, the signal to be amplified with a pulse cos (around 6 GHz, but this is not essential, other values ​​can be used) which is of low intensity, and a pump pulse of controlled intensity, important by its intensity, with a pulse cop not far from cos but for example greater than it, are introduced into the transmission line, which constitutes a wave mixing amplification chain.

[0051] Through a wave mixing phenomenon, which is estimated, without being bound by this explanation, to be based primarily on four-wave mixing—noted in the figure as 4WM for four-wave mixing—the signal at the angular frequency cos φ develops, amplified by wave mixing, at the end of the amplification chain, on the right of the figure. At this end is, of course, the pump signal cop, which has traveled through the chain. There is also at this end one or more complementary or idler waves, not shown because they are not amplified.

[0052] From right to left in the figure, the cosine wave signal, having reached the end of the chain or beyond and having been amplified, is reflected only very partially in the transmission line due to any impedance change, however small. Noise in the frequency range of the cosine wave signal may also be present and travel along the amplification line, from the output and in the direction of the source of the signal to be amplified.

[0053] A pump tone, of controlled intensity, significant in power, of pulsation cop', for example a little further from cos than cop (so cop' > cop) is introduced into the chain by the output, cop' depends on the method of manufacturing the Josephson junctions.

[0054] By a wave mixing phenomenon, which is estimated, without however being bound by this explanation, to be based primarily on a three-wave mixing—noted on the figure 3WM for three wave mixing - the signal at the pulsation cos and the noise at this frequency and at nearby frequencies are attenuated when they travel, in the opposite direction to the intended direction for amplification, through the amplification chain, from output to input.

[0055] At this input end, the pump signal cop', which has traveled through the chain from the output, develops, of course, along with a frequency-shifted wave cos+p', with a much higher frequency. Both are outside the frequencies likely to disturb the source of the signal to be amplified (typically a qubit), because they are far from cos.

[0056] [Fig.2] As shown in [Fig.2], the emissions from the object to be tested DUT (device (under test) 10 and a microwave pump source 20 are, in a 20 mK cryostat chamber, directed respectively towards the two channels of a diplexer 30. The pump signal is processed by a high-pass filter in one channel, and the signal from the object under test by a low-pass filter in the other channel. The two waves are directed by the diplexer 30 via its common port, which then serves as an output to the parametric amplifier 40 according to the invention, also located in the 20 mK cryostat chamber. The signal to be amplified emerges from this port as explained in relation to [Fig. 1]. It is directed to the common gate of a diplexer 50, which is connected via its channel gates to, respectively, a microwave source 60 and an isolator 70 followed by a low-noise amplifier (LNA) 80 located in a higher temperature stage, for example 4 K, which provides the amplified signal to a playback chain 90.The microwaves from the source 60 are filtered by a high-pass filter before being transmitted to the output of the parametric amplifier 40. The waves exiting the parametric amplifier 40 are processed by a low-pass filter before being transferred to the isolator 70. The LNA amplifier 80 produces noise that propagates along the transmission line in the direction of the diplexer 50 but is blocked by the isolator 70. Conversely, no isolator is present on the transmission line between the object under test DUT 10 and the parametric amplifier 40, nor between the parametric amplifier 40 and the diplexer 50. This is a considerable advantage, given the bulk and drawbacks of having such an isolator in a cryostat chamber, typically in close proximity to a qubit or other device under test.The diplexer 30 optionally filters, via the low-pass filter which it interfaces between the parametric amplifier 40 and the object under test DUT 10, the pump tone cop' which has traveled the chain from the output, as well as the frequency-shifted wave cos+p'.

[0057] [Fig.3] Fig.3 shows the isolation obtained in the opposite direction to the amplification, with the system according to the invention. The microwave source 60 provides a pump tone at 10.2 GHz, and this creates a 1 GHz wide isolation band and 20 dB of attenuation gain, which is remarkable.

[0058] [Fig. 4] Figure 4 shows the system gain in either direction, for a pump tone frequency of 10.17 GHz, as a function of the flux applied to the parametric amplifier (x-axis) and as a function of the frequency to be amplified or attenuated (y-axis). The darker the shade, the more the signal is attenuated; the lighter the shade, the more it is amplified. A periodicity of one flux quantum of the parametric amplifier loops is observed along the x-axis. Symmetries of 0 flux quantum, 0.5 flux quantum, and 1 flux quantum are also observed across the x-axis. Attenuation zones are very visible from 0 to 0.5 flux quantum and from 0.5 flux quantum to 1 flux quantum, shifting in frequency as a function of the flux value, with width in frequency and flux decreasing until it becomes zero as we approach 0 and 0.5 flux quantum, values ​​where we no longer observe this attenuation.Thus, as soon as the flux quantum value deviates from 0 and 0.5 flux quantum, it is possible to implement attenuation.

[0059] [Fig. 5] Figure 5 shows the implementation of an embodiment of the invention, with a pump tone for 9 GHz amplification and a pump tone for 12 GHz isolation. For a bandwidth of 250 MHz, an isolation of 20 dB is obtained in the direction to be isolated and a gain of 20 dB in the direction to be amplified.

[0060] Regarding the construction of SNAILs, if we denote ni as the number of Josephson junctions on one arm (the small junctions), and n2 as the number of Josephson junctions on the other arm (the large junctions), then it is preferable that ni be different from n2 (ni n2). In particular, if there is only one small junction, at least two large Josephson junctions are required. Large junctions can be chosen at pH 200 and small junctions at pH 1500.

[0061] The ratio of critical currents between the junctions in each arm (the small and large junctions), as well as the number of junctions in each arm, are parameters for adjusting the presence of attenuation triggered by a pump of a given frequency, and amplification triggered by a pump of another frequency.

Claims

Demands

1. A microwave signal amplifier comprising a chain (40) of nonlinear inductive dipole elements, each forming a superconducting asymmetric loop with Josephson junctions, said chain being arranged between an input of the chain for applying a signal to be amplified of known frequency (10) and an output of the chain at which an output signal is developed, the amplifier further comprising a controllable magnetic flux generation system for circulating a current in said loops, the amplifier further comprising a first microwave pump (20) and a first coupling means (30), the first coupling means coupling said input of the chain to the first pump (20),the first pump (20) generating through the first coupling means (30) a wave in the chain (40) in the direction from input to output and of a frequency set to transfer power to microwaves propagating in a band around the frequency of the signal to be amplified, the amplifier being further characterized in that it further comprises a second microwave pump (60) and a second coupling means (50), the second coupling means (50) coupling said output of the chain to said second pump (60), the second pump (60) generating through the second coupling means (50) a wave in the chain (40) in the direction from output to input, at a frequency different from that of the first pump (20) and so as to attenuate in said direction from output to input microwaves also propagating in a band around the frequency of the signal to be amplified.

2. Microwave signal amplifier according to claim 1, characterized in that the dipole elements of the chain are identical, and that the magnetic flux is, relative to the flux quantum of the loops, set to be non-zero modulo 0.5, and preferably between 0.05 and 0.35, and preferably between 0.1 and 0.

3.

3. Microwave signal amplifier according to claim 1 or claim 2, characterized in that nonlinear asymmetric inductive elements of the chain comprise between their two poles a first and a second branch connected in parallel with each other, the first branch being made up of a network of at least two Josephson junctions in series, the second branch being made up of a single Josephson junction or a second network of junctions Josephson in series, the number of Josephson junctions in the second network being less than the number of Josephson junctions in the first network.

4. Microwave signal amplifier according to any one of claims 1 to 3, characterized in that the dipole elements and the magnetic flux generation system are configured such that the asymmetric loops of successive dipole elements along the chain are subjected to a magnetic flux of similar intensity but opposite in direction from one asymmetric loop to a next loop in the chain, and preferably from one asymmetric loop to the immediately next loop in the chain.

5. Microwave signal amplifier according to any one of claims 1 to 4, characterized in that the asymmetric non-linear inductive elements comprise between their two poles a branch comprising one or more identical small Josephson junctions and a branch comprising one or more identical large Josephson junctions, a critical current ratio r between small junction and large junction being between 0.01 and 0.25, and preferably between 0.05 and 0.

20.

6. Microwave signal amplifier according to any one of claims 1 to 5, characterized in that the non-linear superconducting asymmetric inductive elements comprise between their two poles a branch comprising a single Josephson junction called a small junction and a branch comprising three identical Josephson junctions called large junctions, in series.

7. Microwave signal amplifier according to any one of claims 1 to 6, characterized in that the asymmetric nonlinear inductive elements comprise small and large Josephson junctions, the small Josephson junctions having an inductance between 1300 and 2500 pH, preferably between 1600 and 2200 pH or the large Josephson junctions having an inductance between 100 and 300 pH, preferably between 140 and 260 pH.

8. Microwave signal amplifier according to any one of claims 1 to 7, characterized in that the magnetic flux generation system consists of a single electromagnet developing a uniform magnetic field over the entire chain.

9. A microwave signal amplifier according to any one of claims 1 to 8, characterized in that the chain comprises between 500 and 1300 nonlinear inductive dipole elements, and preferably between 600 and 850.

10. Microwave signal amplifier according to any one of claims 1 to 9, characterized in that the first pump emits a microwave at a frequency between 5.2 and 10.5 GHz, preferably between 6.0 and 10 GHz.

11. Microwave signal amplifier according to any one of claims 1 to 10, characterized in that the second pump emits a microwave at a frequency between 8.4 and 13.5 GHz, preferably between 9.7 and 13.5 GHz.

12. Microwave signal amplifier according to any one of claims 1 to 11, characterized in that the difference in frequencies between the microwaves emitted by the first pump and the second pump is between 2 and 6 GHz, the second pump emitting at a higher frequency than the first.

13. Microwave signal amplifier according to any one of claims 1 to 12, characterized in that the signal to be amplified is present at a frequency of the order of between 5.0 and 7.8 GHz, preferably between 6.0 and 6.4 GHz.

14. Microwave signal amplifier according to any one of claims 1 to 13, characterized in that the first coupling means is a diplexer applying a high-pass filter to the microwaves of the first pump and directing them to the chain, and applying a low-pass filter to the microwaves of the signal to be amplified and also directing them to the chain.

15. Microwave signal amplifier according to any one of claims 1 to 14, characterized in that the second coupling means is a diplexer applying a high-pass filter to the microwaves from the second pump and directing them to the chain, and applying a low-pass filter to the microwaves from the chain and directing them to a playback chain.

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