Fully superconducting Josephson bolometers for gigahertz astronomy

The origin and the evolution of the universe are concealed in the evanescent diffuse extragalactic background radiation (DEBRA). To reveal these signals, the development of innovative ultra-sensitive bolometers operating in the gigahertz band is required. Here, we review the design and experimental realization of two bias-current-tunable sensors based on one dimensional fully superconducting Josephson junctions: the nanoscale transition edge sensor (nano-TES) and the Josephson escape sensor (JES). In particular, we cover the theoretical basis of the sensors operation, the device fabrication, their experimental electronic and thermal characterization, and the deduced detection performance. Indeed, the nano-TES promises a state-of-the-art noise equivalent power (NEP) of about $5 \times 10^{-20}$ W$/\sqrt{\text{Hz}}$, while the JES is expected to show an unprecedented NEP of the order of $10^{-25}$ W$/\sqrt{\text{Hz}}$. Therefore, the nano-TES and JES are strong candidates to push radio astronomy to the next level.

The origin and the evolution of the universe are concealed in the evanescent diffuse extragalactic background radiation (DEBRA). To reveal these signals, the development of innovative ultrasensitive bolometers operating in the gigahertz band is required. Here, we review the design and experimental realization of two bias-current-tunable sensors based on one dimensional fully superconducting Josephson junctions: the nanoscale transition edge sensor (nano-TES) and the Josephson escape sensor (JES). In particular, we cover the theoretical basis of the sensors operation, the device fabrication, their experimental electronic and thermal characterization, and the deduced detection performance. Indeed, the nano-TES promises a state-of-the-art noise equivalent power (NEP) of about 5 × 10 −20 W/ √ Hz, while the JES is expected to show an unprecedented NEP of the order of 10 −25 W/ √ Hz. Therefore, the nano-TES and JES are strong candidates to push radio astronomy to the next level.

I. INTRODUCTION
The universe is permeated by radiation extending over almost all the electromagnetic spectrum, the so-called diffuse extragalactic background radiation (DEBRA) [1]. Particular interest is posed on the portion of the DEBRA covering energies lower than 1 eV, since this range contains information regarding the formation and the evolution of the universe. Indeed, the temperature and the polarization of the cosmic microwave background (CMB) [2][3][4], ranging from 300 MHz to 630 GHz, reveal the early stages of the universe and represent the smoking gun proof of the Big Bang. Furthermore, the emission from stars/galaxies formation [5] and the active galactic nuclei (AGNs) [6] gives rise to the cosmic infrared background (CIB) [7,8], that shows 10% of the power of the CMB. As a consequence, sensitive gigahertz photon detection is fundamental to shed light on different radioastronomy phenomena [9], such as atomic vibrations in galaxy clusters [10], hydrogen atom emission in the galaxy clusters [11], radio burst sources [12], comets [13], gigahertz-peaked spectrum radio sources [14], and supermassive black holes [15].
State-of-the-art GHz/THz detectors for astronomy are the transition edge sensors (TESs) [16][17][18] and the kinetic inductance detectors (KIDs) [19], since they are extremely sensitive and robust. Indeed, TES-based bolometers reached a noise equivalent power (NEP) of the order of 10 −19 W/ √ Hz [20], while KIDs showed a NEP of about 10 −18 W/ √ Hz [21]. To push detection technology towards lower values of NEP, it is necessary a strong reduction of the thermal exchange of the sensor active region, i.e., the portion of the device absorbing the incident radiation, with all the other thermal sinks. To this end, miniaturized superconducting sensors have been realized [22]. Furthermore, several hybrid nano-structures exploiting the Josephson effect [23] have been proposed and realized [24,25]. In particular, cold electron bolometers (CEBs) in normal metal/superconductor tunnel systems were experimentally demonstrated to show a N EP ∼ 3 × 10 −18 W/ √ Hz [26], while gate-tunable CEBs can be realized by substituting the metal with silicon [27] or graphene [28]. Furthermore, detectors based on proximity effect demonstrated a NEP of the order of 10 −20 W/ √ Hz in superconductor/normal metal/superconductor (SNS) junctions [29,30] and 7 × 10 −19 W/ √ Hz in superconductor/graphene/superconductor (SGS) junctions [31]. Finally, an innovative sensor based on the exotic temperature-to-phase conversion (TPC) in a superconducting ring is expected to provide a N EP ∼ 10 −23 W/ √ Hz [32].
Despite the high sensitivity, all these innovative bolometers do not fulfill the strict requirements for being employed in ultra-sensitive space telescopes. In fact, materials, fabrication procedures and structures need to be extensively tested to survive the extreme stress (vibrations, acceleration, radiation, etc.) typical of space missions. Instead, we review recent developments of superconducting radiation sensor based on a structure that shares many technological aspects with the already employed TESs and KIDs. Indeed, the nanoscale transition edge sensor (nano-TES) [36] and the Josephson escape sensor (JES) [37] are envisioned by downsizing the active region of a TES to the nano-scale. In particular, they employ a one dimensional fully superconducting Josephson junction (1D-JJ) as radiation absorber. In full analogy with the widespread TES, these sensors take advantage of the stark variation of the resistance of a superconductor while transitioning to the normal-state. Furthermore, the resistance versus temperature characteristics of a 1D-JJ can be tuned by varying the bias current. As a consequence, in principle the sensitivity of the nano-TES and the JES can be in situ controlled. In addition, the nano-TES showed a thermal fluctuation limited NEP of about 5 × 10 −20 W/ √ Hz [36], while the JES is expected to provide a NEP of the order of 10 −25 W/ √ Hz [37]. In addition to gigahertz astronomy, these sensors could be employed in medical imaging [33], industrial quality controls [34] and security applications [35].
This review is organized as follows. Section II covers the theoretical bases of the nano-TES and JES highlighting their structure and operating principle. Section III introduces the thermal and electrical model employed to calculate the performance of the sensors, such as noise equivalent power and response time. Section IV describes the experimental realization of the nano-TES and the JES. In particular, the nano-fabrication, the thermal, spectral and electronic transport measurements are shown. Section V reports the sensing performance deduced from the experimental data. Finally, Sec. VI resumes the results and opens to new applications for the nano-TES and the JES detectors.

II. SENSORS STRUCTURE AND OPERATING PRINCIPLE
The sensors presented in this Review, i.e., the nano-TES [36] and the JES [37], can be described as a 1D fully superconducting Josephson junction (1D-JJ). A 1D-JJ is realized in the form of a superconducting nanowire (A), with both lateral dimensions [thickness (t) and width (w)] smaller than its coherence length (ξ A ) and the London penetration depth of the magnetic field (λ L,A ), separating two superconducting lateral banks (B), as schematically shown in Fig. 1(a). The 1D nature of the JJ provides a twofold advantage. On the one hand, λ L,A w, t ensures homogeneous supercurrent density in the JJ and uniform penetration of A by an out-of-plane magnetic field. On the other hand, ξ A > w, t leads to uniform superconducting properties and constant superconducting wave function along Properties of a 1D fully superconducting Josephson junction. (a) Schematic representation of a 1D fully superconducting JJ, where a superconducting nanowrire A is contacted by two superconducting leads B obeying to ∆A ∆B (with ∆A and ∆B the superconducting energy gap of the nanowire and the leads, respectively). (b) Energy of the washboard potential normalized with respect to the zero-temperature Josephson energy as a function of the phase difference across a JJ for different values of bias current. The energy barrier (δU ) for the escape of the phase particle from the WP is indicated. (c) Energy barrier normalized with respect to the zero-temperature Josephson energy (δU/EJ,0) calculated as a function of critical current (top) and bias current (bottom). the nanowire cross section.
The electronic transport properties of a 1D-JJ can be described through the overdamped resistively shunted junction (RSJ) model [38], where the dependence of the stochastic phase difference [ϕ(t)] over the 1D-JJ on the bias current (I) is given by where e is the electron charge, R N is the normal-state resistance, is the reduced Planck constant and I C is the critical current. The thermal noise generated by the shunt resistor (R N ) is given by δI th (t)δI th (t ) = K B T R N δ(t − t ), where k B is the Boltzmann constant and T is the temperature. Within the RSJ model, the transition of the junction to the resistive state is attributed to 2π phase-slip events [38,39]. The phase slips can be viewed as the movements of a phase particle in a tilted washboard potential model (WP) under the action of friction forces. In particular, the WP takes the form For a 1D-JJ composed of a superconducting nanowire, the escape energy barrier can be written as [40] δU (I, Indeed, the effective WP profile strongly depends on both bias current (I) through the junction and Josephson energy E J = Φ 0 I C /2π [40], where Φ 0 2.067×10 −15 Wb is the flux quantum. In particular, by rising I the phase-slip energy barrier (δU ) lowers, similarly to the result of decreasing E J , and the WP tilts proportionally to the value of the bias current, as shown in Fig. 1(b). Furthermore, Eq. 3 shows that δU is suppressed faster by rising I than by suppressing I C [see Fig. 1(c)]. As a consequence, the transition to the dissipative state can be more efficiently induced by rising the bias current than by decreasing the Josephson energy. In addition, we note that E J (and thus I C ) can be suppressed by applying an out-of-plane magnetic field. Since a magnetic field can be problematic for several applications and broadens the superconductor-to-dissipative transition [41], we will focus on the impact of I on the transport properties of the 1D-JJ. Since the nanowire normal-state resistance is very low, the 1D-JJ can be efficiently described by the RSJ model in the overdamped limit. Within this model, the resulting voltage (V ) versus temperature (T ) characteristics of a 1D-JJ for different values of I and E J is given by [42] V (I, E J , T ) = R N   I − I C,0 Im where I C,0 is the zero-temperature critical current and I µ (x) is the modified Bessel function with imaginary argument Thus, the current dependent resistance versus temperature characteristics [R(T )] of the 1D-JJ can be evaluated by calculating the current derivative of the voltage drop From each R(T ) curve we can define two temperatures related to the superconductor-to-normal-state transition: the effective critical temperature (T C ) and the escape temperature (T e ), as shown in Fig. 1(e). In particular, T C is the temperature corresponding to half of the normal-state resistance [R(T C ) = R N /2], while T e (I) is the maximum value of temperature providing a zero resistance of the nanowire [R(T e ) = 0]. These two temperatures define two distinct operating conditions for the 1D-JJ: the nano-TES operates at T C , i.e., at the middle of the superconductorto-normal-state transition, and the JES operates at T e , i.e., deeply in the superconducting state. Indeed, T C and T e strongly depend on the bias current, as shown in Fig. 1(f). As a consequence, both nano-TES and JES are in situ current-tunable radiation sensors.

III. THEORY OF NANO-TES AND JES BOLOMETERS
The behavior of superconducting bolometers strongly depends on the predominant heat exchange mechanisms occurring in their active region. The thermal model describing all the main thermal exchange mechanisms occurring in A is the same for the nano-TES and the JES, as schematically shown in Fig. 2(a). Here, P in is the power associated with the absorption of the external radiation, while P A-B represents the energy out-diffusion for the active region to the lateral leads kept at the bath temperature (T bath ). We notice that depending on the device operation, nano-TES or JES, the bath temperature is set to T C (I) or T e (I), respectively. The lateral electrodes can act as energy filters (P A-B → 0), the so-called Andreev mirrors [43], when their critical temperature (T C,B ) is much higher than the zerocurrent critical and escape temperatures of the active region [T C,B T C (0), T e (0)], that are the maximum operating temperatures. Therefore, heat exchange with lattice phonons (P e-ph ) is the predominant thermal relaxation channel in the active region. In the TES operation, A is always kept almost in the normal-state thus yielding an electron-phonon coupling [17,44] where V A is the nanowire volume, and Σ A is its electron-phonon coupling constant. On the contrary, since the JES operates at T e (I), the latter can be substantially smaller than T C depending on I [see Fig. 1 where ∆ A is the superconducting energy gap in A, thus showing an exponential suppression with respect to the normal-state at very low temperatures. As a consequence, the performance of a JES radiation detector are expected to be considerably better than that of a nano-TES operating at the same temperature. The transition to the normal-state driven by radiation absorption generates Joule heating in A, thus rising T A and creating thermal instability. For TES bolometers, this issue is solved by a biasing circuit implementing the so-called negative electrothermal feedback (NETF). Similarly, the nano-TES and the JES could be biased with the circuitry shown in Fig 2(b). The shunt resistor (R S ) guarantees that the current (I) flowing through the sensor (R) is limited when the active region undergoes the superconducting to normal-state transition. In TES operation, the sensor is biased at T C (R = R N /2) so that the condition for the shunting resistor reads R S = IR N /[2(I Bias −I)], where I Bias is the current provided by the generator. In JES-mode, the device has to be biased at T e (I),i.e., at R = 0, and the role of R S is to limit the current flow through the sensing element below the retrapping current (I R ) [46], that is the switching current at which a diffusive superconducting wire switches into the dissipationless state from the normal-state during a current down-sweep. This happens for R S ≤ R N I R /I and brings A quickly back to the superconducting state after radiation absorption. Finally, in both configurations the variations of the current circulating in the inductor (L), as a consequence of radiation absorption, can be measured via a conventional SQUID amplifier.
In the next sections, we will show all the relations describing the principal figures of merit for the nano-TES and the JES bolometers.

A. Nano-TES bolometer performance
The noise equivalent power (NEP) represents the minimum power that can be detected above the noise level. Thus, the NEP is the most important figure of merit for a nano-TES bolometer. Taking into account the equivalent circuit shown in Fig. 2, the total N EP of the nano-TES is given by the [47,48] where N EP T F N,nano-T ES is associated with the thermal fluctuations, N EP Jo is due to the Johnson noise, while N EP R S arises from the shunt resistor. For a nano-TES operating at T A T C , the thermal fluctuations limited N EP takes the form [49] where Υ = n/(2n + 1) accounts for the temperature gradient between the quasiparticles in A and all the other thermal sinks (with n = 5 for pure and n = 4, 6 for dirty metals), and G th,nano-T ES is the thermal conductance of all heat losses.
Since T C T C,B , the main thermalization channel for A is the electron-phonon coupling (P e-ph ). Furthermore, the 1D-JJ is always kept in the partially dissipative state (at R N /2) for the nano-TES operation. So, the electron-phonon coupling of a normal-metal diffusive thin film (P e-ph,n , see Eq. 6) is employed [44]. The resulting thermal conductance for a nano-TES (G th,nano-T ES ) can be calculated through the temperature derivative of the electron-phonon energy relaxation [17] The Johnson noise is originated by the electronic transport through A when the nano-TES is in the normal-state and takes the form [49] where V is the voltage drop, f is the signal bandwidth, α = dR dT T R is the electrothermal parameter accounting for the sharpness of the phase transition from the superconducting to the normal-state [17], and τ ef f is the effective circuit time constant (see Eq. 15). Finally, the charge fluctuations through R S provide a contribution [49] where L 0 = α/n is the loop gain. Since the shunting resistor needs to satisfy R sh R A , the contribution of N EP sh is usually negligible compared to Johnson noise. Indeed, in superconducting bolometers, the thermal fluctuations contribution dominates over N EP Jo and N EP R S . Thus, we can consider N EP tot = N EP T F N,nano-T ES .
The time response of the detector can be calculated by solving the time dependent energy balance equation that takes into account all the exchange mechanisms after radiation absorption [44]. In particular, the re-thermalization (to T bath ) of the quasiparticles in A has an exponential dependence on time. The associated time constant (τ nano-T ES ) can be calculated as the ratio between the thermal capacitance and the thermal conductance of A where C e,nano-T ES is the electron heat capacitance. The latter is written where γ A is the Sommerfeld coefficient of the active region. We note that τ nano-T ES is the intrinsic recovery time of A. This term does not take into account the Joule heating due to the current flowing through the sensor in the dissipative state. By considering the circuitry implementing the NETF [see Fig. 2(b)], the pulse recovery time becomes [17] For τ ef f << τ nano-T ES , i.e., when the pulse recovery time is much shorter than the intrinsic time constant of A, the overheating into the active region is decreased, thus compensating for the initial temperature variation and avoiding the dissipation through the substrate.

B. JES bolometer performance
The JES operates at T e (I), that is fully in the superconducting state. Since the current injection does not change the energy gap of the active region (∆ A ∼ const), only the effective critical temperature of A changes with I, while the intrinsic values of critical temperature (T i C ) is unaffected. As a consequence, all figures of merit of a JES are calculated deeply in the superconducting state, thus ensuring high sensitivity.
In full analogy with the nano-TES, the thermal fluctuations are the limiting factor for the sensitivity of a JES bolometer. The related contribution to the NEP reads where G th,JES is the thermal conductance in the superconducting state. The latter takes the form [50] where the first term refers to the electron-phonon scattering, while the second term stems from the recombination processes. In Eq. 17, ς(5) is the Riemann zeta function,∆ = ∆ A /k B T is the normalized energy gap of A,h = h/k B T represents exchange field (0 in this case), f 1 (x) = 3 n=0 C n x n with C 0 ≈ 440, C 1 ≈ 500, C 2 ≈ 1400, C 3 ≈ 4700, and f 2 (x) = 2 n=0 B n x n with B 0 = 64, B 1 = 144, B 2 = 258. We note that the thermal conductance for a JES is exponentially damped compared to the nano-TES, due to the operation in the superconducting state. Thus, we expect the JES to be extremely more sensitive than the nano-TES, that is N EP T F N,JES N EP T F N,nano-T ES . The JES speed in given by the relaxation half-time (τ 1/2 ), which reads [32] where τ JES is the JES intrinsic thermal time constant. The latter is calculated by substituting the JES parameters in Eq. 13, thus considering C e,JES and G th,JES in deep superconducting operation. The electron heat capacitance needs to be calculated at the current-dependent escape temperature [T e (I)], thus in the superconducting state, and takes the form where Θ Damp is the low temperature exponential suppression with respect to the normal metal value. The suppression is written [51] Θ Finally, the electronic heat capacitance is given by

IV. EXPERIMENTAL REALIZATION OF JES AND NANO-TES
The nano-TES and JES are experimentally realized and tested thanks to two different device architectures: an auxiliary device and the proper nano-sensor. On the one hand, the auxiliary device was employed to determine the superconducting energy gap and the thermal properties of the material composing the one-dimensional active region. On the other hand, the measurements performed on the proper nanosensor provided dependence of the R(T ) characteristics on the bias current.
Both devices were fabricated during the same evaporation process, ensuring the homogeneity of the properties of A. In particular, they were fabricated by electron-beam lithography (EBL) and 3-angles shadow mask evaporation onto a silicon wafer covered with 300 nm of thermally grown SiO 2 . The evaporation was performed in an ultra-high vacuum electron-beam evaporator with a base pressure of about 10 −11 Torr. The first step was the evaporation of a 13-nm-thick Al layer at an angle of -40 • and then oxidized by exposition to 200 mTorr of O 2 for 5 minutes to obtain the tunnel probes of the auxiliary device. In a second step, the Al/Cu bilayer (t Al = 10.5 nm and t Cu = 15 nm) forming the active region is evaporated at an angle of 0 • . Finally, a second 40-nm-thick Al film was evaporated at an angle of +40 • to obtain the lateral electrodes.

A. Density of states and thermal properties of the active region
The false-color scanning electron microscope (SEM) picture of a typical auxiliary device is shown in Fig. 3(a). The 1D-JJ is formed by 1.5 µm-long (l), 100 nm-wide (w) and 25 nm-thick (t) Al/Cu bilayer nanowire-like active region (purple) sandwiched between the two Al electrodes (blue). To characterize both the energy gap and the thermal properties of A, the device is equipped with two additional Al tunnel probes (green). Figure 3(a) schematically represents the experimental set up employed to carry out the spectral characterization of the active region in a filtered He 3 -He 4 dry dilution refrigerator. The IV tunnel characteristics of A are performed by applying a voltage (V ) and measuring the current (I) flowing between one lateral electrode and a tunnel probe.
For T < 0.4T C , the energy gap of a superconductor follows ∆(T ) = ∆ 0 , where ∆ 0 is its zero-temperature value [38]. Typically, aluminum thin films show a T C ≥ 1.2 K, that is the bulk Al critical temperature [52]. Therefore, the superconducting gap of the superconducting tunnel probes is temperature independent up to at least 500 mK. On the contrary, superconductivity in A is expected to be strongly suppressed due to inverse proximity effect [38]. Therefore, this structure allows to determine the zero-temperature superconducting energy gap of the active region (∆ 0,A ). The IV characteristics were measured at the base temperature (T = 20 mK) and well above the expected critical temperature of A, as shown in Fig. 3(b). At the base temperature, the JJ switches to the normal-state when the voltage bias reaches V = ±(∆ A,0 + ∆ P,0 )/e [44], where ∆ 0,P is the zero-temperature gap the Al probe. Instead, at T bath = 250 mK the transition occurs at V = ±∆ P,0 /e, since A is in the normal-state. In addition, the tunnel resistance of the JJ takes the values R I 12 kΩ. The difference between the curves recorded at 20 mK and and 250 mK is highlighted by Fig. 3(c). The measurement at T bath = 250 mK (purple) shows a value of the zero-temperature energy gap of the Al probe ∆ 0,P 200 µeV, indicating a critical temperature T C,P = ∆ P,0 /(1.764k B ) 1.3 K. Furthermore, the difference between the results obtained at 20 mK and 250 mK leads to ∆ A,0 23 µeV pointing towards a critical temperature T C,A 150 mK.
We now focus on the heat exchange properties of the active region. The schematic representation of the experimental setup employed is shown in Fig. 3(d). The left Josephson junction operates as a thermometer: it was current-biased at I t and the resulting voltage drop (V t ) reflects the variations of the electronic temperature in A [44]. Instead, the right JJ was voltage-biased at V h > ∆ A,0 + ∆ P,0 )/e to work as heater [44].
The geometry of the device guarantees that the electronic temperature of the lateral superconducting electrodes and the tunnel probes are equal to the phonon bath temperature (T bath ). By contrast, the quasiparticles temperature of the active region is the fundamental thermal variable in the experiment. Since T A T C,B for all the measurements, the lateral banks serve as perfect Andreev mirrors (P A-B = 0). Therefore, the power injected by the heater (P h ) relaxes only via electron-phonon interaction P e−ph and out-diffuses through the tunnel junction acting as thermometer (P t ). The resulting quasi-equilibrium thermal exchange model is as schematically represented in Fig. 3(e). Since the active region is in the normal-state, the power exchanged via electron-phonon interaction is described by Eq. 6, while the power flowing through the thermometer reads [44] where R t = 11.6 kΩ is the normal-state tunnel resistance of the thermometer, and f 0 (E, T A,bath ) = [1 + exp (E/k B T A,bath )] is the Fermi-Dirac distribution of the active region and the superconducting probe, respectively. Above, the normalized density of states of the superconducting probe takes the form [44]: Figure 3(f) shows the dependence of electronic temperature in A on the injected power (P h ) acquired at T bath = 150 mK for five different sets of measurements. The value of T A rises monotonically from T bath = 150 mK to about 270 mK by increasing P h up to ∼ 7 fW.
By solving Eq. 22, it is possible to fit the experimental values of T A as a function of P h . This simple model is in good agreement with the data, as shown by the black line in Fig. 3(f). The extracted value of the electron-phonon coupling constant of the Al/Cu bilayer is Σ A 1.3 × 10 9 W/m 3 K 5 in good agreement with the average of Σ Cu = 2.0 × 10 9 W/m 3 K 5 and Σ Al = 0.2 × 10 9 W/m 3 K 5 [44], weighted with the volumes of the copper and the aluminum layer forming the active region: Since the fit provides P e-ph P t , the presence of the thermometer tunnel barrier has a negligible impact on the determination of Σ A . Furthermore, the electronic temperature in A varies for distances of the order of the electron-phonon coherence length l e−ph = D A τ e−ph 180 µm [44], where D A = (t Al D Al + t Cu D Cu )/(t Al + t Cu ) 5.6×10 −3 m 2 /s is the diffusion constant of the active region and τ e−ph = C/G 6 µs is the electron-phonon scattering time. Since the length of the active region is l = 1.5 µm l e−ph , the electronic temperature in A can be assumed homogeneous.

B. Bias current control of resistance versus temperature characteristics
The realization of a typical 1D-JJ is shown by the scanning electron micrograph displayed in Fig. 4(a). The 1D superconducting active region consists of the same Al/Cu bilayer presented in Sec. IV A, that is t Al = 10.5 nm and t Cu = 15 nm. The width of A is w = 100 nm, while its length is l = 1.5 µm. Finally, the lateral banks are composed of a 40-nm-thick aluminum film. The zero-temperature critical current of this 1D-JJ is I C,0 575 nA.
The resistance R vs temperature characteristics and of the Al banks were obtained by conventional four-wire lowfrequency lock-in technique at 13.33 Hz in a filtered He 3 -He 4 dry dilution refrigerator. The current was generated by applying a voltage (V ac ) to a load resistor (R L ) of impedance larger than the device resistance (R L = 100 kΩ R), as shown in Fig. 4(a). In particular, the device showed a normal state resistance R N 77 Ω.
To prove that the Al/Cu bilayer can be considered a uniform superconductor, we need to demonstrate that it respects the Cooper limit [53,54], that is the contact resistance between the two layers is negligible and the thickness of each component is lower than its coherence length. Since its large surface area, the Al/Cu interface can be considered fully transparent, i.e., its resistance is negligibly small with comparison to R N . Furthermore, the superconducting Al film fulfils ξ Al = D Al /∆ Al 80 nm t Al = 10.5 nm, where D Al = 2.25 × 10 −3 m 2 s −1 is its diffusion constant of Al and ∆ Al 200 µeV is its superconducting energy gap. Concurrently, the normal copper film respects ξ Cu = D Cu /(2πk B T ) 255 nm t Cu = 15 nm, with D Cu = 8 × 10 −3 m 2 s −1 the copper diffusion constant. We note that the temperature is chosen to the worst case scenario T = 150 mK. As a consequence, the Al/Cu bilayer lies within the Cooper limit ad can be considered a single superconducting material. We now focus on the 1D nature of the fully superconducting nanowire Josephson junction. The superconducting coherence length in A is given by 220 nm, where N Al = 2.15 × 10 47 J −1 m −3 and N Cu = 1.56 × 10 47 J −1 m −3 are the density of states at the Fermi level of Al and Cu, respectively. Therefore, the bilayer shows a constant pairing potential along the out-of-plane axis, since the Cooper pairs coherence length is much larger than its thickness (ξ a t = t Al + t Cu = 25.5 nm). Furthermore, ξ A w = 100 nm. So, the active region is one dimensional with respect to the superconducting coherence length. In addition, the London penetration depth for the magnetic field of A can be calculated from λ L,A = ( wt A R N )/(πµ 0 l∆ A,0 ) 970 nm, where µ 0 is the magnetic permeability of vacuum. Since λ L,A t, w, A is 1D with respect to the London penetration depth, too.
The magnetic field generated at the wire surface by the maximum possible bias current is B I,max = µ 0 I C,0 /(2πt) 5 µT. This value is orders of magnitude lower than the critical magnetic field of A. So, the self generated magnetic field does not affect the properties of the device. Furthermore, the superconducting properties of the Al/Cu bilayer dominate the behavior of A. In fact, the energy gap expected for a non-superconducting Al/Cu bilayer as originated by lateral proximity effect is E g 3 D A /l 2 5 µeV [55]. This value is about 1/4 of the measured ∆ A (see Sec. IV A).
The device in Fig.4(a) fulfills all the requirements of a 1D-JJ (see Sec. II). Therefore, it can be used to investigate the impact of I on the R(T ) characteristics. To this end, excitation currents with amplitude ranging from 15 nA to 370 nA were imposed through the device. Figure 4(b), shows that the R(T ) characteristics monotonically move towards low temperatures by rising the current from ∼ 3% and ∼ 65% of I C,0 . Furthermore, the resistance versus temperature characteristics preserve the same shape up to the largest bias currents.
Despite the R(T ) curves shift towards low temperatures by increasing the bias current, the active region electronic temperature (T A ) at the middle of the superconducting-to-dissipative-state transition under current injection does not coincide with T bath . In fact, Joule dissipation (for R = 0) causes the quasiparticles overheating in A yielding T A > T bath . Therefore, the operation of the sensor as a nano-TES is not possible without the additional shunting resistor [see Fig. 2(b)]. By contrast, the operation as a JES (at R = 0) guarantees that the electronic temperature of A coincides with the bath temperature.
From the R vs T curves we can specify the current-dependent escape temperature [T e (I)]. The values of T e are shown in Fig. 4(c) as a function of I C,0 /I for two different devices. The escape temperature is monotonically reduced by rising the bias current with a minimum value ∼ 20 mK for I = 370 nA, that is ∼ 15% of the intrinsic critical temperature of the active region, T i C ∼ 130 mK. As a consequence, the bias current is the ideal tool to in situ tune the properties of the 1D-JJ when operated as a JES.

V. PERFORMANCE DEDUCED FROM THE EXPERIMENTAL DATA
Here, we show the deduced performance of the 1D-JJ based bolometers operated both as nano-TES (at T C ) and JES (at T e ). To this end, the experimental data (∆, thermal and transport properties of A) showed in Sec. IV are substituted in the theoretical models presented in Sec. III.

A. Nano-TES bolometer experimental deduced performance
The thermal fluctuations between the electrons and phonons in the active region are the limiting factor for the noise equivalent power of a nano-TES [44], as described in Sec. III A. Indeed, the contributions related to the Johnson noise and the shunting resistor are negligibly small [36]. Despite the R(T ) characteristics are modulated by the bias current, Joule heating restricts the operation of the nano-TES at I → 0. As a consequence, the values of N EP T F N,nano-T ES can be only extracted for the lowest experimental values of I. Table I shows the N EP T F N,nano-T ES of two different 1D-JJs. In particular, the thermal fluctuations limited N EP of sample 1 (N EP T F N, 1 5.2 × 10 −20 W/ √ Hz) is lower than that of sample 2, since it can be operated at lower temperature (T C,1 < T C,2 ) and its thermal losses are reduced (G th,1 6.7×10 −15 W/K and G th,2 9.3×10 −15 W/K). This sensitivity is one order of magnitude better than state-of-the-art transition edge sensors [20], since G th,nano-T ES is drastically reduced thanks to the small dimensions of A and the presence of efficient Andreev mirrors.
The intrinsic time constant of the 1D-JJ (τ ) can be calculated from Eq. 13. Here, the heat capacitance is given by Eq. 14 taking the value C e,1 = 4 × 10 −20 J/K and C e,2 = 4.2 × 10 −20 J/K for sample 1 and 2, respectively, where the Sommerfeld coefficient of the active region is calculated as the average of the two components The presence of the bias circuit producing the NETF speeds up the response of a nano-TES bolometer. In fact, effective detector time constant becomes τ 1 10 ns for sample 1 and τ 2 200 ns for sample 2. The difference between the two devices arises from the values of the electrothermal parameter (α 1 2742 and α 2 121, respectively), as shown by Eq. 15.
It is interesting to note that, in principle, the nano-TES is fully tunable through the current injection. In fact, the critical temperature, i.e., the temperature giving R(T C ) = R N /2, can be varied by I, as shown in Fig. 1(d). In order to be I-tunable, the electronic temperature of the active region should be not affected by Joule overheating. This condition is fulfilled when I 2 R N P e-ph,n , that is when electron-phonon relaxation is able to fully balance the Joule dissipation in A.

B. JES bolometer experimental deduced performance
Also for the JES, the noise equivalent power is limited by thermal fluctuations between the electron and phonon systems in A [44]. Other limitations to the resolution can arise from the measurement of the superconducting to normal-state transition, which we assume it is optimized to be sub-dominant. The values of N EP T F N,JES can be extracted by substituting in Eq. 16 the measured parameters of the JES, such as I C,0 , R(T ) characteristics, ∆ A and Σ A (see previous sections for details). We note that the performance can be extracted at any value of I, since the operation in the dissipationless superconducting state ensures that T e (I) = T bath [see Fig. 4 As expected, N EP T F N,JES can be in situ finely controlled by tuning I. In particular, it decreases monotonically by increasing the amplitude of bias current, as shown in Fig. 5(a). Notably, the current bias modulates the device sensitivity over about 6 orders of magnitude. Furthermore, the extracted data indicate that the JES [37] reaches best sensitivities several orders of magnitude better than nano-TES bolometers [36] and all other sensors proposed and realized [16-22, 26-35, 48] so far. Specifically, the JES showed unprecedented values of N EP T F N,JES as low as ∼ 1×10 −25 W/ √ Hz for the highest bias current I = 370 nA (I C,0 /I 1.5) corresponding to a working temperature of about 18 mK. This sensitivity arises from the extremely suppressed heat exchange of A with all the thermal sinks (the phonons and the lateral electrodes) due to the combination of very low working temperature and operation deeply in the superconducting state.
The JES time constant (τ 1/2 ) can be calculated by the combination of Eqs. 13 and 18. As for the TES, it is proportional to the ratio between the electron heat capacitance and the electron-phonon heat conductance in A [44]. Figure 5(a) shows the dependence of the JES time constant deduced from the experimental data on the amplitude of I. As expected, τ 1/2 is monotonically suppressed by rising I, since the thermalization of A is exponentially suppressed by decreasing the working temperature. In particular, τ 1/2 varies between ∼ 1 µs at I C,0 /I 42 and ∼ 100 ms at I C,0 /I 1.5.
The tunability of the JES properties allows to choose between moderate sensitivity/fast response and extreme sensitivity/slow response by simply varying the bias current within the same structure. As a consequence, the same bolometer could fulfill the requirements of different applications.

VI. CONCLUSIONS
This paper reviews a new class of superconducting bolometers [16-22, 26-37, 48] owing the possibility of being finely in situ tuned by a bias current. This family of sensors includes the nanoscale transition edge sensor (nano-TES) [36] and the Josephson escape sensor (JES) [37], which take advantage of the strong resistance variation of a superconductor when transitioning to the normal-state. These bolometers employ a one dimensional fully superconducting Josephson junction (1D-JJ) as active region. On the one hand, this enables the modulation of the R(T ) characteristics of the device by varying I. On the other hand, the lateral superconducting electrodes ensure exponentially suppressed thermal losses, the so-called Andreev mirrors effect.
The 1D-JJ is theoretically analyzed from an electronic and thermal transport point of view. In particular, the current dependence of the resistance versus temperature characteristics and of the electro-phonon thermalization are predicted. Furthermore, the equations of the main figures of merit of a bolometer, such as the noise equivalent power and response time are calculated both in the nano-TES and JES operations.
A complete series of electronic and thermal experiments allowed extracting all the parameters of the device active region, such as the current-dependent R(T ) characteristics, the density of states and the electron-phonon thermal relaxation. These data allow determining the detection performance of bolometers based on the nano-TES and the JES.
The nano-TES reaches a total noise equivalent power of about 5 × 10 −20 W/ √ Hz limited by thermal fluctuations, that is one order of magnitude better than state-of-the-art conventional transition edge sensors [20]. In addition, the negative electrothermal feedback ensures a very fast sensing response τ ef f 10 ns.
The JES showed the possibility of in situ tuning the sensitivity by changing the biasing current. The thermal fluctuation limitation to NEP can be lowered down to the unprecedented value of ∼ 1 × 10 −25 W/ √ Hz. On the contrary, the sensing speed decreases significantly (up to about 100 ms), due to the poor thermalization of the active region when operated fully in the superconducting state.