^{1,a)}, M. A. Laakso

^{1}and T. T. Heikkilä

^{1}

### Abstract

We study the proximity Josephson sensor in both bolometric and calorimetric operation and optimize it for different temperature ranges between 25 mK and a few kelvin. We investigate how the radiation power is absorbed in the sensor and find that the irradiated system is typically in a weak nonequilibrium state. We show in detail how the proximity of the superconductors affects the device response: for example, via changes in electron-phonon coupling and out-of-equilibrium noise. In addition, we estimate the applicability of graphene as the absorber material.

The authors thank Francesco Giazotto, Pertti Hakonen, Panu Helistö, Leonid Kuzmin, Arttu Luukanen, and Andrei Zaikin for useful discussions. J.V. is supported by the Finnish Foundation for Technology Promotion whereas T.T.H. acknowledges the support from the Academy of Finland and MAL from the Finnish Academy of Science and Letters.

I. INTRODUCTION

II. DETECTOR

A. Basic operating principle

B. Detailed discussion

1. Coupling to radiation

2. Parameters and conditions

III. OPERATION

A. Bolometer

B. Calorimeter

C. Optimization

1. Length

2. Graphene

IV. CONCLUSION

### Key Topics

- Superconducting detectors
- 38.0
- Superconducting proximity effects
- 26.0
- Superconductivity
- 21.0
- Graphene
- 18.0
- Diffusion
- 17.0

## Figures

Illustration of the detector with normal (N) and superconducting (S) components. Incident radiation is coupled to the normal-conducting absorber via the antennas in contact to the superconductors.

Illustration of the detector with normal (N) and superconducting (S) components. Incident radiation is coupled to the normal-conducting absorber via the antennas in contact to the superconductors.

Critical Josephson current as a function of electron temperature . We use ratio for , corresponding to Nb energy gap .

Critical Josephson current as a function of electron temperature . We use ratio for , corresponding to Nb energy gap .

Relative contributions to the electron energy balance of the system defined in Eq. (2). At all energies , the magnitude of the input (radiation contribution) must equal to the sum of the magnitudes of the other three processes which contribute to energy relaxation. The result is obtained for a typical set of operating and materials parameters and, most notably, and .

Relative contributions to the electron energy balance of the system defined in Eq. (2). At all energies , the magnitude of the input (radiation contribution) must equal to the sum of the magnitudes of the other three processes which contribute to energy relaxation. The result is obtained for a typical set of operating and materials parameters and, most notably, and .

Fraction of incident radiation power converted into thermal response in a PJS detector. The results are given as a function of for and as a function of for (inset). The curves are obtained for a typical set of materials parameters defined in Sec. II B.

Fraction of incident radiation power converted into thermal response in a PJS detector. The results are given as a function of for and as a function of for (inset). The curves are obtained for a typical set of materials parameters defined in Sec. II B.

Nonequilibrium distribution resulting from irradiation and a set of relevant equilibrium distributions. Notice that the curves for the actual nonequilibrium distribution and the equilibrium distribution used to approximate this are nearly on top of each other. The difference between these two is magnified in the inset. The figure is obtained for the same set of parameters used in Fig. 3. In this case the input power is large so that the bath temperature is small compared to the final . Here , so is also clearly smaller than the temperature of an equivalent equilibrium system heated with the same power, .

Nonequilibrium distribution resulting from irradiation and a set of relevant equilibrium distributions. Notice that the curves for the actual nonequilibrium distribution and the equilibrium distribution used to approximate this are nearly on top of each other. The difference between these two is magnified in the inset. The figure is obtained for the same set of parameters used in Fig. 3. In this case the input power is large so that the bath temperature is small compared to the final . Here , so is also clearly smaller than the temperature of an equivalent equilibrium system heated with the same power, .

Comparison between numerical result for thermal conductance of the electron-phonon heat link and two exponential fitting curves: one valid to good degree of accuracy for (green) and one, where the suppression of is determined by the energy minigap (red). is given in proportion to the thermal conductance in the incoherent case.

Comparison between numerical result for thermal conductance of the electron-phonon heat link and two exponential fitting curves: one valid to good degree of accuracy for (green) and one, where the suppression of is determined by the energy minigap (red). is given in proportion to the thermal conductance in the incoherent case.

Nonequilibrium noise of the PJS under heating , with (coherent—red) and without (incoherent—blue) the corrections from the proximity effect. We compare the exact results to the analytical approximations of Eqs. (10) (incoherent) and Eq. (7) (coherent) valid at the limits and (dashed lines). In the inset, we show how the noise of the coherent system can be approximated by the exponential law of Eq. (7) (dashed line) for a large temperature range.

Nonequilibrium noise of the PJS under heating , with (coherent—red) and without (incoherent—blue) the corrections from the proximity effect. We compare the exact results to the analytical approximations of Eqs. (10) (incoherent) and Eq. (7) (coherent) valid at the limits and (dashed lines). In the inset, we show how the noise of the coherent system can be approximated by the exponential law of Eq. (7) (dashed line) for a large temperature range.

Base NEP (with negligible power load) for proximity and normal conductor as function of . The proximity effect decreases NEP by the factor in our example at .

Base NEP (with negligible power load) for proximity and normal conductor as function of . The proximity effect decreases NEP by the factor in our example at .

Comparison between the numerical result for the electronic heat capacity of the coherent (proximity) and the incoherent case.

Comparison between the numerical result for the electronic heat capacity of the coherent (proximity) and the incoherent case.

Time constant of the PJS as a function of electron temperature on a log-log scale. The coherent corrections from the proximity effect (red) are compared to the incoherent result (blue).

Time constant of the PJS as a function of electron temperature on a log-log scale. The coherent corrections from the proximity effect (red) are compared to the incoherent result (blue).

Detector resolving power for some operating temperatures. Note that the curves for are nearly on top of each other.

Detector resolving power for some operating temperatures. Note that the curves for are nearly on top of each other.

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