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Joydip Sarkar, Krishnendu Maji, Abhishek Sunamudi, Heena Agarwal, Priyanka Samanta, Anirban Bhattacharjee, Rishiraj Rajkhowa, Meghan P. Patankar, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Mandar M. Deshmukh

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[Kerr non-linearity enhances the response of a graphene Josephson bolometer](https://mdr.nims.go.jp/datasets/6e0e9c07-be39-4998-ab89-93062fb6c7b6)

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Kerr non-linearity enhances the response of a graphene Josephson bolometerArticle https://doi.org/10.1038/s41467-025-62480-9Kerrnon-linearity enhances the responseof agraphene Josephson bolometerJoydip Sarkar 1 , Krishnendu Maji1, Abhishek Sunamudi 1,2, Heena Agarwal1,Priyanka Samanta1, Anirban Bhattacharjee1, Rishiraj Rajkhowa 1,Meghan P. Patankar1, Kenji Watanabe 3, Takashi Taniguchi 4 &Mandar M. Deshmukh 1Bolometers are radiation sensors that are central to wide areas such as darkmatter search, radio astronomy, material science, and qubit readouts, amongothers. There have been different kinds of bolometer realizations in the recentpast. The challenge is to have a single device that combines high sensitivity,broad bandwidth, and a fast readout scheme. Here we demonstrate the usageof Josephson parametric amplifiers (JPA) as highly sensitive bolometers. Ourkey finding is that the Kerr non-linearity of the JPA boosts the device’s sensi-tivity. When the bolometer is biased in the non-linear regime, it enhances theup-converted signals (~100 times), resulting in an order of magnitudeimprovement in sensitivity compared to the linear regime. In the non-linearbiasing, we achieve a NEP ~ 500 aW/ffiffiffiffiffiffiHzp. Our device offers a fast detectionscheme with a thermal time constant of 4.26 μs and an intrinsic JPA timeconstant of 70 ns. Our work integrates a JPA into a bolometer, enabling a fastand sensitive operation compared to previously studied graphene-based bol-ometers. Our study demonstrates a way forward to improve the quantumsensors based on 2Dmaterials by leveraging the inherent non-linear response.Sensing single photons in the radio frequency (RF) range is challengingbecause of the low photon energies compared to THz or near-infrared(NIR). However, sensitive bolometers in the radio frequency range areat the heart of radio astronomy and darkmatter search experiments1,2.There are various types of bolometers utilizing different physicalplatforms, such as transition edge sensor (TES)3, microwave kineticinductance detector (MKID)4, quantum dot-based5, superconductingqubit-based6,7, graphene-based8,9, graphene Josephson junction (JJ)-based10–12, and superconducting nanowire-based (SNSPD)13 sensorsamong others. The key performancemetrics of any bolometer includenoise equivalent power (NEP), response time (τ), instantaneous fre-quency bandwidth, and operational frequency range. However,achieving optimal performance across all these metrics in a singledevice is challenging. Currently, thebestNEP formicrowavephotons is10−22 W/ffiffiffiffiffiffiffiffiHzpusing a superconducting qubit-based bolometer7. How-ever, this device operates within a narrow bandwidth of ~50MHz andrequires a long integration time. Whereas, the fastest graphene-basedbolometer operates with a very short thermal relaxation time of 35 ps9.Nonetheless, its NEP is relatively modest at 10−12 W/ffiffiffiffiffiffiffiffiHzp. Therefore,efforts are required to improve all these aspects at a single-device level.Over the past decade, single-photon bolometers based on gra-phene have gained popularity because of their high performance acrossa broad electromagnetic spectrum and their rapid response times.Graphene has many attractive electrical and thermal properties, ren-dering it a promising material for bolometry and calorimetry. At thecharge neutrality, graphene has a vanishing density of states, resulting insmall heat capacity and electron-to-phonon thermal coupling, which arehighly desirable properties for bolometers8. It has been shown thatReceived: 7 February 2025Accepted: 22 July 2025Check for updates1Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Mumbai, India. 2Indian Institute of ScienceEducation and Research Kolkata, Mohanpur, West Bengal, India. 3Research Center for Functional Materials, National Institute for Materials Science,Tsukuba, Japan. 4International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan.e-mail: joydips581@gmail.com; deshmukh@tifr.res.inNature Communications |         (2025) 16:7043 11234567890():,;1234567890():,;http://orcid.org/0000-0003-2493-664Xhttp://orcid.org/0000-0003-2493-664Xhttp://orcid.org/0000-0003-2493-664Xhttp://orcid.org/0000-0003-2493-664Xhttp://orcid.org/0000-0003-2493-664Xhttp://orcid.org/0009-0008-3382-7174http://orcid.org/0009-0008-3382-7174http://orcid.org/0009-0008-3382-7174http://orcid.org/0009-0008-3382-7174http://orcid.org/0009-0008-3382-7174http://orcid.org/0009-0006-4854-0497http://orcid.org/0009-0006-4854-0497http://orcid.org/0009-0006-4854-0497http://orcid.org/0009-0006-4854-0497http://orcid.org/0009-0006-4854-0497http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1401-1080http://orcid.org/0000-0002-1401-1080http://orcid.org/0000-0002-1401-1080http://orcid.org/0000-0002-1401-1080http://orcid.org/0000-0002-1401-1080http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62480-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62480-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62480-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62480-9&domain=pdfmailto:joydips581@gmail.commailto:deshmukh@tifr.res.inwww.nature.com/naturecommunicationsgraphene efficiently absorbs photons across a wide frequency spectrumstarting from GHz to NIR9,14,15. The short electron-electron scatteringtime in graphene facilitates rapid equilibration of energy from absorbedphotons16,17. Recently, superconductor-normal-superconductor (SNS)Josephson junctions have been used for bolometry harnessing the sen-sitivity of JJs10–12,18–20. While these experiments have demonstrated highlysensitive operations, some utilize a low-frequency switching scheme tooperate the device, which limits the bolometer’s response time. Addi-tionally, all these experiments show very narrow bandwidth operationand none of them have exploited the non-linear response of a JJ forsensing. Hence, there is scope for improving the sensitivity, responsetime, and bandwidth of these devices, and we focus on these aspects inour work.To devise a highly sensitive and fast bolometer, we employ agraphene-based JPA architecture. JPAs are widely used for quantumsensing and readout purposes in circuit quantum electrodynamics(cQED) experiments21. Because of the high sensitivity of the JPA non-linearity and quantum noise-limited operation, such devices have thepotential to sense at individual photon levels with minimalbackaction22–24. While the previous realizations of graphene-basedbolometers have exploited the temperature-dependent resistance,inductance, or switching events in JJs, the temperature-dependentnon-linear Josephson inductance hasbeenunexplored. In thiswork,wedemonstrate a graphene JPA as a highly sensitive bolometer. Weimplement a separate heater line inside the device to inject RF signalsonto the graphene flake. We measure the heater-modulated sidebandresponse of the bolometer and extract the NEP and response time ofthe device experimentally.ResultsDevice descriptionFigure 1 a–c shows the schematic, optical image, and circuit model ofthe bolometer device. The device contains a superconducting copla-nar waveguide (CPW) where the central line is terminated to theground through a lumped element LC resonator made from a parallelplate capacitor and a graphene JJ, which serves as an inductor. Thedevice is designed to have a low-quality factor (~10) using a directlycoupled architecture that helps in fast readout from the device. The JJbd20 µmacHeatingONOFFFrequencyNon-linear resonatorGraphenePhasehBNgraphenehBNSDHC-1 C-2SDGH0 2 4 6 8 10(V)4.04.55.05.56.06.5(GHz)−180−90090180(degree)5.0 5.5 6.0(GHz)−90090IheaterLstrayLstrayC-2C-1RintLJVg50Ω MicrowavePortFig. 1 | Device image, circuit model, and microwave response of the device.a Shows the schematic of our bolometer device, the Josephson junction (JJ) is madeon an hBN-graphene-hBN stack, where hBN stands for hexagonal boron nitride.Weimplement a separate heater line inside the device to inject the heating signals. Inthe image, S, D, and H imply the source, drain, and heater electrodes, respectively.The inset figure in the dashed box illustrates the working scheme of our devicebased on the resonance frequency shift upon heating. The individual traces indi-cate the phase change at resonance. b Shows a zoomed optical micrograph of ourJosephson parametric amplifier (JPA) bolometer device. The graphene JJ is in par-allel to a series combination of two parallel plate capacitors C-1 and C-2 havingidentical dimensions of 60 × 60μm2. The red dashed line indicates the position ofthe sandwiched graphene flake. In the image, S, D, G, and H indicate the source,drain, gate, and heater electrodes, respectively. The heater line connects to theedge of the extendedgraphene flake, which is substantially away from the junction.When the heater current flows, it causes Joule heating in the extended grapheneflake shared with the JJ; in turn, the generated heat propagates and increases thelocal temperature of the junction. The heater current drains to the ground plane ofthe coplanar waveguide. c Shows the equivalent lumped element circuit model ofthe device, where LJ is the junction inductance, Lstray is the stray inductance, C-1 andC-2 are the two parallel plate capacitors in series, Rint is to account for internallosses in the device, Iheater is the heater current, and Vg is the applied gate voltage tothe JJ. The heater current is sent from a heater port and drains to the ground. Thedevice is connected to a microwave port through a 50Ωmatched environment forreflection-based measurements. d Shows reflected phase (∠S11) of the deviceplotted as a function of signal frequency (fs) and applied gate voltage (Vg). Thelinear resonance frequency of the device (f linres) gets tuned as a function of gating.The gate voltage tunes the linear resonance in a large frequency band of 4−5.7 GHz.The 2π phase change at resonance indicates that the device is over coupled(Qint ≫ Qext) all along the electron doping side. The inset shows a line slice of thephase plot at Vg = 6 V.Article https://doi.org/10.1038/s41467-025-62480-9Nature Communications |         (2025) 16:7043 2www.nature.com/naturecommunicationsis made on an hBN-graphene-hBN stack.Wemake a separate electrodeclose to the JJ (∼10μm away) to inject heating signals onto the gra-phene flake. The graphene JJ and heater are on the same sheet ofgraphene that also serves as the bus for carrying excitations.The essential idea here is that for a JPA, the reflected signal’s phaseis a very sensitive parameter due to its nonlinear nature. Consequently,anyminute heating effect causes a resonance frequency or phase shift inthe device. The current-phase relation (CPR) of the graphene JJ,including the first non-linear term, can be written as Is(ϕ) ≅ (αϕ + βϕ3),for a small ϕ approximation around zero. Where, Is is the supercurrent,ϕ is the phase difference across the junction, α and β are the expansioncoefficients. The Josephson inductance is given by LJðϕÞ= ℏ2e∂Is∂ϕ� ��1,where ℏ is the reduced Planck’s constant and e is the electronic charge.Hence, the non-linear inductance can be approximated asLJ(ϕ)≅ L0 + L2ϕ2, where L0 and L2 are the nonlinear inductor coefficients.This cubic nonlinearity in theCPR, known as theKerr term, gives rise to anonlinear junction inductance that is essential for parametric amplifi-cation. In our JPA bolometer device, we explore the effect of heating andthe consequent phase shift in the device. When the heater signal ismodulated, the resulting phase shift generates frequency up-convertedsideband signals, which we use as markers for sensing.Device characterizationWe begin with a basic microwave characterization of the device andthenmove to the bolometer measurements. We probe the device withlow-powermicrowave signals andmeasure the reflected signals using avector network analyzer (VNA). For DC characterization of the device,see Supplementary Note 1. The measurements were done in a dilutionfridge at 20mK temperature (see Supplementary Note 2 for details onthe setup). We check the gate tunability of the JPA and observe broadtunable resonance over a band of ~2 GHz, see Fig. 1d. Next, we proceedto do bolometer characterization, where we measure the reflectedphase (∠S11) of the device as a function of signal frequency (fs) andapplied dc heater current (Idcheater) at a fixed gate voltage (Vg = 1 V), seeFig. 2a. The Joule heating caused by the heater current reduces theswitching current (Ic) and increases the Josephson inductance of thejunction.Weobserve adecrease in the linear resonance frequencywithheating, consistent with the f linres /ffiffiffiffiIcpprediction. This holdswhen thestray inductance is minimized compared to the Josephson inductance.In our devices the Josephson inductance is at least 3 times larger thanthe stray inductance contribution of the JJ arms. We see a large tun-ability of the resonance frequency with the gate voltage withoutsaturation even at high Vg, as the Josephson inductance dominatesover the stray inductance. In Fig. 2b, we show the line slice of Fig. 2a atdifferent heater currents.Modulated heating experimentsNext, to extract the sensitivity of the bolometer, we perform the heatermodulation experiments. In Fig. 3a, we explain the frequency conver-sion and sideband generation scheme due to modulated heating. Amodulated heater signal causes the JPA phase (∠S11) at a certain fre-quency to oscillate over time, resulting in the generation of sidebandsin the frequency domain. The Joule heating effect of any modulatedcurrent at frequency fh produces sidebands at fs ± 2fh, where fs is thepump signal frequency, set near the resonance. See SupplementaryNote 12 for a theoretical descriptionof theobserved sideband features.Fig. 3b shows the experimental sideband data from the device mea-sured using a spectrumanalyzer,we send a heater signal at a frequencyfh = 1 MHz and heater power Pheater = −78 dBm. We see the up-converted sideband signals at twice the frequencies (2fh = 2MHz)along with the pump signal in the middle. The pump signal is set nearthe non-linear regime of the bolometer with fs = 5.47 GHz,Ps = −79.77 dBm, and Vg = 6 V. The on-flake heating scheme in ourdevice works from DC to 100 MHz heater signal frequencies; seeSupplementary Note 7 for sideband data at different heater fre-quencies and Supplementary Note 8 for different gate voltages. Now,to check the heater sensitivity, in Fig. 3c we plot the right sideband(RSB) signal power measured as a function of the detuned frequency(δf) and heater power. As we increase the heater power the sidebandsignal rises and eventually saturates, indicating saturation of thebolometer.We quantify the sensitivity of our device through the sidebandmeasurements as discussed in Fig. 3c.We have observed that when thebolometer is biased in the non-linear regime, it is very sensitive toheater modulations. Fig. 3d shows a non-linear phase diagram of thebolometer, where we measure the reflected phase (∠S11) of the deviceas a function of microwave signal frequency (fs) and power (Ps). This isthe typical non-linear phase diagram of a JPA with a cubic non-linearterm in the CPR. See Supplementary Note 14 for a calculated phase−300 −200 −100 0 100 200 300Idcheater (nA)4.704.754.804.854.904.95f s(GHz)−90 0 90∠S11 (degree)4.65 4.70 4.75 4.80 4.85 4.90 4.95 5.00fs (GHz)−150−100−50050100150∠S 11(degree)Idcheater (nA)0100200300a bFig. 2 | Resonance frequency shift of the bolometer due to heating. a Shows thelow-power reflected phase (∠S11) of the device as a function of dc heater current(Idcheater) and microwave signal frequency (fs) at Vg = 1 V. The white color in the plotindicates thedecreasing resonant featureof thedevice. The Joule heating causedbythe heater current reduces the switching current (Ic) and increases the Josephsoninductance of the junction. The decrease in the linear resonance frequency withheating is consistent with the f linres /ffiffiffiffiIcpprediction. b Shows the line slice of thecolor plot in (a) for different values of the DC heater currents (Idcheater).Article https://doi.org/10.1038/s41467-025-62480-9Nature Communications |         (2025) 16:7043 3www.nature.com/naturecommunicationsdiagram of the JPA. Next, at each point of this phase diagram, we biasthe bolometer and measure its sideband response for the heaterturnedon andoff. Eventually, we extract the signal-to-noise ratio (SNR)map of the bolometer across the non-linear phase diagram (see Sup-plementary Fig. 4b, c for details). Fig. 3e shows the SNRof the sidebandsignal measured as a function of the pump signal’s frequency (fs) andpower (Ps). Here we keep the gate voltage fixed at Vg = 6 V, set theheater frequency at fh = 1MHz, and measure the right sideband signalpower. In this measurement, the heater power is kept fixed atPheater = −95 dBm for the ON state of the bolometer. We observe thatwhen the bolometer becomes non-linear, there is a high SNR contrastin these regions. These high SNR regions are preferred for biasing thebolometer. See Supplementary Note 15 for the method used in opti-mizing the bias point of the bolometer for heat sensing. We note thatthe protocol used for biasing the bolometer through the SNR mea-surements does not require us to characterize the JPA gain profile, sowe do not have this data for the current Device-1. The measured gainprofile for Device-2 is shown in the Supplementary Fig. 17.We next bias the device at linear and non-linear regimes to com-pare its bolometric sensitivity. Fig. 3f shows the sideband powerplotted as a function of Pheater for linear and non-linear biasing of thebolometer at thebiasingpoints (linear: fs = 5.68GHz,Ps =−97 dBm) and−2 −1 0 1 2(MHz)−100−90−80−70−60−50Signal Power (dBm) 2* =2 MHz=-78 dBm−15 −10 −5 0 5 10 15(Hz)−120−115−110−105−100−95−90−85(dBm)−130 −110 −90RSB power (dBm)5.3 5.4 5.5 5.6 5.7(GHz)−86−84−82−80−78−76−74−72(dBm)−90 0 90(degree)5.2 5.3 5.4 5.5 5.6 5.7(GHz)−86−84−82−80−78−76−74−72(dBm)20 25 30 35SNR (dB)bacd effsfs+2fhfs-2fhFrequency Time FrequencyONOFFHeater Reflected signal phase Reflected signal phaseSideband power5.5 6.0(GHz)−90090Phase−120 −115 −110 −105 −100 −95 −90 −85(dBm)−140−130−120−110−100−90−80−70Right side band power (dBm)FrequencyLinearNon-linear Reflected phaseLinear regimeNon-linear regimeEnhanced responseFig. 3 | Graphene JPA as a sensitive bolometer. a Shows the sideband generationscheme. Amodulatedheater signal causes the phase (∠S11) at a certain frequency tooscillate over time, leading to thegeneration of sidebands in the frequencydomain.The Joule heating effect of any modulated current at frequency fh produces side-bands at fs ± 2fh, where fs is the pump signal frequency. b Shows a sidebandspectrum of the bolometer device. The signal power is measured at the spectrumanalyzer. Herewe set the heater signal at fh = 1MHz, which causes the Joule heatingin the device and hence modulation of the resonance at 2fh. Consequently, we seetwo sidebands around the pump signal at fs ± 2fh. Here, δf is the detuned frequencyfrom the pump signal set at fs = 5.47 GHz. The Vg is set to 6 V and the heater powerPheater = −78dBm. c Shows the right sideband (RSB) signal power measured as afunction of heater power (Pheater) and detuned frequency (δf). Here we zoom in onthe right sideband as shown by the red dashed circle in (b) and then resolve it as afunction of Pheater. The x-axis δf is the detuned frequency from the right sideband in(b). As we increase the heater power, the sideband signal rises and eventuallysaturates. d Shows the non-linear phase diagram of the JPA, as a function of signalfrequency (fs) and power (Ps). The Vg is kept at 6 V, which fixes the linear resonanceat low powers. With increasing signal power, the JPA becomes nonlinear, and theresonance starts to shift. An increase in power pushes the JPA towards a criticalpoint beyond which any further increase in power makes it unstable (dark greyregion). The inset shows the phase response at fixed powers marked by the purpleand orange dashed horizontal lines on (d), in the low and high power regimes,respectively. e Shows the signal-to-noise ratio (SNR) map of the sideband signalmeasured as a function of pump signal frequency (fs) and power (Ps). Here we keepthe Vg at 6 V, set the fh = 1MHz, Pheater = −95 dBm, resolution bandwidth of thespectrum analyzer at 1 Hz, andmeasure the right sideband signal power at differentpoints of the non-linear phase diagram of (d). We observe that when the JPA bol-ometer becomes non-linear, there is highSNR contrast in these regions. f Shows thesideband power plotted as a function of Pheater for linear and non-linear biasing ofthe bolometer at the points (linear: fs = 5.68 GHz, Ps = −97 dBm) and (non-linear:fs = 5.39GHz, Ps = −76.87 dBm) respectively, marked by the purple hexagon andorange star in e. In the non-linear regime, the sideband signal is ~22 dB higher, andthe sideband starts to rise in ~10 dB lower heater powers than that of the linearregime. This indicates that the device is more sensitive when operating in non-linear biasing. The inset schematic illustrates the phase sensitivity in the non-linearregimeover the linear regime. The dashed horizontal lines indicate the noise floors.Article https://doi.org/10.1038/s41467-025-62480-9Nature Communications |         (2025) 16:7043 4www.nature.com/naturecommunications(non-linear: fs = 5.39GHz, Ps = −76.87 dBm), respectively.We find in thenon-linear regime, the sideband signal is ~22 dB higher, and the signalstarts to rise at ~10 dB lower heater powers than that of the linearregime. This indicates that the device ismore sensitivewhen operatingin non-linear biasing. We see around 6 dB increase in the noise floor inthe non-linear regime, which is possibly set by the JPA gain and thesystem noise of the amplification chain. However, the SNR is nowimproved by 16 dB than that of the linear regime. The usage of a JPAhelps us to enhance the bolometer response in two ways. First, in thenon-linear regime, the device can sense smaller heat signals comparedto the linear regime. This is due to the narrowing line width of thedevice (see Fig. 3d inset), which gives better sensitivity to the non-linear regime. Secondly, the JPA amplifies the upconverted sidebandsignals, as seen by the enhancement in the sideband power. Thisis a unique aspect of our integrated JPA bolometer device. Next,we extract the NEP of the device from the data shown in Fig. 3f, atthe non-linear biasing. Supplementary Fig. 5 shows the extracted NEPof the bolometer. The best NEP value for fh = 1MHz is ~500 aW/ffiffiffiffiffiffiffiffiHzp.In graphene bolometer devices, an open question in the field is theextent to which the injected heat couples to the JJ channel.We accountfor the fact that a finite fraction of the heat injected into the grapheneheater leaks to the phonon bath before reaching the JJ. Theheat transfer from the hot electrons of graphene to the hBN phononsis a surprising observation. We experimentally verify this heattransduction next.Control experiment to study phononic heat transferThere are two possible routes for the heat to reach the JJ – first, the hotelectrons diffuse to the junction, and second, the phonons excited inthe substrate carry heat to the JJ. To test the relative efficacy of thesetwo channels we first study a device with a contiguous grapheneconnecting the heater and the JJ; subsequently, we sever the galvanicconnection by etching the graphene in the same device—disconnecting the heater and JJ electrically. After severing the galvanicconnection, we eliminate the channel of hot electrons perturbing the JJresponse while still allowing for the phonons to affect the JJ. In ourcontrol experimentwith an etched graphene heater device (see Fig. 4a,b), we observe that even after isolating the graphene heater and the JJby introducing a cut in the graphene, heat can still propagate to the JJvia the phonons in the hBN. This phonon-mediated heat transfercauses a shift in the resonance frequency, as shown in Fig. 4c. Thisindicates that a finite portion of the heat injected into the device leaksto the substrate phonons. Notably, this response is seen despiteinterfacial Kapitza resistance at multiple interfaces. Studies utilizingscanning probes have demonstrated that hot electrons in graphenedissipate heat to atomic defects through resonant inelastic scatteringfor cooling25,26. However, such cooling processes at the device level,particularly in configurations involving small JJ channels, remain lar-gely unexplored and challenging27. Here, our control experimentprovides insights into heat dissipation to substrate phonons via atomicdefects. Our finite element simulations estimate that approximately~ 35% of the heat injected at the heater is lost to the phonon bath, asdetailed in Supplementary Note 11.Time constant measurementsNext, we measure the time constant of the bolometer experimentally.The response time of a bolometer quantifies the time required toexcite and reset a bolometer. Using the graphene heater port, we heatthe bolometer using short DC pulses sent in sequences while simul-taneously probing its response with a pump signal at the resonancefrequency of 4.848GHz. The heater pulse width is set at 50μs. Wemeasure the digitized quadrature signal of the pump tone using ahomodyne demodulation scheme (see Supplementary Note 6 forsetup details). The quadrature signals (I,Q) are plotted as a function oftime, see Fig. 5a. An exponential fit to the rising and falling edge yieldsthe thermal time constants τon = 4.45μs and τoff = 4.26μs. The data isa cbJJ arm-1JJ arm-2heater inheater outcuth-BNh-BNGrheatpathelectron diffusion: Xe-p coupling: ✔−1500 −1000 −500 0 500 1000 1500(nA)−125−100−75−50−2502550Resonance frequency shift: (MHz)=5.15 GHzBefore gr-heater etchingAfter gr-heater etchingFig. 4 |Heat conduction throughphononchannels. a Shows anoptical imageof acontrol device (Device-4) for testing the heat conduction contribution of electronsand phonons. The JJ and the heater electrode share the same graphene flakemarked by a dashed black line. After measuring one round of the device response,we etch the graphene heater to create a galvanic discontinuity between the heaterand the JJ. The scale bar is 2μm. b Shows the cross-sectional schematic of the hBN-gr-hBN stack. The white cut region shows the galvanic discontinuity for electrondiffusion. We fully etch the top hBN, the graphene flake, and a little bit of bottomhBN (∼5 nm) to ensure a full cut in graphene. In the heterostructure, the top hBNthickness is ~20nm, and the bottom hBN thickness is ~60nm. The only possibleway for the heat to reach the JJ is through substrate phonons of hBN. c Showsresonance frequency shift as a function of DC Joule heating as described in Fig. 2a.After etching the graphene, the device still gets heated through the substratephonons and shows a shift in the resonance frequency.Article https://doi.org/10.1038/s41467-025-62480-9Nature Communications |         (2025) 16:7043 5www.nature.com/naturecommunicationstaken at a fixed gate voltage and measured with averaging over mul-tiple pulse sequences. Understanding the contributions of differentheat-conducting channels is key to enhancing the time response of athermal detector28. In our studies, we find that the rise and fall timesare similar, about a few μs but varying across devices. See Supple-mentary Note 13 for the measured time constants on other devices.The fact that there are sources for the transduction of hot elec-trons into phonons close to the JJ makes the defect-mediated phononscrucial in understanding the thermal response of our device. Paststudies using the scanning probe technique show that there are atomicdefects along the rough edges of the graphene sample, which con-tribute significantly to the transduction of hot electrons intophonons25. The path of electron diffusion into the JJ devices typicallyhas a narrow entrance, through one open side (~300nm) of the gra-phene segment. This could restrict the heating of the junction fromelectron diffusion. Hence, atomic defects along the rough edges of the1D contacts, formed after etching graphene, could play an importantrole in the conversion of hot electrons into phonons, thereby heating40 60 80 100 120time ( s)−10123Digitized quadratures (arb. units)I quadratureQ quadraturefit: =4.45 0.04 sfit: =4.26 0.02 s40 60 80 100 120time ( s)−10−505101520253035Digitized quadratures (arb. units)I quadratureQ quadraturefit: =0.09 0.001 sfit: =0.07 0.001 s4.6 4.8 5.0 5.2(GHz)−95−90−85−80−75(dBm)−90 0 90(degree)86 88 90 92 94time ( s)10−310−210−1100Normalized digitized quadratures (arb. units)(dBm)-90.0-84.3-81.6-80.7-80.0-79.4-78.8a bc dsquare pulse microwave pulseFig. 5 | Time constants of the bolometer. a Shows the measured thermal timeconstant of the bolometer. We heat the bolometer using a short DC square pulseand simultaneously probe its responsewith apump signal at 4.848GHz in the linearbiasing of the device. The heater pulse width is set at 50 μs. We measure thedigitized quadrature signal of the pump tone using a homodyne demodulationscheme. The quadrature signals (I, Q) are plotted as a function of time. An expo-nential fit to the rising and falling edge yields the thermal time constantsτon = 4.45μs and τoff = 4.26μs. b Shows themeasured intrinsic time constant of theJPA.Weprobe the JPAusing anamplitude-modulatedmicrowave pulse, in the linearbiasing of the device. Themicrowavepulse ismadeusing apump signal of 4.88GHzmixed with a square pulse for amplitudemodulation. The square pulse width is setat 50μs. We measure the digitized quadrature signal of the pump pulse using ahomodyne demodulation scheme. The quadrature signals (I, Q) are plotted as afunction of time. An exponential fit to the rising and falling edge yields the intrinsicJPA time constants τon = 90 ns and τoff = 70 ns. c Shows the non-linear phasediagram of the JPA plotted as a function of signal frequency (fs) and power (Ps). Thegate voltage is kept atVg = 2 V.d Shows themeasured intrinsic time constant of theJPA for different pump signal powers marked by colored dots in the non-linearphase diagram of (c). We probe the JPA using amplitude-modulated microwavepulses. We measure the digitized quadrature signal of the pump pulse using ahomodyne demodulation scheme. The quadrature signals are plotted as a functionof time. For small signal powers, the device responds fast; however, for large signalpowers, the device becomes non-linear and eventually dissipative; hence, theresponse time lags and develops multiple time constants, evident from the slopechange in the log scale.Article https://doi.org/10.1038/s41467-025-62480-9Nature Communications |         (2025) 16:7043 6www.nature.com/naturecommunicationsthe JJ. Similarly, for heat removal, the substrate phonons play a crucialrole in thermalizing the graphene’s electrons to the bath. Our under-standing of the microscopic mechanism is qualitative at present andcould explain the similarity of rise and fall times. Further studies areneeded in the future todisentangle the effects of atomic defects on theinterconversion of electrons into phonons and resulting thermalproperties. One can fabricate vdW superconducting contacts (e.g,NbSe2) to graphene without etching graphene to avoid defects andstudy their contributions further. In the Supplementary Note 16, wediscuss the possible heat transfer mechanism in our device.Next, to verify that the bolometer’s time response is not con-strained by the intrinsic time scale of the JPA, we measure the timeresponse of the JPA. We drive the JPA with an amplitude-modulatedmicrowave pulse and simultaneously probe it through the digitizedquadrature signals using a homodyne demodulation scheme (seeSupplementary Note 6 for setup details). During this experiment, theheater is not energized. At relatively low powers, the JPA exhibits afaster responsewith τon = 90ns and τoff = 70 ns, as shown in Fig. 5b. Theresponse time of the JPA is limited by the intrinsic bandwidth of thedevice when operating close to the non-linear regime. Next, we varythe signal power of the microwave pulse to drive the JPA from thelinear regime to the non-linear regime and eventually to the normalstate of the JJ, following the probing pointsmarked by the coloreddotsin Fig. 5c. In the linear regime, the JPA responds quickly, but as thepower increases, the response slows down, as shown in Fig. 5d. Thisincrease in response time at high power is expected in the non-linearregime of the JPA, where the internal bandwidth of the devicedecreases and also due to local heating at the JJ.DiscussionIn summary, we report the experimental realization of a bolometerdevice using a graphene JPA. The Kerr non-linearity of the JPA helpsin enhancing the bolometer’s sensitivity. When the bolometer isbiased in the non-linear regime, it enhances the sideband signals(~100 times), resulting in an order of magnitude improvement insensitivity compared to the linear regime. We achieve a best NEP~ 500 aW/ffiffiffiffiffiffiHzp. We experimentally measure a fast thermal timeconstant of the bolometer of 4.26 μs. The sensitive and fast readoutis a key feature of our device that will improve upon previous sensingschemes that relied on shifts in switching histograms to demonstrateexquisite sensitivity. Our device has the potential to sense single THzand NIR photons via a direct irradiation mechanism, where the gra-phene flake acts as a bus for carrying the hot electrons from theheated regions to the JJ, leading to a frequency shift in the device.The sensitivity of the bolometer can be improved further by usingsuperconductors with a smaller energy gap, such as aluminum, forfabricating the JJs. Another approach could involve substrate engi-neering to enhance heat coupling to the JJ.Our work extends the pathway for the exploration of 2D van derWaals materials-based devices for future-generation quantum sensors.Fast broadband bolometers have versatile applications in readoutprocesses for cQED experiments29,30, suggesting that our device couldalso be utilized for similar measurements. Recent experiments onMKIDs and SNSPDs have demonstrated significant pixel multiplexingcapabilities in bolometer devices13,31, which could also be adapted inlarge-scale graphene JPA bolometer devices for multiplexing applica-tions. Furthermore, the nonlinear sensitivity enhancement, a criticalfeature unutilized in MKIDs and SNSPDs, is feasible within our devicearchitecture while still enabling fast readout capabilities similar tothose of MKIDs and SNSPDs.MethodsThe device fabrication process consists of a few steps. First, we patternthe coplanar waveguide (CPW) on SiO2/Si substrate by standarde-beam lithography. The CPW is made of MoRe sputtered film ofthickness 40 nm. Next, we make the MoRe-Al2O3-Al parallel platecapacitors (see Fig. 1b) by fixed-angle uniform rotation evaporation ofAl2O3 and Al for thicknesses of 50 and 70 nm, respectively. Then, weprepare the hBN-graphene-hBN-graphite stack. We follow the scotchtape exfoliation of graphene and hBN crystals. A thick graphite flake isused for the bottom gate. We use PC (Poly(bisphenol A carbonate))/PDMS (polydimethylsiloxane) stamps for assembling the flakes. Oncethe stack is ready, we drop it on the CPW substrate. Next, we followstandard e-beam lithography for defining the JJ contacts on graphene.We etch the top hBN using CHF3/O2 reactive ion etching. Next, we dothe MoRe sputtering to make the superconducting contacts of thick-ness 40 nm. Before deposition, we do an in-situ argon (Ar) plasmacleaning of the contacts. After sputtering, the resist lift-off is done inhigh-purity acetone. The device gets ready for characterization at thisstage. Sometimes we face poor transparency of the contacts. In suchcases, vacuum annealing at 350 °C in the forming gas environmenthelps to improve the transparency significantly.Data availabilityThe experimental data used in the main text figures are available inZenodo, with the identifier https://doi.org/10.5281/zenodo.15195742.Additional data related to this study are available from the corre-sponding authors upon request.Code availabilityThe codes related to this study are available from the correspondingauthors upon request.References1. Paolucci, F., Ligato, N., Germanese, G., Buccheri, V. & Giazotto, F.Fully superconducting Josephson bolometers for gigahertzastronomy. Appl. Sci. 11, 746 (2021).2. Braine, T. et al. Extended search for the invisible axionwith the axiondark matter experiment. Phys. Rev. Lett. 124, 101303 (2020).3. DeVisser, P. J., Baselmans, J. J. 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Pac. 132, 125005 (2020).AcknowledgementsWe thank Vibhor Singh, Eli Zeldov, Vishal Ranjan, and R. Vijay for theirhelpful discussions and comments. We thank Kishor V. Salunkhe,Gaurav Bothara, Ritajit Kundu, Mahesh Hingankar, and Digambar A.Jangade for useful discussions and experimental assistance. Thismaterial is based upon work supported by the Air Force Office ofScientific Research under award number FA2386-23-1-4031. Weacknowledge the Nanomission grant SR/NM/NS-45/2016 and DSTSUPRA SPR/2019/001247 grant along with the Department of AtomicEnergy of Government of India 12-R&D-TFR-5.10-0100 for support.Preparation of hBN single crystals is supported by the ElementalStrategy Initiative conducted by the MEXT, Japan (Grant NumberJPMXP0112101001) and JSPS KAKENHI (Grant Numbers 19H05790and JP20H00354).Author contributionsJ.S. fabricated the devices, led the measurements, and analyzed thedata. K.M. and P.S. helped with measurements and analysis. A.S., H.A.,and P.S. assisted in the device fabrication. R.R. and A.S. assisted in thefinite element simulations. A.B. assisted in the time constant measure-ments.M.P.P. assisted inmicrowavePCB fabrications. K.W. andT.T. grewthe hBN crystals. J.S. and M.M.D. wrote the manuscript with input fromeveryone. M.M.D. supervised the project.FundingOpen access funding provided by Department of Atomic Energy.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-62480-9.Correspondence and requests for materials should be addressed toJoydip Sarkar or Mandar M. Deshmukh.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-62480-9Nature Communications |         (2025) 16:7043 8http://arxiv.org/abs/2410.22433https://doi.org/10.1038/s41467-025-62480-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Kerr non-linearity enhances the response of a graphene Josephson bolometer Results Device description Device characterization Modulated heating experiments Control experiment to study phononic heat transfer Time constant measurements Discussion Methods Data availability Code availability References Acknowledgements Author contributions Funding Competing interests Additional information