How can self-cavity plasmon polaritons be probed at millikelvin temperatures?

Why millikelvin sub-THz spectroscopy is hard

Van der Waals heterostructures show self-cavity resonances from sub-terahertz to terahertz frequencies, which makes them attractive for cavity-modified phases of matter. Probing those resonances requires high frequency resolution while the sample stays at millikelvin temperature, and the paper states that existing methods struggle to deliver both at once. The obstacles it names are concrete: the small length scale of van der Waals heterostructures pushes the relevant near-field response into the tens to hundreds of GHz, beyond conventional microwave spectroscopy; plasmonic cavities built from non-superconducting metals are intrinsically lossy, limiting quality factors and sensitivity; and optics-based probes complicate operation at millikelvin temperatures.

The paper's response is to change both the cavity and the readout. The cavity is a parallel-plate, or broadside, structure of two high-kinetic-inductance superconducting layers separated by a thin dielectric, which the authors call a kinetic inductance broadside cavity. The readout is a frequency-domain spectrometer built from a Josephson tunnel junction. Neither component alone would answer the question; the claim is that together they make sub-THz cavity-matter spectroscopy possible in the quantum limit, where k_BT is much smaller than hf.

A junction that emits and detects sub-THz light

The spectrometer uses one Josephson junction as both source and detector. A DC voltage bias V_JJ drives an oscillating AC current at frequency ω_J/2π = 2eV_JJ/h, about 483.6 GHz per mV, so the emission frequency is tuned by voltage rather than by a laser or a microwave generator. Emission stops at 4Δ/h, where Δ is the superconducting quasiparticle gap; for standard thin-film aluminium junctions this ceiling is roughly 190 GHz.

Detection works through inelastic Cooper pair tunneling in the same junction. When the electromagnetic environment dissipates power at ω_J, Cooper pairs tunnel inelastically to supply it, and the DC current follows I_DC = I_0² Re[Z_in(ω_J)]/2V_JJ. Because the emission is narrow-band, the DC current becomes a frequency-sensitive probe of the real part of the environment's input impedance. The practical consequence the authors emphasize is that only DC biasing is needed, which reduces complexity and cost relative to direct sub-THz technology. On-chip AC powers are at the femtowatt to picowatt scale, mostly dissipated in the Pt biasing lines, and all measurements are performed at a base temperature of about 10 mK with no detectable rise in mixing-chamber temperature during operation.

Superconducting layers shrink the cavity volume

The cavity itself is the second ingredient. Disordered NbN films made by magnetron sputtering carry high kinetic inductance L_k, corresponding to low superfluid stiffness, while keeping a high critical temperature. Sandwiched around a thin hBN dielectric, they support plasmonic modes with linear dispersion, sometimes called acoustic plasmons, whose phase velocity scales as (εL_k/d)^-1 and comes out near c/100. That slow velocity is what lets cavities only a few tens of microns long host modes at sub-THz frequencies.

The paper quantifies the payoff in two ways. The superconducting layers define self-cavity structures with electromagnetic volume compression of order 10^7, and the out-of-plane vacuum electric field fluctuations are about two orders of magnitude larger than the longitudinal fluctuations in typical coplanar resonators. The authors argue this makes KIBC modes especially suitable for coupling to displacement-field-tuned phases and excitations.

The first test used the simplest structure, two NbN plates separated by hBN. The extracted spectrum shows a sharp peak at 50 GHz and a large dip near 150 GHz, identified as the λ/2 and 3λ/2 KIBC modes, plus a smaller peak near 100 GHz assigned to the λ mode and a small dip near 160 GHz consistent with a mode whose wavevector has components along both z and y. A multi-parameter fit of an effective circuit model, including shunt-resistance loss on the NbN layers, accounts for all modes observed up to 150 GHz. The fitted mode frequencies correspond to a plasmon velocity of about 3.4×10^6 m/s, approaching the Fermi velocity of graphene, roughly 10^6 m/s.

Graphene adds a density-tunable matter mode

The next device replaced one NbN layer with monolayer graphene, producing a hybrid graphene/superconductor mode the authors call a screened nonlocal graphene plasmon, or SNGP. Contacts to both the NbN and the graphene allow the graphene carrier density to be tuned by electrostatic field effect, so the same device yields a spectrum at each gate voltage. A prominent mode near 120 GHz at high density (V_gate ≈ −5 V) drops sharply as the gate voltage is reduced and broadens considerably at charge neutrality; a weaker mode near 40 GHz also redshifts and gradually disappears as density is reduced.

The notable result here is lifetime. The bilayer device shows a graphene plasmon lifetime of roughly τ ≈ 15 ps, which the authors describe as surprisingly long and consistent with v_p^SNGP τ/L ≈ 1, where L is the cavity length. Their interpretation is that the SNGP mode lifetime is likely limited by the device size through edge scattering rather than by intrinsic graphene loss. That reading matters for anyone judging whether these cavities could reach the quality factors needed for cavity-modified phases: the loss being measured is, in the authors' account, partly a geometric boundary effect.

Avoided crossings show light-matter hybridization

The third structure is the one that addresses strong coupling directly: a NbN/graphene/NbN trilayer. It supports two confined plasmon modes. In one, the electric field between the top NbN and graphene points the same way as the field between graphene and the bottom NbN, so little current flows in graphene and the mode depends weakly on graphene kinetic inductance; the authors identify this as the KIBC, or cavity, mode. In the other, the fields are sourced from the graphene layer, making it sensitive to graphene's electrodynamic properties; this is the SNGP, or matter, mode. The paper notes that high-kinetic-inductance superconducting layers make such a combined cavity-plus-matter spectrum straightforward in this band, whereas lossy normal metals such as Au would not support their own cavity modes at these frequencies.

The measured spectra show both kinds of feature: minimally dispersing modes around 62, 130, and 175 GHz, with the 62 GHz mode the strongest sharp feature, and dispersing modes near 40 GHz and near 120 GHz at high carrier density. A third dispersing feature cuts through the nondispersing mode around 170 GHz, producing an avoided crossing. Comparing the data with calculated dispersion for an infinite NbN/graphene/NbN trilayer at q = π/34 µm, matching the 34 µm cavity length, lets the authors label each harmonic: strongly dispersing features are SNGP modes, weakly dispersing ones are KIBC modes. A level crossing between KIBC(3λ/2) and SNGP(5λ/2) is expected near 170 GHz, and the authors interpret the observed avoided crossing as hybridization of those two modes caused by the couplers, which break spatial homogeneity. That is the basis for their claim of strong light-matter coupling between confined plasmonic modes.

Two extra peaks at 94 GHz and 147 GHz cannot be explained as KIBC harmonics. The authors instead assign them to coupler modes C1 and C2 arising from a thin capacitive interface between the Nb couplers and the NbN, and note that these coupler modes also show signatures of hybridization with graphene modes at sub-GHz coupling. The circuit model reproduces all observed modes but with some discrepancies in frequency or amplitude for some modes and avoided crossings, which the authors attribute to uncertainty in the coupler properties.

What the coupling strength and model leave open

The coupling scale is set by the spectrometer's resolution rather than by a fitted coupling constant alone. The paper states that sub-GHz frequency resolution lets the team observe couplings down to the 1–2 µeV level, far below the resolution of optics-based methods. That is the number to compare when asking whether a given material's collective mode is within reach of this platform.

The model has a stated blind spot. The authors note that recently predicted cavity-induced effects on electronic structure itself, such as effective mass renormalization, would also appear in these experiments as shifts in mode frequencies and may not be captured by their circuit model. They propose that KIBCs probed with Josephson spectroscopy offer a promising route to distinguishing such back-action effects in future experiments. Until then, a frequency shift in this architecture cannot be assigned cleanly to a cavity-modified material response rather than to a change in the passive electromagnetic environment.

Where this platform changes the comparison

The paper's own priority is not a single record number but a combination that earlier approaches could not hold together: volume compression of order 10^7, plasmon velocities near c/100, low loss from superconducting NbN, graphene plasmon lifetimes around 15 ps apparently limited by device size, and a spectrometer that works at about 10 mK with femtowatt-to-picowatt on-chip power. The authors also point out that the high effective momentum of the KIBC structure can push into regimes where collective modes with a vanishing coupling matrix element at zero momentum become visible.

The forward-looking claim is that the same instrument allows simultaneous in situ transport measurements in a single device, which the authors leave to future work, and that optimizing dielectric thickness, dielectric constant, and kinetic inductance could yield another order of magnitude in vacuum field amplitude with corresponding reductions in plasmon velocity. For a reader deciding whether this platform is relevant, the decisive comparison is therefore between the 1–2 µeV coupling resolution and the energy scale of the collective mode of interest, with the caveat that mode-frequency shifts from cavity back-action are not yet separable from ordinary environmental shifts in the present model.

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