Superconducting terahertz emitters based on stacks of intrinsic Josephson junctions (IJJs) in Bi2Sr2CaCu2O8+δ (Bi-2212) emit coherent radiation through the synchronized ac Josephson oscillations of hundreds to thousands of junctions, but single stacks are limited to output powers below about 100 microwatts by Joule self-heating; mutual synchronization demonstrated to date with direct phase-sensitive evidence involves only two emitters, and the best collective emission from multi-mesa arrays (three mesas, without phase-sensitive evidence) remains below roughly 1 mW. The source paper (Tsujimoto et al., Phys. Rev. Applied 13, 051001 (2020)) used full Stokes-parameter polarization analysis of two simultaneously biased mesas to prove phase synchronization mediated by Josephson plasma waves in the superconducting base crystal, and left open the follow-on problems: determine the inter-mesa coupling matrix VmV_m (whether its diagonal or non-diagonal elements dominate), understand and mitigate the self-heating that limits power and may prevent synchronization among multiple mesas, and extend mutual synchronization beyond two mesas and characterize the resulting coherence. A 2024 study confirms that Joule heating still prevents synchronization of more than three stacks on a common base crystal; it demonstrates only an alternative two-stack route through a shared gold contact layer and leaves larger arrays open. The problem remains open.

Background

The layered cuprate superconductor Bi2Sr2CaCu2O8+δ (Bi-2212) behaves as a natural stack of intrinsic Josephson junctions (IJJs) — superconducting electrode pairs separated by insulating BiO layers, roughly 670 junctions per micrometer of crystal thickness along the c-axis. By the ac Josephson effect, a dc voltage VV applied across a Josephson junction drives an alternating supercurrent at frequency f=V/Φ0f = V/\Phi_0, where Φ0\Phi_0 is the magnetic flux quantum (2.07×10−152.07\times10^{-15} Wb, giving 483.6 GHz per millivolt), so millivolt-scale biases place the oscillations in the terahertz range. A mesa — a small pillar photolithographically patterned from a Bi-2212 single crystal on a remaining base crystal — emits coherent terahertz radiation when the thousands of junctions in the stack synchronize, which occurs when the Josephson oscillation resonates with an electromagnetic cavity mode of the mesa geometry (typically a standing wave along the mesa width). This physics underlies superconducting solid-state terahertz sources demonstrated since 2007, which are broadly tunable and monolithically fabricated but limited in power.

Two limitations define the problem. First, Joule self-heating: Bi-2212 is a poor thermal conductor, dissipation can drive part of the mesa above its superconducting transition temperature (a 'hot spot'), and heating caps the output power of a single stack at values below roughly 100 μW. Second, scaling by synchronization: the output power of an ideal coherent array should grow as the square of the number of synchronized junctions, so synchronizing many mesas is the most promising route to milliwatt-class sources. Benseman et al. (Applied Physics Letters 103, 022602 (2013)) reported collective emission from three adjacent mesas on a common base crystal with output up to about 0.61 mW (610 μW), but the evidence was power enhancement, not a direct measurement of phase locking. Theory by Lin and Koshelev (Physica C 491, 24 (2013)) proposed that the coupling agent is the Josephson plasma wave (JPW) — an electromagnetic plasma mode of the layered superconductor, polarized along the c-axis and propagating in the superconducting planes — traveling through the base crystal between mesas.

Tsujimoto et al. (Phys. Rev. Applied 13, 051001 (2020)) supplied the missing phase-sensitive evidence for two mesas. They biased two mesas (A1, A2) simultaneously and measured the full set of Stokes parameters (S0S_0–S3S_3, the standard four quantities characterizing the polarization state of a quasi-monochromatic wave) by passing the emitted beam through a quarter-wave plate (a device delaying one linear polarization component relative to the orthogonal one by a quarter period) and a wire-grid polarizer (an array of parallel metal wires that transmits the electric-field component perpendicular to the wires). The simultaneous-emission polarization was described as a linear superposition of the two individual emissions with a complex amplitude ratio β/α\beta/\alpha: its argument is the phase difference between the Josephson oscillations of the two mesas, and its modulus measures the interaction strength. The observed axial ratio (ratio of major to minor axis of the polarization ellipse; infinite for perfectly linear polarization) jumped from about 2 (individual emission) to about 24 (simultaneous emission), demonstrating a fixed phase relation and hence mutual synchronization, most plausibly mediated by small-amplitude Josephson plasmons propagating in the base crystal. The formalism introduces a 4×44\times4 perturbation matrix VmV_m coupling the two-mesa Josephson-plasmon states; the paper notes that VmV_m may contain non-diagonal elements and that its symmetry 'involves a general question in non-linear physics regarding the symmetry of the matrix'. The theory also predicts singular states of 'perfect polarization' (infinite axial ratio, attributed to coherent excitation of the Josephson plasmon) when ∣β/α∣<0.9|\beta/\alpha|<0.9 and the phase difference arg⁡(β/α)\arg(\beta/\alpha) is near 45° or 135° — while the experiment achieved ∣β/α∣≈0.9|\beta/\alpha|\approx0.9, just outside this regime, so the singular states were not realized.

Problem Statement

The problem, as posed by the unresolved issues of Tsujimoto et al. (Physical Review Applied 13, 051001 (2020)), is to scale mutually synchronized intrinsic Josephson junction terahertz emitters from the demonstrated two-mesa (and, at the power level only, three-mesa) regime to a genuinely multi-mesa coherent source. Concretely: (1) determine the inter-mesa coupling matrix VmV_m — the perturbation coupling the Josephson-plasmon states of the individual mesas, including whether its diagonal or non-diagonal elements dominate and what symmetry it has — with an evidence-backed analysis; (2) understand and mitigate the self-heating and thermal gradients in Bi-2212 mesa arrays that limit output power and may prevent synchronization among multiple mesas; and (3) establish whether mutual synchronization of a larger number of mesas than two is achievable and characterize the resulting coherence properties (inter-mesa phase relations, linewidth, output power and its scaling with the number of mesas). These components jointly serve one overarching objective — a phase-synchronized Bi-2212 emitter array whose output power and coherence follow from an understood, characterization-backed inter-mesa coupling mechanism.

References

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