With superconductors that use the Josephson effect, it is also possible to generate coherent millimetre waves and THz photons on a chip, typically between 100 GHz and 10 THz (refs. ). JJs naturally convert d.c. voltages to high-frequency electric currents, resulting in electromagnetic radiation that crosses the THz gap, where 1 mV equals about 0.483 THz. While the emission power from a single junction is normally in the picowatt regime, a device that contains multiple junctions emitting in phase at the same frequency can dramatically increase the output power, reaching microwatt levels. The frequency of generated THz radiation is determined only by the material's superconducting energy gap. In superconductors with low transition temperatures (T), the frequency is often limited to the millimetre-wave (sub-THz) range. However, in high-transition temperature (high-T) superconductors, the frequency can reach around f = 15 THz. Because of their broad frequency range, these high-T superconductors are especially attractive for applications that require higher-frequency THz radiation.

Interconnected JJs may self-synchronize with a collective radiation field and emit coherently via a quantum-stimulated emission mechanism involving Cooper pairs and photons. The underlying physical mechanism of synchronization is identical to the quantum description of a group of superradiant atoms in a resonating cavity. The output power scales with the square of the number of active junctions N. In general, such an N dependence indicates coherence in a system of N oscillators. The connection between a single JJ and a quantum radiating two-level atom demonstrates that spontaneous and stimulated emission and absorption can occur in JJs. Two-dimensional (2D) JJ arrays made of underdamped Nb-Al-AlO-Nb junctions, which are macroscopic and non-identical objects with no shunt resistors, coupled to a high-quality factor (Q) cell resonance (Fig. 2a) emit quantum coherent radiation at f = 150 GHz in the same way that atoms in a laser emit. The emission frequency is equivalent to a high-Q resonance in the structure formed by the array and the ground plane. This resonance stimulates sharp, self-induced steps in the current-voltage characteristics of the array. The power coupled to the detector is measured as a function of the number of junctions that are biased at the resonant step. In such a scenario, no detectable power is observed if the number of active junctions is below a critical threshold (N). This behaviour is analogous to the threshold phenomenon in lasers (where coherent radiation appears only when the gain exceeds the losses, indicating the presence of population inversion), underlining their potential as efficient coherent millimetre-wave and THz radiation sources. Above N, the detected power scales with the square of the number of active junctions, reaching a d.c.-a.c. power conversion efficiency of nearly 17%. In comparison, arrays that synchronize via classical coupling processes have a maximum a.c.-d.c. conversion efficiency of only 1%. The emission power from a single JJ is relatively small, but it can be largely enhanced in a superradiant manner by using either planar or vertical JJ arrays with several synchronized junctions (N ≫ 1). Synchronization is often facilitated by a resonant electromagnetic mode, such as a cavity mode (a standing electromagnetic wave), which can be established either within an external cavity or within the dielectric substrate. To achieve an emission power at the milliwatt level, very large arrays (such as that shown in Fig. 2b) containing approximately N ≈ 10-10 JJs would be required. Considering the achievable integration density, such arrays would typically have a size of L ≈ 1 cm, which is significantly larger than λ even at millimetre-wave frequencies. However, as the size of the planar 2D array increases, so does the complexity of achieving synchronization. The challenge originates from variations in junction parameters, which statistically increase with N, as well as unequal environmental conditions for the inner and outer JJs. In addition, large phase delays along the array hinder the synchronization process. In the non-resonant scenario, synchronization can be accomplished using a unidirectional travelling wave along the array, which functions in a way similar to a travelling wave (Beverage) antenna. The primary feature of this travelling-wave domain is a strong forward-backwards asymmetry in the radiation pattern, with the majority of the power radiated in the direction of the wave's propagation. This behaviour differs significantly from the resonant standing wave scenario, in which the radiation pattern is symmetric by definition. As a result, the form of the radiation pattern makes it easy to distinguish between these two operational modes. The previously described planar 2D JJ arrays were artificially produced structures, the large-scale fabrication of which is quite challenging. In comparison, 1D arrays of JJs naturally grow in layered high-T superconductor BiSrCaCuO (BSCCO). Devices based on BSCCO are emerging compact sources of coherent continuous-wave electromagnetic radiation in the millimetre-wave and THz frequency bands. In BSCCO, the junctions are naturally identical. They are evenly spaced with two junctions per unit-cell c-axis edge length of 1.533 nm, forming stacks of JJs (Fig. 2c). The superconducting CuO layers of BSCCO, coupled with the intrinsic Josephson effect, can maintain high voltages across junctions. Owing to the large superconducting energy gap, BSCCO devices can produce powerful, coherent radiation spanning the THz gap with emission powers of free-space radiation of several hundred microwatts and emission linewidths as low as 6 MHz at 600 GHz (refs. ). The efficient excitation of high-frequency currents is an important consideration in the development of superconducting sources. This can be accomplished by triggering resonances such as the Fiske resonance using a junction bias. Similar to a laser cavity, the stimulation of an electromagnetic cavity resonance within the sample generates a macroscopic coherent state, causing a large number of junctions to oscillate in phase. Modern flux-flow oscillators provide microwatt-level powers at frequencies ranging from 400 GHz to 600 GHz, with emission linewidths as small as ~0.6 MHz. 1D or 2D arrays of phase-locked JJs result in much larger emission powers; for example, an array of 1,968 junctions delivers 160 μW at a frequency of 240 GHz. Phase locking is critical, and it can be accomplished by placing the junctions in a microwave stripline at half-wavelength intervals on a common ground plane linked to a resonant cavity or loading the array with an external inductor-capacitor-resistor circuit (LCR) resonance circuit. The radiation power of an array depends on the array geometry and the external circuitry. The power of a 1D series-connected array scales as N (where N is the number of phase-locked junctions) for an unmatched load (for which the effective array resistance is smaller than the load resistance) and N for a matched load. The emission linewidth decreases as 1/N for all array types. Examinations of devices with various cavity geometries (from square to rectangular, cylindrical, triangular and pentagonal, as shown in Fig. 2d) fabricated using different techniques and under varying conditions reveal that the a.c. Josephson effect is the principal driving mechanism for the radiation in BSCCO THz sources. While cavity resonance (Table 1) contributes to increased radiation strength, the two mechanisms act together during the emission process. The combination of the a.c. Josephson effect and cavity resonance is critical to produce stronger and coherent THz radiation. In such THz sources the radiation power efficiency (RPE; the ratio of emitted to dissipated power) drops quickly, especially in the low THz region. The measured RPE for BSCCO single-crystal-based devices with both large and small mesas is below 1%, lower than the theoretical limit of 50%. An impedance mismatch between the device and the open space mostly causes this lower efficiency. In general, a low RPE results from poor impedance matching, as JJs are significantly smaller than wavelengths, with interlayer distances as small as 1 nm. As a result, JJs act as microdipoles with low far-field emissions. In the end, the radiation is supported by the device's passive (but larger) elements, such as the BSCCO crystal and electrodes, which operate as matching antennas. To ensure impedance matching, the emission must be optimized via precise microwave design. Self-heating is an important issue encountered in all cryogenic devices.

Given the limited cooling capacity of tiny cryostats (typically sub-watt at low temperatures), devices with a 1% RPE would be unable to output much more than 1 mW. The THz emission power (P) of cryogenic sources is restricted by the cooling power (P) and RPE; P < RPE × P must be satisfied. In the case of compact cryocoolers that have low cooling power, the best way to boost the emission power is to improve the RPE. THz sources based on BSCCO whisker-type crystals with intermediate-sized mesa structures, as shown in Fig. 2e, could provide a solution to these issues. Various approaches can be used to detect THz radiation, such as in situ detection with a device on the same whisker, on-chip detection with electrically isolated devices and off-chip detection with a bolometer. Furthermore, the radiative cooling process can be used to determine the absolute value of the emitted power. Whisker-based BSCCO THz sources can achieve RPEs of up to 12%, resulting in an emission power in the far field of around P ≃ 0.11 mW. The increase in efficiency (an order of magnitude greater than equivalent devices produced on traditional BSCCO single crystals) is related to better impedance matching with free space. This can be attributed mainly to the turnstile antenna-like design of the devices, which reduces parasitic capacitance between the crystal and the electrode. By minimizing unnecessary capacitance, the device improves impedance matching with open space, allowing more effective THz radiation emission. One of the most efficient techniques for improving the radiation intensity is to synchronize several mesas to release radiation simultaneously. Once two mesas operate in series, the combined emission intensity surpasses the total of their separate outputs. For instance, coherent THz emission can be achieved in devices with up to three mesas coupled in parallel, with the intensity scaling roughly proportionally to the number of synchronized mesas squared. Experimental results show an emission intensity of 0.61 mW, demonstrating the efficiency of this method. The polarization of the radiation emitted from individually biased mesas, together with the coupling matrix that describes the interaction of Josephson plasma waves between mesas, provides insight into how each mesa contributes to the overall synchronized emission when multiple mesas are simultaneously biased. Quantitative measurements of the polarization of the output electromagnetic wave allow an estimation of how each mesa affects the overall synchronized radiation. Comparing the emission properties of parallel and series couplings of identical mesas (like the devices shown in Fig. 2f) is especially relevant, because the coupling matrix might evolve when identical bases are employed, potentially resulting in different synchronization dynamics. In an emission mesa, where a thousand stacked intrinsic JJs (IJJs) oscillate coherently as a macroscopic JJ, the common voltage bias caused by parallel couplings should create synchronized oscillations across the macroscopic junctions. On the other hand, the common current bias caused by series couplings provides useful information on the performance of a smaller number of stacked IJJs. Inter-mesa coupling becomes critical, especially when two or three mesas are used in common voltage bias or common current bias modes. Studying the polarization of the electromagnetic waves generated by the mesas, both in the case of single mesa emission and in coupled emission modes, provides important information about their synchronization dynamics, revealing how the individual oscillators phase-lock and contribute to coherent collective radiation. In the common voltage bias mode, the emission has a unimodal frequency spectrum, indicating strong coupling between the mesas. In contrast, the common current bias mode generates uncoupled emissions with a bimodal frequency spectrum. The coupled emission state is effectively a superposition of independent emissions of radiation that are influenced by inter-mesa couplings. The coefficients of this linear combination form the interaction matrices between mesas. These interaction matrices indicate the harmonically oscillating plasmons within the superconducting substrate that facilitate the interaction of the nonlinear Josephson plasma oscillations in the mesas. The principles underlying powerful THz emissions from different devices have been investigated, demonstrating that BSCCO-based devices can produce THz radiation with frequencies ranging from 1 to 11 THz (ref. ), but the self-heating issue must be solved for these BSCCO emitters to generate THz waves at frequencies lower than 200 GHz. Self-heating causes hot areas in the stack, which reduce the voltage across the JJs. One approach to address this issue is using sandwich-structure devices that can boost the cooling efficiency. These developments have also increased the emission frequency beyond 2 THz. At frequencies below 200 GHz, Josephson plasma frequency (f) and resonant cavity modes dominate the THz emission frequency. The f is dependent on temperature and follows the relation f(T) ∝ (j(T)) with a cutoff emission frequency around 4f. Here, j refers to the JJ critical current density. At relatively cold bath temperatures (T), f is saturated, resulting in a constant cutoff emission frequency at the bottom end of the spectrum. When T rises, f falls, finally reaching zero when T reaches the critical temperature T, resulting in a lower low-frequency cutoff. Moreover, the activation of collective cavity resonances across the entire stack boosts the THz emission, with the emission frequency determined by a particular resonance mode. As a result, BSCCO stacks with low-frequency resonance modes can emit THz waves with adequate power in the lower frequency range. THz emitters with square gold-BSCCO-gold mesas (with T = 88.6 K) on sapphire substrates (Fig. 2g) can extend the emission frequency to f = 0.15 THz, generating a power output of 0.18 μW at T = 75 K and 85 K (ref. ). The operating temperatures of these devices notably exceed the boiling point of liquid nitrogen (77 K). In pushing the operation temperature of BSCCO devices higher than 77 K, an emitter with mesa of BSCCO doped with 0.16 holes per Cu atom with T = 86.5 K (Fig. 2h) generates THz radiation of 130 μW coherent power at f = 0.456 THz at T = 77.4 K (ref. ). This progress shows that implementing a BSCCO crystal with a different Bi/Sr stoichiometry could reach equivalent THz power levels at higher temperatures, resulting in a T higher than 86.5 K. This change may provide more thermal flexibility, making these devices better suited for emerging technologies and quantum applications that require stable operation at high temperatures. Another approach to address the thermal conductivity issue is to use standalone stacks that are connected by gold layers and share a common gold layer. This design shown in Fig. 2j benefits from the thermal conductivity of gold being significantly higher than that of the BSCCO base crystals, while its patterning remains relatively straightforward. In this device, the two oscillators exhibit phase correlations within ±0.4 GHz of their centre frequencies, ranging from 745 to 765 GHz. However, strong phase gradients in the beams radiated from both mutually locked and unlocked stacks seem to play a crucial role, probably reducing the detected emission power due to destructive interference. This effect may stem from higher-order cavity modes excited within individual stacks. The mutual interaction facilitated by the common gold layer could offer new possibilities for mitigating Joule heating, potentially enabling the synchronization of more stacks. This approach may also allow the synchronization of smaller stacks, which are less susceptible to strong phase gradients. BSCCO devices can generate coherent THz frequency signals with high-speed modulation reaching up to 40 GHz when 3 GHz sinusoidal waves on a d.c. bias of about 2 V are superimposed on 840-890 GHz carrier waves radiated by the device. As previously discussed, the JJs embedded within BSCCO emit THz waves with frequencies precisely proportional to V, following the relation f = 2eV/h. By modifying V, the Josephson plasma emission frequency can be modulated, allowing dynamic control over the output THz frequency, as schematically shown in Fig. 2i. The modulated signals generate discrete comb-like features, as defined by a Bessel function sum, with the spacing between each comb tooth corresponding to the modulation frequency. On-chip gigahertz-bandwidth frequency-modulated Josephson plasma emission requires precise control of the temporal behaviour of almost a thousand identical IJJs, which are naturally stacked in a vertical 1D array. As mentioned above, each IJJ is around 1.533 nm thick and has two junctions per unit cell that are evenly spaced. In BSCCO, superconductivity is limited to 2D planes held together by weak van der Waals interactions between the layers. One of the most difficult challenges in implementing frequency modulation in BSCCO-based sources has been regulating the temperature changes produced by the higher modulation amplitude of the bias voltage. With precise electrical biasing and gigahertz synchronization of the phase emission of numerous IJJs of the device, the right choice of cavity geometry may address this issue. The detailed fundamental physics of electromagnetic wave radiation from JJs is explained in previous reports. For application purposes (Fig. 2k), BSCCO THz sources have several distinct benefits. These include chip integrability, very small footprints, low power dissipation, monolithic generation of linearly and circularly polarized coherent THz waves, narrow emission linewidths of less than 10 MHz and the ability to cover a wide bandwidth across the THz gap. They also have a high RPE, which is promising for application domains from metrology, tomography and imaging to future ultrafast communication and computing networks.