Information exchange in a cryostat: challenges

Conventionally, information between room-temperature equipment and superconducting electronics is transmitted through coaxial RF cabling. Because cooling power quickly diminishes with decreasing temperature, diligent mechanical design and a careful choice of materials is required to strike a suitable balance between bandwidth and heat conduction. This is because both bandwidth and heat conduction in conventional cabling depend on resistivity, which does not apply to optical fibres. Still, scaling conventional RF cabling up to a few hundred cables is possible, and in fact implemented in cryostats used for state-of-the-art qubit experiments [11]. In terms of the quantitative figures of merit, a highly optimistic estimate of the heat leak per bit for conventional cabling from 55 K to 4 K would be 1300 aJ/bit, a figure greatly exceeding our target for a first generation optical data bus.

The question of transmitting data from 4 K to a mK stage requires separate consideration, because superconducting cables are an option, ensuring low thermal conductivity. Nevertheless, optical fibres have the long-term potential of providing even more bandwidth for the same footprint, thanks to their extremely high-bandwidth, small diameter and negligible cross-talk.

Data input

On the OE conversion side, we tackle the challenging task to combine the state-of-the art of single photon detection with the state-of-the art of high-speed detectors. Superconducting nanowires single-photon detectors (SNSPDs) have reached unprecedented quantum efficiency (exceeding 90%) but their detection rate is typically limited well below 1 GHz [12,13]. The state of the art of high-speed PDs is represented by uni-traveling-carrier photodiodes, exceeding 300 GHz bandwidth but, being diodes, they can hardly be operated at cryogenic temperatures, due to carrier freeze-out, and can hardly detect a few photons. A competing emerging technology is plasmonic PDs, that have recently exceeded 100 GHz [14], and are naturally suited for nanoscale miniaturization and for cryogenic operation, as they don’t rely on dopants. We stress that SFQ circuits typically have input and output impedances of only a few ohms, meaning relatively large working currents (10÷100 μA) and sub-mV voltages. This is an issue for OE converters based on photodiodes and EO converters based on light emitters, since the photon energy sets the natural voltage scale at ≈ 1 V. Instead, typical currents through SNSPDs are comparable to typical SFQ currents, and the rising edge of an SNSPD pulse is sharp (~ 100 ps), approaching the natural time scale of low-critical-current-density SFQ circuits. Indeed, readout of SNSPDs by superconducting logic has been proposed and demonstrated for the purposes of reducing the number of coaxial output lines in multi-pixel SNSPDs [15–19]. All those cases involved inherently long and slow (≈ 100 MHz) SNSPDs, which are not suitable to drive SFQ circuits at full speed.

Data output: a first approach based on efficient modulation

The EO conversion side is even more challenging for existing technologies. The low signal levels of the electrical output of SFQs (10÷103 µV) and the high-speed requirements call for EO interfaces which can operate with mV (or lower) driving voltages and ~ 0.1÷1 aJ energy per bit levels, unless RF signal amplification is used. Electro-optic modulation beyond 100 GHz have been demonstrated by several modulator concepts, but plasmonic modulators offer unprecedented small footprint, low power consumption and low driving voltages, due to enhanced interaction between the optical field and electro-optic material. The state-of-the-art plasmonic modulators developed by ETH have reached modulation bandwidths up to 500 GHz [20] and power consumption in the sub-fJ/bit range [21], with driving voltages < 1 V. In the aCryComm project, we aim to develop further plasmonic modulators to enable high speed and (ultra) low-power consumption at cryogenic temperatures. The best plasmonic modulators reported to date, rely on the Pockels effect in polymers with EO coefficients up to 400 pm/V for bulk and up to 230 pm/V when integrated in a slot on a chip [22]. Even stronger Pockels effect (r42 = 700 pm/V) have been found in barium titanate (BTO) in plasmonic modulators by ETH [23]. Nevertheless, experiments at 4 K showed a significant 70% reduction of the nonlinear coefficient of BTO [24,25], whereas some EO polymers measured at 7 K had only about 10% decrease, suggesting that some polymeric materials may maintain most of their optical properties in this temperature range. The performance and durability of electro-optic materials in the mK regime, instead, remain mainly unexplored. Beside the challenges and unknowns, one good news of working at cryogenic temperatures is that the propagation losses of the plasmonic modes will be significantly reduced [26–28], which allows longer devices, and therefore lower driving voltages and power consumption, so to be more compatible with SFQ requirements.

Data output: a second approach based on nanoscale light sources

We will also explore a complementary approach for fast and low-energy EO interfaces, using directly modulated nanoscale light sources instead of modulating an externally generated light signal. In terms of high-speed and low energy per bit performance, vertical cavity surface emitting lasers (VCSEL) and distributed feedback (DFB) lasers present the current SoA of conventional directly modulated semiconductor light sources, with ~ 100 fJ/bit for modulation at 100 GHz. Our breakthrough solution is to exploit similar gain materials as in macroscopic lasers to create nanoscale light sources with subwavelength dimensions that can operate at cryogenic temperatures. Even though nanolasers and nanoLEDs based on metal-clad III-V semiconductor pillars are under extensive development for optical interconnects operating at room temperature [29], cryogenic operation requires completely different optical and electrical considerations. Doped regions must be carefully designed taking into account carrier freeze-out, and metal contacts are taken very close to the gain region, effectively acting also as a part of the optical cavity. In contrast to traditional macroscopic light emitters, a metal-clad semiconductor light source, has extremely small device volume (smaller than a cubic wavelength in the medium), which has a number of important consequences: (i) The cavity supports only one or a few optical modes in the gain band which increases the spontaneous emission coupling factor (β) to the lasing mode, reducing the lasing threshold. The extreme case of only one allowed mode with β→1 enables thresholdless lasing without a clear transition from spontaneous to stimulated emission [30]. (ii) A metal-clad semiconductor nanocavity has a low or moderate cavity quality factor yet it still provides strong Purcell enhancement of the emission owing to the ultra-small mode volume. Consequently, the device has short radiative lifetime of the excited state and short photon lifetime in the cavity mode, allowing ultrafast response in both LED and laser operation. To this end, the direct electrical modulation of InGaAs/InP based nanolasers has already been demonstrated for operation at 77 K [31]. (iii) The energy per bit for high speed operation scales down with the device volume [32]. In aCryComm, we develop two parallel lines of technology: one using InGaAs/GaAs quantum dots as the gain medium for 950÷1100 nm wavelengths [33] and the other based on InGaAs/InP materials for the 1550 nm telecom band [34]. The current SoA in direct electrical modulation of metal-clad nanolasers is 30 MHz modulation speed for operation at 77 K using InGaAs/InP materials [31], with modulation speed in this demonstration limited by the electrical cables used in the cryostat. The metal-clad semiconductor nanolasers are expected to achieve modulation bandwidths exceeding 100 GHz [35]. We stress that the hybrid cavity mode becomes more and more plasmonic in nature when the volume is reduced, leading to the increase of lasing threshold as a result of losses in the metal. However, these losses become significantly lower when moving to cryogenic temperatures [26–28], which brings also a number of major advantages, such as a significant reduction of leakage current, and lower non-radiative losses in the semiconductor. We have here a unique opportunity to shrink the cavity to unprecedented small sizes, and to aim at a significant leap over the current SoA of electrically driven nano-light-sources in terms of both energy efficiency and modulation speed by exploiting the advantages brought by the cryogenic operation at 4 K and mK temperatures. This will also give us a chance to scale down the device volume to approach the quantum regime where the optical energy per bit is minimized down to the single photon level. It should be noted that the cryogenic high-speed performance of electrically pumped nanolasers is still largely unknown. Therefore, as an alternative approach we will consider optically pumped and electrically modulated III-V semiconductor light emitters in high-Q optical cavities [36]. This approach allows for separating pumping and signal modulation which provides more degrees of freedom for optimizing the speed and energy efficiency of the EO-interface, therefore mitigating the risks linked with carrier freezing at cryogenic temperatures.


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