Three-Terminal Photonic Heat Transistor

• Three-Terminal Photonic Heat Transistor is a device that modulates, amplifies, and switches photonic heat currents between three reservoirs using a controlled gate terminal.
• Implemented in diverse architectures—from superconducting circuits to radiative setups—it exploits quantum coherence, impedance matching, and NDTC to achieve high thermal gains.
• These devices enable thermal logic, advanced cryogenic sensor integration, and efficient energy management, bridging quantum and classical thermal technologies.

A three-terminal photonic heat transistor is a device or system that enables the modulation, amplification, and switching of heat currents transported via electromagnetic (photonic) channels between three distinct reservoirs or terminals. Such devices realize the thermal analog of an electronic transistor, but with photons as carriers and heat flux as the controlled observable. Architectures span the quantum to mesoscopic scale and are implemented across a range of platforms: superconducting circuits, hybrid semiconductor–superconductor devices, variable-range-hopping disordered semiconductors, and tailored radiative geometries employing phase-change or plasmonic materials. Central to the heat transistor operation is the presence of a gate or modulation terminal capable of controlling (switching or amplifying) the heat flow between two other terminals—the source and the drain—through photonic coupling, often exploiting quantum coherence, impedance matching, or negative differential thermal conductance.

1. Device Architectures and Physical Principles

Three-terminal photonic heat transistors are realized in both solid-state and circuit-QED environments. Distinct physical implementations include:

• Quantum circuits: Superconducting flux qubits or qubit–qutrit systems, capacitively or inductively coupled to multiple resonators, each terminated with metallic resistors serving as thermal baths. For example, a superconducting loop with three Josephson junctions (flux qubit) connects to three $\lambda/2$ resonators, each coupled to its own resistor at controlled temperature, facilitating full quantized phonon/photonic heat transfer between terminals (Gubaydullin et al., 2021). In more abstracted models, direct strong coupling between a two-level (qubit) and a three-level system (qutrit) establishes selective coherent energy-exchange channels (Guo et al., 2019).
• Hybrid nanoelectronic platforms: Semiconductor–superconductor architectures, such as devices with two resistive InAs reservoirs acting as source and drain, interconnected non-galvanically through large-area capacitors and a gate-tunable Josephson junction (JoFET). The JoFET’s impedance (inductive/resistive, controlled electrostatically) modulates photonic heat transfer, enabling magnetic-field-free gate operation and enhanced thermal modulation at sub-100 mK (Battisti et al., 20 Oct 2025, Pioldi et al., 6 Feb 2025).
• Radiative geometries: Planar configurations in which source, drain, and gate bodies exchange heat via thermal radiation, with the gate often composed of a phase-change material (e.g., VO$_2$) exhibiting abrupt emissivity changes at its transition temperature. Heat transfer can be dramatically modulated by small changes in gate temperature, owing to changes in spectral optical properties (Li et al., 2024).
• Disordered semiconductors and variable-range hopping systems: Devices in which strong temperature-dependent impedance and now-established negative differential thermal conductance (NDTC) regions allow for amplified control over photonic heat currents and enable temperature or current amplification with gains exceeding unity (Pioldi et al., 6 Feb 2025).

A key element in all architectures is the photonic channel, realized via either electromagnetic resonators/waveguides or free-space radiative coupling, acting as the information-carrying medium for thermal signals.

2. Theoretical Framework

The physics underpinning photonic heat transistors is governed by open quantum system formalism and Landauer-type heat transport theory.

• Quantum master equations: For coupled artificial atoms or superconducting qubits, Lindblad-type master equations describe the evolution of the reduced density matrix, accounting for coherent interactions between system degrees of freedom (qubit/qutrit, resonators) and dissipative coupling to distinct thermal reservoirs. Steady-state heat currents $J_\mu$ through each terminal are computed via energy-resolved transition rates, with the output current (e.g., $J_R$ for the drain) sensitive functions of the gate/control parameters (e.g., gate bath temperature $T_M$, gate voltage $V_g$) (Guo et al., 2019, Majland et al., 2019).
• Landauer–Büttiker transport formalism: For systems in which energy transfer is limited by impedance mismatches (e.g., photonic waveguide connections or resistive-capacitive-coupled circuits), the net photonic heat current between any two terminals $i$ and $k$ is given by

$$J_\gamma = \int_0^\infty \tau_{ik}(\omega) \hbar \omega [n_i(\omega)-n_k(\omega)] \frac{d\omega}{2\pi}$$

where $\tau_{ik}(\omega)$ is the mode-resolved transmission probability, and $_2$0 denotes the Bose population at the reservoir temperature (Pioldi et al., 6 Feb 2025, Battisti et al., 20 Oct 2025). Crucially, $_2$1 can display strong non-monotonic temperature or control dependence, enabling NDTC and signal amplification.

• Radiative transfer theory: For systems dominated by free-space or guided thermal radiation, heat flux is determined by spectral radiance integrals, weighted by view factors, spectral emissivities, and geometric arrangement, with the net drain and source fluxes expressed as

$_2$2

where $_2$3 is the controllable emissivity of the gate material. The transistor effect emerges from steep changes in $_2$4 near phase transitions or from engineered NDTC regions (Li et al., 2024).

3. Transistor Action: Switching, Amplification, and Negative Differential Thermal Conductance

Photonic heat transistors replicate the essential functionalities of electronic transistors: switching (on/off), amplification, and controllable signal flow. Principal mechanisms include:

• Switching: A low gate-control parameter (e.g., low $_2$5 or low $_2$6) results in negligible source-to-drain heat current (off state). As the gate value exceeds a critical threshold, the heat current sharply increases (on state). Quantitatively, this is reflected in the output current $_2$7 (or $_2$8) rising from an experimentally undetectable baseline to a finite, often maximized value over a narrow range of gate control (Guo et al., 2019, Li et al., 2024, Battisti et al., 20 Oct 2025).
• Amplification and NDTC: The amplification factor or thermal gain is defined by

$_2$9

For photonic systems with NDTC, an increase in gate temperature or voltage can paradoxically result in an increase of the source-to-drain heat current—even as the temperature difference decreases. This occurs in regimes where improved impedance matching or selective occupancy of system eigenstates outweighs the reduced thermal gradient (Pioldi et al., 6 Feb 2025, Guo et al., 2019). Reported thermal gains in photonic implementations reach values up to $J_\mu$015 (cryogenic implants) and exceeding 20 (phase-change radiative systems).

• Physical origin of NDTC: In disordered semiconductors with variable-range hopping, NDTC arises from the rapid decrease in device resistance with increasing temperature, leading to non-monotonic behavior in the photonic conductance and creating windows where $J_\mu$1 (Pioldi et al., 6 Feb 2025). In radiative platforms, abrupt emissivity transitions of the gate material or finely tuned relay slabs enable sharp changes in thermal resistance and transmission (Li et al., 2024, Messina et al., 2012).

4. Experimental Implementations and Performance Metrics

Photonic heat transistors have been experimentally realized across diverse platforms, with critical parameters including on/off ratio, amplification, and transimpedance. Representative architectures and their performance are summarized below:

Platform / Reference	Switching/Amplification	Key Operating Regime / Parameter
Superconducting qubit circuits (Gubaydullin et al., 2021)	On/off ratio $J_\mu$21.2 at sub-K temperatures; $J_\mu$3 aW	Magnetic flux sweep modulates qubit splitting
Radiative VO$J_\mu$4 RTT (Li et al., 2024)	$J_\mu$5 up to 22.6, switching ratio $J_\mu$6, $J_\mu$7	Gate $J_\mu$8 across VO$J_\mu$9 insulator–metal transition, $J_R$0 K
Variable-range-hopping PHA (Pioldi et al., 6 Feb 2025)	Amplification $J_R$1 in mK regime	Disordered Ge:Ga islands, NDTC via temperature tuning
InAsOI JoFET (Battisti et al., 20 Oct 2025)	$J_R$2 mK, $J_R$3 mK/V	Gate voltage sweeps JoFET from inductive to resistive regime, $J_R$4 mK

Table entries highlight the breadth of regimes (from millikelvin cryogenic to near-room-temperature operation), the diversity of gate control schemes (thermal bath, gate voltage, phase transition), and achieved amplification and switching ratios.

5. Representative Theoretical and Experimental Models

• Qubit–Qutrit Quantum Thermal Transistor: Strong coherent coupling between qubit and qutrit (respectively driven by independent heat baths) produces a system Hamiltonian

$J_R$5

The system exhibits multi-region amplification, with a stable region where gain $J_R$620, and a robustness of output current to fluctuations at the cold terminal (Guo et al., 2019). Mapping to circuit-QED or all-optical settings is feasible by engineering appropriate level structures and photon-reservoir couplings.

• Three-Body Photon Heat Tunneling: Inserting a passive relay between two near-field separated bodies (e.g., SiC–Drude metal–SiC) can enhance the photon heat flux by up to $J_R$760%, via the relay’s support of additional evanescent transmission channels. Proper choice of relay thickness ($J_R$8) and material properties tuned to surface-mode resonance is critical (Messina et al., 2012).
• Field-Effect Control via JoFET: The use of a gate-tunable Josephson field-effect transistor enables a transition between a low-impedance (inductive) and high-impedance (resistive) regime, strongly modulating the photonic transmission between source and drain. The Landauer formalism directly quantifies output heat and maps its dependence on the gate voltage (Battisti et al., 20 Oct 2025).

6. Applications and Outlook

Photonic heat transistors have been advanced as enabling components for:

• Thermal logic and signal routing: Implementation of logic gates, thermal memory, and heat-based amplifiers is explicitly demonstrated based on switching and NDTC-enabled gain. Such circuits are extendable to hybrid analog-digital architectures in quantum computing and cryogenic classical/quantum electronics (Pioldi et al., 6 Feb 2025, Guo et al., 2019).
• Cryogenic quantum technologies: High transimpedance and low-temperature operation (<100 mK) position these devices for integration with superconducting qubits and on-chip bolometers, where galvanic isolation and nonlocal routing of heat are essential (Battisti et al., 20 Oct 2025, Gubaydullin et al., 2021). Modulation far exceeding that achieved in single-electron-transistor or SQUID-based devices is reported.
• Active thermal management and sensors: Rapid, large-magnitude modulation of heat current (thermal gains >10) enables design of sensitive temperature preamplifiers, thermal routers, and active management systems for radiation sensors (Li et al., 2024, Battisti et al., 20 Oct 2025).
• Near-field energy harvesting and conversion: Relay-enhanced amplification in near-field tunneling opens the possibility of distance-extended thermal control and infrared spectroscopic applications, by leveraging additional surface-polariton channels (Messina et al., 2012).

Future developments are anticipated in high-speed, low-inertia designs (via metasurfaces and 2D materials), ultra-coherent quantum-coherent devices, and scalable, fully non-galvanic photonic logic architectures.

7. Limitations and Fundamental Considerations

Several intrinsic and extrinsic factors constrain device performance:

• Speed and inertia: Macroscopic devices employing phase-change materials or relying on radiative transfer are limited in response time by thermal inertia, typically to the s–ms scale, though circuit-based platforms operating with GHz photons and artificial atoms achieve much higher bandwidth (Li et al., 2024, Ronzani et al., 2018).
• Flux and tuning range: Far-field radiative coupling exhibits lower conductance than near-field or circuit implementations; near-field geometries, impedance matching, and the use of active tuning elements (e.g., gate-controlled Josephson induction) can address this.
• Thermal noise and stability: Robustness to temperature fluctuations at the cold terminal is achievable, particularly in quantum transistor designs with high output insensitivity in certain control regimes (Guo et al., 2019). However, losses and decoherence can limit operational fidelity.
• Fabrication constraints: Realization of devices with strong NDTC, high impedance-matching contrasts, ultra-low electron–phonon coupling, and non-galvanic isolation requires precise material engineering at the nanoscale and high-quality dielectric and superconducting interfaces (Battisti et al., 20 Oct 2025, Pioldi et al., 6 Feb 2025).

These considerations drive ongoing research into optimized geometries, new material systems, and advanced control schemes for next-generation caloritronic and quantum thermal circuitry.