Wireless Josephson Parametric Amplifier

• Wireless Josephson Parametric Amplifier is a microwave amplifier based on Josephson junctions that employs wireless coupling (via waveguides, antennas, or cavity fields) to minimize losses and impedance mismatches.
• It uses nonlinear resonators and parametric pumping to achieve near-quantum-limited gain with low added noise, leveraging techniques such as four-wave mixing and flux pumping.
• Current designs focus on impedance engineering and integrated RF functionality to optimize gain, bandwidth (from 9 GHz to over 20 GHz), and tunability for advanced quantum applications.

Searching arXiv for recent and foundational papers on wireless Josephson parametric amplifiers and closely related architectures. arXiv search query: "Wireless Josephson parametric amplifier" A wireless Josephson parametric amplifier (WJPA) is a Josephson-junction-based, near-quantum-limited microwave amplifier whose signal port is not defined by a conventional wired microstrip or coplanar line, but instead by a microwave waveguide, slotline, cavity field, antenna, or related near-field structure integrated into the package or electromagnetic environment. In the literature, closely related devices appear under both “wireless Josephson amplifier” and “wireless Josephson parametric amplifier.” The common objective is to eliminate or reduce waveguide–coax–planar transitions, wirebonds, hybrids, directional couplers, printed-circuit traces, and other auxiliary microwave components that introduce loss, impedance mismatch, and limited tunability (Narla et al., 2014, Hao et al., 15 Aug 2025).

1. Historical emergence and scope

The earliest explicit wireless implementation in this lineage is the “wireless Josephson amplifier” of 2014, which coupled a lumped Josephson amplifier directly to the propagating mode of a rectangular waveguide by an on-chip dipole antenna, with no intermediary planar microwave feedlines, wirebonds, hybrids, or input directional couplers (Narla et al., 2014). That device was motivated by the integration problems posed by 3D cavity implementations, especially the transitions between waveguide, coaxial cables, and planar circuits, and by the fact that auxiliary microwave components are sources of spurious losses and impedance mismatches that limit measurement efficiency and amplifier tunability.

A later development is the 2025 realization of a WJPA operating above $20~\mathrm{GHz}$, where the wireless design is implemented through a waveguide-to-slotline transition integrated into a 3D package (Hao et al., 15 Aug 2025). That work explicitly frames the wireless architecture as a response to the losses and impedance mismatches that become problematic at high frequencies. It reports more than $20~\mathrm{dB}$ of gain across a tunable frequency range of $21\text{--}23.5~\mathrm{GHz}$, with a typical dynamic bandwidth of $3~\mathrm{MHz}$, and an added noise of approximately two photons.

The term is not uniformly delimited across all JPA literature. A technical review published in 2025 states that “Wireless Josephson Parametric Amplifier (WJPA) is not a term explicitly defined in the paper,” but then characterizes the relevant building blocks as Josephson parametric amplification combined with on-chip resonators, near-field coupling, and impedance-engineered structures (Salmanogli et al., 17 Jul 2025). Related work on 3D cavity JPAs and impedance-transformed JPAs similarly treats wireless coupling as an architectural question rather than a distinct amplification mechanism (Mahboob et al., 2022, Qing et al., 2023). This suggests that WJPA is best understood as a coupling and packaging paradigm for JPAs, not as a separate parametric-amplifier species.

2. Parametric amplification physics in wireless form

Wireless Josephson parametric amplifiers remain Josephson parametric amplifiers in the strict circuit-theory sense. What changes is the way the nonlinear resonator couples to its environment, not the nonlinear mechanism itself (Kono et al., 15 Apr 2026). The active element is still a Josephson junction or SQUID-based nonlinear inductance, and amplification still arises from parametric pumping.

For a lumped resonator with mode operator $a$, a general effective description used for a wireless implementation above $20~\mathrm{GHz}$ is

$$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$

where $\omega_r$ is the bare resonant frequency, $K$ is the Kerr coefficient, and $H_\text{pump}$ describes the interaction with an external pump drive (Hao et al., 15 Aug 2025). In that device, the amplifier is operated as a single-pump four-wave-mixing device, with

$20~\mathrm{dB}$0

After linearization around a large coherent pump amplitude,

$20~\mathrm{dB}$1

with $20~\mathrm{dB}$2 proportional to $20~\mathrm{dB}$3 (Hao et al., 15 Aug 2025).

Flux-pumped wireless-relevant architectures are described by the standard degenerate JPA Hamiltonian. In the broadband CPW-based impedance-transformed JPA, the flux is modulated as

$20~\mathrm{dB}$4

with $20~\mathrm{dB}$5, and the rotating-wave Hamiltonian becomes

$20~\mathrm{dB}$6

where $20~\mathrm{dB}$7 and $20~\mathrm{dB}$8 is the pump-dependent parametric coupling (Qing et al., 2023). The quartic term regularizes the divergence at the parametric instability and is important for saturation and squeezing performance, but for small-signal gain it is neglected.

The corresponding input–output description gives the power gain

$20~\mathrm{dB}$9

with $21\text{--}23.5~\mathrm{GHz}$0 in the strong-coupling limit (Qing et al., 2023). Parametric instability occurs as

$21\text{--}23.5~\mathrm{GHz}$1

A recurring point in the WJPA literature is that the pump and nonlinearity remain local even when the signal coupling becomes wireless. In the CPW impedance-transformed design, the device is clearly flux-pumped: DC flux bias sets $21\text{--}23.5~\mathrm{GHz}$2, an RF tone at $21\text{--}23.5~\mathrm{GHz}$3 is applied on the flux line, and the RF signal to be amplified is injected and extracted through the linear CPW port (Qing et al., 2023). For WJPA, this means that “wireless” does not imply pump-free or bias-free operation; it means that the signal port is realized through a shaped electromagnetic environment rather than conventional wiring.

3. Coupling architectures and electromagnetic implementations

The foundational wireless architecture used a sapphire chip mounted inside a WR-90 rectangular waveguide supporting the fundamental TE$21\text{--}23.5~\mathrm{GHz}$4 mode between $21\text{--}23.5~\mathrm{GHz}$5 (Narla et al., 2014). The chip was placed at a distance $21\text{--}23.5~\mathrm{GHz}$6 from a shorted wall so that the electric field at the chip location was maximal, and two galvanically connected pads formed a dipole antenna. In that design, the antenna acts as a coupling capacitor $21\text{--}23.5~\mathrm{GHz}$7 between the resonator and the waveguide mode, and the external quality factor obeys

$21\text{--}23.5~\mathrm{GHz}$8

In the short-dipole limit $21\text{--}23.5~\mathrm{GHz}$9, so $3~\mathrm{MHz}$0, which provides a direct electromagnetic design knob for bandwidth without changing the resonant frequency (Narla et al., 2014).

The high-frequency WJPA of 2025 replaces the dipole-waveguide interface by a waveguide-to-slotline transition in WR42 geometry, $3~\mathrm{MHz}$1, supporting $3~\mathrm{MHz}$2 (Hao et al., 15 Aug 2025). The slotline is defined in superconducting tantalum on sapphire and acts as the feedline for a flux-tunable lumped resonator consisting of an Al/AlO$3~\mathrm{MHz}$3 SQUID shunted by interdigitated capacitors. The slotline has characteristic impedance $3~\mathrm{MHz}$4, is shorted at one end, and the resonator is coupled at $3~\mathrm{MHz}$5, chosen to correspond to approximately a quarter wavelength at $3~\mathrm{MHz}$6. The taper profile for the waveguide-to-slotline transition is

$3~\mathrm{MHz}$7

with $3~\mathrm{MHz}$8, $3~\mathrm{MHz}$9, and $a$0. HFSS simulations show return loss $a$1 and insertion loss $a$2 over $a$3 (Hao et al., 15 Aug 2025).

A cavity-mediated variant appears in the three-dimensional Josephson parametric amplifier. There, the nonlinear element is not in-line with the cavity feedline; instead, a SQUID embedded in a two-dimensional dipole resonator couples capacitively to the fields of a 3D cavity (Mahboob et al., 2022). The SQUID circuit is therefore coupled to the measurement mode through cavity fields rather than direct transmission-line wiring. This is a “wireless-like” coupling scheme in which the cavity inherits an effective Kerr nonlinearity from the SQUID resonator.

The CPW-based impedance-transformed JPA is not itself labeled wireless, but it is directly relevant because it realizes a single-mode, lumped-element, flux-pumped JPA embedded in a non-$a$4 environment via a distributed-element impedance transformer implemented as a single horn-like CPW line (Qing et al., 2023). The gap is fixed at $a$5, the center conductor width is tapered from $a$6 to $a$7, and the characteristic impedance decreases from $a$8 to approximately $a$9 following a Klopfenstein taper. The paper explicitly notes that the linear CPW environment can be shaped arbitrarily, including into antenna or quasi-free-space structures (Qing et al., 2023). This places impedance engineering at the center of WJPA design.

4. Experimental realizations and reported performance

Several realizations define the present experimental range of wireless and wireless-adjacent Josephson parametric amplification.

Platform	Coupling modality	Reported performance
Wireless Josephson Amplifier (Narla et al., 2014)	WR-90 waveguide + on-chip dipole antenna	$20~\mathrm{GHz}$0 band; about $20~\mathrm{GHz}$1 of amplitude gain-bandwidth product; up to $20~\mathrm{GHz}$2 gain; $20~\mathrm{GHz}$3 bandwidth at $20~\mathrm{GHz}$4 gain; $20~\mathrm{GHz}$5
Wireless JPA above $20~\mathrm{GHz}$6 (Hao et al., 15 Aug 2025)	WR42 waveguide-to-slotline transition	$20~\mathrm{GHz}$7 gain across $20~\mathrm{GHz}$8; typical dynamic bandwidth $20~\mathrm{GHz}$9; example $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$0 bandwidth; $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$1 at $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$2 maximum gain; added noise $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$3 photons
3D JPA (Mahboob et al., 2022)	3D cavity field coupled to embedded SQUID resonator	Gain $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$4; $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$5 gain gives $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$6 bandwidth; $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$7 compression point $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$8; half a quantum of added noise
Broadband CPW IMPA (Qing et al., 2023)	Horn-like CPW impedance transformer	Instantaneous bandwidth $$H = \hbar \omega_r a^\dagger a + \frac{K}{2} a^\dagger a^\dagger a a + H_\text{pump},$$9 for $\omega_r$0 gain; average saturation power $\omega_r$1; operating-frequency tuning over $\omega_r$2; near quantum-limited added noise

The 2014 wireless amplifier demonstrated that a direct waveguide-coupled architecture could achieve performance on par with conventional sample holders while simplifying assembly and increasing tunability (Narla et al., 2014). The 2025 high-frequency realization extended the concept to K-band operation, explicitly targeting elevated-temperature superconducting qubit platforms and the suppression of thermal photons by moving readout into the $\omega_r$3 range (Hao et al., 15 Aug 2025).

The 3D cavity implementation shows that cavity-mediated coupling can still support high gain, quantum-limited operation, and $\omega_r$4-class compression even when the nonlinearity is physically separated from the signal port by the cavity mode structure (Mahboob et al., 2022). The CPW impedance-transformed device shows that bandwidth and saturation power can be improved substantially by lowering the effective environmental impedance from $\omega_r$5 to $\omega_r$6, while maintaining a simple planar geometry (Qing et al., 2023).

A broader non-wireless but directly relevant benchmark is the high-saturation-power JPA with a three-pole matching network and two parallel rf-SQUID arrays totaling $\omega_r$7 junctions, which reaches a $\omega_r$8 bandwidth of $\omega_r$9, gain of $K$0, and $K$1 compression around $K$2 to $K$3 (Naaman et al., 2017). This indicates the performance that impedance matching and distributed nonlinearity can make available to future WJPA architectures.

5. Noise performance, impedance environment, and back-action

The principal noise benchmark remains the quantum limit for phase-preserving amplification,

$K$4

Wireless implementations are evaluated against this same limit.

In the 2014 waveguide-coupled device, room-temperature spectrum-analyzer measurements gave an upper bound

$K$5

with $K$6 (Narla et al., 2014). At high gain, the noise visibility reached about $K$7, so less than $K$8 of the power at room temperature was due to HEMT noise. The paper attributes part of the improved tunability to the simpler impedance environment presented by the waveguide.

The 2025 WJPA uses Y-factor measurements with a variable temperature source and a qubit-based photon number calibration (Hao et al., 15 Aug 2025). Because broadband Johnson noise from the heated source can saturate the amplifier, the gain is measured as a function of source temperature and the output noise is scaled by the temperature-dependent gain. Across the $K$9 amplifier bandwidth, the system-added noise is approximately $H_\text{pump}$0 photons. For a phase-preserving amplifier at $H_\text{pump}$1, the standard quantum limit is $H_\text{pump}$2 photon, so the reported system-added noise is about four times the quantum limit (Hao et al., 15 Aug 2025).

In the broadband CPW-based impedance-transformed JPA, the equivalent input noise temperature is inferred from signal-to-noise-ratio improvement relative to the following HEMT, whose noise temperature is taken as $H_\text{pump}$3 (Qing et al., 2023). That work reports noise temperature approaching the quantum limit across the $H_\text{pump}$4 band where $H_\text{pump}$5, and also demonstrates negligible back-action on a transmon qubit. The saturation-power calibration is performed by fitting the readout resonator reflection, ac Stark shift, and measurement-induced dephasing to obtain the intracavity photon number $H_\text{pump}$6, then using

$H_\text{pump}$7

A recurrent misconception is that a wireless architecture automatically removes environmental sensitivity. The literature does not support that view. The 2026 study of a high-gain, large-bandwidth JPA shows that gain spectra can exhibit pronounced sensitivity to weak reflections in the input-output waveguide caused by impedance mismatches in the microwave environment, and that Fabry–Pérot-type interference must be incorporated into the input–output model to reproduce the observed spectral structure (Kono et al., 15 Apr 2026). The high-frequency WJPA likewise reports a parasitic mode near $H_\text{pump}$8 and residual gain and phase ripples due to interface mismatches in the microwave chain (Hao et al., 15 Aug 2025). Wireless coupling can simplify the impedance environment, but it does not make the electromagnetic environment irrelevant.

6. Design trajectories and related amplifier directions

The main design trajectory in WJPA research combines three elements: minimal interconnect complexity, deliberate impedance engineering, and increasingly integrated RF functionality. The CPW impedance-transformed JPA is exemplary in this respect: compared with earlier broadband IMPAs that required multilayer microstrip, lossy dielectrics, or finely patterned interdigitated capacitors, it realizes the transformer as a single planar CPW taper with no discrete elements, no multilayer fabrication, and feature sizes compatible with photolithography and simple RIE (Qing et al., 2023). For a future WJPA, the same paper identifies a continuously tapered, planar impedance transformer between the local nonlinear element and an external coupling structure, potentially a chip-scale antenna rather than a coax line.

Another trajectory is cavity mediation. The 3D JPA shows that dispersive nonlinearity injection into a high-Q 3D cavity can provide $H_\text{pump}$9 gain, half-quantum noise, and $20~\mathrm{dB}$00 compression while keeping the nonlinear SQUID element separate from the signal port (Mahboob et al., 2022). This is structurally compatible with 3D cQED, in which qubits and amplifiers share cavity fields rather than direct line connections.

Integration of auxiliary RF functions is developing in parallel. Although the 2025 on-chip RF-component KIT concerns a kinetic-inductance TWPA rather than a Josephson amplifier, it demonstrates microfabricated bias tees and directional couplers that reduce the installation footprint by a factor of nearly five, eliminate all external lossy microwave components previously required to operate the amplifier, and achieve a $20~\mathrm{dB}$01 $20~\mathrm{dB}$02 bandwidth with median true gain of $20~\mathrm{dB}$03 and median system noise of $20~\mathrm{dB}$04 quanta (Howe et al., 5 Mar 2025). The associated analysis explicitly presents these ideas as transferable to WJPA. This suggests a route toward a WJPA module in which bias networks, pump routing, and matching structures are co-fabricated with the Josephson device.

Directional and array-based concepts provide a further extension. The proposed topological Josephson parametric amplifier array uses a one-dimensional array of non-linearly coupled Kerr resonators with synthetic gauge fields and nonlocal squeezing to realize gains exceeding $20~\mathrm{dB}$05 over a bandwidth ranging from hundreds of MHz to GHz and reverse isolation suppressing backward noise by more than $20~\mathrm{dB}$06 across all frequencies (2207.13728). Its external ports are the formal interface where, in a WJPA setting, one could replace the guided microwave line by an antenna or wireless coupling structure. A plausible implication is that directionality and wireless integration need not be treated as separate design goals.

Finally, traveling-wave Josephson metamaterial amplifiers based on three-wave mixing offer a distributed alternative. A serial array of flux-biased one-junction SQUIDs can realize strong quadratic nonlinearity with vanishing cubic Kerr term, giving broadband gain over several GHz and natural phase matching (Zorin et al., 2017). Although this is a TWPA rather than a JPA, its broadband, nonresonant behavior is directly relevant to wireless front ends that must interface to broadband antennas or resonators.

Taken together, these works define WJPA not as a single canonical circuit, but as a family of Josephson parametric amplifiers in which the signal interface is migrated from conventional hardwired microwave plumbing into a deliberately engineered electromagnetic environment. The central technical problem is therefore twofold: to preserve near-quantum-limited parametric amplification, and to control the impedance, reflections, pump routing, and parasitic modes of the wireless coupling structure with at least the same rigor as the Josephson circuit itself (Narla et al., 2014, Hao et al., 15 Aug 2025, Kono et al., 15 Apr 2026).