In our recent study [arXiv:2601.03407] we showed that a hybrid non-degenerate parametric amplifier could be realized for a microwave mode and an ensemble of NV-centers (or other spins) by parametrically driving the spin ensemble. The parametric driving was sinusoidal at the sum of the spin and cavities frequencies. Here we consider whether the performance of the amplifier can be improved by using a more complex drive. Employing numerical optimization, we find that the optimal driving is primarily a sum of harmonics of the sum frequency. The optimal drive, which is essentially a square wave, ramps up the amplification rate by about 40 %, while limiting the drive to four harmonics improves the amplification by about 22 %.
In our recent study [arXiv:2601.03407] we showed that a hybrid non-degenerate parametric amplifier could be realized for a microwave mode and an ensemble of NV-centers (or other spins) by parametrically driving the spin ensemble. The parametric driving was sinusoidal at the sum of the spin and cavities frequencies. Here we consider whether the performance of the amplifier can be improved by using a more complex drive. Employing numerical optimization, we find that the optimal driving is primarily a sum of harmonics of the sum frequency. The optimal drive, which is essentially a square wave, ramps up the amplification rate by about 40 %, while limiting the drive to four harmonics improves the amplification by about 22 %.
Abstract We introduce an implementation of a non-degenerate parametric amplifier in which the signal and idler modes, respectively, a microwave mode and an ensemble of spins (e.g., nitrogen-vacancy centers in diamond), are operated in their linear regime. This paramp, which amplifies signals in both parts at room and cryogenic temperatures, can be used to generate both the two-mode and single-mode squeezing of either system. It requires merely modulating the frequency of the spin ensemble at the sum of the cavity and spin frequencies (providing the classical pump) with the two systems sufficiently detuned. This effect is remarkable given that modulating a spin ensemble by itself produces neither amplification nor squeezing, unlike modulating an oscillator, and that an off-resonant perturbative analysis would suggest that modulating the spin ensemble merely parametrically drives the cavity mode. With typical cavity parameters including a cavity quality factor Q = 10<4/sup>, and a 1 GHz modulation amplitude, the microwave signal can be amplified by approximately 18 dB in 1.7 μs, with a resonant bandwidth of about 0.5 MHz. At 10 mK with the same modulation amplitude and a cavity and spin Q = 5×10<4sup> it generates approximately 5 dB of squeezing. We also examine the experimental requirements for implementation.
We introduce an implementation of a non-degenerate parametric amplifier in which the signal and idler modes, respectively, a microwave mode and an ensemble of spins (e.g., nitrogen-vacancy centers in diamond), are operated in their linear regime. This paramp, which amplifies signals in both parts at room and cryogenic temperatures, can be used to generate both the two-mode and single-mode squeezing of either system. It requires merely modulating the frequency of the spin ensemble at the sum of the cavity and spin frequencies (providing the classical pump) with the two systems sufficiently detuned. This effect is remarkable given that modulating a spin ensemble by itself produces neither amplification nor squeezing, unlike modulating an oscillator, and that an off-resonant perturbative analysis would suggest that modulating the spin ensemble merely parametrically drives the cavity mode. With typical cavity parameters including a cavity quality factor~Q=104, and a 1 GHz modulation amplitude, the microwave signal can be amplified by approximately $18~\mbox{dB}$ in $1.7~\mbox{$μ$s}$, with a resonant bandwidth of about $0.5~\mbox{MHz}$. At $10~\mbox{mK}$ with the same modulation amplitude and a cavity and spin Q=5×104 it generates approximately $5~\mbox{dB}$ of squeezing. We also examine the experimental requirements for implementation.
Parametric amplification is essential for quantum measurement, enabling the amplification of weak microwave signals with minimal added noise. While Josephson-junction-based amplifiers have become standard in superconducting quantum circuits, their magnetic sensitivity, limited saturation power, and sub-kelvin operating requirements motivate the development of alternative nonlinear platforms. Here we demonstrate a two-mode kinetic-inductance parametric amplifier based on a pair of capacitively coupled Kerr-nonlinear resonators fabricated from NbTiN and NbN thin films. The distributed Kerr nonlinearity of these materials enables nondegenerate four-wave-mixing amplification with gains approaching 40 dB, gain-bandwidth products up to 6.9 MHz, and 1-dB compression powers two to three orders of magnitude higher than those of state-of-the-art Josephson amplifiers. A coupled-mode theoretical model accurately captures the pump-induced modification of the hybridized modes and quantitatively reproduces the observed signal and idler responses. The NbN device exhibits a significantly larger Kerr coefficient and superior gain-bandwidth performance, highlighting the advantages of high-kinetic-inductance materials. Our results establish coupled kinetic-inductance resonators as a robust platform for broadband, high-power, and magnetically resilient quantum-limited amplification, offering a scalable route for advanced readout in superconducting qubits, spin ensembles, quantum dots, and other microwave-quantum technologies.
One of the primary requirements for superconducting quantum information processors is high-fidelity, quantum non-demolition qubit readout. In superconducting circuits, we perform measurements with quantum-limited microwave amplifiers. These amplifiers are based on microwave cavities and powered by Josephson-junction based nonlinearities, which we drive to parametrically modulate the circuit and generate gain. However, cavity-based amplifiers generally suffer from a fixed gain-bandwidth product, a limited dynamic range, and the absence of directionality, and so they must be operated with external lossy microwave commercial components such as circulators. Many of these limitations can be circumvented by combining multiple parametric processes in a few-mode device, in particular by combining parametric drives which produce gain and those which produce gainless photon conversion. By combining balanced gain and conversion processes between a pair of modes, we have demonstrated transmission-only, phase-sensitive, gain-bandwidth-free amplification. We have also used measurements of transmon qubits with this mode of amplification to demonstrate its practical utility. More, by combining multiple instances of imbalanced gain and conversion processes among three modes, we have realized devices with non-reciprocal, transmission-only amplification, matched ports, and a large, gain-independent bandwidth. One of the biggest challenges in tuning multiple parametric processes is both inherent and dynamically-generated higher order nonlinearities in the device, which shift mode frequencies and parametric coupling strengths with pump power, preventing accurate balancing of the parametric processes. These can be controlled through engineering the Hamiltonian of the nonlinear element, in this thesis either a linearly-shunted Josephson Ring Modulator or SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements), which for certain applied flux values can minimize or even change the sign of higher-order even nonlinearities. Additionally, we have explored a range of circuit parameters, allowing us to also control the relative size of odd-order nonlinearities. We have developed a series of prototypes which implement these concepts, and have achieved both high-dynamic range singly pumped amplifiers, and a promising platform for multi-parametric devices. We conclude by presenting recent progress towards implementing multiple parametric schemes that generates a practical directional amplifier, and discuss the remaining obstacles to a truly ideal parametric amplifiers.
Optimally detuned parametric amplification amplifies a signal in a resonator that is driven off-resonance, with respect to a signal mode, using a far-detuned pump. This pump establishes a parametric drive strength, and is "far-detuned" in that its detuning from the signal mode is greater than the drive strength. The amplitude and frequency of the pump are chosen so that the eigenfrequency of the resulting Bogoliobov mode matches a photonic loss rate of the Bogoliobov mode. In this case, a signal coupled into the Bogoliobov mode will be amplified with a gain that is broader and flatter than that achieved with conventional parametric amplification, and is not limited by a gain-bandwidth product. Optimally detuned parametric amplification may be used for degenerate or non-degenerate parametric amplification, and may be used to amplify microwaves, light, electronic signals, acoustic waves, or any other type of signal that can be amplified using conventional parametric amplification.
Optimally detuned parametric amplification amplifies a signal in a resonator that is driven off-resonance, with respect to a signal mode, using a far-detuned pump. This pump establishes a parametric drive strength, and is "far-detuned" in that its detuning from the signal mode is greater than the drive strength. The amplitude and frequency of the pump are chosen so that the eigenfrequency of the resulting Bogoliobov mode matches a photonic loss rate of the Bogoliobov mode. In this case, a signal coupled into the Bogoliobov mode will be amplified with a gain that is broader and flatter than that achieved with conventional parametric amplification, and is not limited by a gain-bandwidth product. Optimally detuned parametric amplification may be used for degenerate or non-degenerate parametric amplification, and may be used to amplify microwaves, light, electronic signals, acoustic waves, or any other type of signal that can be amplified using conventional parametric amplification.