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.
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.
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 Superconducting resonator parametric amplifiers are potentially important components for a wide variety of fundamental physics experiments and utilitarian applications. We propose and realise an operating scheme that achieves amplification through the use of non-degenerate pumps, which addresses two key challenges in the design of parametric amplifiers: non-continuous gain across the amplification band and pump tone removal. We have experimentally demonstrated the non-degenerate pumping scheme using a half-wave resonator amplifier based on NbN thin-film, and measured a peak gain of 26 dB and 3-dB bandwidth of 0.5 MHz. The two non-degenerate pump tones were positioned ∼10 ∼ 10 bandwidths above and below the frequency at which peak gain occurs. We have found the non-degenerate pumping scheme to be more stable compared to the usual degenerate pumping scheme in terms of gain drift over time, by a factor of 4. This scheme also retains the usual flexibility of NbN resonator parametric amplifiers in terms of reliable amplification in a ∼4 ∼ 4 K environment, and is suitable for cross-harmonic amplification. The use of pump tones at different frequencies allows phase-sensitive amplification when the signal tone is degenerate with the idler tone. A gain of 23 dB and squeezing ratio of 6 dB were measured.
A fundamental result of quantum mechanics is that the fluctuations of a bosonic field are given by its temperature T. An electromagnetic mode with frequency ω in the microwave band has a significant thermal photon occupation at room temperature according to the Bose-Einstein distribution nˉ=kBT/ℏω. The room temperature thermal state of a 3 GHz mode, for example, is characterized by a mean photon number nˉ∼2000 and variance Δn2≈nˉ2. This thermal variance sets the measurement noise floor in applications ranging from wireless communications to positioning, navigation, and timing to magnetic resonance imaging. We overcome this barrier in continuously cooling a ∼3 GHz cavity mode by coupling it to an ensemble of optically spin-polarized nitrogen-vacancy (NV) centers in a room-temperature diamond. The NV spins are pumped into a low entropy state via a green laser and act as a heat sink to the microwave mode through their collective interaction with microwave photons. Using a simple detection circuit we report a peak noise reduction of −2.3±0.1dB and minimum cavity mode temperature of 150±5K. We present also a linearized model to identify the important features of the cooling, and demonstrate its validity through magnetically tuned, spectrally resolved measurements. The realization of efficient mode cooling at ambient temperature opens the door to applications in precision measurement and communication, with the potential to scale towards fundamental quantum limits.
We report the observation of zero-point noise squeezing by means of a Josephson- junction parametric amplifier, which has been used previously to squeeze 4.2 K thermal noise1. To observe quantum noise squeezing, a number of improvements were made on the apparatus; these include the in stallation of two low-noise cryogenic high- electron-mobility-transistor (HEMT) amplifiers, which boosted the detector sensitivity an order of magnitude to 215 K. The Josephson- junction parametric amplifier was cooled to 30 mK and was operated in the degenerate mode with the signal carrier frequency at 19.16 GHz. At this frequency the vacuum noise floor is hv/2k = 0.46 K. In the deamplified quadrature a drop in the noise of 0.223 K was observed relative to the pump-off noise floor. The pump-off noise floor was established to be within 3.4 + 2.0% of the vacuum noise floor by varying the temperature of the cold termination at the parametric amplifier's input from 30 mK to 1K. A probe signal at the input of the first HEMT amplifier was used to establish that the detector system saturation was less than 7 × 10−4 dB. We have thus observed squeezing 47% ± 8% below the vacuum noise floor.
Parametric oscillations are well studied phenomena, with applications in amplification, quantum optics, and quantum information processing. They can occur as a parameter of a system, such as the resonant frequency, is being modulated or “pumped” by an external field. A nonlinearity of the system can then transfer power from the pumping frequency to two frequencies called signal and idler. When the signal falls within a resonance, and when the pump amplitude exceeds an instability threshold, parametric oscillations occur. When signal and idler fall within the same resonance, the pumping is called degenerate.Due to somewhat different implementations, in combination with rich nonlinear physics, the details of the parametric oscillations can differ in different systems. In this work, we expand on the research done on parametric oscillations using a superconducting microwave resonator with a tunable boundary condition. Previously, a degenerate Josephson parametric oscillator (JPO) has been demonstrated by modulation of this boundary condition at twice the resonator's resonant frequency. We further use the JPO to implement a novel read-out method for a superconducting qubit. Moreover, we demonstrate a different, nondegenerate regime of the JPO, which we denote the NJPO, by modulating the frequency at the sum of two resonant frequencies of a multimode resonator.Both the JPO qubit read-out and the NJPO have applications within quantum information processing. The perhaps most promising platform for quantum information processing is represented by the circuit-QED architecture with superconducting resonators and artificial atoms, where the two lowest atomic levels represent the qubit. We make these circuits using lithographic techniques, and control and measure them at low temperature using microwaves. The qubit's state is fragile and difficult to read out with high fidelity. To this end, we have developed a method based on the JPO, in which the qubit state is mapped onto a zero-amplitude or a large-amplitude state of the JPO. We achieved a large contrast (185±15 photons), therefore eliminating the need for a following quantum-limited parametric amplifier. Our readout fidelity was 81.5 %, and by carefully modeling we can distinguish fidelity loss from the qubit and the readout, respectively. This analysis displays an actual readout fidelity of 98.7 %.An alternative model for quantum computing is based on continuous variables, and uses harmonic oscillators instead of qubits. Entangled states, which can be used as quantum resources, can then be created, for example, by two-mode squeezing of the oscillator ground state. The state of the NJPO produces correlated oscillations in its two modes, which might be useful for continuous-variable quantum computing. In this work we fully characterize the classical properties of the NJPO, and show good quantitative agreement with a theoretical model.