We study the dynamics of a driven atomic Josephson junction that we propose as a parametric amplifier. By periodically modulating the position of the barrier, we induce a small current across the junction, serving as our input signal. The pump field is implemented by modulating the barrier height at twice the Josephson plasma frequency. The resulting dynamics exhibit parametric amplification of the signal through nonlinear mixing between the signal and pump fields, which is encoded in a specific microscopic pattern of density waves and phase excitations that can be addressed within the experimental cold-atom capabilities. This work paves the way for tunable amplifiers in atomtronic circuits, with potential applications in several fields including precision measurements and quantum information processing. At the same time, our analysis provides the microscopic explanation of the general notion of parametric amplification occurring in nonlinear coherent devices.
We study the dynamics of a driven atomic Josephson junction that we propose as a parametric amplifier. By periodically modulating the position of the barrier, we induce a small current across the junction, serving as our input signal. The pump field is implemented by modulating the barrier height at twice the Josephson plasma frequency. The resulting dynamics exhibit parametric amplification of the signal through nonlinear mixing between the signal and pump fields, which is encoded in a specific microscopic pattern of density waves and phase excitations that can be addressed within the experimental cold-atom capabilities. This work paves the way for tunable amplifiers in atomtronic circuits, with potential applications in several fields including precision measurements and quantum information processing. At the same time, our analysis provides the microscopic explanation of the general notion of parametric amplification occurring in nonlinear coherent devices.
Linear parametric amplification is a key operation in information processing. Our interest here is quantum-limited parametric amplification, i.e., amplification of quantum signals while adding the minimum amount of noise allowed by quantum mechanics, which is essential for any viable implementation of quantum information processing. We describe parametric amplifiers based on the dispersive nonlinearity of Josephson junctions driven with appropriate tones playing the role of pumps. We discuss two defining characteristics in the architecture of these amplifiers: the number of modes occupied by the signal, idler, and pump waves and the number of independent ports through which these waves enter into the circuit. The scattering properties of these amplifiers are also reviewed. The main focus of this work are the computations of the dynamic range and phase-space distributions of the fluctuations of the modes of the amplifiers.
This short and opinionated review starts with the concept of quantum signals at microwave frequencies and focuses on the principle of linear parametric amplification. This process emerges from the dispersive nonlinearity of Josephson junctions driven with appropriate tones. We discuss two defining characteristics of the corresponding amplifying devices: i) the number of modes excited by the signal, idler and pump waves and ii) the number of independent ports through which these waves enter into the circuit.
The recent developments in quantum technologies, as well as advanced detection experiments, have raised the need to detect extremely weak signals in the microwave frequency spectrum. To this aim, the Josephson travelling wave parametric amplifier, a device capable of reaching the quantum noise limit while providing a wide bandwidth, has been proposed as a suitable cryogenic front-end amplifier. This work deals with the numerical study of a Josephson travelling wave parametric amplifier, without approximations regarding the nonlinearity of the key elements. In particular, we focus on the investigation of the system of coupled nonlinear differential equations representing all the cells of the Josephson travelling wave parametric amplifier, with proper input and output signals at the boundaries. The investigation of the output signals generated by the parametric amplification process explores the phase-space and the Fourier spectral analysis of the output voltage, as a function of the parameters describing the pump and signal tones that excite the device. Beside the expected behavior, i.e., the signal amplification, we show that, depending on the system operation, unwanted effects (such as pump tone harmonics, incommensurate frequency generation, and noise rise), which are not accounted for in simple linearized approaches, can be generated in the whole nonlinear system.
Recent advancements in quantum technologies and advanced detection experiments have underscored the pressing need for the detection of exceedingly weak signals within the microwave frequency spectrum. Addressing this challenge, the Josephson Traveling Wave Parametric Amplifier (JTWPA) has been proposed as a cryogenic front-end amplifier capable of approaching the quantum noise limit while providing a relevant bandwidth. This research is centered on a comprehensive numerical investigation of the JTWPA, without resorting to simplifications regarding the nonlinearity of the essential components. Specifically, this study focuses on a thorough examination of the system, characterized by coupled nonlinear differential equations representing all components of the device. Proper input and output signals at the device's boundaries are considered. The analysis of the output signals undergoing the parametric amplification process involves a detailed exploration of phase-space dynamics and Fourier spectral analysis of the output voltage. This study is conducted while considering the parameters ruling the response of the device under pump and signal excitations. In addition to the expected signal amplification, the findings reveal that the nonlinear nature of the system can give rise to unforeseen phenomena, depending on the system's operational conditions, which include: the generation of pump tone harmonics, modulation of the signal gain, and incommensurate frequency generation—effects that are not easily accommodated by simplistic linearized approaches.
We present the theory of a Josephson parametric amplifier employing two-pump sources. Our calculations are based on input-output theory, and can easily be generalized to any coupled system involving parametric interactions. We analyze the operation of the device, taking into account the feedback introduced by the reaction of the signal and noise on the pump power, and in this framework, compute the response functions of interest---signal and idler gains, internal gain of the amplifier, and self-oscillation signal amplitude. To account for this back action between signal and pump, we adopt a mean-field approach and self-consistently explore the boundary between amplification and self-oscillation. The coincidence of bifurcation and self-oscillation thresholds reveals that the origin of coherent emission of the amplifier lies in the multiwave mixing of the noise components. Incorporation of the back action leads the system to exhibit hysteresis, dependent on parameters such as temperature and detuning from resonance. Our analysis also shows that the resonance condition itself changes in the presence of back action and this can be understood in terms of the change in plasma frequency of the junction. The potential of the double-pump amplifier for quantum-limited measurements and as a squeezer is also discussed.
In the last few years, several groups have proposed and developed their own platforms demonstrating quantum-limited linear parametric amplification, with evident applications in quantum information and computation, electrical and optical metrology, radio astronomy, and basic physics concerning axion detection. Here, we propose a short review on the physics behind parametric amplification via metamaterials composed by coplanar waveguides embedding several Josephson junctions. We present and compare different schemes that exploit the nonlinearity of the Josephson current-phase relation to mix the so-called signal, idler, and pump tones. The chapter then presents and compares three different theoretical models, developed in the last few years, to predict the dynamics of these nonlinear systems in the particular case of a 4-wave mixing process and under the degenerate undepleted pump assumption. We will demonstrate that, under the same assumption, all the results are comparable in terms of amplification of the output fields.