Abstract: We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TWPAs) in order to investigate five experimental phenomena related to their operations, namely the effect of impedance mismatch, the presence of upper idler modes, the presence of quantum and thermal noise, the generation of squeezed states, and the preservation of pre-squeezed states during amplification. Our analysis uses momentum operators to describe the spatial evolution of quantised modes along a TWPA. We calculate the restriction placed on pump amplitude as well as amplifier gain as a result of impedance mismatch between a TWPA and its external system. We apply our analysis to upper idler modes and demonstrate that they will result in suppressed gain. We show that an ideal TWPA is indeed quantum-limited—i.e. it introduces a half-quantum of zero-point fluctuation which is the minimum possible noise contribution for a phase-preserving linear amplifier. We analyse the thermal noise associated with a TWPA by considering the effect of distributed sources along an amplifier transmission line. Our analysis predicts a doubling of thermal noise in the high gain limit as a result of wave-mixing between signal and idler modes. We study the operation of a TWPA in the presence of a DC bias current, and have shown that highly squeezed states can in principle be generated. However, amplifying a pre-squeezed state using a non-degenerate TWPA generally reduces the squeezing advantage.
Abstract: We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TWPAs) in order to investigate five experimental phenomena related to their operations, namely the effect of impedance mismatch, the presence of upper idler modes, the presence of quantum and thermal noise, the generation of squeezed states, and the preservation of pre-squeezed states during amplification. Our analysis uses momentum operators to describe the spatial evolution of quantised modes along a TWPA. We calculate the restriction placed on pump amplitude as well as amplifier gain as a result of impedance mismatch between a TWPA and its external system. We apply our analysis to upper idler modes and demonstrate that they will result in suppressed gain. We show that an ideal TWPA is indeed quantum-limited—i.e. it introduces a half-quantum of zero-point fluctuation which is the minimum possible noise contribution for a phase-preserving linear amplifier. We analyse the thermal noise associated with a TWPA by considering the effect of distributed sources along an amplifier transmission line. Our analysis predicts a doubling of thermal noise in the high gain limit as a result of wave-mixing between signal and idler modes. We study the operation of a TWPA in the presence of a DC bias current, and have shown that highly squeezed states can in principle be generated. However, amplifying a pre-squeezed state using a non-degenerate TWPA generally reduces the squeezing advantage.
Abstract We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TWPAs) in order to investigate five experimental phenomena related to their operations, namely the effect of impedance mismatch, the presence of upper idler modes, the presence of quantum and thermal noise, the generation of squeezed states, and the preservation of pre-squeezed states during amplification. Our analysis uses momentum operators to describe the spatial evolution of quantised modes along a TWPA. We calculate the restriction placed on pump amplitude as well as amplifier gain as a result of impedance mismatch between a TWPA and its external system. We apply our analysis to upper idler modes and demonstrate that they will result in suppressed gain. We show that an ideal TWPA is indeed quantum-limited—i.e. it introduces a half-quantum of zero-point fluctuation which is the minimum possible noise contribution for a phase-preserving linear amplifier. We analyse the thermal noise associated with a TWPA by considering the effect of distributed sources along an amplifier transmission line. Our analysis predicts a doubling of thermal noise in the high gain limit as a result of wave-mixing between signal and idler modes. We study the operation of a TWPA in the presence of a DC bias current, and have shown that highly squeezed states can in principle be generated. However, amplifying a pre-squeezed state using a non-degenerate TWPA generally reduces the squeezing advantage.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.
Superconducting traveling-wave parametric amplifiers (TWPAs) are essential elements for enhancing the signal-to-noise ratio (SNR) and thus the read-out fidelity of superconducting qubits because of their high gain and near quantum-limited noise. However, the impact of the pump source, e.g., phase noise on these amplifiers, has not yet been studied. In this work, we show that among the two amplification processes in JTWPAs, the three-wave mixing (3WM) process is more sensitive to the pump phase noise than the four-wave mixing (4WM) process. We show that the even-order nonlinearity of 4th order and above in three-wave mixing is responsible for more than 10 dB increase of phase noise at high frequency offsets within the phase noise mask as the power of the pump increases. A polynomial model of the amplifier and cyclo-stationary property of phase noise also corroborate with the simulations. The Harmonic Balance (HB) periodic noise analysis tool and Leeson phase noise model in Keysight Advanced Design System (ADS) simulator were used in this study.
Abstract The development of superconducting travelling-wave parametric amplifiers (TWPAs) over the past decade has highlighted their potential as low-noise amplifiers for use in fundamental physics experiments and industrial applications. However, practical challenges, including signal-idler contamination, complex pump injection and cancellation, impedance mismatch, and the reciprocal nature of the device, have made it challenging to deploy TWPAs in real-world applications. In this paper, we introduce an innovative solution to these issues through phase-controlled balanced-TWPA architectures. These architectures involve placing two TWPAs in parallel between a pair of broadband couplers. By carefully controlling the phases of the tones propagating along the TWPAs, we can effectively separate the signal and idler tones, as well as the pump(s), using a straightforward injection and cancellation mechanism. The balanced-TWPA architecture offers versatility and flexibility, as it can be reconfigured either intrinsically or externally to suit different application needs. In this manuscript, we provide a comprehensive discussion of the working principles of the balanced-TWPA, including various configurations designed to meet diverse application requirements. We also present the expected gain-bandwidth products in comparison to traditional TWPAs and conduct tolerance analysis to demonstrate the feasibility and advantages of the balanced-TWPA architecture. By addressing the practical challenges associated with TWPAs, the balanced-TWPA architecture represents a promising advancement in the field, offering a more practical and adaptable solution for a wide range of applications.
In this paper, we present a density operator description for a dissipative-dispersive Josephson traveling-wave parametric amplifier. A quantum master equation has been derived for the description of dissipation and thermal fluctuations that arise from lossy dielectric substrates. The formalism is especially effective in the dispersive case. Based on the equation of motion of the system density operator, we investigate the amplification performance by predicting the signal gain and the total photon number, considering amplifier phase-mismatch present in real devices. In addition to the gain investigation, we perform a two-mode squeezing analysis for such structures.
The advent of ultra-low noise microwave amplifiers revolutionized several research fields demanding quantum-limited technologies. Exploiting a theoretical bimodal description of a linear phase-preserving amplifier, in this contribution we analyze some of the intrinsic properties of a model architecture (i.e., an rf-SQUID based Josephson Traveling Wave Parametric Amplifier) in terms of amplification and noise generation for key case study input states (Fock and coherent). Furthermore, we present an analysis of the output signals generated by the parametric amplification mechanism when thermal noise fluctuations feed the device.