New results for quantum limits to light amplifiers are derived which hold in both linear and nonlinear domains of operation. The relative advantages of squeezing the pump and idler modes of the amplifier are discussed.
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.
Waveguide-based optical parametric amplification (OPA) is advantageous in generating broadband or pulsed squeezed vacuum. To enhance the squeezing level, it is crucial to clarify its limiting factors. In this study, we develop a numerical method which allows us to derive the squeezing level in waveguide OPA. Based on the developed method, we investigate the effect of the higher-order mode of the pump light, which generates noise due to the OPA between the fundamental mode and the higher-order mode. We also investigate the effect of optical loss in the waveguide. Specifically, we formulated coupled equations that take into account the degenerate OPA between the pump and signal both in the fundamental mode, and the non-degenerate OPA between the pump in the higher-order mode, the signal in the fundamental mode, and the idler in the higher-order mode. By solving the coupled equations, we can express the quantum state as a linear combination of annihilation and creation operators, and the squeezing level can be derived from its coefficients. The analysis allowed us to quantify the effect of OPA on the fundamental and higher-order modes, and the requirement for mode matching of pump light with the fundamental mode. We also analyzed the effect of loss in the waveguide based on the same procedure. The results show the loss in the waveguide to have less effect than the same loss at the output of the waveguide. These results provide important design criteria of waveguide OPA for squeezing.