Optimally Detuned Parametric Amplification, and Associated Devices

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.

Dec 13, 20200 citations

Degenerate parametric amplification with time-dependent pump amplitude and phase

Maurice T. Raiford

A quantum-statistical treatment of degenerate (single-mode) parametric amplification is given in which the pump is allowed to have time-dependent amplitude and phase. This relaxes earlier restrictions of a constant pump in exact resonance with the signal. Solutions are obtained for the case where the ratio of the time derivative of the pump phase to the coupling strength between pump and signal is constant. This includes the special case of simple offresonance, where the pump has a constant frequency differing from twice the signal frequency by a given amount (and has constant amplitude). The Wigner distribution for the signal mode is obtained (the $P$ distribution does not in general exist as a well-defined function beyond a finite time interval for this process) and is used to determine the time development of the expectation values of various field operators of interest, such as field strengths and fluctuations. A critical point exists in the solution for the photon annihilation operator such that the behavior of the solution and the resulting quantities which it determines is divided into an exponential region and an oscillatory region. The critical point defines, from the expectation value for the photon number, the condition for amplification. For the case of simple off-resonance, this gives the frequency range of amplification. A calculation without using the rotating-wave approximation is given in the Appendix which shows that, to first order, the same range is obtained as when the approximation is used. The effect of damping is given, showing, e.g., how it slows the growth rate of the signal (in the region of amplification) and how it narrows the frequency range of amplification. The effect of a time-dependent pump (and damping) on the breakdown of the $P$ distribution is also described.A quantum-statistical treatment of degenerate (single-mode) parametric amplification is given in which the pump is allowed to have time-dependent amplitude and phase. This relaxes earlier restrictions of a constant pump in exact resonance with the signal. Solutions are obtained for the case where the ratio of the time derivative of the pump phase to the coupling strength between pump and signal is constant. This includes the special case of simple offresonance, where the pump has a constant frequency differing from twice the signal frequency by a given amount (and has constant amplitude). The Wigner distribution for the signal mode is obtained (the $P$ distribution does not in general exist as a well-defined function beyond a finite time interval for this process) and is used to determine the time development of the expectation values of various field operators of interest, such as field strengths and fluctuations. A critical point exists in the solution for the photon annihilation operator such that the behavior of the solution and the resulting quantities which it determines is divided into an exponential region and an oscillatory region. The critical point defines, from the expectation value for the photon number, the condition for amplification. For the case of simple off-resonance, this gives the frequency range of amplification. A calculation without using the rotating-wave approximation is given in the Appendix which shows that, to first order, the same range is obtained as when the approximation is used. The effect of damping is given, showing, e.g., how it slows the growth rate of the signal (in the region of amplification) and how it narrows the frequency range of amplification. The effect of a time-dependent pump (and damping) on the breakdown of the $P$ distribution is also described.

Physical Review AMay 1, 197445 citations

Signal_Amplification_System_by_Parametric_Down-Conversion

Walter Ayala

This version develops a preregisterable and falsifiable experimental framework for investi-gating parametric optical amplification of weak biomedical signals.The framework explicitly distinguishes spontaneous parametric down-conversion fromseeded parametric amplification and treats the latter as the primary amplification mechanism.The signal path is modeled asweak optical input → parametric amplifier → loss/filtering → detector → statistical inference.The theoretical model is based on a two-mode Bogoliubov transformation,aˆs,out = uaˆs,in + vaˆ†i,in,with|u|2 − |v|2 = 1for the ideal lossless case.The framework separately models amplifier gain, quantum noise, optical loss, detectorinefficiency, electronic noise, pump noise, phase noise, mode mismatch, gain saturation, andpump depletion.Two operating modes are considered:1. phase-insensitive amplification, in which both quadratures are amplified and unavoidablequantum noise is introduced;2. phase-sensitive amplification, in which one selected quadrature can be amplified withlower added noise under appropriate phase matching.The primary endpoint is a prespecified detector-level signal-to-noise metric comparing theparametric amplifier with a gain-matched reference architecture.Secondary endpoints include the measured noise figure, effective gain, detection threshold,and downstream classification performance.The v3.1 framework introduces preregistered performance thresholds, a locked test set,independent calibration, blocked randomization, blinded analysis where feasible, hierarchical. statistical models, uncertainty propagation, multiplicity control, negative-control experiments,saturation diagnostics, and explicit falsification criteria.The proposal does not claim a universal amplification advantage, quantum supremacy, orclinical diagnostic capability.This version develops a preregisterable and falsifiable experimental framework for investi-gating parametric optical amplification of weak biomedical signals.The framework explicitly distinguishes spontaneous parametric down-conversion fromseeded parametric amplification and treats the latter as the primary amplification mechanism.The signal path is modeled asweak optical input → parametric amplifier → loss/filtering → detector → statistical inference.The theoretical model is based on a two-mode Bogoliubov transformation,aˆs,out = uaˆs,in + vaˆ†i,in,with|u|2 − |v|2 = 1for the ideal lossless case.The framework separately models amplifier gain, quantum noise, optical loss, detectorinefficiency, electronic noise, pump noise, phase noise, mode mismatch, gain saturation, andpump depletion.Two operating modes are considered:1. phase-insensitive amplification, in which both quadratures are amplified and unavoidablequantum noise is introduced;2. phase-sensitive amplification, in which one selected quadrature can be amplified withlower added noise under appropriate phase matching.The primary endpoint is a prespecified detector-level signal-to-noise metric comparing theparametric amplifier with a gain-matched reference architecture.Secondary endpoints include the measured noise figure, effective gain, detection threshold,and downstream classification performance.The v3.1 framework introduces preregistered performance thresholds, a locked test set,independent calibration, blocked randomization, blinded analysis where feasible, hierarchical. statistical models, uncertainty propagation, multiplicity control, negative-control experiments,saturation diagnostics, and explicit falsification criteria.The proposal does not claim a universal amplification advantage, quantum supremacy, orclinical diagnostic capability.

Sep 24, 20260 citations

Introduction to parametric amplification of quantum signals with Josephson circuits

Ananda Roy, Michel Devoret

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.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.

arXiv:1605.00539Comptes Rendus PhysiqueAug 1, 2016167 citations

Degenerate parametric amplifier with a nonclassical pump

Mark S. Hillery, Daoqi Yu, János A. Bergou

The degenerate parametric amplifier is usually studied within the context of the parametric approximation.

Annual Meeting Optical Society of AmericaJan 1, 19930 citations

Hybrid non-degenerate parametric amplifier for a microwave cavity mode and an NV ensemble

Roman Ovsiannikov, Kurt Jacobs, Andrii G. Sotnikov +2 more

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~ $Q=10^4$ , 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 $Q=5\times 10^4$ it generates approximately $5~\mbox{dB}$ 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~$Q=10^4$, 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 $Q=5\times 10^4$ it generates approximately $5~\mbox{dB}$ of squeezing. We also examine the experimental requirements for implementation.

quant-pharXiv:2601.03407Jan 8, 20260 citations

P

distribution does not in general exist as a well-defined function beyond a finite time interval for this process) and is used to determine the time development of the expectation values of various field operators of interest, such as field strengths and fluctuations. A critical point exists in the solution for the photon annihilation operator such that the behavior of the solution and the resulting quantities which it determines is divided into an exponential region and an oscillatory region. The critical point defines, from the expectation value for the photon number, the condition for amplification. For the case of simple off-resonance, this gives the frequency range of amplification. A calculation without using the rotating-wave approximation is given in the Appendix which shows that, to first order, the same range is obtained as when the approximation is used. The effect of damping is given, showing, e.g., how it slows the growth rate of the signal (in the region of amplification) and how it narrows the frequency range of amplification. The effect of a time-dependent pump (and damping) on the breakdown of the

P

distribution is also described.

Q=10^4

, 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\times 10^4

it generates approximately $5~\mbox{dB}$ of squeezing. We also examine the experimental requirements for implementation.