Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum and Semiclassical Optics Journal of the European Optical Society Part B

The Cummings-Tavis model as a nonlinear quantum amplifier

D Kouznetsov-Kallistratova, Rommer Alex Ortega Martínez

Published Aug 1, 1995• 3 citations
Publisher

Abstract

A system of N identical two-level atoms interacting with the single mode of the boson field is considered in the rotating-wave approximation. The solution of the Schrodinger equation with the initial condition of all atoms excited and the field in the coherent state is discussed. The resulting state is interpreted as an amplified state of the field correlated with the state of the system of atoms. The system of atoms is interpreted as an example of a nonlinear quantum amplifier. The algorithm to calculate the amplitude of the field at the output and its uncertainty is described. The relation of the mean value of the output field to the input one is interpreted as the amplification coefficient. The uncertainty of the output field is interpreted in terms of the noise of the amplifier. The dependencies of the noise on the amplification coefficient are plotted for several values of N. The noise is compared with the noise of an ideal linear amplifier of the same amplification coefficient. Conditions at which the nonlinear amplifier has less noise than the linear amplifier are found. Uncertainties of quadrature components which correspond to the amplitude and phase of the field are calculated. It is shown that only one of them has an uncertainty less than the uncertainty in the case of the ideal linear amplifier. Another definition of the amplification coefficient of the nonlinear quantum amplifier is suggested. The differential amplification coefficient gives the simple lower bound of the noise of the nonlinear amplifier. It prohibits the construction of a nonlinear amplifier with a signal-to-noise ratio better than that of an ideal linear amplifier. General bounds of the minimal noise in nonlinear amplifiers are compared with results for a particular amplifier.

DOI
10.1088/1355-5111/7/4/009

Related papers

How to characterize the nonlinear amplifier

D Kouznetsov-Kallistratova, Carlos Flores Cotera

The conception of the amplification of the coherent field is formulated. The definition of the coefficient of the amplification as the relation between the mean value of the field at the output to the value at the input and the definition of the noise as the difference between the number of photons in the output mode and square of the modulus of the mean value of the output amplitude are considered. Using a simple example it is shown that by these definitions the noise of the nonlinear amplifier may be less than the noise of the ideal linear amplifier of the same amplification coefficient. Proposals to search another definition of basic parameters of the nonlinear amplifiers are discussed. This definition should enable us to formulate the universal fundamental lower limit of the noise which should be valid for linear quantum amplifiers as for nonlinear ones.

•May 1, 1994•1 citation

Quantum noise limits for nonlinear, phase-invariant amplifiers

Dmitri A. Kouznetsov, Roberto Ortega-Martı́nez, Daniel Rohrlich

Any quantum device that amplifies coherent states of a field while preserving their phase generates noise. A nonlinear, phase-invariant amplifier may generate less noise, over a range of input field strengths, than any linear amplifier with the same amplification. We present explicit examples of such nonlinear amplifiers and derive lower bounds on the noise generated by a nonlinear, phase-invariant quantum amplifier.

arXiv:cond-mat/9407011•Physical Review A•Aug 1, 1995•9 citations

Quantum noise in light amplifiers

Matthew J. Collett, Daniel F. Walls

The principal problem of light amplifiers is to find a means to amplify a coherent amplitude without decreasing the SNR. Consider a signal with amplitude squeezed quantum fluctuations, that is, less noise in the amplitude quadrature than the phase quadrature. The objective is to find a phase sensitive amplifier, which, while amplifying the coherent amplitude, adds quantum noise preferentially to the phase quadrature. We take as a concrete model for the amplifier an intracavity parametric amplifier. We go beyond the usual linear analysis and include the nonlinear regime where pump depletion is important. We find that in the linear region the quantum noise added by the amplification process may be reduced by squeezing the idler mode, while in the nonlinear regime the quantum fluctuations from the pump become more important. These results are of direct application to practical light amplifiers.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Quantum Noise in Linear Amplifiers

H. A. Haus, James A. Mullen

The classical definition of noise figure, based on signal-to-noise ratio, is adapted to the case when quantum noise is predominant. The noise figure is normalized to "uncertainty noise." General quantum mechanical equations for linear amplifiers are set up using the condition of linearity and the requirement that the commutator brackets of the pertinent operators are conserved in the amplification. These equations include as special cases the maser, the parametric amplifier, and the parametric up-converter. Using these equations the noise figure of a general amplifier is derived. The minimum value of this noise figure is equal to 2. The significance of the result with regard to a simultaneous phase and amplitude measurement is explored.

Physical Review•Dec 1, 1962•318 citations

Quantum limits on noise in linear amplifiers

Carlton M. Caves

How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Oct 15, 1982•1,723 citations

A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices

B. M. Rodríguez-Lara, Francisco Soto, Alejandro Zárate Cárdenas +1 more

The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.

arXiv:1303.5892•Optics Express•May 17, 2013•53 citations
A system of N identical two-level atoms interacting with the single mode of the boson field is considered in the rotating-wave approximation. The solution of the Schrodinger equation with the initial condition of all atoms excited and the field in the coherent state is discussed. The resulting state is interpreted as an amplified state of the field correlated with the state of the system of atoms. The system of atoms is interpreted as an example of a nonlinear quantum amplifier. The algorithm to calculate the amplitude of the field at the output and its uncertainty is described. The relation of the mean value of the output field to the input one is interpreted as the amplification coefficient. The uncertainty of the output field is interpreted in terms of the noise of the amplifier. The dependencies of the noise on the amplification coefficient are plotted for several values of N. The noise is compared with the noise of an ideal linear amplifier of the same amplification coefficient. Conditions at which the nonlinear amplifier has less noise than the linear amplifier are found. Uncertainties of quadrature components which correspond to the amplitude and phase of the field are calculated. It is shown that only one of them has an uncertainty less than the uncertainty in the case of the ideal linear amplifier. Another definition of the amplification coefficient of the nonlinear quantum amplifier is suggested. The differential amplification coefficient gives the simple lower bound of the noise of the nonlinear amplifier. It prohibits the construction of a nonlinear amplifier with a signal-to-noise ratio better than that of an ideal linear amplifier. General bounds of the minimal noise in nonlinear amplifiers are compared with results for a particular amplifier.
The conception of the amplification of the coherent field is formulated. The definition of the coefficient of the amplification as the relation between the mean value of the field at the output to the value at the input and the definition of the noise as the difference between the number of photons in the output mode and square of the modulus of the mean value of the output amplitude are considered. Using a simple example it is shown that by these definitions the noise of the nonlinear amplifier may be less than the noise of the ideal linear amplifier of the same amplification coefficient. Proposals to search another definition of basic parameters of the nonlinear amplifiers are discussed. This definition should enable us to formulate the universal fundamental lower limit of the noise which should be valid for linear quantum amplifiers as for nonlinear ones.
The principal problem of light amplifiers is to find a means to amplify a coherent amplitude without decreasing the SNR. Consider a signal with amplitude squeezed quantum fluctuations, that is, less noise in the amplitude quadrature than the phase quadrature. The objective is to find a phase sensitive amplifier, which, while amplifying the coherent amplitude, adds quantum noise preferentially to the phase quadrature. We take as a concrete model for the amplifier an intracavity parametric amplifier. We go beyond the usual linear analysis and include the nonlinear regime where pump depletion is important. We find that in the linear region the quantum noise added by the amplification process may be reduced by squeezing the idler mode, while in the nonlinear regime the quantum fluctuations from the pump become more important. These results are of direct application to practical light amplifiers.
The classical definition of noise figure, based on signal-to-noise ratio, is adapted to the case when quantum noise is predominant. The noise figure is normalized to "uncertainty noise." General quantum mechanical equations for linear amplifiers are set up using the condition of linearity and the requirement that the commutator brackets of the pertinent operators are conserved in the amplification. These equations include as special cases the maser, the parametric amplifier, and the parametric up-converter. Using these equations the noise figure of a general amplifier is derived. The minimum value of this noise figure is equal to 2. The significance of the result with regard to a simultaneous phase and amplitude measurement is explored.
How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.