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

arXiv:2309.16087 · Physica Scripta

Temporal evolution of a driven optomechanical system in the strong coupling regime

L. Medina-Dozal, J. Récamier, H. M. Moya-Cessa, Francisco Soto, R. Román-Ancheyta, I. Ramos-Prieto, Alejandro R. Urzúa

Published Dec 14, 2023• 6 citations
arXivHTMLPDF

Abstract

Abstract We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, G/ω m , is not negligible compared to one, i.e., the system operates in the strong-coupling regime. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement. In contrast to other works, our approach does not use the standard linearized description in the optomechanical interaction. Therefore, highly non-classical (non-Gaussian) states of light emerge during the time evolution.

DOI
10.1088/1402-4896/ad15cf

Related papers

Lie algebraic approach to quantum driven optomechanics

A Paredes-Juárez, I. Ramos-Prieto, Manuel Berrondo +1 more

Abstract We present an approximate Lie algebraic method to deal with a forced optomechanical Hamiltonian. We show that the approximations made in order to linearize the interaction Hamiltonian are fully justified by means of a comparison between a purely numerical calculation of the number of photons, phonons and linear entropy using the full Hamiltonian and the results obtained by means of our approximate time evolution operator.

Physica Scripta•Oct 31, 2019•5 citations

Time-evolution of nonlinear optomechanical systems: interplay of mechanical squeezing and non-Gaussianity

Sofia Qvarfort, Alessio Serafini, André Xuereb +3 more

Abstract We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the non-Gaussian state and its closest Gaussian reference state. We find that the addition of a constant mechanical squeezing term to the standard optomechanical Hamiltonian generally decreases the overall non-Gaussian character of the state. For sinusoidally modulated squeezing, the two second-order differential equations mentioned above take the form of the Mathieu equation. We derive perturbative solutions for a small squeezing amplitude at parametric resonance and show that they correspond to the rotating-wave approximation at times larger than the scale set by the mechanical frequency. We find that the non-Gaussianity of the state increases with both time and the squeezing parameter in this specific regime.

arXiv:1908.00790•Journal of Physics A Mathematical and Theoretical•Dec 23, 2019•28 citations

Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model

Luis Medina-Dozal, Irán Ramos-Prieto, José Récamier

In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator U^(t) for the forced optomechanical system (as a product of exponentials) and take the JC Hamiltonian as an interaction. We transform the later with U^(t) to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable.

arXiv:2008.03839•Entropy•Dec 5, 2020•6 citations

Parametric oscillator in a Kerr medium: evolution of coherent states

R. Román-Ancheyta, Manuel Berrondo, J. Récamier

We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction-picture representation and use an exact time-evolution operator for the time-independent part of the Hamiltonian. We approximate the interaction-picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time-evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator’s frequency. We analyze the probability amplitude, the auto-correlation function, and the Husimi distribution function for different Hamiltonian parameters. We find very good agreement between our approximate results and converged numerical calculations.

arXiv:1503.01050•Journal of the Optical Society of America B•Jul 16, 2015•12 citations

Time evolution of coupled multimode and multiresonator optomechanical systems

David Edward Bruschi

We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanicallike interactions. We find the analytical expression for the full time evolution of the system and compute the expectation value of relevant quantities of interest. Among the most interesting ones, we are able to compute the first-order quantum bipartite coherence between pairs of subsystems, and the analytical expression for the mixedness induced by the nonlinear interaction in the reduced state of the mechanical oscillators. Finally, we also compare our results with a linearized version of the system, and we find a regime where there are qualitative and quantitative differences in the behavior of some measurable quantities. Our results can, therefore, be used to describe the full time-evolution of the system to characterize its nonlinear character and explore the validity of the linearization approach.

arXiv:1812.06879•Journal of Mathematical Physics•Jun 1, 2019•18 citations

Strongly driven cavity quantum electrodynamical-optomechanical hybrid system

Xuxin Wang, Jiahe Pan, Tobias J. Kippenberg +1 more

Hybrid quantum systems harness the distinct advantages of different physical platforms, yet their integration is not always trivial due to potential incompatibilities in operational principles. Here, we theoretically propose and demonstrate a scheme for generating non-Gaussian mechanical states using a strongly driven hybrid system that combines cavity quantum electrodynamics (QED) and cavity optomechanics. Our protocol prepares a non-Gaussian cavity state in the dispersive regime of cavity QED and subsequently transfers it to a mechanical oscillator using the optomechanical interaction enhanced by a coherent cavity drive. While non-Gaussian cavity state control in cavity QED is well established in the dispersive regime, its behavior under strong cavity drive, essential for cavity optomechanics, remains largely unexplored. To bridge this gap, we develop an efficient simulation framework to model cavity QED dynamics in the high-photon-number regime. We show that a strong cavity drive can coherently displace the cavity state with minimal perturbations, effectively decoupling it from the qubit. The resulting large coherent cavity field enhances the optomechanical coupling strength, enabling high-fidelity transfer of non-Gaussian cavity states to the mechanical mode. These results reveal new dynamical features of driven cavity QED and open a pathway toward realizing non-Gaussian mechanical quantum memories and sensors.

quant-pharXiv:2512.07788•Physical Review A•Dec 9, 2025•0 citations
Abstract We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, G/ω m , is not negligible compared to one, i.e., the system operates in the strong-coupling regime. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement. In contrast to other works, our approach does not use the standard linearized description in the optomechanical interaction. Therefore, highly non-classical (non-Gaussian) states of light emerge during the time evolution.
Abstract We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the non-Gaussian state and its closest Gaussian reference state. We find that the addition of a constant mechanical squeezing term to the standard optomechanical Hamiltonian generally decreases the overall non-Gaussian character of the state. For sinusoidally modulated squeezing, the two second-order differential equations mentioned above take the form of the Mathieu equation. We derive perturbative solutions for a small squeezing amplitude at parametric resonance and show that they correspond to the rotating-wave approximation at times larger than the scale set by the mechanical frequency. We find that the non-Gaussianity of the state increases with both time and the squeezing parameter in this specific regime.
In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator U^(t) for the forced optomechanical system (as a product of exponentials) and take the JC Hamiltonian as an interaction. We transform the later with U^(t) to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable.
We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction-picture representation and use an exact time-evolution operator for the time-independent part of the Hamiltonian. We approximate the interaction-picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time-evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator’s frequency. We analyze the probability amplitude, the auto-correlation function, and the Husimi distribution function for different Hamiltonian parameters. We find very good agreement between our approximate results and converged numerical calculations.
We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanicallike interactions. We find the analytical expression for the full time evolution of the system and compute the expectation value of relevant quantities of interest. Among the most interesting ones, we are able to compute the first-order quantum bipartite coherence between pairs of subsystems, and the analytical expression for the mixedness induced by the nonlinear interaction in the reduced state of the mechanical oscillators. Finally, we also compare our results with a linearized version of the system, and we find a regime where there are qualitative and quantitative differences in the behavior of some measurable quantities. Our results can, therefore, be used to describe the full time-evolution of the system to characterize its nonlinear character and explore the validity of the linearization approach.
Hybrid quantum systems harness the distinct advantages of different physical platforms, yet their integration is not always trivial due to potential incompatibilities in operational principles. Here, we theoretically propose and demonstrate a scheme for generating non-Gaussian mechanical states using a strongly driven hybrid system that combines cavity quantum electrodynamics (QED) and cavity optomechanics. Our protocol prepares a non-Gaussian cavity state in the dispersive regime of cavity QED and subsequently transfers it to a mechanical oscillator using the optomechanical interaction enhanced by a coherent cavity drive. While non-Gaussian cavity state control in cavity QED is well established in the dispersive regime, its behavior under strong cavity drive, essential for cavity optomechanics, remains largely unexplored. To bridge this gap, we develop an efficient simulation framework to model cavity QED dynamics in the high-photon-number regime. We show that a strong cavity drive can coherently displace the cavity state with minimal perturbations, effectively decoupling it from the qubit. The resulting large coherent cavity field enhances the optomechanical coupling strength, enabling high-fidelity transfer of non-Gaussian cavity states to the mechanical mode. These results reveal new dynamical features of driven cavity QED and open a pathway toward realizing non-Gaussian mechanical quantum memories and sensors.