I. Ramos-Prieto, ∗ R. Román-Ancheyta, J. Récamier, M. Berrondo, and H. M. Moya-Cessa Instituto de... more I. Ramos-Prieto, ∗ R. Román-Ancheyta, J. Récamier, M. Berrondo, and H. M. Moya-Cessa Instituto de Ciencias F́ısicas, Universidad Nacional Autónoma de México, Apdo. Postal 48-3, Cuernavaca, Morelos 62251, Mexico Instituto Nacional de Astrof́ısica Óptica y Electrónica, Calle Luis Enrique Erro No. 1, Santa Maŕıa Tonantzintla, Pue., 72840, Mexico Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA (Dated: May 31, 2021)
Journal of Physics A: Mathematical and Theoretical, 2012
ABSTRACT A generalization of the time-dependent Jaynes–Cummings Hamiltonian is considered includi... more ABSTRACT A generalization of the time-dependent Jaynes–Cummings Hamiltonian is considered including nonlinear terms in the field and/or an intensity-dependent coupling term. Using algebraic methods we find the corresponding time evolution operator of the problem as a product of exponential operators. Also, we study the effect of the atomic motion in the cavity on its quantum state. We found that, when the atom is vibrating classically with a small amplitude A0 (in comparison with the effective length of the cavity L), i.e. A0 ≪ L, the effects of the atom’s motion are negligible but when A0 ∼ L/4, the state of the atom changes drastically. Our study is devoted to a Jaynes–Cummings Hamiltonian with an additional Kerr medium.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2011
ABSTRACT The Jaynes–Cummings Hamiltonian with deformed operators of the field is considered; as a... more ABSTRACT The Jaynes–Cummings Hamiltonian with deformed operators of the field is considered; as a particular case the Kerr-like medium is obtained via an appropriate deformation function. We find that, for an appropriate choice of the parameter of the deformation function, states of the uncoupled basis with a selected fixed number of quanta are in resonance, providing a maximum probability of transition of the atom for these states. Under this condition one may find an appropriate value of the coupling constant such that complete revivals are obtained.
Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la un... more Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la unam. Primera edición electrónica: 3 de diciembre de 2014
Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la un... more Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la unam. Primera edición electrónica: 2012
We present a formalism to incorporate high order effects of the pump field on the fourwave mixing... more We present a formalism to incorporate high order effects of the pump field on the fourwave mixing signal for a two-level system immersed in a thermal bath. We derive analytical expressions for the nonlinear polarization in terms of the field amplitude and thermal noise parameters
Alternative algebraic techniques to approximate a given Hamiltonian by a harmonic oscillator are ... more Alternative algebraic techniques to approximate a given Hamiltonian by a harmonic oscillator are described both for time-independent and time-dependent systems. The authors apply them to the description of a one dimensional atom-diatom collision. From the resulting evolution operator, they evaluate vibrational transition probabilities as well as other time-dependent properties. As expected, the ground vibrational state becomes a squeezed state during the collision.
In this work we analyze the time evolution of an atomic system in the presence of an electromagne... more In this work we analyze the time evolution of an atomic system in the presence of an electromagnetic field. The interaction between the field and the system is modeled within the dipole approximation. As a zero approximation we first model the system with a harmonic oscillator and consider the field as classical. As is well known, in this case the quantal result is identical with the classical one. Then we model the system with a Morse oscillator which we expand keeping up to fourth order terms in the displacement coordinate. We compare the response of the system for different depths of the potential and different intensities of the field.
Even harmonic molecules display a nonlinear behavior when driven by an inhomogeneous field. We ca... more Even harmonic molecules display a nonlinear behavior when driven by an inhomogeneous field. We calculate the response of single harmonic molecules to a monochromatic time and space dependent electric field E(r, t) of frequency ω employing exact algebraic methods. We evaluate the responses at the fundamental frequency ω and at successive harmonics 2ω, 3ω, etc. as a function of the intensity and of the frequency of the field and compare the results with those of first and second order perturbation theory.
Submitted for the DAMOP11 Meeting of The American Physical Society Dynamical Mean-Field Approach ... more Submitted for the DAMOP11 Meeting of The American Physical Society Dynamical Mean-Field Approach to Anharmonic Oscillators under Time-Dependent Perturbations JEAN-FRANCOIS VAN HUELE, MANUEL BERRONDO, Brigham Young University, JOSE RECAMIER, Universidad Nacional Autonoma de Mexico — We consider the effect of a time-dependent perturbation on an anharmonic oscillator. By expressing the anharmonic oscillator in terms of deformed ladder operators, we obtain the energy spectrum of the unperturbed problem in terms of the quanta of the number operator and an anharmonicity parameter. The combined presence of quadratic terms in the unperturbed Hamiltonian and of the time-dependent perturbation does not lead to a closed algebra and an exact solution. Introducing the mean field in the unperturbed term allows us to obtain a closed algebra with a time-dependent frequency in the unperturbed term. Through factorization of the corresponding evolution operator, the dynamical problem is reduced to a s...
espanolCalculamos probabilidades de transicion entre estados vibracionales de una molecula diatom... more espanolCalculamos probabilidades de transicion entre estados vibracionales de una molecula diatomica inducidas por un atomo incidente. El modelo prototipo trata el movimiento de traslacion relativo como una variable clasica. Los estados vibracionales de la molecula diatomica se tratan cuanticamente en terminos del operador de evolucion, sin involucrar funciones de onda. Las ecuaciones de movimiento correspondiente se acoplan cuasi-clasicamente. A manera de ilustracion presentamos aplicaciones a la dependencia temporal de probabilidades de transicion para diferentes estados inicial y final asi como para un ensamble canonico de condiciones iniciales. EnglishWe calculate transition probabilities between vibrational levels of a diatomic molecule induced by an incident atom. Our prototype model is constructed treating the relative translation of the colliding species as a classical variable. The vibrational states of the diatomic molecule are treated quantum mechanically in terms of the ...
In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hami... more 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 a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode... more We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium and a two-level atom. We obtain approximate expressions for the time-evolution operator valid at short times and/or low average photon number. We have found an interplay between the effect of the nonlinear Kerr medium, which is to decrease the growth of photon generation from the vacuum state, and that of the two-level atom, which is to increase the photon generation. We explore an ample range of Hamiltonian parameters going from the resonant to the dispersive regimes.
We present an approximate Lie algebraic method to deal with a forced optomechanical Hamiltonian. ... more 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.
We study the temporal evolution of a coherent state under the action of a parametric oscillator i... more We study the temporal evolution of a coherent state under the action of a parametric oscillator immersed in a nonlinear Kerr-like medium. Applying a self consistent method we obtain an approximate time evolution operator. This operator behaves like a squeezing operator due to the temporal dependence of the oscillator's frequency. We analyze Mandel's parameter, the presence of squeezing in the field quadratures and the generation of photons from the vacuum state.
I. Ramos-Prieto, ∗ R. Román-Ancheyta, J. Récamier, M. Berrondo, and H. M. Moya-Cessa Instituto de... more I. Ramos-Prieto, ∗ R. Román-Ancheyta, J. Récamier, M. Berrondo, and H. M. Moya-Cessa Instituto de Ciencias F́ısicas, Universidad Nacional Autónoma de México, Apdo. Postal 48-3, Cuernavaca, Morelos 62251, Mexico Instituto Nacional de Astrof́ısica Óptica y Electrónica, Calle Luis Enrique Erro No. 1, Santa Maŕıa Tonantzintla, Pue., 72840, Mexico Department of Physics and Astronomy, Brigham Young University, Provo, UT 84602, USA (Dated: May 31, 2021)
Journal of Physics A: Mathematical and Theoretical, 2012
ABSTRACT A generalization of the time-dependent Jaynes–Cummings Hamiltonian is considered includi... more ABSTRACT A generalization of the time-dependent Jaynes–Cummings Hamiltonian is considered including nonlinear terms in the field and/or an intensity-dependent coupling term. Using algebraic methods we find the corresponding time evolution operator of the problem as a product of exponential operators. Also, we study the effect of the atomic motion in the cavity on its quantum state. We found that, when the atom is vibrating classically with a small amplitude A0 (in comparison with the effective length of the cavity L), i.e. A0 ≪ L, the effects of the atom’s motion are negligible but when A0 ∼ L/4, the state of the atom changes drastically. Our study is devoted to a Jaynes–Cummings Hamiltonian with an additional Kerr medium.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2011
ABSTRACT The Jaynes–Cummings Hamiltonian with deformed operators of the field is considered; as a... more ABSTRACT The Jaynes–Cummings Hamiltonian with deformed operators of the field is considered; as a particular case the Kerr-like medium is obtained via an appropriate deformation function. We find that, for an appropriate choice of the parameter of the deformation function, states of the uncoupled basis with a selected fixed number of quanta are in resonance, providing a maximum probability of transition of the atom for these states. Under this condition one may find an appropriate value of the coupling constant such that complete revivals are obtained.
Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la un... more Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la unam. Primera edición electrónica: 3 de diciembre de 2014
Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la un... more Esta edición fue preparada por el Instituto de Física y el Instituto de Ciencias Físicas de la unam. Primera edición electrónica: 2012
We present a formalism to incorporate high order effects of the pump field on the fourwave mixing... more We present a formalism to incorporate high order effects of the pump field on the fourwave mixing signal for a two-level system immersed in a thermal bath. We derive analytical expressions for the nonlinear polarization in terms of the field amplitude and thermal noise parameters
Alternative algebraic techniques to approximate a given Hamiltonian by a harmonic oscillator are ... more Alternative algebraic techniques to approximate a given Hamiltonian by a harmonic oscillator are described both for time-independent and time-dependent systems. The authors apply them to the description of a one dimensional atom-diatom collision. From the resulting evolution operator, they evaluate vibrational transition probabilities as well as other time-dependent properties. As expected, the ground vibrational state becomes a squeezed state during the collision.
In this work we analyze the time evolution of an atomic system in the presence of an electromagne... more In this work we analyze the time evolution of an atomic system in the presence of an electromagnetic field. The interaction between the field and the system is modeled within the dipole approximation. As a zero approximation we first model the system with a harmonic oscillator and consider the field as classical. As is well known, in this case the quantal result is identical with the classical one. Then we model the system with a Morse oscillator which we expand keeping up to fourth order terms in the displacement coordinate. We compare the response of the system for different depths of the potential and different intensities of the field.
Even harmonic molecules display a nonlinear behavior when driven by an inhomogeneous field. We ca... more Even harmonic molecules display a nonlinear behavior when driven by an inhomogeneous field. We calculate the response of single harmonic molecules to a monochromatic time and space dependent electric field E(r, t) of frequency ω employing exact algebraic methods. We evaluate the responses at the fundamental frequency ω and at successive harmonics 2ω, 3ω, etc. as a function of the intensity and of the frequency of the field and compare the results with those of first and second order perturbation theory.
Submitted for the DAMOP11 Meeting of The American Physical Society Dynamical Mean-Field Approach ... more Submitted for the DAMOP11 Meeting of The American Physical Society Dynamical Mean-Field Approach to Anharmonic Oscillators under Time-Dependent Perturbations JEAN-FRANCOIS VAN HUELE, MANUEL BERRONDO, Brigham Young University, JOSE RECAMIER, Universidad Nacional Autonoma de Mexico — We consider the effect of a time-dependent perturbation on an anharmonic oscillator. By expressing the anharmonic oscillator in terms of deformed ladder operators, we obtain the energy spectrum of the unperturbed problem in terms of the quanta of the number operator and an anharmonicity parameter. The combined presence of quadratic terms in the unperturbed Hamiltonian and of the time-dependent perturbation does not lead to a closed algebra and an exact solution. Introducing the mean field in the unperturbed term allows us to obtain a closed algebra with a time-dependent frequency in the unperturbed term. Through factorization of the corresponding evolution operator, the dynamical problem is reduced to a s...
espanolCalculamos probabilidades de transicion entre estados vibracionales de una molecula diatom... more espanolCalculamos probabilidades de transicion entre estados vibracionales de una molecula diatomica inducidas por un atomo incidente. El modelo prototipo trata el movimiento de traslacion relativo como una variable clasica. Los estados vibracionales de la molecula diatomica se tratan cuanticamente en terminos del operador de evolucion, sin involucrar funciones de onda. Las ecuaciones de movimiento correspondiente se acoplan cuasi-clasicamente. A manera de ilustracion presentamos aplicaciones a la dependencia temporal de probabilidades de transicion para diferentes estados inicial y final asi como para un ensamble canonico de condiciones iniciales. EnglishWe calculate transition probabilities between vibrational levels of a diatomic molecule induced by an incident atom. Our prototype model is constructed treating the relative translation of the colliding species as a classical variable. The vibrational states of the diatomic molecule are treated quantum mechanically in terms of the ...
In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hami... more 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 a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode... more We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium and a two-level atom. We obtain approximate expressions for the time-evolution operator valid at short times and/or low average photon number. We have found an interplay between the effect of the nonlinear Kerr medium, which is to decrease the growth of photon generation from the vacuum state, and that of the two-level atom, which is to increase the photon generation. We explore an ample range of Hamiltonian parameters going from the resonant to the dispersive regimes.
We present an approximate Lie algebraic method to deal with a forced optomechanical Hamiltonian. ... more 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.
We study the temporal evolution of a coherent state under the action of a parametric oscillator i... more We study the temporal evolution of a coherent state under the action of a parametric oscillator immersed in a nonlinear Kerr-like medium. Applying a self consistent method we obtain an approximate time evolution operator. This operator behaves like a squeezing operator due to the temporal dependence of the oscillator's frequency. We analyze Mandel's parameter, the presence of squeezing in the field quadratures and the generation of photons from the vacuum state.
Uploads
Papers by José Récamier