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Manipulação do pulso superradiante via interações atômicas

Paulo Hisao Moriya

Published Feb 28, 2012• 0 citations
Publisher

Abstract

The superradiant phenomena is characterized by atomic dipoles ordering process in excited samples moderately denses, that occours due to the atomic induced correlations developed not directly but by the coherent radiation emitted by atoms themselves.The superradiant process evolves from a total disorder at t = 0, attain a maximum order in a time τ ∝ N -1 creating a radiation pulse whose intensity follows the sech 2 law and its peak is proportional to N 2 , thereafter the dipoles relax to a disordered equilibrium state.In this essay, we deal with the interaction between two cavity modes ω a and ω b and a classical pump with a system of N two-level atoms, whose atomic transition frequencies ω 0 .We consider a resonant interaction between atoms and mode ω a and a dispersive coupling of atoms with mode ω b , which couple the atomic sample, and the classical pump.In order to obtain how sech 2 law changes, we use the method of nonlinear small rotations to obtain effective Hamiltonian, expliciting dipolar interaction between atoms.Finally, after write the effective master equation, we use the mean-field approximation and Lewis and Riesenfeld method to obtain the mean features of this phenomena to our system.

DOI
10.11606/d.76.2012.tde-07052012-135135

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The superradiant phenomena is characterized by atomic dipoles ordering process in excited samples moderately denses, that occours due to the atomic induced correlations developed not directly but by the coherent radiation emitted by atoms themselves.The superradiant process evolves from a total disorder at t = 0, attain a maximum order in a time τ ∝ N -1 creating a radiation pulse whose intensity follows the sech 2 law and its peak is proportional to N 2 , thereafter the dipoles relax to a disordered equilibrium state.In this essay, we deal with the interaction between two cavity modes ω a and ω b and a classical pump with a system of N two-level atoms, whose atomic transition frequencies ω 0 .We consider a resonant interaction between atoms and mode ω a and a dispersive coupling of atoms with mode ω b , which couple the atomic sample, and the classical pump.In order to obtain how sech 2 law changes, we use the method of nonlinear small rotations to obtain effective Hamiltonian, expliciting dipolar interaction between atoms.Finally, after write the effective master equation, we use the mean-field approximation and Lewis and Riesenfeld method to obtain the mean features of this phenomena to our system.
A superradiant pulse emitted by a sample of two-level atoms can be combined with superabsorption in order to increase the speed of the excitation interplay. We showcase this with two different experiments, first by subjecting the atomic sample to a competition between dissipation and amplification, the latter being a time-dependent multi-modal linear pumping; second, by coupling the atomic sample with a single mode of a high finesse cavity. The mean-field approximation was used in both cases. In the first, to solve the Schrödinger equation for the resulting time-dependent nonlinear Hamiltonian exactly we use the Lewis and Riesenfeld method. In the second case, we obtain a quantum master equation in the Lindblad form and solve it numerically. We observe that, in particular, the higher the number of atoms on the sample the higher will be the frequency of the interplay in comparison with that coming from the Jaynes-Cummings model. For a certain regime of parameters this system also leads to a superradiant laser, whose characteristics we discuss. These results show that many-particle effects can be further explored for the implementation of quantum information processes as well as for constructing of a superradiant laser. At last, we study non-Hermitian PT-symmetric bosonic nonautonomous Hamiltonians under linear and parametric amplifications. We present a generic approach to solve these Hamiltonians through the use of non-unitary similarity transformations. The choice for the metric associated with these transformations has a dramatic impact on the pseudo-Hermitian operators of the system.
In this work we will deal with the effects of a coherent electromagnetic field acting on an atomic dipole gas confined to a cavity.It is known from ( 5) that in such conditions, if we a have moderately dense sample of N 2-level atoms, we can observe the presence of superradiance, i.e., the enhanced emission of a coherent pulse of intensity proportional to N 2 and, in a smaller scale, the enhanced absorption as well ( 14).When coupling this sample to a quantum electromagnetic field via Tavis-Cummings interaction we are able to enhance even more the superabsorption as well as the superemission to a lesser degree in such a way as to almost equate the intensities of both processes and give rise to interleaved oscillations between them in both field and sample resulting in the phenomenon of many-body Rabi oscillations described in (1).However, it is to expect that, due to momentum conservation, such a phenomenon would cause a deflection on the atoms of the sample in a small time interval, after which we would have a mesoscopic superposition containing all the information related to the prior state.Our main goal is the study of the deflection suffered by the atoms of such a sample and how it relates to the state before the emission.We solve the time-dependent non-linear Hamiltonian related to the superradiant emission/superabsorption via the Lewis-Riesenfeld invariant method.At the end we will show how the macroscopic states were prepared to obtain our results.
A superradiant pulse emitted by a sample of two-level atoms can be combined with superabsorption in order to increase the speed of the excitation interplay.We showcase this with two different experiments, first by subjecting the atomic sample to a competition between dissipation and amplification, the latter being a time-dependent multi-modal linear pumping; second, by coupling the atomic sample with a single mode of a high finesse cavity.The mean-field approximation was used in both cases.In the first, to solve the Schrödinger equation for the resulting time-dependent nonlinear Hamiltonian exactly we use the Lewis and Riesenfeld method.In the second case, we obtain a quantum master equation in the Lindblad form and solve it numerically.We observe that, in particular, the higher the number of atoms on the sample the higher will be the frequency of the interplay in comparison with that coming from the Jaynes-Cummings model.For a certain regime of parameters this system also leads to a superradiant laser, whose characteristics we discuss.These results show that many-particle effects can be further explored for the implementation of quantum information processes as well as for constructing of a superradiant laser.At last, we study non-Hermitian PT -symmetric bosonic nonautonomous Hamiltonians under linear and parametric amplifications.We present a generic approach to solve these Hamiltonians through the use of non-unitary similarity transformations.The choice for the metric associated with these transformations has a dramatic impact on the pseudo-Hermitian operators of the system.
Here we present an approach to the problem of superradiance in dense atomic samples, when dipolar interactions arise between atoms. Our treatment consists of the sequential use of the Holstein-Primakoff and mean-field approximations, from which we derive master equations for the strong and weak couplings of the sample with the reservoir. We find, in both cases, that the radiation emission presents remarkable features, with characteristic emission times much shorter and intensities much higher than those of Dicke superradiance. In particular, for strong sample-reservoir coupling, a whole comb of superpulses occurs within an envelope with the above-mentioned characteristic emission times much shorter and intensities much higher than those of Dicke superradiance.
The superradiant emission is considered for a radiating system constituted by N dressed spin-1/2 magnetic dipoles, described by a nonlinear single particle Hamiltonian that is derived under a mean field approximation. This Hamiltonian describes adequately the transient regime of the emission process: The intensity of the radiation follows the sech2 law and its peak is proportional to N2. Then, one considers the application of a periodic time-dependent transverse magnetic field and we study the behavior of the emission that becomes periodically pulsed.
In this paper we attempt to unify the theoretical treatment of a variety of cooperative interaction phenomena occurring in resonantly interacting radiation-matter systems. The system consists of a multimode optical field interacting with NNN resonant atoms in a region of large spatial extent. The field and atoms may or may not be coupled to reservoirs. We derive a set of coupled master equations for the reduced matter and radiation density operators of the composite system in the first Born approximation, using a method due to Bogoliubov. These equations describe within a single framework phenomena involving superradiant emission and coherent propagation. In the first place, our theory generalizes existing formulations of the superradiance problem by treating the radiation field as part of the dynamical system rather than as a reservoir. Hence, our equations describe stimulated interaction effects, which are entirely absent in the usual superradiance master equations. Moreover, our equations contain terms describing the self-consistent interaction of an average field with a set of polarizable atoms, as in the coupled Bloch and Maxwell equations of the theory of coherent pulse propagation, and enable us to describe fluctuations, arising from incoherent emission, about the average behavior described by the Bloch-Maxwell theory. We solve formally the dynamical equation for the radiation density operator and obtain a displaced multivariate Gaussian distribution centered on the solution of the Maxwell wave equation, which has as parameters the first and second moments of the matter density operator. Then we derive and discuss the field and atomic-moment equations, both in the wave-number and position representations. The moment equations enable us to show the relationship between descriptions of superradiant damping based on the Bloch equations and those based on the existence of correlated atomic states, including both as special cases. We introduce reduced matter moments, which allow us to separate incoherent- and coherent-emission effects and enable us to discuss the question of the closure of the moment equations. Then we consider cases where the behavior of the atomic system is dominated by a strong coherent pump wave or where the atoms are in a symmetric correlated state and show how the slowly-varying-envelope approximation simplifies the radiation-moment equations in these two cases. In the former case, we obtain an approximate theory which consists, in lowest order, of the Bloch-Maxwell equations with radiative-damping terms, plus an equation describing the time development of the correlation function for field fluctuations. Returning to our general formalism, we relate the usual parameters of the theory of radiative decay and of resonant interactions to the more general quantities appearing in our spatial analysis. Finally, we discuss the importance of the stimulated-emission terms appearing in our theory and describe several extensions, including the introduction of inhomogeneous broadening.