Controlling subluminal to superluminal behavior of group velocity in an f-deformed Bose–Einstein condensate beyond the rotating wave approximation

Abstract

In this paper, we investigate tunable control of the group velocity of a weak probe field propagating through an f-deformed Bose-Einstein condensate of Λ -type three-level atoms beyond the rotating wave approximation. For this purpose, we use an fdeformed generalization of an effective two-level quantum model of the three-level -configuration without the rotating wave approximation in which the Gardiner's phonon operators for Bose-Einstein condensate are deformed by an operator-valued function,, of the particle-number operator . Corrections produced by the counter-rotating terms appear in the first order as an intensitydependent detuning and in the second order as an intensitydependent atom-field coupling. We consider the collisions between the atoms as a special kind of f-deformation where the collision rate Λ ) (n f n η , the group velocity of the probe pulse changes, from subluminal to superluminal and (iii) beyond the rotating wave approximation, the subluminal and superluminal behaviors of the probe field are enhanced.

Controlling the repetition rate of a mode-locked laser using anf-deformed Bose–Einstein condensate

“…The creation and annihilation operators â † and â, respectively, for photons in the probe field are introduced and by assuming a strong coupling field its intensity is replaced by a c-number parameter. Details of the model are to be found in [24,25], so we summarize only the main features here. In the absence of the RWA, the total Hamiltonian of the system can be written as an effective two-level Hamiltonian in the following form [25]:…”

“…Details of the model are to be found in [24,25], so we summarize only the main features here. In the absence of the RWA, the total Hamiltonian of the system can be written as an effective two-level Hamiltonian in the following form [25]:…”

“…It has been shown that by considering a BEC in the case of finite number of atoms N, the operators of the BEC obey the f -deformed commutation relation of the Heisenberg-Weyl algebra such that, as N → ∞, the usual commutation relation of the Heisenberg-Weyl algebra is regained [23]. In addition, by considering the effect of collisions between the atoms within the condensate, we can apply the extra deformation on the intrinsically deformed operators for the BEC [24,25]. Therefore, the f -deformed BEC can be realized by considering the BEC in the case of a finite number of atoms and taking into account the collision effects.…”

“…Therefore, the f -deformed BEC can be realized by considering the BEC in the case of a finite number of atoms and taking into account the collision effects. Such a system exhibits nonlinear characteristics, such that the nonlinearity increases by adjusting the collision rate κ and the total number of atoms N. Also it improves conditions for realizing the slow light and negative propagation velocities [24,25].…”

“…In this work, we propose a theoretical method, based on an f -deformed BEC introduced inside the resonator of a mode-locked laser, to achieve repetition rate tunability. We have recently shown [25] that, by applying the deformation on atomic operators of a BEC medium beyond the rotating wave approximation (RWA), it is possible to obtain large nonlinearity that leads to an enhanced slow light and negative propagation velocity. Slow light propagation can lead to a reduction of the effective repetition rate of the laser and negative group velocity propagation can lead to an enhancement of the effective repetition rate of the laser.…”