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Journal of Physics B Atomic Molecular and Optical Physics

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

Zahra Haghshenasfard, Michael G Cottam

Published Dec 16, 2011• 1 citation
Publisher

Abstract

Investigations are made for the possibility of using an f-deformed Bose–Einstein condensate (BEC) inside the resonator of a mode-locked laser to achieve tunable control of the repetition rate. Slow light propagation of the probe field through the f-deformed BEC may lead to a large observable increase in the cavity round-trip delay and, therefore, to a reduction in the effective repetition rate of the laser. Conversely, negative propagation velocity through the f-deformed BEC can lead to a decrease in the cavity round-trip and to an increase in the effective repetition rate. Simulations are presented using an f-deformed BEC of Λ-type three-level atoms beyond the rotating wave approximation. Collisions between the atoms are considered as a special kind of f-deformation where the collision rate κ is regarded as the deformation parameter. In particular, it is found that the repetition rate can be controlled effectively by changing the collision rate κ, the total number of atoms N and the parameter λ for the counter-rotating terms.

DOI
10.1088/0953-4075/45/2/025501

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Investigations are made for the possibility of using an f-deformed Bose–Einstein condensate (BEC) inside the resonator of a mode-locked laser to achieve tunable control of the repetition rate. Slow light propagation of the probe field through the f-deformed BEC may lead to a large observable increase in the cavity round-trip delay and, therefore, to a reduction in the effective repetition rate of the laser. Conversely, negative propagation velocity through the f-deformed BEC can lead to a decrease in the cavity round-trip and to an increase in the effective repetition rate. Simulations are presented using an f-deformed BEC of Λ-type three-level atoms beyond the rotating wave approximation. Collisions between the atoms are considered as a special kind of f-deformation where the collision rate κ is regarded as the deformation parameter. In particular, it is found that the repetition rate can be controlled effectively by changing the collision rate κ, the total number of atoms N and the parameter λ for the counter-rotating terms.
In this paper, we investigate the propagation of a weak optical probe pulse in an f-deformed Bose- Einstein condensate (BEC) of a gas with the -type three- level atoms in the electromagnetically induced transparency (EIT) regime. We use an f- deformed generalization of an effective two- level quantum model of the three- level configuration in which the Gardiner phonon operators for BEC are deformed by an operator- valued function, f(n), of the particle- number operator n. With making use of the quantum approach of the angular momentum theory we obtain the eigenvalues and eigenfunctions of the system up to first order approximation. We consider the collisions between the atoms as a special kind of f- deformation. The collision rate k is regarded as the deformation parameter and light propagation in the deformed BEC is analyzed. In particular, we show that the absorptive and dispersive properties of the deformed condensate can be controlled effectively by changing the deformation parameter k and the total number of atoms. We find that by increasing the value of k the group velocity of the probe pulse changes, through deformed condensate, from subluminal to superluminal.
We review and critically evaluate our proposal of a pulse amplification scheme based on two Bose-Einstein condensates inside the resonator of a mode-locked laser. Two condensates are used for compensating the group velocity dispersion. Ultraslow light propagation through the condensate leads to a considerable increase in the cavity round-trip delay time, lowers the effective repetition rate of the laser, and hence scales up the output pulse energy. It has been recently argued that atom-atom interactions would make our proposal even more efficient. However, neither in our original proposal nor in the case of interactions, limitations due to heating of the condensates by optical energy absorption were taken into account. Our results show that there is a critical time of operation,  0.3~0.3 0.3 ms, for the optimal amplification factor, which is in the order of ∼102\sim 10^2∼102 at effective condensate lengths in the order of ∼50\sim 50∼50 μμμm. The bandwidth limitation of the amplifier on the minimum temporal width of the pulse that can be amplified with this technique is also discussed.
In this paper, we investigate the spectrum of light scattered from a Bose-Einstein condensate in the framework of -deformed boson.We use an -deformed quantum model in which the Gardiner's phonon operators for BEC are deformed by an operator-valued function,, of the particle-number operator n .We consider the collisions between the atoms as a special kind of -deformation.The collision rateκ is regarded as the deformation parameter and the spectrum of light scattered from the deformed BEC is analyzed.In particular, we find that with increasing the values of deformation parameters κ and N 1 = η ( , total number of condensate atoms) the scattering spectrum shows deviation from the spectrum associated with nondeformed Bose-Einstein condensate.
In this paper, we investigate the spontaneous emission of an f -deformed Bose–Einstein condensate of a gas with N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially excited. We apply an f -deformed quantum model in which Gardiner's phonon operators are deformed by an operator-valued function of the particle number operator . We consider the collisions between the atoms as a special kind of f -deformation where the collision rate κ is regarded as a corresponding deformation parameter. The time evolution of the expectation value of the atomic inversion is presented, the phenomenon of collective collapses and revivals is shown and the effects of deformation on the cooperative behaviour of the system are discussed.
In this study, we explore the dynamics of slow and fast light propagation in a system consisting of a Bose-Einstein condensate (BEC) acting as a mechanical oscillator coupled to an optical parametric amplifier (OPA) within a fixed-mirror cavity. The system's response is investigated through a comprehensive analysis of the transmission spectrum, output probe field characteristics (real and imaginary components), group delay, and Goos-Hänchen shift (GHS). Our findings reveal that variations in the effective coupling strength and the OPA gain have a profound impact on the system's behavior. Specifically, as the OPA gain increases, a Fano-like resonance emerges, enhancing the transparency window and altering the dispersion, which in turn influences the group delay. The GHS is shown to be sensitive to both the incident angle and the BEC-cavity coupling strength. These results offer valuable insights into the intricate interplay between the probe field, the mechanical oscillator, and the amplified modes of the OPA, highlighting the role of these interactions in shaping the propagation of light in such systems.
Abstract In this paper, we investigate the effect of atomic collisions on the phase transition form the normal to the superradiant phase in a one-dimensional Bose–Einstein condensate (BEC) trapped inside an optical cavity. Specifically, we show that driving the atoms from the side of the cavity leads to the excitation of modes in the edges of the first Brillouin zone of every energy band, which results in the two-mode approximation of the BEC matter field in the limit of weak coupling regime. The nonlinear effect of atom–atom interaction shifts the threshold of the quantum phase transition of the BEC and also affect the power low behavior of quantum fluctuations in the total particle number. Besides, we show the possibility of controlling the quantum phase transition of the system through the s -wave scattering frequency when the strength of the transverse pumping has been fixed.