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Physical Review A

Effect of dephasing on transient and steady-state entanglement in a quantum-beat laser

Eyob Alebachew Sete

Published Dec 5, 2011• 12 citations
Publisher

Abstract

We study the role of dephasing on entanglement evolution in a two-photon quantum-beat laser. We rigorously derived the pertinent master equation by taking into account dephasing, spontaneous emission, and cavity losses. The dephasing rate, in general, is lager than the rates of other dissipation processes and might influence the realizable quantum properties of the cavity field. We investigate the extent to which the dephasing rate affects the transient as well as steady-state entanglement between the cavity modes. We show that the coherence induced by initial coherent superposition of atomic levels leads to transient as well as steady-state entanglement, which turns out to be susceptible to decoherence. However, the entanglement created via coherence induced by a strong laser field exists for only short times and is relatively robust against decoherence.

DOI
10.1103/physreva.84.063808

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We study the role of dephasing on entanglement evolution in a two-photon quantum-beat laser. We rigorously derived the pertinent master equation by taking into account dephasing, spontaneous emission, and cavity losses. The dephasing rate, in general, is lager than the rates of other dissipation processes and might influence the realizable quantum properties of the cavity field. We investigate the extent to which the dephasing rate affects the transient as well as steady-state entanglement between the cavity modes. We show that the coherence induced by initial coherent superposition of atomic levels leads to transient as well as steady-state entanglement, which turns out to be susceptible to decoherence. However, the entanglement created via coherence induced by a strong laser field exists for only short times and is relatively robust against decoherence.
Detailed derivation of the master equation and corresponding time evolution of the cavity radiation of coherent beat laser in terms of the ccc-number variables associated with the normal ordering is presented. Although the obtained expressions in general turn out to have the same form as when dephasing is not taken into consideration, there is clear evidence that the quantum features of the cavity radiation can be significantly affected by the rate of dephasing. It is shown based on intuitive argument that the degree of two-mode squeezing and entanglement decrease with the rate of dephasing. Moreover, a thorough study of the effects of the rate at which the atomic coherent superposition is decaying is expected to aid in determining the actual available various quantum properties of the generated radiation.
A steady state analysis of the nonclassical features and statistical properties of the cavity radiation of a two-photon coherent beat laser is presented. Results show that the degree of two-mode squeezing, detectable entanglement and intensity of the cavity radiation can increase with the deviation of the phase fluctuations of the laser employed in preparing the atoms, but decrease with the increasing rate at which the induced coherence superposition decays. Although it is found that varying the phase fluctuations and dephasing can lead to modification in the quantum features and statistical properties of the radiation, it does not alter the similarity in the nature of the degree of entanglement detectable by the criteria following from Duan—Giedke—Cirac—Zoller and logarithmic negativity in a perceivable manner. Since the intensity and quantum features can be readily enhanced, this system is expected to be a viable source of a strong robust entangled (squeezed) light under various conditions. Moreover, comparison of the mean number of photon pairs with intensity difference shows that the chance of inciting a two-photon process can be enhanced by changing the rate of dephasing and phase fluctuations.
A steady state analysis of the nonclassical features and statistical properties of the cavity radiation of a twophoton coherent beat laser is presented.Results show that the degree of two-mode squeezing,detectable entanglement and intensity of the cavity radiation can increase with the deviation of the phase fluctuations of the laser employed in preparing the atoms,but decrease with the increasing rate at which the induced coherence superposition decays.Although it is found that varying the phase fluctuations and dephasing can lead to modification in the quantum features and statistical properties of the radiation,it does not alter the similarity in the nature of the degree of entanglement detectable by the criteria following from Duan-Giedke-Cirac-Zoller and logarithmic negativity in a perceivable manner.Since the intensity and quantum features can be readily enhanced,this system is expected to be a viable source of a strong robust entangled (squeezed) light under various conditions.Moreover,comparison of the mean number of photon pairs with intensity difference shows that the chance of inciting a two-photon process can be enhanced by changing the rate of dephasing and phase fluctuations.
We consider a two-photon laser in a cascade configuration coupled to an ordinary vacuum reservoir via a partially transmitting mirror. The impacts of the dephasing and the phase fluctuation on the entanglement, two-mode squeezing, and the intensity of the intracavity radiation are studied at steady-state. It so happens that the initial atomic coherence is the cause for the quantum properties of the cavity radiation even in the presence of the decoherence. We show that the dephasing rates and the phase fluctuations hurt the amount of squeezing and entanglement of the intracavity radiation. However, the dephasing rate leads to an increase in the intensity of the cavity radiation. Moreover, the phase fluctuation degrades the intensity of the intracavity radiation near to the initial maximum atomic coherence and it enhances otherwise.
A detailed derivation of the master equation and the corresponding time evolution of the cavity radiation of a coherent beat laser when the atoms are initially prepared in a partial coherent superposition is presented. It turns out that the quantum features and intensity of the cavity radiation are considerably modified by the phase fluctuation arising due to the practical incapability of preparing atoms in the intended perfect coherent superposition. New terms having opposite signs than the contribution of the driving radiation emerged in the master equation. This can be taken as an indication of a competing effect between the two in the manifestation of the nonclassical features. This, on the other hand, means that there is a chance to regain the quantum properties that might have been lost due to faulty preparation in engineering the driving mechanism and vice versa. In light of this, quite remarkably, the cavity radiation is shown to exhibit nonclassical features including two-mode squeezing and entanglement when there is no driving and when the atoms are initially prepared in a partial maximum atomic coherence superposition, contrary to earlier predictions for the case of perfect coherence.
A detailed analysis of the dynamics of the cavity radiation of a coherently pumped correlated emission laser is presented. The phase fluctuation and dephasing are found to affect the time evolution of the two-mode squeezing and intensity significantly. The intensity and degree of the two-mode squeezing increase at early stages of the process with time, but this trend changes rapidly afterwards. It is also shown that they increase with phase fluctuation and dephasing in the strong driving limit; however, the situation appears to be opposite in the weak driving limit. This essentially suggests that the phase fluctuation and dephasing weaken the coherence induced by a strong driving mechanism so that the spontaneous emission gets a chance. Moreover, the degree of two-mode squeezing turns out to increase with the rate of injection of the atoms into the cavity only at early stages, whereas the mean photon number increases throughout the lasing process. The other important aspect of the phase fluctuation, in this regard, is the relaxation of the time at which the maximum squeezing is manifested as well as the time in which the radiation remains in a squeezed state.