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Physical Review A

Influence of pump-phase fluctuations on entanglement generation using a correlated spontaneous-emission laser

Shahid Qamar, Han Xiong, Muhammad Suhail Zubairy

Published Jun 6, 2007• 38 citations
Publisher

Abstract

In this paper, we study the effect of phase fluctuations of the pump field upon the entanglement generation in a two-photon correlated emission laser (CEL). We consider initial vacuum and coherent state for the two-cavity modes. In both cases, we find reduction in the entanglement due to the phase fluctuations. However, our results indicate that entanglement generation is highly sensitive to phase fluctuations when we have initial coherent state in the two modes.

DOI
10.1103/physreva.75.062305

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In this paper, we study the effect of phase fluctuations of the pump field upon the entanglement generation in a two-photon correlated emission laser (CEL). We consider initial vacuum and coherent state for the two-cavity modes. In both cases, we find reduction in the entanglement due to the phase fluctuations. However, our results indicate that entanglement generation is highly sensitive to phase fluctuations when we have initial coherent state in the two modes.
The fundamental source of noise in laser and optical amplifier is spontaneous emission. However, it is possible to reduce this noise by preparing the gain medium (atoms) in coherent superposition of states. There are essentially two schemes for generating atomic coherence in optical amplifiers. \n \nFirst scheme involves the preparation of atoms in a coherent superposition of states before injecting them inside the cavity. In the other scheme atoms (initially pumped incoherently) are continuously driven by an external pump field inside the cavity. Almost all the studies concerning the quenching of spontaneous emission noise in optical amplifiers, based on the notion of atomic coherent superposition, ignore the finite bandwidth of the field that is responsible for generating coherence. In this dissertation, we have examined the effect of the finite bandwidth associated with the phase fluctuations of the driving field on a number of noise quenching schemes. \n \nIt is known that coherent preparation of atoms can, under certain conditions, lead to noise-free amplification and almost 50 percent phase squeezing in a two-photon correlated emission laser. We study the effect of phase fluctuations in the injected atoms on the phase noise of the field in these systems. We discuss the conditions under which squeezing is preserved in the two-photon linear amplifiers. We also show that, even for very large phase fluctuations in the injected atoms, almost 50 percent phase squeezing can be achieved. The corresponding gain is however significantly reduced. \n \nWe also study a system of phase-sensitive amplifier where atoms are prepared in a coherent superposition of states by a strong classical field. We study the role of pump phase fluctuations associated with the finite linewidth on the quantum statistical properties of the radiation field. A study of output field characteristics reveals that the presence of a weak pump field gives rise to equal variances in both the field quadratures which are independent of linewidth. On the other hand, the presence of strong pump field alters the output field characteristics with the generation of squeezing which is later on destroyed due to the presence of 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.
We develop a nonlinear theory of a two-photon correlated-spontaneous-emission laser (CEL) by using an effective interaction Hamiltonian for a two-level system coupled by a two-photon transition. Assuming that the active atoms are prepared initially in a coherent superposition of two atomic levels involved in the two-photon transition, we derive a master equation for the field-density operator by using our quantum theory for coherently pumped lasers. The steady-state properties of the two-photon CEL are studied by converting the field master equation into a Fokker-Planck equation for the antinormal-ordering Q representation of the field-density operator. Because of the injected atomic coherence, the drift and diffusion coefficients become phase sensitive. This leads to laser phase locking and an extra two-photon CEL gain. The laser field can build up from a vacuum in the no-population-inversion region, in contrast to an ordinary two-photon laser for which triggering is needed. We find an approximate steady-state solution of the Q representation for the laser field, which consists of two identical peaks of elliptical type. We calculate the phase variance and, for any given mean photon number, obtain the minimum variance in the phase quadrature as a function of the initial atomic variables. Squeezing of the quantum noise in the phase quadrature is found and it exhibits the following features: (1) it is possible only when the laser intensity is smaller than a certain value; (2) it becomes most significant for small mean photon number, which is achievable in the no-population-inversion region; and (3) a maximum of 50% squeezing can be asymptotically approached in the small laser intensity limit. As a by-product we also study the ordinary two-photon laser and find, e.g., photon-number variance and laser linewidth.
Analysis of the effects of external pumping on the quantum features of cavity radiation of the two-photon correlated emission laser is presented. It turns out that the pumping process induces the atomic coherence responsible for the entanglement of the cavity radiation as well as the correlation between the photon numbers belonging to different modes, despite the arising vacuum fluctuations. The photon number correlation is found to be very close to 2 where the entanglement is relatively better. Moreover, the mean number of photon pairs decreases with the amplitude of the driving radiation which is one of the practical limitations associated with the pumping mechanism. It is also shown that the mean photon number of the radiation in mode b is less than one-third of that in mode a.
We discuss the generation and evolution of entangled light in a correlated spontaneous emission laser. The master equation for the two-mode field in a cavity is derived and solved analytically. The time-dependent characteristic function in the Wigner representation for the two-mode field is obtained. It shows that the two-mode field in the cavity evolves in a two-mode Gaussian state. The entanglement degree of the two-mode field in the cavity increases initially, then decreases, and finally vanishes as the field evolves from an initial vacuum. The period of the entanglement is extended as the intensity of the driving field is increased. It is found that the entanglement still exists even when the two-mode squeezing disappears. During the entanglement period, the intensity of the field is amplified. The entanglement for the initial field being a two-mode squeezed vacuum and the entanglement of the output field are also discussed.
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.