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Physical Review A

Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition

Gao‐xiang Li, Hua-Tang Tan, Mihai Macovei

Published Nov 20, 2007• 87 citations
Publisher

Abstract

The entanglement properties of two mode fields generated from four-wave mixing are discussed in the system of an ensemble of $V$-type three-level atoms embedded in a two-mode cavity, in which the atomic transitions from the two excited states to the ground state are driven by one strong and one relative weak laser field, respectively. The nondegenerate four-wave mixing process occurs in the strong laser-driven transition, which is also coupled by the two cavity modes. With the help of the auxiliary atomic transition driven by the weak laser field and adjusting the frequency difference of the two modes, highly squeezed and entangled light with high intensity can be generated.

DOI
10.1103/physreva.76.053827

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The entanglement properties of two mode fields generated from four-wave mixing are discussed in the system of an ensemble of VVV-type three-level atoms embedded in a two-mode cavity, in which the atomic transitions from the two excited states to the ground state are driven by one strong and one relative weak laser field, respectively. The nondegenerate four-wave mixing process occurs in the strong laser-driven transition, which is also coupled by the two cavity modes. With the help of the auxiliary atomic transition driven by the weak laser field and adjusting the frequency difference of the two modes, highly squeezed and entangled light with high intensity can be generated.
In this paper we propose a scheme in which two-mode entanglement in a steady state is produced by using two lasers to resonantly drive a single four-level atom embedded inside a two-mode optical cavity. In this scheme, atomic coherence induced by a classical laser plays an important role in the process of preparing the entangled state. With the coupling of a strong control field, direct two-photon transition is generated and the relatively weak pump field induces the parametric interaction between two photons, which makes them entangle with each other. By numerical calculation, we find that the degree of entanglement depends strongly on the Rabi frequencies of the classical laser fields and the cavity losses.
We study a nondegenerate three-level cascade laser coupled to a two-mode vacuum reservoir, by employing the stochastic differential equations associated with the normal ordering. The amplification of the properties of squeezing and entanglement of the cavity light is investigated. We have found that there is an entanglement between the states of the light generated in the cavity, due to the strong correlation of the light emitted, when the atom decays from the top level to the bottom level via the intermediate one. We have also obtained that the two cavity modes are strongly entangled, and the degree of entanglement is directly related to the two-mode squeezing.
In this paper, we discuss the generation and evolution of continuous-variable entanglement in a two-mode single-atom laser, where the atomic coherence is induced by two classical microwave fields, which drive the corresponding fine atomic transitions. The results show that the intensity of the microwave field can influence effectively the entanglement properties of the cavity field. In addition, our numerical results also show that the intensity and the period of entanglement between the two cavity modes as well as the total mean photon number of the cavity field can be increased synchronously by adjusting the corresponding frequency detuning.
The generation of two-mode Gaussian-type entangled states of the cavity field is studied in a quantum beat laser, where three-level atoms of the VVV-type level configuration are coupled to two quantized modes of the cavity field and two upper levels of the atom are driven by a strongly classical field. According to Simon's criterion that is a necessary and sufficient condition for the inseparability of two-mode Gaussian states with a general form of covariance matrices, we analytically and numerically investigate the influence of phase and Rabi frequency of the classical driving field, cavity loss, and the purity and nonclassicality of the initial state of the cavity field on the entanglement property of the resulting two-mode Gaussian state. In the limit of weak cavity loss and strong driving, we show that the cavity field can be periodically into an ideal two-mode entangled Gaussian-type state.
We investigate the generation of two-mode-entangled light from a laser-driven three-level $\mathbsf{V}$-type atom inside a cavity by taking into account spontaneously generated quantum interference between two atomic decay channels. We show that under some conditions, the system can reduce to a nondegenerate parametric amplifier which is responsible for the entanglement between the two cavity modes. Compared to the case without the quantum interference, it is found that the entanglement of the cavity field can be significantly enhanced by the interference when the relative phase of the two pumping lasers $\ensuremath{\delta}\ensuremath{\phi}=\ensuremath{\pi}$.