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Physical Review A

Generation of two-mode Gaussian-type entangled states of light via a quantum beat laser

Aiping Fang, Yilong Chen, Fuli Li, Hongrong Li, Pei Zhang

Published Jan 25, 2010• 33 citations
Publisher

Abstract

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 $V$-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.

DOI
10.1103/physreva.81.012323

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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 study the entanglement dynamics of two-mode Gaussian state (TMGS) in a quantum beat laser driven by two classical fields in Raman configuration using Simon's criterion of quantum state separability. The two modes of the cavity field are considered initially in general single-mode Gaussian states. The effect of the non-classicality, purity, and relative phase of the cavity modes on the entanglement phenomenon is studied thoroughly. We show that in the presence of cavity decay rates, the higher the non-classicality of the initial states, the higher is the inseparability of the evolved TMGS of the cavity field. The inseparability, on the other side, is independent of the purity of the initial states. Moreover, the time scale of the entangled state increases with the relative intensity of the driving fields, whereas the relative phase switches the entangled state into the disentangled state of the cavity field and vice versa. The quantum statistics of the mean photons number of the cavity field is analyzed.
We consider a quantum beat laser [Scully and Zubairy, Phys. Rev. A 35 752 (1987)] as a source of entangled radiation. The system essentially consists of three-level atoms inside a doubly resonant cavity such that coherence is introduced by driving the upper two levels with a strong classical field of Rabi frequency $\ensuremath{\Omega}$. We study the dynamics of this system for different values of Rabi frequencies in the presence of cavity losses. It is shown that entanglement can be generated in this system for different initial states of the field in the two modes.
We propose a scheme for the entanglement generation of two cavity modes using a four-level Raman-driven quantum-beat laser (QBL). The atomic coherence is generated by a Raman-type two-photon process. Two different sufficient conditions for entanglement generation have been investigated. The effect of cavity losses and strength of the driving fields on entanglement generation is studied for different initial states of the resonant cavity modes. The results are in agreement with the earlier scheme for the entanglement generation using a directly driven quantum-beat laser. We observe entanglement generation even for high cavity losses and with low strength of the driving fields. Further, there is no dipole-forbidden transition in the Raman-driven QBL system. Thus the proposed scheme for the entanglement generation is experimentally more viable as compared to the previous directly driven QBL system.
Abstract Quantum discord, an appropriate measure of quantum correlation, is analyzed in a two-mode Gaussian state of the cavity field evolved by a system of quantum beat laser. In the laser system, two arbitrary single-mode Gaussian states of the cavity fields and an external classical field couple to the atomic lasing medium. We calculate the time-dependent expression for the quantum discord both analytically and numerically, by following the reduced density matrix equation of the resulting cavity field. In this framework, we investigate the generation and control of Gaussian quantum discord in the two-mode Gaussian state of the cavity field at the output in terms of the purity and non-classicality of the two input cavity modes, the Rabi frequency of the classical driving field, the relative phase of the coupling parameters, and the damping rates of the cavity modes. The behaviour of quantum discord appears oscillatory due to the quantum beats in the output cavity field developed by the classical driving field in the medium as time passes. Moreover, we find that quantum discord switches on and off while adjusting the relative phase of the coupling parameters. Analysis of the analytical results agrees well with our numerical simulations.
We analyze the quantum correlations between side modes of a quantum beat laser when a two-level atomic medium is driven strongly by a classical field. The squeezing and the entanglement generation of the cavity radiation are investigated. It turns out that there is neither squeezing nor entanglement when the strong driving field is resonant with the atomic transition but the generated light exhibits both two-mode squeezing and entanglement when the driving field is tuned away from the atomic transition.
We study the quantum steering of a two-mode Gaussian state evolved by a simple quantum beat laser with the cavity field being initially in arbitrary two single-mode Gaussian states and the lasing medium being driven by a strong classical field. In presence of the cavity damping, the quantum steering time of the two-mode Gaussian state increases with the relative intensity of the coupling fields, whereas the relative phase switches the steerable states into the non-steerable and vice versa. We further show that the higher the non-classicality of the initial cavity modes, the longer the time of steerability in the two-mode Gaussian state. Nonetheless, the quantum steering is irrespective of the influence from the purity of the initial cavity modes of the laser system.