The Quantum Analysis of Nonlinear Optical Parametric Processes with Thermal Reservoirs

Abstract

In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. Particularly, the enhancement of squeezing and the amplification of photon entanglement of the two-mode cavity light are investigated. It is found that the two cavity modes are strongly entangled and the degree of entanglement is directly related to the two-mode squeezing. Despite the fact that the entanglement and squeezing decrease with the increment of the mean photon number of the thermal reservoir, strong amount of these nonclassical properties can be generated for a considerable amount of thermal noise with the help of the nonlinear crystal introduced into the laser cavity. Moreover, the squeezing and entanglement of the cavity radiation enhance with the rate of atomic injection.

Generation of Entangled Light from a Nondegenerate Three-Level Laser Coupled to a Two-Mode Vacuum Reservoir

“…Since the coupling constant is taken to be small, we restrict ourselves to a linear analysis that includes dropping the higher order terms in . Employing the linear and adiabatic approximation schemes in the good cavity limit, we get the equation of evolution of the density operator for the cavity modes in the absence of damping through the coupled mirror in the form [14]…”

“…A pair of particles is taken to be entangled in quantum theory, if its states cannot be expressed as a product of the states of its individual constituents. The preparation and manipulation of these entangled states that have nonclassical and nonlocal properties lead to a better understanding of the basic quantum principles [13,14], if the density operator for the combined state cannot be described as the product of the density operators of the constituents,…”

“…Three-level lasers have been an interesting area of research over the years in light of its capability to produce radiations with various quantum properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The quantum properties of light are attributed to the atomic coherence that can be induced either by preparing the atoms initially in a coherent superposition of the top and bottom levels [1,14,15], by coupling these levels of the atom with a strong classical pumping radiation [2,[8][9][10][11], or by using these mechanisms together [5]. Such mechanism imposes a constraint on the populations of atoms in the bottom and top levels in which transitions to and from could not be made in the electric dipole approximation.…”

“…The two modes 1 and 2 to be at resonance with the two transitions |3⟩ → |2⟩ and |2⟩ → |1⟩ are dipole-allowed, and the direct transition between level |3⟩ and level |1⟩ to be dipole-forbidden sitive measurements [28], and quantum telecloning [29]. Hence, an interest in understanding the entanglement creation and quantification has gained the attention of several authors [10,[13][14][15][30][31][32][33][34][35]. In general, the degree of entanglement degrades, as it interacts with the environment.…”

“…Moreover, many schemes have been proposed to produce a strong entangled light from a three-level laser using different techniques theoretically [6,7,[13][14][15]35]. Some authors have studied the effect of a parametric amplifier on the quantum properties of light generated by a three-level laser [7].…”