<p>This work investigates the entanglement and squeezing properties of light produced by a non-degenerate, coherently driven three-level laser operating within a closed cavity, which is coupled to a two-mode vacuum reservoir through a single-port mirror. To facilitate the analysis, the noise operators are expressed in normal order. Using the master equation approach, we derive the time evolution equations for the atomic operators. Based on the steady-state solutions of the derived evolution equations, we evaluated several key properties of the cavity radiation: the mean and variance of the photon number, the quadrature variance, the degree of entanglement, the normalized second-order correlation function for the two-mode field, the linear correlation coefficient between the modes, and the intensity difference fluctuations. Our findings indicate that increasing the stimulated emission rate leads to a notable enhancement in the average photon number. Additionally, the mean photon number increases with the amplitude of the pumping mode interacting with the parametric amplifier (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>). Enhanced squeezing is observed with increasing <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation> within the range (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(0 \le \varepsilon \le 0.03\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <mi>ε</mi> <mo>≤</mo> <mn>0.03</mn> </mrow> </math></EquationSource> </InlineEquation>), with the highest observed squeezing at <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varepsilon = 0.03\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>=</mo> <mn>0.03</mn> </mrow> </math></EquationSource> </InlineEquation> (70.4%). Even in the absence of a pump mode, squeezing is present but at a lower level. The parametric amplifier enhances both squeezing and entanglement by amplifying the pumping mode, leading to increased photon generation and stronger quantum correlations. Notably, there is a direct correlation between squeezing and entanglement, indicating that increased entanglement is associated with greater squeezing.</p>

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Impact of a Parametric Amplifier on the Entanglement and Squeezing Properties of a Coherently Driven Three-Level Atom in a Closed Cavity

  • Aliyyi Adem

摘要

This work investigates the entanglement and squeezing properties of light produced by a non-degenerate, coherently driven three-level laser operating within a closed cavity, which is coupled to a two-mode vacuum reservoir through a single-port mirror. To facilitate the analysis, the noise operators are expressed in normal order. Using the master equation approach, we derive the time evolution equations for the atomic operators. Based on the steady-state solutions of the derived evolution equations, we evaluated several key properties of the cavity radiation: the mean and variance of the photon number, the quadrature variance, the degree of entanglement, the normalized second-order correlation function for the two-mode field, the linear correlation coefficient between the modes, and the intensity difference fluctuations. Our findings indicate that increasing the stimulated emission rate leads to a notable enhancement in the average photon number. Additionally, the mean photon number increases with the amplitude of the pumping mode interacting with the parametric amplifier ( \(\varepsilon \) ε ). Enhanced squeezing is observed with increasing \(\varepsilon \) ε within the range ( \(0 \le \varepsilon \le 0.03\) 0 ε 0.03 ), with the highest observed squeezing at \(\varepsilon = 0.03\) ε = 0.03 (70.4%). Even in the absence of a pump mode, squeezing is present but at a lower level. The parametric amplifier enhances both squeezing and entanglement by amplifying the pumping mode, leading to increased photon generation and stronger quantum correlations. Notably, there is a direct correlation between squeezing and entanglement, indicating that increased entanglement is associated with greater squeezing.