Phase-to-amplitude conversion noise in squeezed-vacuum-state generation from a semiconductor laser

S. Inoue; S. Machida; Y. Yamamoto; H. Ohzu

doi:10.1364/JOSAB.10.002121

Journal of the Optical Society of America B
Vol. 10,
Issue 11,
pp. 2121-2129
(1993)
•https://doi.org/10.1364/JOSAB.10.002121

Phase-to-amplitude conversion noise in squeezed-vacuum-state generation from a semiconductor laser

S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu

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S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, "Phase-to-amplitude conversion noise in squeezed-vacuum-state generation from a semiconductor laser," J. Opt. Soc. Am. B 10, 2121-2129 (1993)

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Abstract

An excess phase-to-amplitude conversion noise was observed in the interferometric cancellation for the coherent excitation of the squeezed output from an injection-locked laser. We show theoretically that this phase-to-amplitude conversion noise can be eliminated and that it is possible to generate squeezed vacuum states by the use of a semiconductor laser system.

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Symbol	Expression
B₁	A₂A₃A₅ + A₁(A₅² + A₆²) − A₀A₂A₄A₆
B₂	A₀A₄A₆ − A₃A₅
B₃	A₁A₆
B₄	A₁A₅
B₅	−A₀B₁
B₆	A₀A₄A₅ + A₃A₆
B₇	A₂A₃ + A₁A₅
B₈	A₀A₂A₄ − A₁A₆
C₅	$\frac{r_{0}}{C_{4}}$
C₆	C₁ + C₃C₁₀C₁₁
C₇	C₃(C₁₀C₁₂ − 1)
C₈	C₃C₁₀ − 1
C₉	C₃C₄C₁₀
C₀	$\frac{1}{{C_{3}}^{2} + {C_{4}}^{2}}$
C₁₁	−C₂F₀
C₁₂	C₃² + C₄(C₄ + F₀)
D₁	$\frac{B_{2}}{B_{1}} C_{6} + \frac{B_{6}}{B_{5}} C_{7}$
D₂	$\frac{B_{3}}{B_{1}} C_{6} + \frac{B_{7}}{B_{5}} C_{7}$
D₃	$\frac{B_{4}}{B_{1}} C_{6} + \frac{B_{8}}{B_{5}} C_{7}$
D₄	$\frac{B_{2}}{B_{1}} C_{11} + \frac{B_{6}}{B_{5}} C_{12}$
D₅	$\frac{B_{3}}{B_{1}} C_{11} + \frac{B_{7}}{B_{5}} C_{12}$
D₆	$\frac{B_{4}}{B_{1}} C_{11} + \frac{B_{8}}{B_{5}} C_{12}$

Correlation Function	Expression
〈Ĥ_r(t)Ĥ_r(u)〉	$\frac{1}{4} [\frac{1}{τ_{p}} + 〈 {\tilde{E}}_{c υ} 〉 + 〈 {\tilde{E}}_{υ c} 〉] δ (t - u)$
〈Ĥ_i(t)Ĥ_i(u)〉	$\frac{1}{4} [\frac{1}{τ_{p}} + 〈 {\tilde{E}}_{c υ} 〉 + 〈 {\tilde{E}}_{υ c} 〉] δ (t - u)$
$〈 {\tilde{F}}_{c} (t) {\tilde{F}}_{c} (u) 〉$	$[p + \frac{N_{c 0}}{τ_{sp}} + 〈 {\tilde{E}}_{c υ} 〉 ({A_{0}}^{2} + 1) + 〈 {\tilde{E}}_{υ c} 〉 {A_{0}}^{2}] δ (t - u)$
$〈 {\tilde{F}}_{c} (t) {\hat{H}}_{r} (u) 〉$	$- \frac{A_{0}}{2} [〈 {\tilde{E}}_{c υ} 〉 + 〈 {\tilde{E}}_{υ c} 〉] δ (t - u)$
$〈 {\tilde{F}}_{c} (t) {\hat{H}}_{i} (u) 〉$	0
〈Ĥ_r(t)Ĥ_i(u)〉 + 〈Ĥ_i(t)Ĥ_r(u)〉	0
$〈 {\hat{f}}_{r} (t) {\hat{f}}_{r} (u) 〉$	$\frac{1}{4} δ (t - u)$
$〈 {\hat{f}}_{i} (t) {\hat{f}}_{i} (u) 〉$	$\frac{1}{4} δ (t - u)$
$〈 {\hat{f}}_{r} (t) {\hat{f}}_{i} (u) 〉 + 〈 {\hat{f}}_{i} (t) {\hat{f}}_{r} (u) 〉$	0
$〈 {\hat{H}}_{r} (t) {\hat{f}}_{r} (u) 〉 = 〈 {\hat{f}}_{r} (t) {\hat{H}}_{r} (u) 〉$	$\frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (cos ϕ_{0}) δ (t - u)$
$〈 {\hat{H}}_{i} (t) {\hat{f}}_{i} (u) 〉 = 〈 {\hat{f}}_{i} (t) {\hat{H}}_{r} (u) 〉$	$\frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (sin ϕ_{0}) δ (t - u)$
$〈 {\hat{H}}_{r} (t) {\hat{f}}_{i} (u) 〉 = 〈 {\hat{f}}_{i} (t) {\hat{H}}_{r} (u) 〉$	$- \frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (sin ϕ_{0}) δ (t - u)$
$〈 {\hat{H}}_{i} (t) {\hat{f}}_{i} (u) 〉 = 〈 {\hat{f}}_{i} (t) {\hat{H}}_{i} (u) 〉$	$\frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (cos ϕ_{0}) δ (t - u)$

Symbol	Expression
B₁	A₂A₃A₅ + A₁(A₅² + A₆²) − A₀A₂A₄A₆
B₂	A₀A₄A₆ − A₃A₅
B₃	A₁A₆
B₄	A₁A₅
B₅	−A₀B₁
B₆	A₀A₄A₅ + A₃A₆
B₇	A₂A₃ + A₁A₅
B₈	A₀A₂A₄ − A₁A₆
C₅	$\frac{r_{0}}{C_{4}}$
C₆	C₁ + C₃C₁₀C₁₁
C₇	C₃(C₁₀C₁₂ − 1)
C₈	C₃C₁₀ − 1
C₉	C₃C₄C₁₀
C₀	$\frac{1}{{C_{3}}^{2} + {C_{4}}^{2}}$
C₁₁	−C₂F₀
C₁₂	C₃² + C₄(C₄ + F₀)
D₁	$\frac{B_{2}}{B_{1}} C_{6} + \frac{B_{6}}{B_{5}} C_{7}$
D₂	$\frac{B_{3}}{B_{1}} C_{6} + \frac{B_{7}}{B_{5}} C_{7}$
D₃	$\frac{B_{4}}{B_{1}} C_{6} + \frac{B_{8}}{B_{5}} C_{7}$
D₄	$\frac{B_{2}}{B_{1}} C_{11} + \frac{B_{6}}{B_{5}} C_{12}$
D₅	$\frac{B_{3}}{B_{1}} C_{11} + \frac{B_{7}}{B_{5}} C_{12}$
D₆	$\frac{B_{4}}{B_{1}} C_{11} + \frac{B_{8}}{B_{5}} C_{12}$

Correlation Function	Expression
〈Ĥ_r(t)Ĥ_r(u)〉	$\frac{1}{4} [\frac{1}{τ_{p}} + 〈 {\tilde{E}}_{c υ} 〉 + 〈 {\tilde{E}}_{υ c} 〉] δ (t - u)$
〈Ĥ_i(t)Ĥ_i(u)〉	$\frac{1}{4} [\frac{1}{τ_{p}} + 〈 {\tilde{E}}_{c υ} 〉 + 〈 {\tilde{E}}_{υ c} 〉] δ (t - u)$
$〈 {\tilde{F}}_{c} (t) {\tilde{F}}_{c} (u) 〉$	$[p + \frac{N_{c 0}}{τ_{sp}} + 〈 {\tilde{E}}_{c υ} 〉 ({A_{0}}^{2} + 1) + 〈 {\tilde{E}}_{υ c} 〉 {A_{0}}^{2}] δ (t - u)$
$〈 {\tilde{F}}_{c} (t) {\hat{H}}_{r} (u) 〉$	$- \frac{A_{0}}{2} [〈 {\tilde{E}}_{c υ} 〉 + 〈 {\tilde{E}}_{υ c} 〉] δ (t - u)$
$〈 {\tilde{F}}_{c} (t) {\hat{H}}_{i} (u) 〉$	0
〈Ĥ_r(t)Ĥ_i(u)〉 + 〈Ĥ_i(t)Ĥ_r(u)〉	0
$〈 {\hat{f}}_{r} (t) {\hat{f}}_{r} (u) 〉$	$\frac{1}{4} δ (t - u)$
$〈 {\hat{f}}_{i} (t) {\hat{f}}_{i} (u) 〉$	$\frac{1}{4} δ (t - u)$
$〈 {\hat{f}}_{r} (t) {\hat{f}}_{i} (u) 〉 + 〈 {\hat{f}}_{i} (t) {\hat{f}}_{r} (u) 〉$	0
$〈 {\hat{H}}_{r} (t) {\hat{f}}_{r} (u) 〉 = 〈 {\hat{f}}_{r} (t) {\hat{H}}_{r} (u) 〉$	$\frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (cos ϕ_{0}) δ (t - u)$
$〈 {\hat{H}}_{i} (t) {\hat{f}}_{i} (u) 〉 = 〈 {\hat{f}}_{i} (t) {\hat{H}}_{r} (u) 〉$	$\frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (sin ϕ_{0}) δ (t - u)$
$〈 {\hat{H}}_{r} (t) {\hat{f}}_{i} (u) 〉 = 〈 {\hat{f}}_{i} (t) {\hat{H}}_{r} (u) 〉$	$- \frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (sin ϕ_{0}) δ (t - u)$
$〈 {\hat{H}}_{i} (t) {\hat{f}}_{i} (u) 〉 = 〈 {\hat{f}}_{i} (t) {\hat{H}}_{i} (u) 〉$	$\frac{1}{4} {(\frac{1}{τ_{p e}})}^{1 / 2} (cos ϕ_{0}) δ (t - u)$

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Equations (58)

Journal of the Optical Society of America B