We study the fourth-order squeezing in the most general case of superposition of two coherent states by considering (ΔXθ)4 where Xθ = X1 cosθ +X2 sinθ,X1 +iX2 = a is annihilation operator, θ is real, = Z1 + Z2, and are coherent states and Z1,Z2,α,β are complex numbers. We find the absolute minimum value 0.050693 for an infinite combinations with α ? β = 1.30848exp[±i(π∕2) + iθ], Z1∕Z2 = exp(α?β ? αβ?) with arbitrary values of α + β and θ. For this minimum value of (ΔXθ)4, the expectation value of photon number can vary from the minimum value 0.36084 (for α + β = 0) to infinity. We note that the variation of (ΔXθ)4 near the absolute minimum is less flat when the expectation value of photon number is larger. Thus the fourth-order squeezing can be observed at large intensities also, but settings of the parameters become more demanding.
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机译：我们通过考虑（ΔXθ） 4 （其中X θ =）来研究两个相干态叠加的最一般情况下的四阶压缩X 1 cosθ+ X 2 sinθ，X 1 + iX 2 = a是an灭算符，θ是实数，= Z 1 + Z 2 ，是相干态，Z 1 ，Z 2 ，α，β是复数。我们找到无限大组合α？的绝对最小值0.050693。 β= 1.30848exp [±i（π∕ 2）+iθ]，Z 1 ∕ Z 2 = exp（α？β？αβ ？），且具有任意值α+β和θ。对于（ΔXθ） 4 的最小值，光子数的期望值可以从最小值0.36084（对于α+β= 0）变化到无穷大。我们注意到，当光子数的期望值较大时，（ΔXθ） 4 在绝对最小值附近的变化不太平坦。因此，也可以在大强度下观察到四阶压缩，但是参数的设置变得更加苛刻。
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