Merge pull request #130 from karolpezet/squeezefix

proper squeeze update

src/spin.jl

@@ -83,3 +83,20 @@ Spin down state for the given Spin basis.
 """
 spindown(::Type{T}, b::SpinBasis) where T = basisstate(T, b, b.shape[1])
 spindown(b::SpinBasis) = spindown(ComplexF64, b)
+
+
+"""
+    squeeze([T=ComplexF64,] b::SpinBasis, z)
+
+Squeezing operator ``S(z)=\\exp{\\left(\\frac{z^*\\hat{J_-}^2 - z\\hat{J}_+}{2 N}\\right)}`` for the 
+specified Spin-``N/2`` basis with optional data type `T`, computed as the matrix exponential. Too
+large squeezing (``|z| > \\sqrt{N}``) will create an oversqueezed state.
+"""
+function squeeze(::Type{T}, b::SpinBasis, z::Number) where T
+    N = Int(length(b)-1)
+    z = T(z)/2N
+    Jm = sigmam(b)/2
+    Jp = sigmap(b)/2
+    exp(conj(z)*dense(Jm)^2 - z*dense(Jp)^2)
+end
+squeeze(b::SpinBasis, z::T) where {T <: Number} = squeeze(ComplexF64, b, z)

test/test_spin.jl

@@ -113,4 +113,21 @@ antikommutator(x, y) = x*y + y*x
 @test 1e-11 > norm(sm*spinup(spinbasis) - spindown(spinbasis))
 @test 1e-11 > norm(sp*spindown(spinbasis) - spinup(spinbasis))
 
+# squeeze operator test SPIN
+Nspins = 500
+b_spin = SpinBasis(Nspins//2)
+s1 = squeeze(b_spin,0.23*sqrt(Nspins)*exp(1im*0.23*pi))
+s2 = s1*spindown(b_spin);
+
+# Heisenberg uncertainty test
+@test abs(variance(sigmax(b_spin)/2,s2)*variance(sigmay(b_spin)/2,s2)) ≥ abs2(expect(sigmaz(b_spin)/2,s2))/4
+
+# small squeezing test
+x1 = 0.023
+s1 = squeeze(b_spin,x1*sqrt(Nspins));
+s2 = s1*spindown(b_spin);
+
+@test isapprox(2*log(real(variance(sigmax(b_spin)/2,s2))/Nspins*4) , -x1*sqrt(Nspins), atol=1e-2)
+@test isapprox(2*log(real(variance(sigmay(b_spin)/2,s2))/Nspins*4) , x1*sqrt(Nspins), atol=1e-2)
+
 end # testset