Experimental demonstration of macroscopic quantum coherence in Gaussian states

We witness experimentally the presence of macroscopic coherence in Gaussian quantum states using a recently proposed criterion [E. G. Cavalcanti and M. D. Reid, Phys. Rev. Lett. 97 170405 (2006)]. The macroscopic coherence stems from interference between macroscopically distinct states in phase space, and we prove experimentally that a coherent state contains these features with a distance in phase space of $0.51\pm 0.02$ shot noise units. This is surprising because coherent states are generally considered being at the border between classical and quantum states, not yet displaying any nonclassical effect. For squeezed and entangled states the effect may be larger but depends critically on the state purity.

Figure 1

(Color online) $P\left(x\right)$ is one of the marginal distributions of the Wigner function. Binning of one quadrature variable into negative, intermediate, and positive regions, with intermediate distance $S$.

Figure 2

According to Heisenberg’s uncertainty relation the minimum variance of $p$ increases when restricting the distribution of $x$ values to one subspace. The smaller variance of $p$ in full space is evidence for the overall state being a coherent superposition of the subspace states.

Figure 3

(Color online) Contour plot of the maximum distance $S_{\mathit{max}}$, which can be proven with a squeezed state of given purity and squeezing. Symbols denote the measured values.

Figure 4

(Color online) Experimental setup for measuring a quadrature probability distribution of squeezed states. SHG, second harmonic generator; MCC, mode cleaning cavity; LO, local oscillator; HD, balanced homodyne detecter.

Figure 5

(Color online) Quadrature $x$ probability density distributions of binned regions and unbinned data of a squeezed beam ($30\mathrm{mW}$ pump power) with distance $S=0.83\pm 0.02$ SNU. The subspace probability distributions are each separately normalized.

Figure 6

(Color online) Value of the left-hand side of inequality (3) vs distance $S$ for different squeezed states and the vacuum coherent state. A value smaller than one proves the existence of a generalized superposition of distance $S$.