Conditional preparation of a nonclassical state in the continuous-variable regime: Theoretical study

We study the characteristics of the quantum state of light produced by a conditional preparation protocol totally performed in the continuous-variable regime. It relies on conditional measurements on quantum intensity correlated bright twin beams emitted by a nondegenerate optical parametric oscillator above threshold. Analytical expressions as well as computer simulations of the selected state properties and preparation efficiency are developed and show that a sub-Poissonian state can be produced by this technique. Projection onto a given trigger value is studied and then extended to a finite band. The continuous-variable regime offers the unique possibility to improve dramatically the preparation efficiency by choosing multiple selection bands and thus to generate a great number of sub-Poissonian states in parallel.

Figure 1

(Color online) Proposed conditional measurement protocol in the continuous-variable regime. A ND-OPO generates above threshold orthogonally polarized and quantum intensity correlated bright twin beams which are detected by high efficiency photodiodes. The continuously varying signal photocurrent is kept only when the idler photocurrent takes a given value or falls inside a narrow band.

Figure 2

(Color online) The dotted rectangle models a ND-OPO which can be described by a source of perfect intensity correlated beams plus a partition process generated by two symmetric beam splitters with intensity transmission $T$ and reflection $R$. The “gemellity” $G$ of the beams is found to be equal to the loss coefficient $R$.

Figure 3

Conditional variance as a function of the Fano factor for different initial intensity correlation between signal and idler beams, measured by the “gemellity” $G$. Values of $G$ as small as $0.1$ have been obtained experimentally [15].

Figure 4

(Color online) Photon probability distributions of conditionally prepared state. The probability distributions are all normalized to 1 at their maxima for clarity of the plots. The horizontal unit is the width $\sigma =\sqrt{{\overline{n}}^{\prime }}$ of the Poisson distribution of same mean intensity. Thick curves give the initial Gaussian distribution and dashed ones correspond to a coherent state of same mean intensity. Arrows give the extension of the selection band. (a),(b) The selection band is centered on the mean value $(\alpha =0)$. The bandwidth is $\Delta =0.1\sigma$ for (a) and $10\sigma$ for (b). A large band results in a wide distribution (kurtosis coefficient lower than 3). (c),(d) The band is centered on $\alpha =10\sigma$: $\Delta =0.1\sigma$ for (c) and $10\sigma$ for (d). Noncentral selection band results in an asymmetry of the distribution (non-null skewness) $(F^{\prime }=100,G=0.18)$.

Figure 5

Kurtosis coefficient of the conditionally selected state according to the selection bandwidth normalized to $\sigma =\sqrt{{\overline{n}}^{\prime }}$ (b): zoom for small bandwidth $(\alpha =0,F^{\prime }=100,G=0.18)$.

Figure 6

(a) Intensity noise on the reduced state and (b) preparation probability (proportion of selected points) as a function of the selection bandwidth normalized to $\sigma$ $(\alpha =0,F^{\prime }=100,G=0.18)$.

Figure 7

Preparation probability as a function of the center of the narrow $\Delta =0.1\sigma$ selection band $(F^{\prime }=100,G=0.18)$.

Figure 8

Experimental multiband selection. The horizontal unit is the width $\sigma$ of the Poisson distribution of same mean intensity. Independent bands of width $\Delta =0.2\sigma$ have been implemented. Band are separated by $4\sigma$ in (a) and $2\sigma$ in (b) $(F^{\prime }=100,G=0.18)$.