Interference of macroscopic beams on a beam splitter: phase uncertainty converted into photon-number uncertainty

Abstract

Squeezed-vacuum twin beams, commonly generated through parametric downconversion, are known to have perfect photon-number correlations. According to the Heisenberg principle, this is accompanied by a huge uncertainty in their relative phase. By overlapping bright twin beams on a beam splitter, we convert phase fluctuations into photon-number fluctuations and observe this uncertainty as a typical 'U-shape' of the output photon-number distribution. This effect, although reported for atomic ensembles and giving hope for phase super-resolution, has never been observed for light beams. The shape of the normalized photon-number difference distribution is similar to the one that 7 These two authors contributed equally.

Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

“…In contrast to the TMSVS, the pair coherent states exhibit sub-Poissonian photon statistics in each mode. Recently, Spasibko et al [25] experimentally examined the interference effects and photon-number fluctuations from TMSVS whose twin beams fall on opposite sides of a beam splitter.…”

Molecular interferometers: effects of Pauli principle on entangled-enhanced precision measurements

“…We found that condensate depletion reduces the odd/even discrete structure of the typical U-shaped particle distribution that arise when measuring the different numbers of particles populating both modes. Such an odd/ even fluctuation reduction is very similar to that caused by particle losses [5,6,8]. Condensate depletion also renders the standard deviation of the interfering mBECs to be smaller, as compared with the one given by the ideal BECs interference of bosonic atoms.…”

“…For k a 1 4 F = ( ) (Green dots) the probability of the different population imbalances match the ideal bosonic behavior (gray shaded histogram), whereas for k a 1 1 F = ( ) the even/odd particle fluctuations almost vanishes. Particle losses and/or the absence of single-particle resolution in the experiments also render even/odd fluctuations vanishes [5,6]. Nevertheless, the U-shape of the probability distribution, considered in the literature as an indicator for possible entanglement-enhanced phase resolution [4][5][6][7][8], is preserved.…”

“…However, we show that the increase in phase uncertainty is not so significant such that entanglement-enhanced precision measurements are also feasible with mBECs. This is because the U-shape of the particle distribution, indicating many-particle entanglement [5,6], is preserved for small values of the interference phase θ = 1. We also analyze the phase uncertainty considering a Gaussian noise in the particle detectors, and show how the effects of quantum depletion increase with the detection noise.…”

“…Twin Fock states, i.e. states with two orthogonal modes populated by the same number of particles, have been produced with both, photons [4,5] and ultracold bosonic atoms [6][7][8]. However, entangled-enhanced precision measurements of the resulting interference phase have been performed only in the case of ultracold bosonic atoms [6,8].…”