Quantum Properties of a Single Beam Splitter

Abstract

When a single beam-splitter receives two beams of bosons described by Fock states (Bose-Einstein condensates at very low temperatures), interesting generalizations of the two-photon Hong-Ou-Mandel effect take place for larger number of particles. The distributions of particles at two detectors behind the beam splitter can be understood as resulting from the combination of two effects, the spontaneous phase appearing during quantum measurement, and the quantum angle. The latter introduces quantum "population oscillations", which can be seen as a generalized Hong-Ou-Mandel effect, although they do not always correspond to even-odd oscillations.Keywords Quantum mechanics · Bose-Einstein condensates · Quantum optics · Hong-Ou-Mandel effect · Beam splitter Beam splitters are an essential component of many experiments designed to observe quantum effects. They are involved in experimental and theoretical schemes that both Helmut Rauch and Daniel Greenberger have studied. Indeed, the famous neutron experiments of H. Rauch and colleagues [1, 2] were made possible by the realization of an appropriate device allowing neutron beams to be split into two coherent beams, which can then be recombined and give rise to various interesting quantum interference effects. The observation of equally famous quantum GHZ (Greenberger, Horne and Zeilinger) violations of local realism [3,4] may also require the use of photon F. Laloë ( ) Laboratoire Kastler Brossel, ENS,

Nonmonotonic quantum-to-classical transition in multiparticle interference

“…Therefore, this term gives rise to a three-particle interference signal through coherent superposition of indistinguishable three-particle paths, with amplitude ffiffi ffi 2 p α ffiffiffiffiffiffiffiffiffiffiffiffi 1 − α 2 p . In general, when N/2 particles enter at each input mode, the event probability for detecting m particles in output mode c and n particles in output mode d, defined as an (m, n)-event, is given by the following: for the different distinguishability types are determined by the geometry of the experimental setup (25,26), computed by mapping input on output modes via the following:…”

NOON states via a quantum walk of bound particles

“…We expect that when the bound particle impinges the splitting field because it behaves like an effective single particle, the output state, measured at the endpoints, will be |ψ(t * ) 1L = 1 √ 2 (|2, 0 + i|0, 2 ), namely we generate a NOON state with two particles (here |2 = (a † ) 2 |0 / √ 2). On the other hand if the two particles are non interacting U/J = 0, the effect of the splitting field is to produce also a non-zero probability P 1L (t * ) to have one particle in each end [68]. We show, for a L = 5 chain with U/J = 5 in Fig.…”

“…In the non-interacting case U/J = 0 when three particles are initially located in the first site |ψ(0) ∝ (a † 1 ) 3 |0 an ideal beam splitter transformation generates as output a state with probabilities [68]: P 111 = P LLL = 1/8, P 1LL = P 11L = 3/8 where we define P jkl (t) = | 0|a i a j a k |ψ(t) | 2 1+δ i j +δ jk +δ ik +2δ i j δ jk the probability to have the three particles in the sites i, j, k. We expect that when the onsite interaction is strong enough, the bound particle behaves as an effective single bound particle, thus the terms P 1LL , P 11L are suppressed and the output state at the end points effectively results in the NOON state |ψ(t * ) 1L = 1…”

Degree of polarization as a measurable quantity for a quantum optical field containing variously polarized photons

“…Parallel measurement on the same photon is impossible due to the non-cloning theorem. Using a quantum beam splitter is acceptable as it modifies the state of the photon in a welldefined way [9,10]. For example, in the case of a 50:50 non-polarizing beam splitter with no phase shift, simple calculation shows that:…”