Quantum State Reconstruction of the Single-Photon Fock State

Abstract

We have reconstructed the quantum state of optical pulses containing single photons using the method of phase-randomized pulsed optical homodyne tomography. The single-photon Fock state 1> was prepared using conditional measurements on photon pairs born in the process of parametric down-conversion. A probability distribution of the phase-averaged electric field amplitudes with a strongly non-Gaussian shape is obtained with the total detection efficiency of (55+/-1)%. The angle-averaged Wigner function reconstructed from this distribution shows a strong dip reaching classically impossible negative values around the origin of the phase space.

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

“…To accurately determine the Wigner function value on the axis, W (θ = π 2 , φ = 0) = n (−1) n ρ nn , that depends only on the population terms ρ nn , we average the photon distributions g(n β ) over four angles β and thereby reduce the fitting parameters to just ρ nn , n ≤ 4. This is equivalent to constructing a rotationally symmetric Wigner function from the angle-averaged marginal distribution [17]. We obtain ρ 00 = 0.32±0.03, ρ 11 = 0.66±0.04 with negligible higherorder population terms, giving W ( π 2 , 0) = −0.36 ± 0.08, to be compared to W ( π 2 , 0) = −1 for the perfect first Dicke state.…”

“…An important goal is the creation of entangled states of many-particle systems while retaining the ability to characterize the quantum state and validate entanglement. Entanglement can be verified in a variety of ways, with one of the strictest criteria being a negative-valued Wigner function [16,17], that necessarily implies that the entangled state has a non-Gaussian wavefunction. To date, the metrologically useful spin-squeezed states [1][2][3][4][5][6][7][8][9][10] have been produced in large ensembles.…”

Conditional generation of arbitrary multimode entangled states of light with linear optics

“…For instance in the scheme described in Fig. 5, one can first produce the states |f j and store them in a memory before proceeding with the production of the entangled state (19). Suppose that the state |f j can be prepared with the probability P j .…”

“…Several setups for the generation of twomode N -photon path-entangled states have been suggested [14,15,16,17,18]. Recently, the experimental conditional preparation of a single-photon Fock state with negative Wigner function has been reported [19].…”

Practical photon number detection with electric field-modulated silicon avalanche photodiodes

“…In combination with parametric down-conversion sources, photon number detection can also be used for the generation and conditioning of photonic Fock states 10 , as well as more complex quantum light states 11 . Furthermore, many applications beyond pure quantum information processing, such as quantum imaging 12 , tomography 13,14 and interferometry 15 , have been suggested to require error-free photon number detection, and extensive efforts [16][17][18][19][20][21][22][23][24][25][26][27][28][29] have therefore been devoted to developing photon number resolving detectors.…”