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Two independent photon pairs versus four-photon entangled states in parametric down conversion

De Riedmatten, H, Scarani, V, Marcikic, I, Acin, A, Wolfgang Tittel, Zbinden, H, Nicolas Gisin

Published Oct 28, 2003• 71 citations
OpenAlex

Abstract

We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t_c is much shorter than the duration of the pump pulse Delta t, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter chi, which is a function of tphc/∆t. We present a direct measurement of chi through a simple experimental setup. The full theoretical analysis is also provided

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We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t_c is much shorter than the duration of the pump pulse Delta t, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter chi, which is a function of tphc/∆t. We present a direct measurement of chi through a simple experimental setup. The full theoretical analysis is also provided
We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t ph c is much shorter than the duration of the pump pulse Δt, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter χ, which is a function of t ph c Δt. We present a direct measurement of χ through a simple experimental set-up. The full theoretical analysis is also provided.
We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t ph c is much shorter than the duration of the pump pulse Δt, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter χ, which is a function of t ph c Δt. We present a direct measurement of χ through a simple experimental set-up. The full theoretical analysis is also provided.
We investigate spectral and temporal features and entanglement of biphoton wave packets formed in spontaneous parametric down-conversion with a pulsed laser pump. The degree of entanglement is characterized by the experimentally measurable parameter RRR defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration $\ensuremath{\tau}$. The function $R(\ensuremath{\tau})$ is shown to have a minimum and even in the minimum, at rather natural conditions, the degree of entanglement is found to be very high (Rmin=73)({R}_{\mathrm{min}}=73)(Rmin​=73). The Schmidt number KKK is found analytically for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of RRR and KKK are found to be identical and numerical coefficients are found to be rather close. Two-time temporal wave function of a biphoton state is investigated in detail, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter Rt{R}_{t}Rt​ (defined as the ratio of durations of the single-particle and coincidence signals) is shown to be very close to the Schmidt number KKK.
Spectral and temporal coincidence and single-particle photon wave packets are described and their widths and durations are found. The degree of entanglement is characterized by the experimentally measurable parameter R defined as the ratio of the coincidence and single-particle spectral widths. In the frequency representation, this parameter is found as a function of the pump-pulse duration. This function is shown to have a minimum and even in the minimum, at rather natural conditions, the parameter R is found to be very high (R=73>>1). The Schmidt number K is found for both short and long pump pulses and interpolated for arbitrary pulse durations. All functional dependences of R and K are found to be identical and numerical difference between them is shown to be not exceeding 20%. Two-time temporal wave function of a biphoton state is investigated in details, and a rather significant difference between the cases of short and long pump pulses is found to occur. In the case of long pulses, the temporal parameter R is defined as the ratio of durations of the single-particle and coincidence signals, and the defined in such a way parameter R is shown to be very close to the Schmidt number K.
The generation of entangled photon pairs by parametric down-conversion from solid state CW lasers with small coherence time is theoretically and experimentally analyzed. We consider a compact and low-cost setup based on a two-crystal scheme with Type-I phase matching. We study the effect of the pump coherence time over the entangled state visibility and over the violation of Bell's inequality, as a function of the crystal length. The full density matrix is reconstructed by quantum tomography. The proposed theoretical model is verified using a purification protocol based on a compensation crystal.
Coherence properties of the down-converted beams generated in spontaneous parametric down-conversion are investigated in detail using an iCCD camera. Experimental results are compared with those from a theoretical model developed for pulsed pumping with a Gaussian transverse profile. The results allow us to tailor the shape of correlation area of the signal and idler photons using pump-field and crystal parameters. As an example, splitting of a correlation area caused by a two-peak pump-field spectrum is experimentally studied.