Biphoton in a Dispersive Medium

We report an experimental study of group-velocity dispersion effect on an entangled two-photon wavepacket, generated via spontaneous parametric downconversion and propagating through a dispersive medium. Even in the case of using CW laser beam for pump, the biphoton wavepacket and the secondorder correlation function spread significantly. The study and understanding of this phenomenon is of great importance for quantum information applications, such as quantum communication and distant clock synchronization. PACS Number: 42.50.-p, 42.50.Dv, 03.65.Ta Typeset using REVTEX 1 Entangled two-photon light has been proved to be useful in quantum metrology [1] and quantum communications [2]. New applications have been recently proposed, such as quantum computing, quantum information processing, and quantum lithography [3]. In all applications, the crucial feature is the measurement of the correlation of the two-photon entangled state. In many cases, the spreading of the biphoton wavepacket and the second-order Glauber correlation function [4] becomes a critical issue, especially for these applications in which the precise timing information is essential, such as synchronization of distant clocks. Consider a very simple experiment. A pair of entangled photons is generated from spontaneous parametric down-conversion(SPDC) [5] and propagates through a dispersive medium. The dispersive medium could be in one path or both paths. Two single-photon counting detectors are used for the detection of the signal and the idler photons, respectively. In most of the two-photon interferometric experiments, coincidence counting rate is the only necessary measured quantity: Rc ∼ ∫ T 0 dt1dt2S(t1 − t2 − t0)G (t1, r1; t2, r2), (1) where G(t1, r1; t2, r2) is the second-order Glauber correlation function [4], S(t1 − t2 − t0) the coincidence window function, which is usually a rectangular function centered at t0, T the data collection time for the coincidence measurement, ti the detection time of the i-th detector and ri the optical path to the i-th detector. The second-order Glauber correlation function is defined as G(t1, r1; t2, r2) =< E (t1, r1)E (t2, r2)E (t2, r2)E (t1, r1) >, (2) where E and E are the negative-frequency and the positive-frequency field operators and ensemble averaging is done over the quantum state. In the stationary case, G depends only on t1−t2. In the case of two-photon state generated via SPDC, G (2) can be represented as the square modulo of the two-photon wave function, or biphoton, ψ(t1, r1; t2, r2) ≡ 〈0|E (t2, r2)E (t1, r1) |Ψ〉 , (3)