Partial Distinguishability in Femtosecond Optical Spontaneous Parametric Down-Conversion

Abstract

Quantum interference is observed using femtosecond parametric down-conversion in the absence of spectral filtering of the down-converted light. The well-known symmetric dip observed in cw polarization-interferometry experiments becomes less pronounced and substantially asymmetric under such pulsed excitation. We show that this asymmetry arises from the partial distinguishability of contributions from space-time segments within the down-conversion crystal. We develop a theory that achieves agreement with experiment by coherently adding intrasegment contributions while incoherently adding intersegment contributions. PACS numbers: 42.50.Dv, 42.65.Re, 42.65.Ky Entangled photon pairs (biphotons) generated via the nonlinear optical process of spontaneous parametric downconversion (SPDC) [1,2] have enabled us to carry out many valuable quantum-optics experiments, particularly during the past few years. These range from fundamental physics experiments that have shed light on the validity of quantum mechanics [3,4] to useful applications such as the determination of detector absolute quantum efficiency [5]. Entangled photon pairs have recently also found a place in unusual but powerful techniques such as quantum cryptography [6] and quantum teleportation [7,8].Almost all of these experiments have made use of stationary streams of biphotons generated by illuminating an anisotropic second-order nonlinear crystal with a continuous-wave (cw) laser pump. The unique possibilities offered by such light sources reside in their entanglement property, which is mathematically described in terms of a composite quantum state that cannot be factored into a produce of single-particle states (entangled states thereby have no classical analogs) [9]. A great variety of quantuminterference experiments have been carried out to examine the unusual second-and fourth-order coherence properties [10,11] of partially entangled biphoton beams.Since ultrafast (sub-ps) pump sources in the ultraviolet and near-ultraviolet have come into their own, it is important to determine the entanglement properties imparted to biphoton beams by very brief pulses of pump light impinging on a nonlinear parametric down-conversion crystal. The reason is simple: entangled photon pairs generated by mode-locked pump lasers emitting femtosecond pulses are expected to be crucial for carrying out important experiments in quantum teleportation [12], entanglement swapping [13], and the production of three-photon entangled [Greenberger-Horne-Zeilinger (GHZ)] states [14]. Several experiments along these lines have already been conducted. Some of these have made use of crystals whose lengths are short relative to the length of the coherent nonlinear interaction region [15]. Others have employed narrow-band interference filters placed immediately before the detectors [12,13,15,16]. The filters serve to lengthen the coherence time of the photons and thereby to increase the fringe visibility in interference experiments. Although the results of both of these types of experiments...

Extended phase-matching conditions for improved entanglement generation

“…If the pump spectrum is not perfectly monochromatic (Ω p > 0), a range of signal-idler sum frequencies exist such that the maximal entanglement property is degraded and the spectra of the two down-converted photons are no longer identical [4]. The drawback of non-identical signal and idler spectra turns out to be critical for many experiments that employ a pulsed pump, because the difference in the spectra introduces distinguishability that is detrimental to quantum interference [3,4,5,7]. On the other hand, it is clear from Eq.…”

“…Furthermore, they allow the use of short-duration pump pulses that increase the experimental signal-idler generation rate compared to that of continuous-wave (cw) pumping. These two advantages are not readily available with the conventional phasematching condition: on one hand the use of long type II phase-matched crystals narrows the spectrum over which the down-converted photons are entangled, and, on the other hand, the use of pulsed pumping reduces the entanglement because the indistinguishability of the downconverted photons is adversely affected [3,4,5].…”

“…4) centered at τ = 0 with a (base-to-base) width of 4π/Ω f , which is determined by the crystal length L. Note that the pump bandwidth Ω p does not play any role in determining the function P − (τ ), which is a unique characteristic of the state |Ψ epm because of the extended phase-matching conditions. It is well known [3,4,5] that, under the conventional phase-matching condition (7) only, the visibility of the Mandel dip decreases when the pump bandwidth is increased. The Mandel dip can be interpreted as the result of destructive quantum interference between the different paths that lead to coincidences at the detectors [13].…”

“…For frequency entanglement generation, the SPDC crystal is usually operated at frequency degeneracy, in which the signal and idler spectra are centered around half the mean frequency of the pump ω p [3,4,5]. This is enforced by imposing the conventional phase-matching condition that requires the crystal's refractive indices to satisfy…”

Stimulated emission of polarization-entangled photons

“…Initially modes a and b are in the vacuum state and the photon pairs are spontaneously created. The fact that modes a and b geometrically diverge, and that horizontally and vertically polarised photons experience different crystal parameters, limits the useful crystal length [27] and thereby prohibits an efficient stimulated emission process. To obtain significant stimulated emission we redirect the spontaneously created photon pairs into the crystal at the same time (tuned by a delay on mirror M3) as the reflected pump pulse passes through the crystal a second time.…”