The rate of absorption of entangled photon pairs is linear in the photon-flux density. We demonstrate that the two-photon absorption cross section is a nonmonotonic function of the entanglement time; it vanishes for certain energy-level configurations and values of the entanglement time. This entanglement-induced two-photon transparency arises from the coherent summation of transition-amplitude contributions over the finite entanglement time. As an example, the entangled two-photon cross

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... for the 1S-2S electronic transition in atomic hydrogen is obtained. [S0031-9007(97)02508-8] PACS numbers: 42.50.Ct, 32.80.Rm, 42.50.Dv, 42.50.Hz Since the 1930s, when two-photon absorption was first described [1], multiphoton processes have received considerable attention as fundamental components of the interaction of light with matter. With classical light, the N-photon absorption and ionization rates vary with the photon-flux density f as f N . These rates also depend on the statistical properties of the light. For example, it has been shown that the off-resonance rate using a thermal light source exceeds that using a coherent light source by a factor of N! [2, 3] . Current interests in classical-light induced multiphoton processes include two-photon fluorescence [4] and two-photon spectroscopy [5] . With the advent of nonclassical light sources [6, 7] , new phenomena in multiphoton processes can be explored. A linear (rather than quadratic) dependence of the two-photon absorption rate on photonflux density has been predicted for sufficiently weak entangled [8, 9] and quadrature squeezed light [10]; indeed, the latter has been recently observed with atomic cesium in a squeezed vacuum [11] . A composite quantum system whose state cannot be factored into a product of single-particle states is said to be entangled [7] ; it has no classical analog. In this Letter, we present a quantum-mechanical calculation of the twophoton (linear) absorption rate with temporally entangled light. Our results reveal a new nonclassical phenomenon-nonmonotonic variations in the absorption rate as a function of the entanglement time. An important feature of these variations is the occurrence of significantly reduced values of the absorption cross section that emerge for certain parameter values, which we term entanglementinduced two-photon transparency. Like electromagnetically induced transparency [12, 13] , which has applications in lasing without inversion [13] and isotope discrimination [14] , entanglement-induced transparency is a quantum interference effect. It is distinguished from the inhibition and enhancement of two-photon absorption using classical light [15] by its dependence on the degree of entanglement of the photon pair and its linear dependence on the photonflux density. As an example, we calculate the effect in the 1S-2S transition of atomic hydrogen [16] . Simple probabilistic model.-We first present a simple probabilistic two-photon absorption model that considers the photons as particles. The process is regarded as having two steps: the first photon initiates a transition to a virtual state and the second photon brings about a transition to the final state. For randomly arriving photons, the probabilistic analysis yields a transition rate R r that depends only on the material's single-photon cross section s and virtual-state lifetime t. The resulting random two-photon absorption rate is R r d r f 2 where the twophoton quadratic cross section is d r s 2 t [17]. Next, consider correlated photon pairs arriving at the absorbing medium with flux density f͞2 photon pairs͞ ͑cm 2 s͒. In this case, the absorption rate of the material depends on the probability j͑T e ͒ that the two photons emitted within the time T e arrive within t and the probability z ͑A e ͒ that the two photons emitted within the area A e arrive within s. Thus, the correlated two-photon absorption rate is R e s e f with cross section s e sj͑T e ͒z ͑A e ͒͞2. This rate must be supplemented by that representing the accidental arrival of pairs within t and s, resulting in the overall two-photon absorption rate R R e 1 R r s e f 1 d r f 2 . (1) It is clear that correlated two-photon absorption dominates random two-photon absorption only when the photon-flux density is sufficiently small. The critical photon-flux density at which the two processes are equal is f c s e ͞d r . For T e ø t and A e ø s, j͑T e ͒ and z ͑A e ͒ are unity, yielding s e d r ͞2st. In the experimentally relevant case in which T e ¿ t and A e ¿ s, the probability functions are j͑T e ͒ t͞T e and z ͑A e ͒ s͞A e , yielding s e d r ͞2A e T e . (2) Quantum-mechanical cross section.-We now obtain a proper quantum-mechanical expression for s e , which we then compare to the results obtained above. Entangled light is assumed to be created by parametric downconversion through a second-order nonlinear optical interaction [7, 18] . This process produces an entangled photon 0031-9007͞ 97͞78(9)͞1679(4)$10.00