Spontaneous emission of a photon by an atom is described theoretically in three dimensions with the initial wave function of a finite-mass atom taken in the form of a finite-size wave packet. Recoil and wave-packet spreading are taken into account. The total atom-photon wave function is found in the momentum and coordinate representations as the solution of an initial-value problem. The atom-photon entanglement arising in such a process is shown to be closely related to the structure of atom and photon wave packets which can be measured in the coincidence and single-particle schemes of measurements. Two predicted effects, arising under the conditions of high entanglement, are anomalous narrowing of the coincidence wave packets and, under different conditions, anomalous broadening of the single-particle wave packets. Fundamental symmetry relations between the photon and atom single-particle and coincidence wave packet widths are established.The relationship with the famous scenario of Einstein-Podolsky-Rosen is discussed.
We show theoretically that high-order thermal ghost imaging has considerably higher visibility and contrast-to-noise ratio than conventional thermal ghost imaging, which utilizes the lowest-order intensity cross correlation of the object and the reference signal. We also deduce the optimal power order of the correlation that gives the best contrast-to-noise ratio.
We show that, although the amount of mutual entanglement of photons propagating in free space is fixed, the type of correlations between the photons that determine the entanglement can dramatically change during propagation. We show that this amounts to a migration of entanglement in Hilbert space, rather than real space. For the case of spontaneous parametric down conversion, the migration of entanglement in transverse coordinates takes place from modulus to phase of the bi-photon state and back again. We propose an experiment to observe this migration in Hilbert space and to determine the full entanglement.Entanglement is one of the truly central features of the quantum world, and it forms the core of many applications based on quantum theory. The observation of entanglement is generally achieved through the measurement of correlations between entangled subsystems. Correlation in quantum systems takes many forms and is open to observation in a variety of ways. Therefore, the determination of the amount of entanglement of quantum states depends on the measurement of the correlations where entanglement resides. This is of paramount importance, since in some experimental configurations one registers types of correlation that might not be appropriate to quantify the entangled nature of the quantum state.In this Communication, we show that the measurement of correlation between paired photons can miss the detection of entanglement entirely. The underlying reason is an interesting migration of entanglement that occurs in Hilbert space, but that depends on coordinate location in real space. This is manifest in photon correlations that show a rich and complex structure that evolves during propagation, although the amount of entanglement is constant. We focus here on entanglement that can become partly or entirely identified with the phase of the state, in which case the measurement of intensity correlations partially or completely misses the existing entanglement. This is an observable manifestation of the "phase entanglement" previously noted [1] for massive particle breakup in an Einstein-Podolsky-Rosen (EPR) scenario.Entangled photons generated in spontaneous parametric down-conversion (SPDC) are particularly open to the observation of this phenomenon. The generated twophoton states have been shown to exhibit entanglement in transverse momentum [2] and in orbital angular momentum [3,4]. Moreover, one can enlarge the Hilbert space of the two-photon state by using several degrees of freedom [5]. The spatial transverse degrees of freedom of photon pairs produced in SPDC have attracted great attention because of the vast Hilbert space involved [6,7], and the availability of techniques to implement the ddimensional quantum channel [8,9,10].Observations of SPDC entanglement have usually been made either in the near zone or the far zone [11]. Interestingly, in the course of photon propagation from the near field zone to the far field zone, the entanglement embedded in the two-photon positional amplitude migrates out of th...
The narrowing of electron and ion wave packets in the process of photoionization is investigated, with the electron-ion recoil taken fully into account. Packet localization of this type is directly related to entanglement in the joint quantum state of the electron and ion, and to Einstein-Podolsky-Rosen localization. Experimental observation of such packet-narrowing effects is suggested via coincidence registration by two detectors, with a fixed position of one and varying position of the other. A similar effect, typically with an enhanced degree of entanglement, is shown to occur in the case of photodissociation of molecules.
We solve the joint open problems of photon localization and single-photon wave functions in the context of spontaneous emission from an excited atom in free space. Our wave functions are well-defined members of a discrete orthonormal function set. Both the degree and shape of the localization are controlled by entanglement mapping onto the atom wave function, even though the atom is remote from the photon.
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