Two-photon interferometry started to play an important role in quantum optics since 1980’s. In that time, Dirac was criticized to be mistaken because he stated in his book, The Principles of Quantum Mechanics , that “photon only interferes with itself. Interference between two different photons never occurs”. Two-photon interference was considered as the interference between two photons. In fact, neither classical theory nor quantum theory suggested the interference between different photons. Classical theory views optical interference the result of coherent superposition between electromagnetic waves. The two-photon interference picture provided reasonable interpretation to that observation too: under the condition of complete overlapping, when the two biphoton amplitudes superpose in phase the joint-detection of the two distant photodetectors reaches its maximum counting rate as the sign of “correlation”. When the optical path difference is increased from zero to unbalanced values, a coincidence curve of “dip” is observed.
Summary form only given. The superposition principle is at the heart of quantum mechanics and plays the central role in interference phenomena in quantum mechanics. Quantum interference differs from classical interference because of particle nature of light. In a quantum mechanical picture, interference occurs because there are indistinguishable ways of an event to occur. Whenever which-path information is given to the system, interference disappears. We have experimentally demonstrated that two-photon interference occurs for biphoton amplitudes arising from two well-separated pump pulses.
In his famous book, The Principles of Quantum Mechanics, Dirac stated that “... photon ... interferes only with itself. Interference between two different photons never occurs.” However, two-photon interference has been demonstrated experimentally. Was Dirac wrong? We report an new experiment in this paper. It demonstrated that two-photon interference can not be considered the interference of two photons. “Two-photon” is not two photons. Two-photon is a single entity, which is just like a photon. We may call it biphoton. Dirac was correct. Biphoton interferes only with itself.
The study of entangled states greatly advanced our understanding about two-photon interferometry. Two-photon interference is not the interference between two photons, it is about a pair of photons interfering with the pair itself. In the language of quantum theory, two-photon interference is the result of superposition between different yet indistinguishable two-photon probability amplitudes. Under certain conditions, the observed second-order interference can be factorized into a product of two individual classic first-order interferences. In this case, the interference is not only observable from the intensity fluctuation correlation measurement, or from the photon number fluctuation correlation measurement, of two photodetectors, but also observable in the counting rate of each individual photodetector. It may not be uneasy to accept the quantum concept of two-photon interference for “classical” thermal radiation. Indeed, the radiation Planck dealt with was “classical” thermal light. Perhaps, no one would even expect observing nontrivial second-order correlation from a laser beam, since laser field is non-Gaussin.
We have experimentally demonstrated two-photon interference between biphoton amplitudes arising from two well-separated pump pulses. It is important to note the following. 1) The pump pulse intensity was low enough so that single counting rates of the detectors were kept much smaller than pulse repetition rates: the probability of having one spontaneous parametric down conversion (SPDC) photon pair per pulse in our experiment is negligible. Hence the interference cannot be explained as two SPDC photons from two pump pulses (one SPDC photon pair from each pulse) interfering at the detectors. The two pump pulses simply provide two biphoton amplitudes which could result in coincidence counts, and interference occurs between these two biphoton amplitudes only when they are indistinguishable. 2) The BBO crystal in our experiment was only 100 /spl mu/m thick, so the two-pulse did not exist in BBO at the same time at any moment. 3) Due to the delays in the interferometer (/spl tau/ /spl tau//sub 1/), the signal-idler never met at the beamsplitter. Therefore, the existence of two-photon interference cannot be viewed as the interference between the signal and idler photons. These three points again emphasize the fact that it is the indistinguishability of the two-photon Feynman alternatives for the biphoton amplitudes which is responsible for the two-photon quantum interference effects.
We report an interference experiment in which the two-photon entangled state interference cannot be pictured in terms of the overlap and bunching of two individual photons on a beamsplitter. We also demonstrate that two-photon interference, or photon bunching effect on a beamsplitter, does not occur if the two-photon Feynman amplitudes are distinguishable, even though individual photons do overlap on a beamsplitter. Therefore, two-photon interference cannot be viewed as interference of two individual photons, rather it should be viewed as two-photon or biphoton interfering with itself. The results may also be useful for studying decoherence management in entangled two-qubit systems as we observe near complete restoration of quantum interference after the qubit pairs, generated by a femtosecond laser pulse, went through certain birefringent elements.
The nature of light, extending from the optical to the x-ray regime, is reviewed from a diffraction point of view by comparing field-based statistical optics and photon-based quantum optics approaches. The topic is introduced by comparing historical diffraction concepts based on wave interference, Dirac’s notion of photon self-interference, Feynman’s interference of space–time photon probability amplitudes, and Glauber’s formulation of coherence functions based on photon detection. The concepts are elucidated by a review of how the semiclassical combination of the disparate photon and wave concepts have been used to describe light creation, diffraction, and detection. The origin of the fundamental diffraction limit is then discussed in both wave and photon pictures. By use of Feynman’s concept of probability amplitudes associated with independent photons, we show that quantum electrodynamics, the complete theory of light, reduces in lowest order to the conventional wave formalism of diffraction. As an introduction to multi-photon effects, we then review fundamental one- and two-photon experiments and detection schemes, in particular the seminal Hanbury Brown–Twiss experiment. The formal discourse of the paper starts with a treatment of first-order coherence theory. In first order, the statistical optics and quantum optics formulations of coherence are shown to be equivalent. This is elucidated by a discussion of Zernike’s powerful theorem of partial coherence propagation, a cornerstone of statistical optics, followed by its quantum derivation based on the interference of single-photon probability amplitudes. The treatment is then extended to second-order coherence theory, where the equivalence of wave and particle descriptions is shown to break down. This is illustrated by considering two photons whose space–time probability amplitudes are correlated through nonlinear birth processes, resulting in entanglement or cloning. In both cases, the two-photon diffraction patterns are shown to exhibit resolution below the conventional diffraction limit, defined by the one-photon diffraction patterns. The origin of the reduction is shown to arise from the interference of two-photon probability amplitudes. By comparing first- and second-order diffraction, it is shown that the conventional first-order concept of partial coherence with its limits of chaoticity and first-order coherence has the second-order analogue of partial entanglement, with its limits corresponding to two entangled photons (“entangled biphotons”) and two cloned photons (“cloned biphotons”), the latter being second-order coherent. The concept of cloned biphotons is extended to the case of
n cloned photons, resulting in a
1/n reduction of the diffraction limit. In the limit of
nth-order collective state are shown to propagate on particle like trajectories, reproducing the 0th-order ray-optics picture. These results are discussed in terms of the linearity of quantum mechanics and Heisenberg’s space–momentum uncertainty principle. Finally, a general concept of coherence based on photon density is developed that in first order is equivalent to the conventional wave-based picture.