According to the identity principle in quantum theory, states of a system consisted of identical particles should maintain unchanged under interchanging between two of the particles. The whole wavefunction should be symmetrized or antisymmetrized. This leads to statistical correlations between particles, which exhibit observable effects. We design an experiment to directly observe such effects for bosons. The experiment is performed with two photons. The effect of statistical correlations is clearly observed when the wavepackets of two photons are completely overlapped, and this effect varies with the degree of overlapping. The results of our experiment substantiate the statistical correlation in a simple way. Experiment reported here can also be regarded as another kind of two-photon Hong-Ou-Mandel interference, occurs in the polarization degree of freedom of photon.
According to the identity principle in quantum theory, states of a system consisted of identical particles should maintain unchanged under interchanging between two of the particles. The whole wavefunction should be symmetrized or antisymmetrized. This leads to statistical correlations between particles, which exhibit observable effects. We design an experiment to directly observe such effects for bosons. The experiment is performed with two photons. The effect of statistical correlations is clearly observed when the wavepackets of two photons are completely overlapped, and this effect varies with the degree of overlapping. The results of our experiment substantiate the statistical correlation in a simple way. Experiment reported here can also be regarded as another kind of two-photon Hong-Ou-Mandel interference, occurs in the polarization degree of freedom of photon.
Usually fermions and bosons behave very differently. Regarding distinguishability, they behave in one and the same way. Two-identical-particle quantum theory is discussed on the example of the deuteron and that of distant correlations, as well as on the example of the real interference and quantum erasure experiments in the Hong–Ou–Mandel two-photon interferometer (with and without polarizers and analyzers). Distinguishability and indistinguishability of two identical photons in the experiments are illustrated. It is demonstrated, using a simple formalism valid simultaneously for fermions and for bosons, that there exists an isomorphism giving theoretical foundation to distinguishing two identical particles. But the distinguishing has a limited range of exact applicability. In most cases of interest, only the indistinguishability approach has a first-principle (and universal) validity.
Interference of light fields, first postulated by Young, is one of the fundamental pillars of physics. Dirac extended this observation to the quantum world by stating that each photon interferes only with itself. A precondition for interference to occur is that no welcher-weg information labels the paths the photon takes; otherwise, the interference vanishes. This remains true, even if two-photon interference is considered, e.g., in the Hong-Ou-Mandel-experiment. Here, the two photons interfere only if they are indistinguishable, e.g., in frequency, momentum, polarization, and time. Less known is the fact that two-photon interference and photon indistinguishability also determine the photon statistics in the overlapping light fields of two independent sources. As a consequence, measuring the photon statistics in the far field of two independent sources reveals the degree of indistinguishability of the emitted photons. In this Letter, we prove this statement in theory using a quantum mechanical treatment. We also demonstrate the outcome experimentally with a simple setup consisting of two statistically independent thermal light sources with adjustable polarizations. We find that the photon statistics vary indeed as a function of the polarization settings, the latter determining the degree of welcher-weg information of the photons emanating from the two sources.
Two photons are said to be identical if they are prepared in the same quantum state. Given the latter, there is a unique way to achieve this. Conversely, there are many different ways of preparing two non-identical photons: they may differ in frequency, polarization, amplitude, etc. Therefore, photon distinguishability depends upon the specific degree of freedom being varied. By means of a careful analysis of the coincidence probability distribution in a Hong–Ou–Mandel experiment, we can show that photon distinguishability can be actually quantified by the rate of distinguishability of photons, an experimentally measurable parameter that crucially depends on both the photon quantum state and the degree of freedom under control.
Abstract Quantum systems with many constituents give rise to a range of conceptual, analytical and computational challenges, hence, the label ‘complex systems’. In the first place, one can think of interactions, described by a many-body Hamiltonian, as the source of such complexity. However, it has gradually become clear that, even in absence of interactions, many-body systems are more than just the sum of their parts. This feature is due to many-body interference. One of the most well-known interference phenomena is the Hong–Ou–Mandel effect, where total destructive interference is observed for a pair of (non-interacting) identical photons. This two-photon interference effect can be generalised to systems of many particles which can be either fermionic or bosonic. The resulting many-particle interference goes beyond quantum statistical effects that are contained in the Bose–Einstein or Fermi–Dirac distributions, and is dynamical in nature. This Tutorial will introduce the mathematical framework for describing systems of identical particles, and explain the notion of indistinguishability. We will then focus our attention on dynamical systems of free particles and formally introduce the concept of many-particle interference. Its impact on many-particle transition probabilities is computationally challenging to evaluate, and it becomes rapidly intractable for systems with large numbers of identical particles. Hence, this Tutorial will build up towards alternative, more efficient methods for observing signatures of many-particle interference. A first type of signatures relies on the detection of a highly sensitive -but also highly fragile- processes of total destructive interference that occurs in interferometers with a high degree of symmetry. A second class of signatures is based on the statistical features that arise when we study the typical behaviour of correlations between a small number of the interferometer’s output ports. We will ultimately show how these statistical signatures of many-particle interference lead us to a statistical version of the Hong–Ou–Mandel effect. The work presented in this Tutorial was one of the four shortlisted finalists of the 2018 DPG SAMOP dissertation prize.
Two-photon Hong-Ou-Mandel (HOM) interference is a fundamental quantum effect with no classical counterpart. The existing research on two-photon interference was mainly limited in one degree of freedom (DOF); hence, it is still a challenge to realize quantum interference in multiple DOFs. Here, we demonstrate HOM interference between two hyperentangled photons in two DOFs of polarization and orbital angular momentum (OAM) for all 16 hyperentangled Bell states. We observe hyperentangled two-photon interference with a bunching effect for ten symmetric states (nine boson-boson states and one fermion-fermion state) and an antibunching effect for six antisymmetric states (three boson-fermion states and three fermion-boson states). More interestingly, expanding the Hilbert space by introducing an extra DOF for two photons enables one to transfer the unmeasurable external phase in the initial DOF to a measurable internal phase in the expanded two DOFs. We directly measured the symmetric exchange phases being 0.012±0.002, 0.025±0.002, and 0.027±0.002 in radian for the three boson states in OAM and the antisymmetric exchange phase being 0.991π±0.002 in radian for the other fermion state, as theoretical predictions. Our Letter may not only pave the way for more wide applications of quantum interference, but also develop new technologies by expanding Hilbert space in more DOFs.
The experimental study of second-order interference with fermions is much more difficult than that with bosons. Inspired by the conclusion that the behavior of two identical classical particles has exactly half fermionic and half bosonic characteristics [Phys. Rev. A88, 012130 (2013)PLRAAN1050-294710.1103/PhysRevA.88.012130], we have studied the second-order interference of fermions via the second-order interference of photons in Hanbury Brown–Twiss and Hong–Ou–Mandel interferometers, respectively. The experimental results are consistent with the theoretical predictions, which may serve as guidance for future interference experiments with fermions. The employed method offers an interesting and convenient way to study the coherence of fermions.