Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.
We examine multiphoton interference with a symmetric
SU(N) beam splitter
SN, an extension of features of the
SU(2) 50/50 beam splitter extended Hong-Ou-Mandel (eHOM) effect, whereby one obtains a zero amplitude (probability) for the output coincidence state (defined by equal number of photons
n/N in each output port), when a total number
n of photons impinges on the
N-port device. These are transitions of the form
∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N, where
n=∑i=1Nni, which generalize the Hong-Ou-Mandel (HOM) effect $|1,1\rangle \overset{S_2}{\to}|1,1\rangle $, the eHOM effect $|n_1,n_2\rangle \overset{S_2}{\to}|\tfrac{n_1+n_2}{2},\tfrac{n_1+n_2}{2}\rangle $, and the generalized HOM effect (gHOM)
∣1⟩⊗N→SN∣1⟩⊗N, which have previously been studied in the literature. The emphasis of this work is on illuminating how the overall destructive interference occurs in separate groups of destructive interferences of sub-amplitudes of the total zero amplitude. We develop symmetry properties for the generalized eHOM effect (geHOM)
∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N involving a zero amplitude governed by Perm(
Λ)=0, for an appropriately constructed matrix
Λ(SN) built from the matrix elements of
SN. We develop an analytical constraint equation for Perm
(Λ) for arbitrary
N that allows us to determine when it is zero. We generalize the SU(2) beam splitter feature of central nodal line (CNL), which has a zero diagonal along the output probability distribution when one of the input states is of odd parity (containing only odd number of photons), to the general case of
N=2∗N′ where
N′∈odd.
Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.
Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.
It is well known that the Hong–Ou–Mandel (HOM) effect can be realized on beam splitters (BSs) in the form of coupled waveguides. It is believed that in this case, the theory is similar to HOM interference on conventional BSs. In this work, it is shown that if a BS is used in the form of a coupled waveguide, the theory of HOM interference can differ significantly from the known one. It is shown that even in the case of completely identical photons, the visibility of V can essentially differ from unity. The developed theory must be taken into account in quantum optical schemes, where BSs are represented mainly as coupled waveguides.
Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.