Measuring the Biphoton Temporal Wave Function with Polarization-Dependent and Time-Resolved Two-Photon Interference

Abstract

We propose and demonstrate an approach to measuring the biphoton temporal wave function with polarization-dependent and time-resolved two-photon interference. Through six sets of two-photon interference measurements projected onto different polarization subspaces, we can reconstruct the amplitude and phase functions of the biphoton temporal waveform. For the first time, we apply this technique to experimentally determine the temporal quantum states of the narrow-band biphotons generated from the spontaneous four-wave mixing in cold atoms. DOI: 10.1103/PhysRevLett.114.010401 PACS numbers: 03.65.Wj, 03.67.Mn, 42.50.Dv Photons are described by their discrete polarization states and field amplitude distribution in continuous time-space domains. The state density matrix in a discrete Hilbert space can be reconstructed using the well-developed quantum-state tomography [1][2][3][4]. To describe the temporal modes of photons, one needs a continuous-variable quantum-state tomography characterizing both the amplitude and the phase functions. Homodyne detection has been proven an efficient probe to characterize photonic (unentangled) Fock and coherent states [5][6][7][8][9][10]. However, most homodyne measurements of bipartite states have only aimed at verifying the entanglement [11][12][13][14][15]. A complete optical homodyne tomography for the time-frequency entangled two-photon (amplitude and phase) temporal waveform still remains a technical challenge [8].There is an increasing interest in fully characterizing narrow-band biphotons because of their applications in realizing efficient light-matter quantum interfaces [16][17][18][19]. Using spontaneous four-wave mixing (SFWM) in cold atoms [20], the sub-MHz biphoton generation with a coherence time on the order of microseconds has been demonstrated [21][22][23]. Such a long coherence time of single photons allows manipulating their temporal waveforms [24][25][26] and their interaction with atoms in the time domain [27][28][29]. Owning to the nanosecond time resolution of commercially available single-photon counting modules (SPCM), the biphoton amplitude temporal profile can be directly measured from the coincidence counts. However, the coincidence counting does not distinguish between a time-frequency entangled state and a temporal-probability mixed state because it does not measure the phase distribution. Although additional evidences, such as the violation of the Cauchy-Schwarz inequality [30] and the antibunching of heralded single photons [31] can indicate the nonclassical properties, they do not provide a complete state information. It is believed that the time-frequency entanglement of biphotons generated from a continuouswave SFWM is naturally endowed by the energy conservation [32], but this claim has not been confirmed experimentally.In this Letter, we propose and implement a technique to measure the temporal wave function of SFWM narrowband biphotons. Using six sets of symmetrized timeresolved two-photon interference measurements in different polarization...

Quantum interference of multi-photon at beam splitter with application in measurement-device-independent quantum key distribution

“…Let us discuss the notion of narrowing of the dip in equation (18). Notice that each term in the summation has a factor e j A B…”

“…A summary for some of these experiments with discussion of temporal distinguishability is given in [12]. The general results for multi-photon quantum interference using traditional HOM interferometer, specifically, for any photon number state with Gaussian spectral distribution, have not been discussed in the literature.Despite that, however, and despite the relative simplicity of the original HOM interferometer setup, it has proven to be useful and important in various applications, for example, in quantum interference of successive single photons from the same emitter [13][14][15][16], to determine the purity of photons emitted by quantum dot [13], in quantum interference between single photons emitted by independent atoms [17], to measure biphoton temporal wavefunction [18], in quantum interference of single photons with different colors via frequencydomain beam splitter [19], and in quantum interference of topological states of light [20].…”

Narrowband biphotons with polarization-frequency-coupled entanglement

“…1(c) agrees well with the theoretical curve obtained numerically following the interaction picture [13], The biphotons have a correlation time of about 50 ns. We also perform a temporal quantum-state tomography [27] and obtain a biphoton bandwidth of about 22 MHz. To describe polarizations, we take the convention in which the wave is observed from the point of view of the source.…”

Theory and applications of toroidal moments in electrodynamics: their emergence, characteristics, and technological relevance

“…Although the history of Maxwell equations and lightmatter interaction started as early as 1861 [1], electromagnetism has been the field of most challenging and rival concepts such as understanding the actual velocity of the information transfer [2], the actual wave function of photons [3][4][5], realization of cloaking, negative refraction, and transferring of the data beyond the diffraction limits using plasmons and metamaterials [6][7][8][9][10][11], and the emergence of the Abraham-Minkowski controversy and the actual linear momentum of light [12,13]. At the heart of our understanding of light-matter interaction, there exist multipole-expansion sets that tell us how to construct the extended electromagnetic sources according to the localized sources with well-known electromagnetic field and radiation patterns.…”