Revisiting self-interference in Young’s double-slit experiments S. Kim1 and Byoung S. Ham1,* 1Center for Photon Information Processing, School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology 123 Chumdangwagi-ro, Buk-gu, Gwangju 61005, South Korea (Submitted on April. 16, 2021 *[email protected]) Abstract: Over the past several decades, single photon-based path interference in Young’s double-slit experiment has been well demonstrated for the particle nature of photons satisfying complementarity theory, where the quantum mechanical interpretation of the single photon interference fringe is given by Born’s rule for complex amplitudes in measurements. Unlike most conventional methods using entangled photon pairs, here, a classical coherent light source is directly applied for the proof of the same self-interference phenomenon. Instead of Young’s double slits, we use a Mach-Zehnder interferometer as usual, where the resulting self-interference fringe of coherent single photons is exactly the same as that of the coherent photon ensemble of the laser, demonstrating that the classical coherence based on the wave nature is rooted in the single photon self- interference. This unexpected result seems to contradict our common understanding of decoherence phenomena caused by multi-wave interference among bandwidth distributed photons in coherence optics. Introduction Young’s double-slit experiments [1] have been studied over the last century using not only the wave nature of coherent light but also the particle nature of electrons [2-4], atoms [5,6], and photons [7-10] for quantum mechanical understanding of self-interference (SI) [11,12]. According to the Copenhagen interpretation, a single photon can be viewed as either a particle nature or a wave nature, so that the Young’s double-slit interference fringe based on single photons has been interpreted as self-interference based on the wave nature, satisfying the complementarity theory [13]. In other words, the single photon-based fringe cannot be compatible with the particle nature simply because a single photon as a minimum energy unit cannot be split into two parts. Thus, quantum superposition of a single photon itself between two paths of Young’s double slits needs to be interpreted in terms of the wave nature via indistinguishable entities or quantum superposition, otherwise the fringe disappears [7,14,15]. This is the essence of the quantum interference in Young’s double-slit experiments for SI satisfying the complementarity in quantum mechanics. Without violating generality, a Mach-Zehnder interferometer (MZI) has replaced the Young’s double slits due to its experimental feasibilities [7,12,14-20]. The SI of single photons in an MZI has also been applied for the proof of quantum features such as quantum erasers [7,15], Franson-type nonlocal correlation [16], and N00N state generations for higher order entangled photon pairs [17-21]. Based on the quantum features of SI in an MZI, indistinguishability between two entities in a paired path has been demonstrated with a polarization basis, where a selection of perpendicularly polarized bases negates the interference fringe due simply to distinguishable entities regardless of mutual coherence [7,14]. So far, those experiments of SI have been performed using quantum particles of single photons generated mostly from spontaneous parametric down conversion (SPDC) processes [15,16,18-20]. Keeping in mind that multi- interference among many waves results in decoherence, each individual photon’s coherence time is supposed to be longer than that of an ensemble of photons. According to the Copenhagen interpretation regarding wave- particle duality or complementarity theory, the particle and wave natures are incompatible with each other. Thus, SI should be related with the wave nature of photons, otherwise the physical reality of a single photon in the paired path would be contradictory. In that sense, the first question for SI in an MZI is whether the coherence time of each single photon is longer than that of an ensemble of photons, resulting in a classical bound. According to the given (measured) bandwidth of a laser, each individual photon’s frequency or wavelength is supposed to be slightly different from the others, resulting in the ensemble coherence length as a classical bound. Thus, it can be assumed that a single photon should have a longer coherence length than . Here, in this paper, we experimentally demonstrate that it is not true; thus, a fundamental question is followed by what the difference between coherent light as a classical entity and a single photon as a quantum entity should be. As 1 long as a coherent state is defined as a linear superposition of Fock states, a laser cannot be treated as a quantum entity [22-24]. By answering these simple questions, we confirm quantum characteristics of MZI via SI. In other words, the Fock state representation of a coherent state may not be applied at least for the MZI. Fig. 1. Schematic of quantum superposition for self-interference in an MZI. L: 405 nm laser, A: attenuator, BS: beam splitter, G1/G2: 500 m glass plate, M: mirror, D1/D2: single photon detector, CCU: coincidence counting unit. μ Figure 1 shows the schematic of coherent photon-based MZI for the test of SI. For this, we set a reference as a classical bound with a typical MZI fringe using a commercial 405 nm laser (Omicron, PhoxX405-120), whose coherence time (length) is = 0.5 ( = 150 ). For a single photon MZI, the 405 nm laser light is attenuated with neutral density filters (OD 10) until a single photon stream is achieved with ~2 Mega counts per a second (cps). To confirm SI, a heralded detection technique is applied, where doubly bunched photons are split into two parts by the first beam splitter (BS) in Fig. 1. Bunched photons grouped into three or more are simply neglected, because their occurrence rates are less than 1% compared with the doubly bunched photons (see Fig. S1 of the Supplementary Information). Thus, the measured single photon-based SI in the present experiments has an error of < 1%. Fig. 2. Attenuated laser light for a single and bunched photons. (a) and (b) From SPCM output D2. (c) On the oscilloscope (some examples). Expansion from the top to the bottom. Yellow/green: D1/D2, where D2 is relocated between the first and second BSs in Fig. 1. In (a), the red (black) dots are from D1 (D2). Figure 2 shows experimental data for both single photons and doubly bunched photons detected by a coincidence counting unit (Altera, DE2) fed by a pair of single photon counting modules (Excelitas SPCM- AQRH 15), whose resolving time and dark count rate are 350 ps and 50 cps, respectively. For Fig. 2, the detector D2 in Fig. 1 is relocated to a position between the first and second BSs before the MZI. Both SPCMs show a ~1 Mcps detection rate as shown by red and black dots in Fig. 2(a), while Fig. 2(b) shows the coincidence detection rate for the doubly bunched photon pairs. The detected coincidence counting rate for the doubly bunched photons is ~12 kcps. As mentioned above, this coincidence counting rate includes three or more bunched photons, resulting in a < 1% error experimentally. With this error, Fig. 2(b) confirms stable coherent 2 photon pair generation by the coherent light source of 405 nm laser, where one photon in each pair is used for the SI experiment, while the other photon is used for the heralded detection to confirm the validity of SI. To visualize the doubly bunched photon pairs, both detector outputs are fed into a fast (500 MHz) digital oscilloscope (Yokogawa, DL9040). As shown in Fig. 2(c), a pair of single photon streams detected by D1 and D2 are observed in both top and middle panels, respectively. Of them are doubly bunched photon pairs occasionally detected as shown in the yellow box of the middle panel (see Figs. S2 and S3 of the Supplementary Information for details). The bottom panel of Fig. 2(c) shows some examples of the doubly bunched photon pairs. The detected number of photon pairs are 11 for 1 ms in the top panel. Figure 3 shows both coherent light-based MZI at 200 W (cw; 405 nm) for the classical bound (upper panels) and the single photon-based SI for the quantum bound (lower panels) with attenuation of the cw light. For the coherent light (cw) MZI, the single photon detector D1μ is blocked, and the SPCM of D2 is replaced by an avalanche silicon photodiode (Thorlabs, APD-110A) connected to the fast digital oscilloscope. For both cases, the fringe is expanded to ~2 cm in diameter using a telescope (see Fig. 1). For the intensity measurement of the fringe, a homemade single slit of width < 1 mm is inserted right after the collimated fringe and is linearly scanned across the fringe cross-section as shown in Fig. 1. The scanning slit-filtered light (photon) is focused onto the detector D2 by a lens, so that the slit scanning position does not affect the measurement efficiency. The number of MZI fringes is preset to be about six, resulting in each fringe width being much wider than the slit width to neglect potential diffraction effects. For the intentional path-length difference of the MZI, identical glass plates (G1 and G2) are inserted in the MZI paths, where one (G1) is changed, while the other (G2) is fixed. For G1 control, one end of the plate is linearly pushed using a picometer (Thorlabs, Z825B) with respect to the other hinged end, resulting in a rotation. The path-length difference of the MZI corresponds to the rotation angle of G1 (see Fig.