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Towards Simultaneous Observation of Path and Interference of a Single Photon in a Modified Mach–Zehnder Interferometer

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Towards Simultaneous Observation of Path and Interference of a Single Photon in a Modified Mach–Zehnder Interferometer 622 Vol. 8, No. 4 / April 2020 / Photonics Research Research Article Towards simultaneous observation of path and interference of a single photon in a modified Mach–Zehnder interferometer 1,† 1,† 1 1,4 2,3 FENGHUA QI, ZHIYUAN WANG, WEIWANG XU, XUE-WEN CHEN, AND ZHI-YUAN LI 1School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China 2College of Physics and Optoelectronics, South China University of Technology, Guangzhou 510641, China 3e-mail: [email protected] 4e-mail: [email protected] Received 27 December 2019; revised 10 February 2020; accepted 11 February 2020; posted 13 February 2020 (Doc. ID 386774); published 1 April 2020 Classical wisdom of wave–particle duality regulates that a quantum object shows either the particle or wave nature but never both. Consequently, it would be impossible to observe simultaneously the complete wave and particle nature of the quantum object. Mathematically the principle requests that the interference visibility V and which- path distinguishability D satisfy an orthodox limit of V 2 D2 ≤ 1. The present work reports a new wave– particle duality test experiment using single photons in a modified Mach–Zehnder interferometer to demonstrate the possibility of breaking the limit. The key element of the interferometer is a weakly scattering total internal reflection prism surface, which exhibits a pronounced single-photon interference with a visibility of up to 0.97 and simultaneously provides a path distinguishability of 0.83. Apparently, the result of V 2 D2 ≈ 1.63 exceeds the orthodox limit set by the classical principle of wave–particle duality for single photons. We expect that more delicate experiments in the future should be able to demonstrate the ultimate limit of V 2 D2 ≈ 2 and shed new light on the foundations of contemporary quantum mechanics. © 2020 Chinese Laser Press https://doi.org/10.1364/PRJ.386774 1. INTRODUCTION of complete destruction of the interference pattern, i.e., 0 1 The wave–particle duality of a quantum object, including pho- V and D . In the third situation, using interferometer tons, electrons, atoms, etc., constitutes one of the conceptual setups with quantum delayed-choice schemes, one can observe cornerstones of quantum physics. The principle dictates that all the simultaneous partial wave and partial particle nature of pho- tons with V ≠ 0 and D ≠ 0 [13,15,16,23], which yet still sat- quantum objects exhibit mutually exclusive behaviors of two 2 2 ≤ 1 intrinsic attributes, namely, being either as wave or as particle isfies the orthodox limit of V D [24]. In summary, – despite enormous efforts, all existing test experiments have depending on how they are measured, but never both [1 10]. – Over the past several decades, numerous studies using gedanken shown no sign of going beyond the principle of wave particle or practical interferometers such as a Mach–Zehnder interfer- duality. ometer (MZI) and Young’s two-slit interferometer in various A rigorous analysis based on full quantum mechanics in the genuine arrangements have been carried out to test the wave– Schrödinger picture reveals that in previous interferometers, ’ particle duality principle of particles. To name a few, there are, such as the delayed-choice scheme of MZI as well as Afshar s for instance, Wheeler’s delayed-choice scheme [6,7,11–16], scheme, the measurement of one entity (either wave or particle Scully’s quantum eraser scheme [8–10], Afshar’s scheme nature) strongly disturbs the other so that the observation of the [17–19], and others [20–23]. The outcomes of all previous test two are exclusive [25,26]. As illustrated in Fig. 1(a), a photon experiments can be summarized into three situations character- sent into the MZI goes either into path X or path Y with each ized by the interference visibility V and which-path distin- 50% probability after the first beam splitter BS1. To know guishability D. In the first situation, one uses a specific setup which path the photon passes and thus the particle property, to achieve perfect observation of the wave nature of the par- one needs to remove the second beam splitter BS2 and check ticle with an interference visibility V 1 at the price of com- the detectors X and Y . To observe the interference pattern and plete loss of the path distinguishability with D 0. In the thus the wave property of the photon, one should keep BS2 and second situation, one applies another setup to distinguish examine the detectors X and Y . However, no matter how smart unambiguously the paths that each particle passes at the cost the design is, it is impossible to observe the wave and particle 2327-9125/20/040622-08 Journal © 2020 Chinese Laser Press Research Article Vol. 8, No. 4 / April 2020 / Photonics Research 623 challenging experiment. The difficulty lies in observing the interference pattern via the WM-MZI. The proposed origi- nal configuration shown in Fig. 1(b) suffers from very low collection efficiency of weakly scattered single photons from the interference screen. For a two-dimensional image with 100 × 100 pixels, the average photon detection rate at each pixel is estimated to be fewer than 0.01 count per second (cps) considering a single-photon source with an emission rate of 100 kcps, a scattering efficiency of 10%, and an overall detec- tion efficiency of 1% for the proposed configuration. To cir- cumvent such a formidable experimental difficulty, we take advantage of the fact that the interference pattern of two plane waves is one dimensional in nature and thus one can use an efficient point detector (an avalanche photodiode, APD) with a movable slit instead of a camera to observe the interference pattern. Moreover, we modify the original high-transmission weak-scattering interference screen in Fig. 1(b) to a high- reflection weak-scattering prism setup so that a microscope ob- jective with a high numerical aperture (NA) could be used to improve the collection of the weakly scattered single photons. The above modifications afford us to experimentally demon- strate single-photon WM-MZI, as discussed in the following sections. Figure 2(a) shows the key element of the WM-MZI, i.e., a Fig. 1. (a) Schematic setup of classical Mach–Zehnder interferom- prism surface that hosts the interference and provides weak eter (MZI) used to test wave–particle duality of a photon. The MZI scattering via a diffusive scattering thin film. The weakly scat- consists of the first beam splitter BS1, two mirrors (M), a phase shift φ tering film is made via casting a droplet of dilute milk. Single ( ), and the second beam splitter BS2. BS2 can either be present in the photons split into two beams are incident upon the prism sur- path, or absent, or controlled by an external (classical or quantum) face at total internal reflection angles with an angle difference of module. (b) Schematic setup of weak-measurement MZI (WM-MZI), θ ≈ 1 75 where an interference screen (denoted by the blue thick lines) with . °. Labeled as beam 1 and beam 2, the two beams exit high transmission and weak scattering replaces BS2. the prism with the same separation angle and are detected by APD1 and APD2, respectively. These two beams interfere on the prism surface to form a one-dimensional interference pat- tern, which evanescently decays into the air side of the surface. nature of the photon simultaneously because the insertion and With a diffusive weak-scattering thin film, incident single pho- removal of BS2 are completely exclusive operations. Yet, as tons are scattered by a small probability and a fraction of that displayed in Fig. 1(b), a modified MZI working in the weak- is collected and detected by APD3 to reveal the interference measurement regime, hereafter called WM-MZI, can largely pattern. Moreover, with weak scattering the total reflection get around the difficult mutual exclusion problem by using an becomes imperfect, having a reflection coefficient R slightly interference screen to replace BS2 in the standard MZI [27]. smaller than unity. We have tested the WM-MZI setup by in- This interference screen exhibits a high transmission and weak cidence of a laser beam and observed a very clear interference scattering of the photon, and essentially becomes a detector pattern at the prism hypotenuse surface, as illustrated by the of interference pattern via weak scattering. A similar idea has right-most image in Fig. 2(a), which confirms that the weak- recently been extended to atom interferometers with weak- scattering prism surface functions nicely as an interference measurement path detectors [28]. Quantum mechanical analy- screen for light. ses show that compared to the standard MZI the proposed Figures 2(b) and 2(c) display the whole experimental setup. WM-MZI has the potential to make simultaneous observation An efficient single-photon source based on spontaneous emis- of interference and which-path information of quantum ob- 1 sion of excited single CdSe/CdS core–shell colloidal quantum jects. Specifically, it can reach the level of V and – D → 1, so that V 2 D2 → 2, which far exceeds the regime dots (QDs) [29 33] is prepared in Room 1 and then by cou- allowed by the principle of wave–particle duality. In this work, pling to the single-mode fiber (SMF) the single photons are we experimentally construct a WM-MZI setup and perform delivered to the WM-MZI setup in Room 2. The challenging single-photon experiment with this new interferometer to test part is to achieve large coupling of the single photons from sin- the wave–particle duality of photons. gle QDs into the SMF [31].
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