Delayed-choice test of quantum complementarity with interfering single photons

Quantum causality emerging in a delayed-choice quantum Cheshire Cat experiment with neutrons

We report an experiment with neutrons in a silicon perfect crystal interferometer, that realizes a quantum Cheshire Cat in a delayed choice setting. In our setup the quantum Cheshire Cat is established by spatially separating the particle and its property (i.e. the neutron and its spin) into the two different paths of the interferometer. The condition for a delayed choice setting is achieved by postponing the choice of path assignment for the quantum Cheshire Cat, i.e. which path is taken by the particle and which by its property, until the point in time when the neutron wave function has already split and entered the interferometer. The results of the experiment suggest not only the fact that the neutrons and its spin are separated and take different paths in the interferometer, but also quantum-mechanical causality is implied, insomuch that the behavior of a quantum system is affected by the choice of the selection at a later point in time.

Experimental display of generalized wave-particle duality

The quantification of wave-particle duality (WPD) by means of measurable features associated to it, such as fringe visibility ($\mathcal {V}$) and path distinguishability ($\mathcal {D}$), led to the establishment of the constraint $\mathcal {V}^{2}+\mathcal {D}^{2} \leq \,1$. The two involved quantities refer to so-called "quantons", physical objects that are capable of generating an interferometric pattern, while being at least partially localizable. Any quanton's internal degree of freedom (DOF) can in principle be used as a path-marker. When the quanton and its internal DOF are simultaneously engaged, new constraints can be derived and experimentally tested. Generalized constraints show how $\mathcal {V}$ and $\mathcal {D}$ relate to other quantifiers and bring to light coherences that might remain otherwise hidden in both quantum and classical light. We submitted two-qubit constraints to experimental tests, using optical light beams. This shows that, despite the rather contrived nature of the constraints, linear optics setups are appropriate to test them. Our experimental results are in very good agreement with theoretical predictions related to the tested constraints. Our results also show that quantifiers such as $\mathcal {V}$ and $\mathcal {D}$ help not only to quantify, but also to generalize the concept of WPD.

Conceiving Particles as Undulating Granular Systems Allows Fundamentally Realist Interpretation of Quantum Mechanics

The strange behavior of subatomic particles is described by quantum theory, whose standard interpretation rejected some fundamental principles of classical physics such as causality, objectivity, locality, realism and determinism. Recently, a granular relativistic electrodynamical model of the electron could capture the measured values of its observables and predict its mass from the stability of its substructure. The model involves numerous subparticles that constitute some tight nucleus and loosely bound envelope allegedly forming real waves. The present study examines whether such a substructure and associated dynamics allow fundamentally realist interpretations of emblematic quantum phenomena, properties and principles, such as wave-particle duality, loss of objectivity, quantization, simultaneous multipath exploration, collapse of wavepacket, measurement problem, and entanglement. Drawing inspiration from non-linear dynamical systems, subparticles would involve realist hidden variables while high-level observables would not generally be determined, as particles would generally be in unstable states before measurements. Quantum mechanics would constitute a high-level probabilistic description emerging from an underlying causal, objective, local, albeit contextual and unpredictable reality. Altogether, by conceiving particles as granular systems composed of numerous extremely sensitive fluctuating subcorpuscles, this study proposes the possible existence of a local fundamentally realist interpretation of quantum mechanics.

Simulation of quantum delayed-choice experiment through a single shot

A fundamental feature of micro objects is the wave-particle duality which is addressed by Bohr's complementarity principle. To observe the wave and particle behaviours, quantum delayed-choice experiments based on linear optics have been realized at the single-photon level. Since they were performed by using a single photon as the input, repeating measurements were required in order to obtain different experimental data and adjusting experimental parameters was necessary prior to each of measurements. Different from the previous works, we here realize a simulation of quantum delayed-choice experiment through a single shot, which employs a classical intense light beam as the input instead of a single photon. Experimentally, we demonstrate the trade-off between distinguishability and visibility of photons in a two-arm interferometer in an intuitive way by utilizing the finite beam profile of the light. We observe the morphing between wave and particle natures of photons via a single shot of a charged-coupled-device camera. Since the image is captured within the exposure time which is several milliseconds, the phase fluctuation is negligible, and therefore our experimental setup is robust against the noise. This work provides a simple and new route to inspect quantum duality, which does not require adjusting experimental parameters frequently and only needs performing measurement once.

A generalized multipath delayed-choice experiment on a large-scale quantum nanophotonic chip

Bohr's complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young's double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interest to study complementarity in multipath interferometric systems. Here, we demonstrate generalized multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalized Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr's multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology.

Wave-Particle Duality Relation with a Quantum Which-Path Detector

According to the relevant theories on duality relation, the summation of the extractable information of a quanton’s wave and particle properties, which are characterized by interference visibility V and path distinguishability D, respectively, is limited. However, this relation is violated upon quantum superposition between the wave-state and particle-state of the quanton, which is caused by the quantum beamsplitter (QBS). Along another line, recent studies have considered quantum coherence C in the l1-norm measure as a candidate for the wave property. In this study, we propose an interferometer with a quantum which-path detector (QWPD) and examine the generalized duality relation based on C. We find that this relationship still holds under such a circumstance, but the interference between these two properties causes the full-particle property to be observed when the QWPD system is partially present. Using a pair of polarization-entangled photons, we experimentally verify our analysis in the two-path case. This study extends the duality relation between coherence and path information to the quantum case and reveals the effect of quantum superposition on the duality relation.

Stereographic geometry of coherence and which-path information

Recently, it was shown that quantum entanglement is an indispensable part of the duality behavior of light. Here we report a surprisingly intimate connection between the stereographic projection and the duality-entanglement nature of a single photon. We show that the duality-entanglement relation [Optica5, 942 (2018)OPTIC82334-253610.1364/OPTICA.5.000942] naturally emerges from the stereographic projection geometry. We demonstrate that this geometry is complementarity sensitive, in the sense that it is sensitive to the particle nature, wave nature, and entanglement nature of a single photon.

Experimental demonstration of wave-particle duality relation based on coherence measure

Wave-particle duality is a typical example of Bohr's complementarity principle that plays a significant role in quantum mechanics. Previous studies used the visibility of an interference pattern to quantify the wave property and used path information to quantify the particle property. However, coherence is the core and basis of the interference phenomenon. If we could use coherence to characterize the wave property, the understanding of wave-particle duality would be strengthened. A recent theoretical work [ Phys. Rev. Lett.116, 160406 (2016)] found two relations between quantum coherence and path information. Here, we demonstrate the new measure of wave-particle duality based on two kinds of coherence measures quantitatively for the first time. The wave property, quantified by the coherence in the l₁-norm measure and the relative entropy measure, can be obtained via tomography of the target state, which is encoded in the path degree of freedom of the photons. The particle property, quantified by the path information, can be obtained via the discrimination of detector states, which is encoded in the polarization degree of freedom of the photons. Our work may deepen people's understanding of coherence and provide a new perspective regarding wave-particle duality.

Quantum twisted double-slits experiments: confirming wavefunctions' physical reality

Are quantum states real? This most fundamental question in quantum mechanics has not yet been satisfactorily resolved, although its realistic interpretation seems to have been rejected by various delayed-choice experiments. Here, to address this long-standing issue, we present a quantum twisted double-slit experiment. By exploiting the subluminal feature of twisted photons, the real nature of a photon during its time in flight is revealed for the first time. We found that photons' arrival times were inconsistent with the states obtained in measurements but agreed with the states during propagation. Our results demonstrate that wavefunctions describe the realistic existence and evolution of quantum entities rather than a pure mathematical abstraction providing a probability list of measurement outcomes. This finding clarifies the long-held misunderstanding of the role of wavefunctions and their collapse in the evolution of quantum entities.

Dynamically unpolarized single-photon source in diamond with intrinsic randomness

Polarization is one of the fundamental properties of light, providing numerous applications in science and technology. While ‘dynamically unpolarized’ single-photon sources are demanded for various quantum applications, such sources have never been explored. Here we demonstrate dynamically unpolarized single-photon emission from a single [111]-oriented nitrogen- vacancy centre in diamond, in which the single-photon stream is unpolarized, exhibiting intrinsic randomness with vanishing polarization correlation between time adjacent photons. These properties not only allow true random number generation, but may also enable fundamental tests in quantum physics.

Information gain versus interference in Bohr's principle of complementarity

We study the wave and particle nature in a symmetric Mach-Zehnder interferometer from the viewpoint of quantum information theory. By introducing either the von Neumann or Zurek's model of quantum measurement, we find that the classical correlation can be used to quantify the particle nature since its monotonicity is similar to the path distinguishability. The environment in Zurek's model induces the emergence of the optimal measuring basis, and reduces the classical and quantum correlation comparing to the von Neumann's model. A way is presented analytically to calculate the quantum correlation of a two-qubit separable state other than X-type.

Tracing the trajectory of photons through Fourier spectrum

By slightly vibrating the mirrors in an interferometer at different frequencies, the photons' trajectory information is stored in the light beam. To read out this information, we record the centroid location of the intensity distribution of output beam and Fourier analyze its time evolution. It is shown that every vibrating mirror contributes a peak in the Fourier spectrum. In other words, we can reveal the trajectory of the photons by figuring out the vibrating mirrors which ever interact with the light beam based on the Fourier spectrum. This techniques is not limited by the vibration amplitude of the mirrors.

Equivalence of wave-particle duality to entropic uncertainty

Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behaviour, yet that wave behaviour disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitatively as an inequality, for example, by Englert and Jaeger, Shimony and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely, the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.

Coherent perfect absorption of path entangled single photons

We examine the question of coherent perfect absorption (CPA) of single photons, and more generally, of the quantum fields by a macroscopic medium. We show the CPA of path entangled single photons in a Fabry-Perot interferometer containing an absorptive medium. The frequency of perfect absorption can be controlled by changing the interferometer parameters like the reflectivity and the complex dielectric constant of the material. We exhibit similar results for path entangled photons in micro-ring resonators. For entangled fields like the ones produced by a down converter the CPA aspect is evident in phase sensitive detection schemes such as in measurements of the squeezing spectrum.

On-chip manipulation of single photons from a diamond defect

Operating reconfigurable quantum circuits with single photon sources is a key goal of photonic quantum information science and technology. We use an integrated waveguide device containing directional couplers and a reconfigurable thermal phase controller to manipulate single photons emitted from a chromium related color center in diamond. Observation of both a wavelike interference pattern and particlelike sub-Poissionian autocorrelation functions demonstrates coherent manipulation of single photons emitted from the chromium related center and verifies wave particle duality.

Quantum erasure with causally disconnected choice

The counterintuitive features of quantum physics challenge many common-sense assumptions. In an interferometric quantum eraser experiment, one can actively choose whether or not to erase which-path information (a particle feature) of one quantum system and thus observe its wave feature via interference or not by performing a suitable measurement on a distant quantum system entangled with it. In all experiments performed to date, this choice took place either in the past or, in some delayed-choice arrangements, in the future of the interference. Thus, in principle, physical communications between choice and interference were not excluded. Here, we report a quantum eraser experiment in which, by enforcing Einstein locality, no such communication is possible. This is achieved by independent active choices, which are space-like separated from the interference. Our setup employs hybrid path-polarization entangled photon pairs, which are distributed over an optical fiber link of 55 m in one experiment, or over a free-space link of 144 km in another. No naive realistic picture is compatible with our results because whether a quantum could be seen as showing particle- or wave-like behavior would depend on a causally disconnected choice. It is therefore suggestive to abandon such pictures altogether.

A quantum delayed-choice experiment

Quantum systems exhibit particle- or wavelike behavior depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics. Its paradoxical nature is best captured in the delayed-choice thought experiment, in which a photon is forced to choose a behavior before the observer decides what to measure. Here, we report on a quantum delayed-choice experiment in which both particle and wave behaviors are investigated simultaneously. The genuinely quantum nature of the photon's behavior is certified via nonlocality, which here replaces the delayed choice of the observer in the original experiment. We observed strong nonlocal correlations, which show that the photon must simultaneously behave both as a particle and as a wave.

Entanglement-enabled delayed-choice experiment

Wave-particle complementarity is one of the most intriguing features of quantum physics. To emphasize this measurement apparatus-dependent nature, experiments have been performed in which the output beam splitter of a Mach-Zehnder interferometer is inserted or removed after a photon has already entered the device. A recent extension suggested using a quantum beam splitter at the interferometer's output; we achieve this using pairs of polarization-entangled photons. One photon is tested in the interferometer and is detected, whereas the other allows us to determine whether wave, particle, or intermediate behaviors have been observed. Furthermore, this experiment allows us to continuously morph the tested photon's behavior from wavelike to particle-like, which illustrates the inadequacy of a naive wave or particle description of light.

Two-slit diffraction with highly charged particles: Niels Bohr's consistency argument that the electromagnetic field must be quantized

We analyze Niels Bohr's proposed two-slit interference experiment with highly charged particles which argues that the consistency of elementary quantum mechanics requires that the electromagnetic field must be quantized. In the experiment a particle's path through the slits is determined by measuring the Coulomb field that it produces at large distances; under these conditions the interference pattern must be suppressed. The key is that, as the particle's trajectory is bent in diffraction by the slits, it must radiate and the radiation must carry away phase information. Thus, the radiation field must be a quantized dynamical degree of freedom. However, if one similarly tries to determine the path of a massive particle through an inferometer by measuring the Newtonian gravitational potential the particle produces, the interference pattern would have to be finer than the Planck length and thus indiscernible. Unlike for the electromagnetic field, Bohr's argument does not imply that the gravitational field must be quantized.