Delayed-choice Experiment Research Articles

Philosophical Aspects of Time in Modern Physics

In classical physics, the concept of time appeared to be well-understood. With space, it provided a kind of stage where the events followed each other in an orderly way. The introduction of relativity and quantum mechanics profoundly changed this intuitive view. To address these challenges, the Aristotelian vision of time and the now is a promising starting point. His approach is compatible with the absence of absolute time and time's granularity, required by relativity and quantum mechanics, respectively. Several issues, like Einstein’s point coincidence argument and Wheeler's delayed choice experiment, enter the discussion. The Aristotelian approach appears to lead to a novel understanding of time in modern physics.

Delayed choice experiments: an analysis in forward time

In this article, we present a detailed analysis of two famous delayed choice experiments: Wheeler’s classic gedanken-experiment and the delayed quantum eraser. Our analysis shows that the outcomes of both experiments can be fully explained on the basis of the information collected during the experiments using textbook quantum mechanics only. At no point in the argument, information from the future is needed to explain what happens next. In fact, more is true: for both experiments, we show, in a strictly mathematical way, that a modified version in which the time-ordering of the steps is changed to avoid the delayed choice leads to exactly the same final state. In this operational sense, the scenarios are completely equivalent in terms of conclusions that can be drawn from their outcomes.

Proposal for sequential Stern–Gerlach experiment with programmable quantum processors

The historical significance of the Stern–Gerlach (SG) experiment lies in its provision of the initial evidence for space quantization. Over time, its sequential form has evolved into an elegant paradigm that effectively illustrates the fundamental principles of quantum theory. To date, the practical implementation of the sequential SG experiment has not been fully achieved. In this study, we demonstrate the capability of programmable quantum processors to simulate the sequential SG experiment. The specific parametric shallow quantum circuits, which are suitable for the limitations of current noisy quantum hardware, are given to replicate the functionality of SG devices with the ability to perform measurements in different directions. Surprisingly, it has been demonstrated that Wigner’s SG interferometer can be readily implemented in our sequential quantum circuit. With the utilization of the identical circuits, it is also feasible to implement Wheeler’s delayed-choice experiment. We propose the utilization of cross-shaped programmable quantum processors to showcase sequential experiments, and the simulation results demonstrate a strong alignment with theoretical predictions. With the rapid advancement of cloud-based quantum computing, such as BAQIS Quafu, it is our belief that the proposed solution is well-suited for deployment on the cloud, allowing for public accessibility. Our findings not only expand the potential applications of quantum computers, but also contribute to a deeper comprehension of the fundamental principles underlying quantum theory.

Why interference phenomena do not capture the essence of quantum theory

Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued that basic interference phenomena force us to accept a number of radical interpretational conclusions, including: that a photon is neither a particle nor a wave but rather a Jekyll-and-Hyde sort of entity that toggles between the two possibilities, that reality is observer-dependent, and that systems either do not have properties prior to measurements or else have properties that are subject to nonlocal or backwards-in-time causal influences. In this work, we show that such conclusions are not, in fact, forced on us by basic interference phenomena. We do so by describing an alternative to quantum theory, a statistical theory of a classical discrete field (the `toy field theory') that reproduces the relevant phenomenology of quantum interference while rejecting these radical interpretational claims. It also reproduces a number of related interference experiments that are thought to support these interpretational claims, such as the Elitzur-Vaidman bomb tester, Wheeler's delayed-choice experiment, and the quantum eraser experiment. The systems in the toy field theory are field modes, each of which possesses, at all times, both a particle-like property (a discrete occupation number) and a wave-like property (a discrete phase). Although these two properties are jointly possessed, the theory stipulates that they cannot be jointly known. The phenomenology that is generally cited in favour of nonlocal or backwards-in-time causal influences ends up being explained in terms of inferences about distant or past systems, and all that is observer-dependent is the observer's knowledge of reality, not reality itself.

Observations of the delayed-choice quantum eraser using coherent photons

Quantum superposition is the cornerstone of quantum mechanics, where interference fringes originate in the self-interference of a single photon via indistinguishable photon characteristics. Wheeler’s delayed-choice experiments have been extensively studied for the wave-particle duality over the last several decades to understand the complementarity theory of quantum mechanics. The heart of the delayed-choice quantum eraser is in the mutually exclusive quantum feature violating the cause-effect relation. Here, we experimentally demonstrate the quantum eraser using coherent photon pairs by the delayed choice of a polarizer placed out of the interferometer. Coherence solutions of the observed quantum eraser are derived from a typical Mach–Zehnder interferometer, where the violation of the cause-effect relation is due to selective measurements of basis choice.

Aspects of wave-particle complementarity in quantum delayed-choice experiments

Quantum delayed-choice experiments are designed to probe the robustness of the complementarity principle. In this proceeding, we revisit the main ideas reported recently in Ref. [Commun. Phys. 5, 82 (2022)] concerning a setup (quantum-controlled reality experiment) that has the same final visibility as the quantum version of Wheeler’s delayed-choice arrangement. Besides the same final statistics, upon an operational criterion of physical realism, the authors claimed a different state of affairs for the wave-and-particle behavior in delayed-choice experiments. To this end, we put forward an analysis by employing the relative entropy of coherence to study how the local wave and particle coherences when the system is traveling inside the interferometer change accordingly to the final observed visibility.

Photon’s Spin Mechanism and Wave-Particle Hybrid Structure. It Exhibits both Wave Property and Particle Property at the Same Time in all Experiments.

The interpretation of single photon double slits Wheeler's delayed choice experiment leads to a weird inference: "what the observer does now can change what happened in the past". It subverts our cognitions. Other interpretations are also in dispute. Is there another possible way that can better explain experiments? For this purpose, we try to reacquaint what is a photon? What structure does it have? How does the structure influence the photon behavior? In 1905 Einstein supposed that the photon is a quantum of EM radiation; according to the quantum interpretation, the probability density of a coherent state undergoes a sinusoidal vibration with time. It will also excite a quantized EM wave. So, our research object must be an EM wave beams. We discover and prove that under the Quantification Law of Charge, there is a kind of axial symmetric EM-wave beam it is a quantum of circularly polarized light. Its energy is concentrated in a very small packet; this energy packet will be proved having the photon properties, like , , spin , obeying B-E statistics and so on; On the other hand, the width of the sodium spectral lines identifies that the energy packet carries a long EM wave beam. They form a wave-particle hybrid structure. It exhibits both wave property and particle property at the time in all experiments. Its interpretation for the single photon double slits Wheeler's delayed choice experiment does not lead to the above strange inference.

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.

The ‘pliable character’ might be the reason for wave-particle duality of light

The delayed-choice experiment is one of the best ways to illustrate the wave-particle duality. The consequences of a quantum delayed-choice experiment have shown that the photon can exhibit dual nature through morphing. There are no hidden variable theories; that can assert the real identities of a photon being a wave and a particle. An open question can emerge, what is the fundamental reason for a photon exposing dual nature. Meanwhile, the recent investigation on photon’s ‘illusive nature’ expounds the apparently unrevealed phenomena like mass posing (zero, real-valued and imaginary rest mass), hidden energy, complex momentum form, and photon possesses this nature for wave-particle duality. The ‘illusive nature’ could interpret why photon does not hold fixed rest mass like another fundamental particles. This article will find out the cause of wave-particle duality from the outcomes of quantum delayed-choice experiments and the ‘illusive nature’ of photons. Furthermore, we will figure out a correlation between dual nature and ‘illusive nature’. Indeed, a photon might manifest dual nature due to its ‘pliable nature’.

Photon Wave-particle Hybrid Structure and Wheeler’s Single Photon Double-slit Delayed Choice Experiment

The interpretation of single-photon double slit Wheeler's delayed choice experiment leads to a weird inference: "what observer does now can change what happened in the past". It subverts our cognitions. Other interpretations are also in dispute. I try to find another possible way that can better explain the experiments. For this purpose, we try to reacquaint what is a photon; what structure it possesses, and how the structure influences photon behavior. In 1905 Einstein supposed that the photon is a quantum of EM radiation; according to the quantum interpretation, the probability density of a coherent state undergoes a sinusoidal vibration with time; it will also excite a quantized EM wave. So we start our research from an axially symmetric EM wave beam. We discovered and proved that under the Quantification Law of Charge, there is a kind of axially symmetric EM-wave beam which is a quantum of circularly polarized light. Its energy is concentrated in a very small packet; this energy packet will be proven to have photon properties, like,, spin , obeying B-E statistics, etc. On the other hand, the width of the sodium spectral lines identifies that the energy packet carries a long EM wave beam. They form a wave-particle hybrid structure. It exhibits both wave property and particle property all the time in the experiments. Its interpretation for the single photon double slits Wheeler's delayed choice experiment does not lead to the above strange inference.

Macroscopic delayed choice and retrocausality: Quantum eraser, Leggett-Garg, and dimension witness tests with cat states

We propose delayed choice experiments carried out with macroscopic qubits, realised as macroscopically-distinct coherent states $|\alpha\rangle$ and $|-\alpha\rangle$. Quantum superpositions of $|\alpha\rangle$ and $|-\alpha\rangle$ are created via a unitary interaction $U(\theta)$ based on a nonlinear Hamiltonian. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality (MrC). We therefore consider weak macroscopic realism (wMR), which specifies a hidden variable $\lambda_{\theta}$ to determine the macroscopic qubit value (analogous to 'which-way' information), independent of any future measurement setting $\phi$. Using entangled states, we demonstrate a quantum eraser where the choice to measure a which-way or wave-type property is delayed. Consistency with wMR is possible, if we interpret the macroscopic qubit value to be determined by $\lambda_{\theta}$ without specification of the state at the level of $\hbar$, where fringes manifest. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the dimension witness inequality applied to the Wheeler-Chaves-Lemos-Pienaar experiment, where measurements need only distinguish the macroscopic qubit states. This negates all two-dimensional non-retrocausal models, thereby suggesting MrC. However, one can interpret consistently with wMR, thus avoiding MrC, by noting extra dimensions, and by noting that the violations require further unitary dynamics $U$ for each system. The violations are then explained as failure of deterministic macroscopic realism (dMR), which specifies validity of $\lambda_{\theta}$ prior to the dynamics $U(\theta)$ determining the measurement setting $\theta$. Finally, although there is consistency with wMR for macroscopic observations, we demonstrate EPR paradoxes at a microscopic level.

The wave function as a true ensemble.

In quantum mechanics, the wave function predicts probabilities of possible measurement outcomes, but not which individual outcome is realized in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which reproduce quantum mechanics violate statistical independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur–Vaidman bomb detector and the extended Wigner’s friends scenario.

Experimental assessment of physical realism in a quantum-controlled device

Bohr’s complementarity principle has been challenged by quantum delayed-choice experiments wherein quantum systems are claimed to behave neither as wave nor as a particle, but in an intermediary way. However, this conclusion has been supported by retro-inference and with no direct link with the system quantum state. Here, we consider a framework that employs an operational criterion of physical reality to diagnosis the system ontology directly from the quantum state at each instant of time. We show that, in disparity with previous proposals, our setup ensures a formal link between the output visibility and elements of reality within the interferometer. An experimental proof-of-principle is provided for a two-spin-1/2 system in an interferometric setup implemented in a nuclear magnetic resonance platform. We discuss how our results validate, to a great extent, Bohr’s original formulation of the complementarity principle and unveil morphing reality states.

Observing wave–particle behavior of entangled atoms in cavity assisted delayed-choice experiment

A scheme is proposed to study the wave–particle duality of two entangled atoms in a cavity-QED framework. Two atoms may exhibit a mutating trend between particle and wave behaviors. This mutating behavior can be post-selected after the atomic states have been recorded on the state selective detectors. In the present proposal, second Hadamard transformation is always present, whereas the probabilities are the same as that in the case, where the state of the second Hadamard can be controlled by an ancilla. The whole scheme revolves around resonant, off-resonant, and Ramsey interactions of two level atoms with the field. To observe the desired behavior, cavity assisted atom-field multiple swappings are employed for tagging as well as for the better control and good fidelity.

Wheeler’s delayed-choice experiment based on Rydberg atoms

The delayed choice gedanken-experiment initially proposed by J A Wheeler reveals the nontrivial features of wave–particle duality in quantum world, that is, the choice of whether to observe the particle/wave character of a quantum system at a delayed time can affect its evolution history. In this work, the Wheeler’s delayed-choice experiment is conducted and tested in a new regime based on a Rydberg-ground level atomic Mach–Zehnder interferometer with optical coherent manipulation. Our quantum system exhibits an excellent single-excitation of the collective atomic state due to the Rydberg blockade effect, and the delayed choice of the interferometer configuration is realized by a quantum random number generator based on high-quality Rydberg single-photon source. Our experimental results demonstrate the Wheeler’s nontrivial time order inversion in this quantum system and confirm the Copenhagen interpretation of the physical reality of quantum state, which means the particle/wave character can only be ascribed to a quantum system when it was measured. This work is encouraging toward testing the foundations of quantum mechanics using the Rydberg atoms.

Mathematical Relation between Concurrence and Intensity of a Photon in the Quantum Delayed-Choice Experiment

I provide the explicit mathematical expression of the correlation between concurrence and the intensity of a photon in the quantum delayed-choice experiment. This shows us that one may observe the wave-particle duality and entanglement simultaneously.

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.

Optical beam splitter, Mach\u2013Zehnder interferometer and the delayed choice issue

John Wheeler's delayed choice thought experiment is often invoked in discussions of the wave-particle duality of quantum physics. Every so often interpretations are offered that do not restrict to straight physics. The key element of the 'Gedankenexperiment' is a Mach–Zehnder interferometer composed of two optical beam splitters. The quantum description of these devices and the treatment of delayed choice experiment in the framework of quantum optics are discussed here.

Modified quantum delayed-choice experiment without quantum control or entanglement assistance

Wheeler's delayed-choice experiment delays the decision to observe either the wave or particle behavior of a photon until after it has entered the interferometer, and the quantum delayed-choice experiment provides the possibility of observing the wave and particle behaviors with a single experimental setup by introducing quantum control. We here propose a modified quantum delayed-choice experiment without quantum control or entanglement assistance, in which a photon can be prepared in a wave-particle superposition state and the morphing behavior of wave-to-particle transition can be observed easily. It is demonstrated that the presented scheme can allow us to rule out classical hidden-variable models in a device-independent manner via violating dimension witness. We also extend the scheme to the situation of two degrees of freedom, first constructing a hybrid quantum delayed-choice experiment which enables a photon respectively exhibits wave and particle behaviors in different degrees of freedom, and then proposing a scheme to prepare the single-photon wave-particle entanglement. This study is not only meaningful to explore the wave-particle complementarity of photons, but also provides potential for the research of the single-particle nonlocality from the perspective of the wave-particle degree of freedom.

The Delayed-Choice Quantum Eraser Leaves No Choice

A realizable delayed-choice quantum eraser, using a modified Mach-Zehnder (MZ) interferometer and polarization entangled photons, is theoretically analyzed here. The signal photon goes through a modified MZ interferometer, and the polarization of the idler photon provides path information for the signal photon. The setup is very similar to the delayed-choice quantum eraser experimentally studied by the Vienna group. In the class of quantum erasers with discrete output states, it is easy to see that the delayed mode leaves no choice for the experimenter. The which-way information is always erased, and every detected signal photon fixes the polarization state of the idler, and thus gives information on precisely how the signal photon traversed the two paths. The analysis shows that the Vienna delayed-choice quantum eraser is the first experimental demonstration of the fact that the delayed mode leaves no choice for the experimenter, and the which-way information is always erased. Additionally it is shown that this argument holds even in a conventional two-slit quantum eraser. Every photon registered anywhere on the screen, fixes the state of the two-state which-way detector in a unique mutually unbiased basis. In the delayed-choice quantum eraser experiments, the role of mutually unbiased basis sets for the which-way detector, has been overlooked till now.