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Register a new userObservation of Four-Photon de Broglie Wavelength by State Projection Measurement
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A measurement process is constructed to project an arbitrary two-mode $N$-photon state to a maximally entangled $N$-photon state (the {it NOON}-state). The result of this projection measurement shows a typical interference fringe with an $N$-photon de Broglie wavelength. For an experimental demonstration, this measurement process is applied to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. Generalization to arbitrary $N$-photon states projection measurement can be easily made and may have wide applications in quantum information. As an example, we formulate it for precision phase measurement.
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Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on the proposal by Wang and Kobayashi (Phys. Rev. A {bf 71}, 021802) that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON state projection measurement to three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON state contribution in these schemes of projection measurement.
Recently, a new interpretation of quantum mechanics has been developed for the wave nature of a photon, where determinacy in quantum correlations becomes an inherent property without the violation of quantum mechanics. Here, we experimentally demonstrate a direct proof of the wave natures of quantum correlation for the so-called coherence de Broglie waves (CBWs) using sub-Poisson distributed coherent photon pairs obtained from an attenuated laser. The observed experimental data coincides with the analytic solutions and the numerical calculations. Thus, the CBWs pave a road toward deterministic and macroscopic quantum technologies for such as quantum metrology, quantum sensing, and even quantum communications, that are otherwise heavily limited due to the microscopic non-determinacy of the particle nature-based quantum mechanics.
A usual assumption in the so-called {it de Broglie - Bohm} approach to quantum dynamics is that the quantum trajectories subject to typical `guiding wavefunctions turn to be quite irregular, i.e. {it chaotic} (in the dynamical systems sense). In the present paper, we consider mainly cases in which the quantum trajectories are {it ordered}, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a H{e}non - Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie - Bohm formalism, namely the influence of order in the so-called {it quantum relaxation} effect. We show that the existence of regular trajectories poses restrictions to the quantum relaxation process, and we give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.
An experiment is performed to demonstrate the temporal distinguishability of a four-photon state and a six-photon state, both from parametric down-conversion. The experiment is based on a multi-photon interference scheme in a recent discovered NOON-state projection measurement. By measuring the visibility of the interference dip, we can distinguish the various scenarios in the temporal distribution of the pairs and thus quantitatively determine the degree of temporal (in)distinguishability of a multi-photon state.
Quantum mechanically, multiple particles can jointly be in a coherent superposition of two or more different states at the same time. This property is called quantum entanglement, and gives rise to characteristic nonlocal interference and stays at the heart of quantum information process. Here, rather than interference of different intrinsic properties of particles, we experimentally demonstrated coherent superposition of two different birthplaces of a four-photon state. The quantum state is created in four probabilistic photon-pair sources, two combinations of which can create photon quadruplets. Coherent elimination and revival of distributed 4-photons can be fully controlled by tuning a phase. The stringent coherence requirements are met by using a silicon-based integrated photonic chip that contains four spiral waveguides for producing photon pairs via spontaneous four-wave mixing. The experiment gives rise to peculiar nonlocal phenomena without any obvious involvement of entanglement. Besides several potential applications that exploit the new on-chip technology, it opens up the possibility for fundamental studies on nonlocality with spatially separated locations.
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