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Register a new userDemonstration of three-photon de Broglie wavelength by projection 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.
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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.
We propose and demonstrate experimentally a projection scheme to measure the quantum phase with a precision beating the standard quantum limit. The initial input state is a twin Fock state $|N,N>$ proposed by Holland and Burnett [Phys. Rev. Lett. {bf 71}, 1355 (1993)] but the phase information is extracted by a quantum state projection measurement. The phase precision is about $1.4/N$ for large photon number $N$, which approaches the Heisenberg limit of 1/N. Experimentally, we employ a four-photon state from type-II parametric down-conversion and achieve a phase uncertainty of $0.291pm 0.001$ beating the standard quantum limit of $1/sqrt{N} = 1/2$ for four photons.
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.
Multi-photon interference is at the heart of the recently proposed linear optical quantum computing scheme and plays an essential role in many protocols in quantum information. Indistinguishability is what leads to the effect of quantum interference. Optical interferometers such as Michaelson interferometer provide a measure for second-order coherence at one-photon level and Hong-Ou-Mandel interferometer was widely employed to describe two-photon entanglement and indistinguishability. However, there is not an effective way for a system of more than two photons. Recently, a new interferometric scheme was proposed to quantify the degree of multi-photon distinguishability. Here we report an experiment to implement the scheme for three-photon case. We are able to generate three photons with different degrees of temporal distinguishability and demonstrate how to characterize them by the visibility of three-photon interference. This method of quantitative description of multi-photon indistinguishability will have practical implications in the implementation of quantum information protocols.
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