John F. Clauser, Jonathan P. Dowling
We show that a Young's N slit interferometer can be used to factor the integer N. The device could factor four- or five-digit numbers in a practical fashion. This work shows how number theory may arise in physical problems, and may provide some insight as to how quantum computers can carry out factoring problems by interferometric means.
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The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for factoring $N$ by means of an N-slit interference experiment is translated into an experiment with a single Mach-Zehnder interferometer. With dispersive phase shifters the ratio of the coherence length to wavelength limits the numbers that can be factored. A conservative estimate permits $N \approx 10^7$. It is furthermore shown, that sine and cosine Fourier coefficients of a real periodic function can be obtained with such an interferometer.
Quantum theory of interference phenomena does not take the diameter of the particle into account, since particles were much smaller than the width of the slits in early observations. In recent experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, analytical description of these cases should include a finite particle size. The generic quantum interference setup is an asymmetric double slit interferometer. We evaluate the wave function of the particle transverse motion using two forms of the solution of Schrodinger's equation in an asymm…
Superposition principle of wave function in multi-slit interference experiment has been widely accepted by many quantum mechanics textbooks, however the expression ${ψ_{AB}} = {ψ_A} + {ψ_B}$ does not strictly hold. The non-classical paths in Feynman path integral provide an explanation to the multi-path interference effect, and can be used to quantitatively analyse the multi-slit interference effect. In this work, we apply quantities in Bohmian mechanics to the measurement of multi-order interference by analysing the contribution of non-classical paths to Bohmian velocity in electron's multi-s…
Kocsis et al. (Science, Reports 3 June 2011, p. 1170) state that the experimentally deduced average photon trajectories are identical to the particle trajectories of Bohm's quantum mechanics. No supporting evidence, however, was provided. The photon trajectories presented in their report do not converge to high probability regions, a familiar and necessary behavior of Bohm trajectories. We reanalyze their data and calculations, conclude that the average photon trajectories do indeed agree with Bohm, and discuss possible interpretations of this result.
Coherence spectroscopy by the Nth power of the measured signal in an interferometer overcoming the diffraction limit
本研究提出对N缝干涉仪的测量信号强度取K次方的方法，在满足散粒噪声极限下突破N缝干涉仪分辨率极限，可应用于现有光谱设备，还能突破量子计量学中的超分辨率极限。
We construct an analog computer based on light interference to encode the hyperbolic function f(ζ) = 1/ζ into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.
We describe a new and distinctive interferometry in which a probe particle scatters off a superposition of locations of a single free target particle. In one dimension, probe particles incident on superposed locations of a single "mirror" can interfere as if in a Fabry-Perot interferometer; in two dimensions, probe particles scattering off superposed locations of a single "slit" can interfere as if in a two-slit Young interferometer. The condition for interference is loss of orthogonality of the target states and reduces, in simple examples, to transfer of orthogonality from target to probe st…
Complementarity lies at the heart of conceptual foundation of orthodox quantum mechanics. The wave-particle duality makes it impossible to tell which slit each particle passes through and still observe an interference pattern in a Young's double-slit experiment. In this paper, this duality is appraised under the standard formulation of quantum mechanics for atom interferometers. It is found that the internal freedoms like electronic states of an atom can be used to detect the which-path information of each atom while uphold the interference pattern of atoms when the center-of-mass motion of at…
Thought experiments based on the double-slit interferometer had a crucial role to develop ideas concerning the wave-particle duality and the Bohr's complementarity principle. Ideally, a slit with a sufficiently low mass recoils due to the passage of the photon. This motion denounces the path taken by the light and suppresses any attempt to observe an interference pattern. In real life, however, available which-way information in such a setup is significantly impaired by the typical magnitudes of photons and slits, making the verification of the effect almost impossible. Here, we extend this di…
We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well latt…
Quantum superposition is the heart of quantum mechanics as mentioned by Dirac and Feynman. In an interferometric system, single photon self-interference has been intensively studied over the last several decades in both quantum and classical regimes. In Born rule tests, the Sorkin parameter indicates the maximum number of possible quantum superposition allowed to the input photons entering an interferometer, where multi-photon interference fringe is equivalent to that of a classical version by a laser. Here, an attenuated laser light in a quantum regime is investigated for self-interference in…
Detector-Conditioned Source-Space Nulls and Null-Mask Loss in a Programmable Two-Slit Interferometer
通过时间反演Young-Afshar配置，将零测试转移到源标签平面，提出探测器条件源空间零点概念，并引入零掩模损耗，分析其与路径可区分性的对偶关系。
Squeezed-slit Bohr-Einstein Interferometer
通过主动量子态工程制备单原子狭缝的压缩态，超越标准量子极限，实现高可见度干涉，并揭示克尔诱导的非高斯动力学。
We introduce a simple experiment involving a double-slit interferometer by which one can learn basic concepts of quantum interference such as which-path marking, quantum erasers, and geometric phases. Each of them exhibits seemingly mysterious phenomena in quantum physics. In our experiment, we use the double-slit interference of visible light with the polarization as an internal state to demonstrate the disappearance of fringes by which-path marking, recovery of interference using quantum erasers, and the rapid shifting of the fringe pattern induced by the geometric phase. We also present a s…
Tunable Einstein-Bohr recoiling-slit gedankenexperiment at the quantum limit
本文利用光镊中三维冷却至运动基态的单原子，忠实实现了爱因斯坦-玻尔可移动缝隙干涉仪，通过动态调谐原子动量波函数证明了其量子本质，并揭示了由原子加热和进动导致的量子到经典转变。
A Bose-Einstein "double-slit" interferometer has been recently realized experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We analyze the interferometric steps by solving numerically the time-dependent Gross-Pitaevski equation in three-dimensional space. We focus on the adiabaticity time scales of the problem and on the creation of spurious collective excitations as a possible source of the strong dephasing observed experimentally. The role of quantum fluctuations is discussed.
We provide an analytical and theoretical study of exotic looped trajectories (ELTs) in a double-slit interferometer with quantum marking. We use an excited Rydberg-like atom and which-way detectors such as superconducting cavities, just as in the Scully-Englert-Walther interferometer. We indicate appropriate conditions on the atomic beam or superconducting cavities so that we determine an interference pattern and fringe visibility exclusive from the ELTs. We quantitatively describe our results for Rubidium atoms and propose this framework as an alternative scheme to the double-slit experiment …
A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to produce a computational result is stored in the phase shifts of the 2^n arms. They can be detected by interferometry that allows us to utilize quantum parallelism. Quantum algorithms are accountable for what interferometers to be constructed to compute particular problems. A standard formalism for constructing the arms has been developed by the extension of cla…
Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a one-to-one relationship. As a result the identification of factors by the maxima is unique. However, for non-integer arguments such as rational numbers this powerful instrument to find factors breaks down. We develop new strategies for factoring numbers using Gauss sums at rational arguments. This approach may find application in a recent suggestion to factor numbe…
Single-slit and two-slit interferometer measurements of electrons are analyzed within the realistic model of particle propagation. In a step by step procedure we show that all current models of interference are essentially non-local and demonstrate that the treatment of the quantum theory of motion is the simplest model for the scalar problem. In particular we give a novel interpretation of the quantum potential Q, which should be regarded as a non-classical and essentially statistical term describing the changes of the quantum ensemble due to a change of the physical environment.
Young double-slit interference with single hard x-ray photons
本研究使用25 keV硬X射线在同步辐射光源进行杨氏双缝干涉实验，通过单光子计数和百万帧叠加成功观测到干涉图样，并客观估计了识别干涉所需的最小光子数，旨在探索低剂量医学X射线相位对比成像的可行性。
The experimental results of Kocsis et al., Mahler et al. and the proposed experiments of Morley et al. show that it is possible to construct "trajectories" in interference regions in a two-slit interferometer. These results call for a theoretical re-appraisal of the notion of a "quantum trajectory" first introduced by Dirac and in the present paper we re-examine this notion from the Bohm perspective based on Hamiltonian flows. In particular, we examine the short-time propagator and the role that the quantum potential plays in determining the form of these trajectories. These trajectories diffe…
Quantum computing (QC) architectures utilizing classical or coherent resources with Gaussian transformations are classically simulable as an indicator of the lack of QC power. Simple optical set-ups utilizing wave-particle duality and interferometers achieve QC speed-up with the cost of exponential complexity of resources in time, space or energy. However, linear optical networks composed of single photon inputs and photon number measurements such as boson sampling achieve solving problems which are not efficiently solvable by classical computers while emphasizing the power of linear optics. I…
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