Some modified two-slit interference experiments were carried out showing an apparent paradox in wave-particle duality. In a typical such experiment, the screen, where the interference pattern is supposed to be formed, is replaced by a converging lens. The converging lens forms the images of the two slits at two spatially separated detectors. It was claimed that each of these two detectors give information about which slit a photon came from, even though they come from the region of interference. These experiments generated a lot of debate. The various refutations pointed out that the controversial claims involved some questionable assumptions. However the refutations were largely philosophical in nature, and one may like to substantiate those with arguments which are testable, at least in principle. Here such an experiment is theoretically analyzed by introducing path markers which are two orthogonal polarization states of the photon. Analyzing the polarization at the two detectors shows that the photons which give rise to interference, and reach a particular detector, always come from both the slits. This provides clarity in understanding such experiments by making use of testable quantum correlations.
Some modified two-slit interference experiments claim to demonstrate a violation of Bohr's complementarity principle. A typical such experiment is theoretically analyzed using wave-packet dynamics. The flaw in the analysis of such experiments is pointed out and it is demonstrated that they do not violate complementarity. In addition, it is quite generally proved that if the state of a particle is such that the modulus square of the wave-function yields an interference pattern, then it necessarily loses which-path information.
We report a quantum eraser experiment which actually uses a Young double-slit to create interference. The experiment can be considered an optical analogy of an experiment proposed by Scully, Englert and Walther. One photon of an entangled pair is incident on a Young double-slit of appropriate dimensions to create an interference pattern in a distant detection region. Quarter-wave plates, oriented so that their fast axes are orthogonal, are placed in front of each slit to serve as which-path markers. The quarter-wave plates mark the polarization of the interfering photon and thus destroy the in…
We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down conversion process, is prepared in a maximally entangled polarization state. A birefringent double-slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled not gate that couples the polarization with the transversal momentum of these photons. The other photon, that acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interf…
A modified double slit experiment of light was implemented. In the experiment, a spatial shape filter is used to manipulate the shape of cross section of laser beam. When this modified laser beam was shined on the double slit, the intensity distribution of laser beam on double slit is asymmetrical. In this way, the laser light was directed to pass through only one or two slits of double slit in different sections. So the which-way information is predetermined before the photons pass through the slits. At the same time, the visible interference pattern can be observed on a monitor screen after …
Recently Kastner has analyzed the issue of visibility in a modified two-slit experiment carried out by Afshar et al, which has been a subject of much debate. Kastner describes a thought experiment which is claimed to show interference with hundred percent visibility and also an "apparent" which-slit information. We argue that this thought experiment does not show interference at all, and is thus not applicable to the Afshar experiment.
Discussions about quantum interference, indistinguishability and superpostion between quantum states goes back to the beginning of quantum mechanics, but the theoretical problem concerning quantitative measures for quantum coherence was only recently solved by Baumgratz et al. [Phys. Rev. Lett. 113 140401 (2014)]. Since then many works have explored one of the possible coherence measures, the l1 norm, which has not yet been experimentally obtained for spatial photonic states in high dimensions. In this article we study states prepared with photons crossing multiple slits and implement the theo…
Fringe visibility and which-way information in Young's double slit experiments with light scattered from single atoms
Massachusetts Institute of Technology（麻省理工学院）；Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；MIT-Harvard Center for Ultracold Atoms（麻省理工学院-哈佛超冷原子中心）
A modified version of Young's experiment by Shahriar Afshar indirectly reveals the presence of a fully articulated interference pattern prior to the post-selection of a particle in a "which-slit" basis. While this experiment does not constitute a violation of Bohr's Complementarity Principle as claimed by Afshar, both he and many of his critics incorrectly assume that a commonly used relationship between visibility parameter V and "which-way" parameter K has crucial relevance to his experiment. It is argued here that this relationship does not apply to this experimental situation and that it i…
A double-slit experiment with entangled photons is theoretically analyzed. It is shown that, under suitable conditions, two entangled photons of wavelength $λ$ can behave like a \emph{biphoton} of wavelength $λ/2$. The interference of these biphotons, passing through a double-slit can be obtained by detecting both photons of the pair at the same position. This is in agreement with the results of an earlier experiment. More interestingly, we show that even if the two entangled photons are separated by a polarizing beam splitter, they can still behave like a biphoton of wavelength $λ/2$. In this…
We propose a new setup to demonstrate quantum eraser, using spin-1/2 particles in a modified Stern-Gerlach setup, with a double slit. The "which-way" information can be erased simply by applying a transverse magnetic field with an additional magnet, resulting in the emergence of two complementary staggered interference patterns. Use of the classic Stern-Gerlach setup, and the unweaving of the washed out interference without any coincident counting, is what makes this proposal novel.
Summary. A modified version of the two-slit experiment is proposed in which the moveable detector/counter used to obtain the fringe distribution by counting single photons at different positions on the screen plane is replaced with a mirror positioned at an angle to the screen plane. A single photon arriving at the mirror through one of the slits is reflected at one of two angles along one of two divergent paths. It is then detected by one of two detectors, one on each of the paths, for different positions of the mirror on the screen plane. This modification results in the ability to generate …
The generally accepted view in quantum theory is that information about which way the quantum system traveled and interference visibility are complementary. In all which-way experiments, however, an intervention takes place in the interference process in order to determine which way the quantum system took. This intervention can imply the tagging of a which-way marker to a quantum system or, for instance, blocking off one of the paths in a Mach-Zehnder interferometer so that one indirectly knows that the quantum system took the other (open) path. It is, however, this intervention that destroys…
The Afshar experiment is a relatively simple two-slit experiment with results that appear to show a discrepancy with the predictions of Bohr's Principle of Complementarity. We report on the results of a calculation using a simpler but equivalent set-up called the modified Afshar experiment. Numerical results are in agreement with the experimental results performed on the Afshar experiment set-up. Calculations show that the level of which-way information and visibility in the Afshar experiement is higher than originally estimated.
It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector componen…
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…
In an analysis of the Afshar experiment R.E. Kastner points out that the selection system used in this experiment randomly separates the photons that go to the detectors, and therefore no which-way information is obtained. In this paper we present a modified but equivalent version of the Afshar experiment that does not contain a selection device. The double-slit is replaced by two separate coherent laser beams that overlap under a small angle. At the intersection of the beams an interference pattern can be inferred in a non-perturbative manner, which confirms the existence of a superposition s…
NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and $b$ are single particle states) have been used for predicting violations of hidden-variable theories (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state/Bose-Einstein condensates as sources in a modified Mach Zender interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is the total number of particles in the two condens…
We propose and analyze a modified ghost-interference experiment, and show that revealing the particle-nature of a particle passing through a double-slit hides the wave-nature of a spatially separated particle which it is entangled with. We derive a nonlocal duality relation, ${\mathcal D}_1^2 + {\mathcal V}_2^2 \le 1$, which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohr's principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brin…
We present a theoretical model which allows to keep track of all photons in an interferometer. The model is implemented in a numerical scheme, and we simulate photon interference measurements on one, two, four, and eight slits. Measurements are simulated for the high intensity regime, where we show that our simulations describe all experimental results so far. With a slightly modified concept we can also model interference experiments in the low intensity regime, these experiments have recently been performed with single molecules. Finally, we predict the result of polarization measurements, w…
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 eras…
Quantum trajectory-based descriptions of interference between two coherent stationary waves in a double-slit experiment are presented, as given by the de Broglie-Bohm (dBB) and modified de Broglie-Bohm (MdBB) formulations of quantum mechanics. In the dBB trajectory representation, interference between two spreading wave packets can be shown also as resulting from motion of particles. But a trajectory explanation for interference between stationary states is so far not available in this scheme. We show that both the dBB and MdBB trajectories are capable of producing the interference pattern for…
NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and $b$ are single particle states) have been used for predicting violations of local realism (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state Bose-Einstein condensates as sources in a modified Mach-Zehnder interferometer can lead to the creation of the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$ is a subset of the total number of particles in the two conde…
We study the quantum communication protocol of remote state preparation (RSP) for pure states of qubits encoded in single photons transmitted through a double slit, the so-called spatial qubits. Two measurement strategies that one can adopt to remotely prepare the states are discussed. The first strategy is the well-known spatial postselection, where a single-pixel detector measures the transverse position of the photon between the focal and the image plane of a lens. The second strategy, proposed by ourselves, is a generalized measurement divided into two steps: the implementation of a two-ou…
