Double-slit Apparatus Research Articles

Dynamics, locality and weak measurements: trajectories and which-way information in the case of a simplified double-slit setup

Dynamics, locality and weak measurements: trajectories and which-way information in the case of a simplified double-slit setup

Plasmon echoes and polarization dynamics in Young's double-slit setup with pulsed light

We consider two closely spaced slits of subwavelength width, pierced in a metal screen, that are illuminated by short, arbitrarily polarized, plane-wave pulses. The $p$-polarized component generates plasmonic pulses propagating on the metal surface between the slits. In addition to the primary transmitted pulses, scattering of the plasmonic pulses by the opposite slit is found to produce secondary (echo) radiation pulses, which causes splitting, shaping, and time-dependent polarization modulation of the radiated pulses in the far field. We study these effects in the linear regime. A previously explored phenomenological model is extended to the time domain and is validated by rigorous numerical calculations. Our analytical and numerical results have implications for the transmission of pulsed light through arrangements of nanoscale apertures with plasmonic coupling.

Proposal to observe path superpositions in a double-slit setup

The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wave function having gone through both slits. In the path integral formulation, this interference involves a superposition of paths, going through either slit, linking the source to the detection point. We show how these paths superpositions can in principle be observed by implementing a series of minimally perturbing weak measurements between the slits and the detection plane. We further propose a simplified protocol in order to observe these ``weak trajectories'' with single photons.

Biphoton phase-space correlations from Gouy-phase measurements using double slits

Quantum correlations encoded in photonic Laguerre-Gaussian modes were shown to be related to the Gouy-phase shifts [Kawase et al., Phys. Rev. Lett. 101, 050501 (2008)], allowing for a nondestructive manipulation of photonic quantum states. In this work, we exploit the relation between phase-space correlations of biphotons produced by spontaneously parametric down-conversion (SPDC) as encoded in the logarithmic negativity (LN) and the Gouy phase as they are diffracted through an asymmetrical double-slit setup. Using an analytical approach based on a double-Gaussian approximation for type-I SPDC biphotons, we show that measurements of Gouy-phase differences provide information on their phase-space entanglement variation, governed by the physical parameters of the experiment and expressed by the LN via covariance matrix elements.

Polarization modulation by surface plasmons in Young's double-slit setup

A simple phenomenological model, justified by rigorous electromagnetic analysis, is used to examine far-field polarization modulation introduced by a metallic screen with two subwavelength slits in uniform, partially polarized illumination. The accuracy of this intuitive model is assessed numerically, by employing the Fourier modal method, as regards the wavelength, the screen metal, and the slit depth, width, and separation. The Stokes parameters and the degree of polarization are evaluated paraxially in the far zone of the slits. We demonstrate that a uniform, partially linearly polarized incident beam can be rendered unpolarized by the nanoslits. Our work provides insight into the pivotal role that surface plasmons have in polarization modulation in photonics.

Resource theory of quantum coherence with probabilistically nondistinguishable pointers and corresponding wave-particle duality

One of the fundamental features of quantum mechanics is the superposition principle, a manifestation of which is embodied in quantum coherence. Coherence of a quantum state is invariably defined with respect to a preferred set of pointer states, and there exist quantum coherence measures with respect to deterministically as well as probabilistically distinguishable sets of quantum state vectors. Here we study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors, that may not even be probabilistically distinguishable. Geometrically, a probabilistically indistinguishable set of quantum state vectors forms a linearly dependent set. We find the free states of the resource theory, and analyze the corresponding free operations, obtaining a necessary condition for an arbitrary quantum operation to be free. We identify a class of measures of the quantum coherence, and in particular establish a monotonicity property of the measures. We find a connection of an arbitrary set of quantum state vectors with positive operator valued measurements with respect to the resource theory being considered, which paves the way for an alternate definition of the free states. We notice that the resource theory of magic can be looked upon as a resource theory of quantum coherence with respect to a set of quantum state vectors that are probabilistically indistinguishable. We subsequently examine the wave-particle duality in a double-slit set-up in which superposition of probabilistically indistinguishable quantum state vectors is possible. Specifically, we report a complementary relation between quantum coherence and path distinguishability in such a set-up.

Irrealism from fringe visibility in matter-wave double-slit interference with initial contractive states

The elements of reality coined by Einstein, Podoslky, and Rosen promoted a series of fundamental discussions involving the notion of quantum correlations and physical realism. The superposition principle applied in the double-slit experiment with matter waves highlights the need for a critical review of the adoption of physical realism in the quantum realm. In this work, we employ a measure of physical irrealism and consider an initial contractive state in the double-slit setup for which position and momentum variables of a single particle are initially correlated. We investigate how the behavior of the irrealism can help us to obtain information about the interference pattern, wavelike, and particle-like properties in the double-slit setup with matter waves. We find that there is a time of propagation that minimizes the irrealism, and around this point the state at the detection screen is squeezed in position and momentum in comparison with the standard Gaussian superposition. Interestingly, we show that the maximum visibility and the number of interference fringes are related to the minimum of the irrealism. Moreover, we demonstrate a monotonic relation between the irrealism and visibility around the time of minimum. Then, we argue how to use these results to indirectly measure the irrealism for position variable from the fringe visibility.

Displacement measurement in a Sagnac interferometer with thermal light second-order correlation

We report a displacement measurement experiment in second-order correlation and subwavelength correlation with thermal light. Our target is a single slit, which is inserted into a Sagnac interferometer to mimic a double-slit apparatus. According to the correlated diffraction pattern, we can predict the excursion of the slit from the optical axis. When the slit is shifted, we can predict the displacement accurately. We also present the mathematical presentations of beam propagation and reflection in comprehensive deduction.

Double-slit interferometry as a lossy beam splitter

We cast diffraction-based interferometry in the framework of post-selected unitary description towards enabling it as a platform for quantum information processing (QIP). We express slit-diffraction as an infinite-dimensional transformation and truncate it to a finite-dimensional transfer matrix by post-selecting modes. Using such a framework with classical fields we show that a customized double-slit setup is effectively a lossy beam splitter in a post-selected sense. Diffraction optics provides a robust alternative to conventional multi-beam interferometry with scope for miniaturization, and also has applications in matter wave interferometry. In this work, the classical treatment of slit-diffraction sets the stage for quantization of fields and implementing higher-dimensional QIP like that done with other platforms such as orbital angular momentum.

Fringe visibility of exotic trajectories for matter waves in a double-slit experiment

We theoretically study the fringe visibility of exotic looped trajectories in double-slit experiments with matter waves. We consider the relative intensity at [Formula: see text] as a function of the time-of-flight from the double-slit to the screen inside the interferometer. This allows us to define a fringe visibility associated with the contribution to the interference pattern given by exotic looped trajectories. We demonstrate that the Sorkin parameter is given in terms of this visibility and of the axial phases which include the Gouy phase. Thus, the effect of exotic looped trajectories can be attested by measuring deviations from unity for the fringe visibility. We show that the effect of exotic trajectories can be increased by adjusting the parameters of the double-slit apparatus in the Fresnel regime.

Observing momentum disturbance in double-slit "which-way" measurements.

Making a "which-way" measurement (WWM) to identify which slit a particle goes through in a double-slit apparatus will reduce the visibility of interference fringes. There has been a long-standing controversy over whether this can be attributed to an uncontrollable momentum transfer. Here, by reconstructing the Bohmian trajectories of single photons, we experimentally obtain the distribution of momentum change. For our WWM, the change we see is not a momentum kick that occurs at the point of the WWM, but rather one that nonclassically accumulates during the propagation of the photons. We further confirm a quantitative relation between the loss of visibility consequent on a WWM and the total (late-time) momentum disturbance. Our results emphasize the role of the Bohmian momentum in giving an intuitive picture of wave-particle duality and complementarity.

Quantum erasure in the near-field

The phenomenon of quantum erasure has shed light on the nature of wave-particle duality and quantum complementarity. A number of quantum erasers have been realized using the far-field diffraction of photons from a Young double-slit apparatus. By marking the path of a photon using an additional degree of freedom, the usual Young interference pattern is destroyed. An appropriate measurement of the system marking the photon’s path allows one to recover the interference pattern. Here quantum erasure is considered in the context of near-field diffraction. To observe interference in the near-field requires the use of two periodic wave functions, so that the usual ‘which way’ marker then becomes a ‘which-wave function’ marker. We determine the propagation distances for which quantum erasure, or more generally the observation of interference between the two periodic wave functions, can be observed. The meaning of wave and particle-like properties in this scenario is discussed. These results could lead to quantum eraser experiments with material particles, for which interference effects are more readily observed in the near-field rather than the far-field.

Time-resolved double-slit interference pattern measurement with entangled photons.

The double-slit experiment strikingly demonstrates the wave-particle duality of quantum objects. In this famous experiment, particles pass one-by-one through a pair of slits and are detected on a distant screen. A distinct wave-like pattern emerges after many discrete particle impacts as if each particle is passing through both slits and interfering with itself. Here we present a temporally- and spatially-resolved measurement of the double-slit interference pattern using single photons. We send single photons through a birefringent double-slit apparatus and use a linear array of single-photon detectors to observe the developing interference pattern. The analysis of the buildup allows us to compare quantum mechanics and the corpuscular model, which aims to explain the mystery of single-particle interference. Finally, we send one photon from an entangled pair through our double-slit setup and show the dependence of the resulting interference pattern on the twin photon's measured state. Our results provide new insight into the dynamics of the buildup process in the double-slit experiment, and can be used as a valuable resource in quantum information applications.

Proposal to Observe the Nonlocality of Bohmian Trajectories with Entangled Photons

Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate this point using a double double-slit setup with path-entangled photons. The Bohmian velocity field for one of the photons can be measured using a recently demonstrated weak-measurement technique. The found velocities strongly depend on the value of a phase shift that is applied to the other photon, potentially at spacelike separation.

A portable double-slit quantum eraser with individual photons

The double-slit experiment has played an important role in physics, from supporting the wave theory of light, via the discussions of the wave–particle duality of light (and matter) to the foundations of modern quantum optics. Today it keeps playing an active role in the context of quantum optics experiments involving single photons. In this paper, we present a truly portable double-slit apparatus which demonstrates both the wave–particle duality of light and the phenomenon of quantum erasing. The device can be operated either with strong laser light and screen projection, or with individual photons, in which case quantum interference and quantum erasing are detected by a photomultiplier whose pulses are rendered acoustically by means of a loudspeaker. Alternatively, the phenomena can be displayed using multimedia projection of oscilloscope traces.

Interférences de type Young avec une source à un seul électron

In the present work we provide experimental evidence for Young-type interferences caused by one single electron acting on a given double-center scatterer which is analogous to an atomic-size double-slit apparatus. The interfering electron is provided by autoionization of a doubly-excited helium atom following the capture of the two H 2 target electrons by a He 2+ incoming projectile ion. In the backward direction, the auto-ionized electron scatters on the two H + centers of the fully ionized target molecule. Here, the auto-ionizing projectile plays the role of a single-electron source, independent of the interferometer provided by the residual two-center target. The present experiment resembles the famous “thought experiment” imagined by Feynman in 1963, in which the quantum nature of the electron is illustrated from a Young-like double-slit experiment. Similarly to the case of Young's experiment with light, the interference effect manifests itself in well defined oscillations in the angular distribution of the scattered electrons. To cite this article: F. Frémont et al., C. R. Physique 9 (2008).

Reduced coherence in double-slit diffraction of neutrons

In diffraction experiments with particle beams, several effects lead to a fringe visibility reduction of the interference pattern. We theoretically describe the intensity one can measure in a double-slit setup and compare the results with the experimental data obtained with cold neutrons. Our conclusion is that for cold neutrons the fringe visibility reduction is due not to decoherence, but to initial incoherence.

Transverse coherence measurement using a folded Michelson interferometer

The transverse coherence of a 1 ps pulsed laser beam was measured using a technique involving a modified Michelson interferometer and separate reference images. Using this technique, the transverse coherence of a selected plane in the laser beam was determined, in this case at the exit of a channel in a metal foil self-drilled by the laser. Images of each arm were used as references. Through this technique, it is possible to use the interference patterns produced with uneven intensity distributions and for pulsed lasers on a single-shot basis. The results of these measurements were then shown to be in agreement with those obtained using a Young's double-slit setup.

Lossy purification and detection of entangled coherent states

In work by Howell and Yeazell [Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. After considering a preparation with nonperfect photodetection, we discuss a random mode of entanglement purification without manual intervention using a number of preparations transmitted over a lossy optical transmission line. An efficiency greater than 1/2 of the purification scheme is required to increase entanglement at all. Furthermore, we study a nondemolition configuration to measure the purity of the state as contrast of interference fringes in a double-slit setup. As a consequence of the relationship between purity and entanglement of formation resulting from treating the entangled coherent states as a state of a bipartite quantum system, the contrast of interference fringes provides a direct means to measure entanglement.

Complementarity and quantum erasure with dispersive atom-field interactions.

The welcher Weg (which-path) detector as described by Scully et al. [Nature 351, 111 (1991)] employs a pair of initially empty micromaser cavities placed in front of a double-slit apparatus in an atomic interferometer. Laser excited atoms spontaneously emit a photon into either cavity thereby marking the atoms' path and thereby destroying the interference. I propose an alternative method wherein at least one of the cavities is prepared in a coherent state with a strong amplitude. Which-path information is obtained by a nonresonant, dispersive type of atom-field interaction associated with quantum nondemolition measurements. Ground-state atoms passing through the cavity remain in the ground state but impart a phase shift to the cavity fields. Velocity selection is shown to affect the visibility of the fringes. An associated quantum eraser is also discussed.