We discuss the interaction between two resonant states in a quantum double-well structure. The behaviour of the resonant states depends on the coupling between the wells, i.e. the height and width of the barrier that separates them. We distinguish a region with resonant tunneling and a region where the two resonances repel each other. The transition between the two regions is marked by a double pole of the S-matrix.
Exceptional points and double poles of the S matrix are both characterized by the coalescence of a pair of eigenvalues. In the first case, the coalescence causes a defect of the Hilbert space. In the second case, this is not so as shown in prevoius papers. Mathematically, the reason for this difference is the bi-orthogonality of the eigenfunctions of a non-Hermitian operator that is ignored in the first case. The consequences for the topological structure of the Hilbert space are studied and compared with existing experimental data.
Theoretical calculations on transmission of quantum states such as Schrödinger cat (SC) states are considered in a periodically poled nonlinear crystal (PPNC). Combinations of various initial states (SC, coherent (C),and vacuum (V)) of light waves at frequencies $ω_{e}$ and $3ω_{e}$ at the input of a PPNC are studied. It is shown that the transmission and interference between superposition of macroscopically distinguishable states can be achieved by using a PPNC. Visualization and analyzes of transmission and interference processes are demonstrated with the help of reduced Wigner quasi-probabi…
An accidental degeneracy of resonances gives rise to a double pole in the scattering matrix, a double zero in the Jost function and a Jordan chain of length two of generalized Gamow-Jordan eigenfunctions of the radial Schroedinger equation. The generalized Gamow-Jordan eigenfunctions are basis elements of an expansion in bound and resonant energy eigenfunctions plus a continuum of scattering wave functions of complex wave number. In this biorthonormal basis, any operator which is a regular function of the Hamiltonian is represented by a complex matrix which is diagonal except for a Jordan bloc…
We perform a nonlocal double-slit interference experiment with pseudothermal light. The experimental result exhibits a typical double-slit interference fringe in the intensity correlation measurement, in agreement with the theoretical analysis by means of the property of the second-order spatial correlation of field.
In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete…
Recent work using spontaneous parametric down-conversion (SPDC) has made possible investigations of the Einstein-Podolsky-Rosen paradox in its original (position-momentum) form. We propose an experiment that uses SPDC photon pairs to measure through which slit a photon passes while simultaneously observing double-slit interference.
For the solid state double-dot interferometer, the phase shifted interference pattern induced by the interplay of inter-dot Coulomb correlation and multiple reflections is analyzed by harmonic decomposition. Unexpected result is uncovered, and is discussed in connection with the which-path detection and electron loss.
We theoretically discuss one-photon and two-photon double-slit interferences for spontaneous and stimulated parametric down-conversions. We show that the two-photon sub-wavelength interference can exist in a general spontaneous parametric down-conversion (SPDC) for both type I and type II crystals. We propose an alternative way to observe sub-wavelength interference by a joint-intensity measurement which occurs for only type I crystal in a higher gain of SPDC. When a signal beam injects into the crystal, it may create two interference patterns by two stimulated down-converted beams, showing no…
The double slit experiment provides a classic example of both interference and the effect of observation in quantum physics. When particles are sent individually through a pair of slits, a wave-like interference pattern develops, but no such interference is found when one observes which "path" the particles take. We present a model of interference, dephasing, and measurement-induced decoherence in a one-dimensional version of the double-slit experiment. Using this model, we demonstrate how the loss of interference in the system is correlated with the information gain by the measuring apparatus…
Spatial interference of quantum mechanical particles exhibits a fundamental feature of quantum mechanics. A two-mode entangled state of N particles known as N00N state can give rise to non-classical interference. We report the first experimental observation of a three-photon N00N state exhibiting Young's double-slit type spatial quantum interference. Compared to a single-photon state, the three-photon entangled state generates interference fringes that are three times denser. Moreover, its interference visibility of $0.49 \pm 0.09$ is well above the limit of 0.1 for spatial super-resolution of…
We consider non-degenerate pump-probe spectroscopy of V-systems under conditions such that interference among decay channels is important. We demonstrate how this interference can result in new gain features instead of the usual absorption features. We relate this gain to the existence of a new vacuum induced quasi-trapped-state. We further show how this also results in large refractive index with low absorption.
The Fraunhofer diffraction intensity distribution of Laguerre-Gaussian beam is studied in an angular-double-slit interferometer. We demonstrate that the spiral phase structure of vortex light can be clearly revealed in this interference geometry, and it gives us an efficient way to distinguish different order of Laguerre-Gaussian beams. This angular-double-slit interference gives us a better understanding to the nature of orbital angular momentum and the interpretation of vortex beams interference phenomenon.
We present a numerical simulation of the double slit interference experiment realized by F. Shimizu, K. Shimizu and H. Takuma with ultracold atoms. We show how the Feynman path integral method enables the calculation of the time-dependent wave function. Because the evolution of the probability density of the wave packet just after it exits the slits raises the issue of the interpreting the wave/particle dualism, we also simulate trajectories in the de Broglie-Bohm interpretation.
We show that interference phenomena plays a big role for the electron yield in ionization of atoms by an ultra-short laser pulse. Our theoretical study of single ionization of atoms driven by few-cycles pulses extends the photoelectron spectrum observed in the double-slit experiment by Lindner et al, Phys. Rev. Lett. \textbf{95}, 040401 (2005) to a complete three-dimensional momentum picture. We show that different wave packets corresponding to the same single electron released at different times interfere, forming interference fringes in the two-dimensional momentum distributions. These struc…
In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in two limiting cases, considering the limits of uncertainty in the position probability distribution. Moreover, we analyze the interference patterns based on a recent proposal called stochastic electrodynamics with spin. Our results show that when the quantum character of the macro-system is decreased, the diffraction pattern becomes more similar to a classic…
Mesoscopic routers and single-pole double-throw switches for electronic heat
Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心（IFIMAC））；Instituto Nicolás Cabrera (INC), Universidad Autónoma de Madrid（马德里自治大学尼古拉斯·卡布雷拉研究所（INC））
Search for the Double Poles of the Scattering Matrix in Light Nuclei
Grand Accélérateur National d’Ions Lourds (GANIL), CEA/DSM - CNRS/IN2P3（重离子国家加速器中心（GANIL））；CAS Laboratory of High precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所高精度核谱学实验室）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
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 systematically report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrodinger (DNLS) equation with both zero boundary condition (ZBC)/non-zero boundary conditions (NZBCs) at infinity and double poles of analytical scattering coefficients. The scattering theories for both ZBC and NZBCs are addressed. The direct problem establishes the analyticity, symmetries and asymptotic behavior of the Jost solutions and scattering matrix, and properties of discrete spectra. The inverse problems are formulated and solved with the aid of the matrix Riemann-Hil…
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…
We study the spectral properties of Spontaneous Parametric Down Conversion in a periodically poled waveguided structure of KTP crystal pumped by ultra-short pulses. Our theoretical analysis reveals a strongly multimode and asymmetric structure of the two-photon spectral amplitude for type-II SPDC. Experimental evidence, based on Hong-Ou-Mandel polarization interference with narrowband filtering, confirms this result.
We propose a quantum interference cooling scheme for a nano-mechanical resonator (NAMR) in a hybrid optomechanical system, where the atoms are trapped in an optomechanical cavity, coupling to an additional optical cavity. The absorption of the optomechanical resonator can be modified by quantum interference effects induced by the atom-cavity and cavity-cavity couplings independently. With the employment of the quantum interference, the desired transition for cooling is enhanced, along with the heating suppression due to the undesired transition. As a result, the NAMR vibration can be cooled do…
We present the experimental characterization of two distant double-slit masks illuminated by chaotic light, in the absence of first-order imaging and interference. The scheme exploits second-order interference of light propagating through two indistinguishable pairs of {\it disjoint} optical paths passing through the masks of interest. The proposed technique leads to a deeper understanding of biphoton interference and coherence, and opens the way to the development of novel schemes for retrieving information on the relative position and the spatial structure of distant objects, which is of int…
Using a neutron double-slit setup, we construct a quantum bit commitment scheme in which time development of quantum states plays an essential role. Our scheme evades the widely accepted no-go theorem by the fact that it is neither possible to stop the time evolution of spreading wave packets, nor is it possible to evolve them backward in time. Moreover, for unstable particles such as neutrons, one cannot delay detecting their positions indefinitely, or they would disintegrate spontaneously and escape detection. We find that using non-stationary states instead of stationary ones, unconditional…
The two-photon ghost interference experiment, generalized to the case of massive particles, is theoretically analyzed. It is argued that the experiment is intimately connected to a double-slit interference experiment where, the which-path information exists. The reason for not observing first order interference behind the double-slit, is clarified.It is shown that the underlying mechanism for the appearance of ghost interference is, the more familiar, quantum erasure.
A double cavity with a quantum mechanical and a classical field is located immediately behind of a double-slit in order to analyse the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path-information can be recorded on the phase of the quantum field. On other hand, if the atom crosses a common node, the interaction is null and no path-information is stored. A quadrature measurement on the quantum field can reveal the path f…
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 present a treatment of the double-slit interference of matter-waves represented by Gaussian wavepackets. The interference pattern is modelled with Green's function propagator which emphasizes the coordinate correlations and phases. We explore the connection between phases and position-momentum correlations in the intensity, visibility and predictability of the wavepackets interference. This formulation will indicate some aspects that can be useful for theoretical and experimental treatment of particles, atoms or molecules interferometry.
We theoretically investigate transport signatures of quantum interference in highly symmetric double quantum dots in a parallel geometry and demonstrate that extremely weak symmetry-breaking effects can have a dramatic influence on the current. Our calculations are based on a master equation where quantum interference enters as non-diagonal elements of the density matrix of the double quantum dots. We also show that many results have a physically intuitive meaning when recasting our equations as Bloch-like equations for a pseudo spin associated with the dot occupation. In the perfectly symmetr…
The Young double-slit interference pattern produced by quantum objects, like photons, that move through a double-slit is regarded, by the conventional Copenhagen interpretation of Quantum Mechanics, as the evidence of the wave-like behaviour potentially contained in the wave function. On the contrary, a more realistic view of this phenomenon considers the quantum object a particle accompanied by a pilot wave which would be the cause of the interference fringes. This paper proposes a feasible experiment, based on an easy variation of the nowadays common double-slit experimental set-ups, aimed a…
Permutations of particle labels are usually used to illustrate the relationship between classical and quantum statistics. We use permutations of attributes/properties of particles to express properties of waves. We express events of the well-known two-double-slit experiment (in regimes that are appropriate to quantum interference and classical interference) in terms of symmetries of permutations of particle labels and attributes. We also obtain a new system called residual interference, and suggest an experiment to detect it.
Due to a transient quantum interference during a wavepacket collision with a potential barrier, a particular momentum, that depends on the potential parameters but is close to the initial average momentum, becomes suppressed. The hole left pushes the momentum distribution outwards leading to a significant constructive enhancement of lower and higher momenta. This is explained in the momentum complex-plane language in terms of a saddle point and two contiguous ``structural'' poles, which are not associated with resonances but with incident and transmitted components of the wavefunction.
Based on a re-formulation of the classical explanation of quantum mechanical Gaussian dispersion (Groessing et al. 2010) as well as interference of two Gaussians (Groessing et al. 2012), we present a new and more practical way of their simulation. The quantum mechanical "decay of the wave packet" can be described by anomalous sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. In a simulation of the double-slit experiment with different slit widths, the phase with this new approach can be implemented as a local quantity. We descri…
Quantum interference is a natural consequence of wave-particle duality in quantum mechanics, and is widely observed at the atomic scale. One interesting manifestation of quantum interference is coherent population trapping (CPT), first proposed in three-level driven atomic systems and observed in quantum optical experiments. Here, we demonstrate CPT in a gate-defined semiconductor double quantum dot (DQD), with some unique twists as compared to the atomic systems. Specifically, we observe CPT in both driven and non-driven situations. We further show that CPT in a driven DQD could be used to ge…
A third-order double-slit interference experiment with pseudo-thermal light source in the high-intensity limit has been performed by actually recording the intensities in three optical paths. It is shown that not only can the visibil- ity be dramatically enhanced compared to the second-order case as previously theoretically predicted and shown experimentally, but also that the higher visi- bility is a consequence of the contribution of third-order correlation interaction terms, which is equal to the sum of all contributions from second-order cor- relation. It is interesting that, when the two …
We carry out a numerical simulation about the occurrence of interference fringes in experiments where an initial Gaussian wave packet evolves inside a billiard domain with two slits on the boundary. Our simulation extends a previous work by Casati and Prosen and it is aimed to test their surprising conclusion that the fringes disappear in the experiments with fully chaotic billiards. According to the results found, we are led to reassess this remarkable effect of classical dynamics on quantum interference. Actually, we highlight another factor which acts on interference: a symmetry condition (…
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 behav…
Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment. The exact quantum mechanical intensity distribution, as well as the corresponding trajectory distribution and the velocity field of a Gaussian wave packet are therewith computed. We utilize no quantum mechanics, but only familiar simulation techniques for diffusion, e.g., finite differences or coupled map lattices (CML).
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. While the direct event-by-event buildup of this interference pattern has been observed for massive particles such as electrons, neutrons, atoms and molecules, it has not yet been measured for massless particles like photons. Here we pr…
We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom. We characterize the state of the emitted atom beams by observing strong number squeezing up to -10 dB in the correlated two-particle modes of emission. We furthermore demonstrate genuine two-particle interference in the normalized second-order correlation function $g^{(2)}$ relative to the emitted atoms.
The validity of the assertion that some recent double-slit interference experiments, conducted by Radin et al., would have tested the possible role of the experimenter's mind in the collapse of the quantum wave function, is questioned. It is emphasized that quantum mechanics doesn't need any psychophysical ingredient to explain the measurement processes, and therefore parapsychologists shouldn't resort to the latter to support the possibility of psychokinesis, but search for more convincing explanations.
We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and thre…
Time double-slit interference experiments have been achieved and presented as complementary to spatial double-slit interference experiments, providing a further confirmation of the wave-particle duality. Numerical solutions of the free particle time dependent Schrödinger equation were presented as explanation of the experimental results, but have been objected to on the basis that the standard non relativistic quantum theory does not have the property of coherence in time. In this note the theoretical and experimental results are derived in a schematic but analytic solution of the TDSE with ap…
People have been paying attention to the role of atoms' complex internal level structures in the research of electromagnetically induced transparency (EIT) for a long time, where the various degenerate Zeeman levels usually generate complex linkage patterns for the atomic transitions. It turns out, with special choices of the atomic states and the atomic transitions' linkage structure, clear signatures of quantum interference induced by the probe and coupling light's polarizations can emerge from a typical EIT phenomena. We propose to study a four state system with double-V linkage pattern for…
We present a fully local treatment of the double slit experiment in the formalism of quantum field theory. Our exposition is predominantly pedagogical in nature and exemplifies the fact that there is an entirely local description of the quantum double slit interference that does not suffer from any supposed paradoxes usually related to the wave-particle duality. The wave-particle duality indeed vanishes in favour of the field picture in which particles should not be regarded as the primary elements of reality and only represent excitations of some specific field configurations. Our treatment i…
The subject of bianyon interference with ultracold atoms is introduced through theoretical investigations pertaining to the second-order momentum correlation maps of two anyons (built upon spinless and spin-1/2 bosonic, as well as spin-1/2 fermionic ultracold atoms) trapped in a double-well optical trap. The two-particle system is modeled according to the recently proposed protocols for emulating an anyonic Hubbard Hamiltonian in ultracold-atom one-dimensional lattices. Because the second-order momentum correlations are mirrored in the time-of-flight second-order interference patterns in space…
We design a computational experiment in which a quantum particle tunnels into a billiard of variable shape and scatters out of it through a double-slit opening on the billiard's base. The interference patterns produced by the scattered probability currents for a range of energies are investigated in relation to the billiard's geometry which is connected to its classical integrability. Four billiards with hierarchical integrability levels are considered: integrable, pseudo-integrable, weak-mixing and strongly chaotic. In agreement with the earlier result by Casati and Prosen [1], we find the bi…
We employ the broken-link model to create a barrier with slits in a two-dimensional lattice. The diffraction and interference patterns of the probability distribution of quantum walkers passing through the slits are analyzed. Simulations were performed using the main types of coins, and display diffraction and interference patterns that depend on the choice of coins.
In a previous paper it has been shown that the interference of the first and second order pole of the Green's function at an exceptional point, as well as the interference of the first order poles in the vicinity of the exceptional point, gives rise to asymmetric scattering cross section profiles. In the present paper we demonstrate that these line profiles are indeed well described by the Beutler-Fano formula, and thus are genuine Fano resonances. Also further away from the exceptional points excellent agreement can be found by introducing energy dependent Fano parameters.
A classical explanation of interference effects in the double slit experiment is proposed. We claim that for every single "particle" a thermal context can be defined, which reflects its embedding within boundary conditions as given by the totality of arrangements in an experimental apparatus. To account for this context, we introduce a "path excitation field", which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a "particle" can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as wel…
As normally used, no commercially available camera has a low-enough dark noise to directly produce video recordings of double-slit interference at the photon-by-photon level, because readout noise significantly contaminates or overwhelms the signal. In this work, noise levels are significantly reduced by turning on the camera only when the presence of a photon has been heralded by the arrival, at an independent detector, of a time-correlated photon produced via parametric down-conversion. This triggering scheme provides the improvement required for direct video imaging of Young's double-slit e…
Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the second-order density matr…
