Molecular matter-wave interferometry enables novel strategies for manipulating the internal mechanical motion of complex molecules. Here, we show how chiral molecules can be prepared in a quantum superposition of two enantiomers by far-field matter-wave diffraction and how the resulting tunnelling dynamics can be observed. We determine the impact of ro-vibrational phase averaging and propose a setup for sensing enantiomer-dependent forces, parity-violating weak interactions, and environment-induced superselection of handedness, as suggested to resolve Hund's paradox. Using ab-initio tunnelling calculations, we identify [4]-helicene derivatives as promising candidates to implement the proposal with state-of-the-art techniques. This work opens the door for quantum sensing and metrology with chiral molecules.
With a microwave-regime cyclic three-state configuration, an enantiomer-selective state transfer~(ESST) is carried out through the two-path interference between a direct one-photon coupling and an effective two-photon coupling. The $π$-phase difference in the one-photon process between two enantiomers makes the interference constructive for one enantiomer but destructive for the other. Therefore only one enantiomer is excited into a higher rotational state while the other remains in the ground state. The scheme is of flexibility in the pulse waveforms and the time order of two paths. We simula…
We propose a simple experimental procedure based on the Elitzur-Vaidman scheme to test the persistence of macroscopic superpositions. We conjecture that its implementation will reveal the persistence of superpositions of macroscopic objects in the absence of a direct act of observation.
Entanglement can modify the interference patterns of multi-particle systems. We analyse, using the path integral formalism, a novel example of multi-particle interference and some unexplored aspects of this phenomenon by considering the two-slit arrangement with two distinguishable particles in a superposition state. The two components of entanglement, multiplicity of multi-particle terms and their coherence, can be studied separately by comparing the patterns of product, mixed and superposition states. This suggests a scheme to detect multi-particle superposition in some favourable cases. Mor…
We propose an experimental scheme to implement a second-order nonlocal superposition operation and its variants by way of Hong-Ou-Mandel interference. The second-order coherent operations enable us to generate a NOON state with high particle number in a heralded fashion and also can be used to enhance the entanglement properties of continuous variable states. We discuss the feasibility of our proposed scheme considering realistic experimental conditions such as on-off photodetectors with nonideal efficiency and imperfect single-photon sources.
We predict the possibility of sharp, high-contrast resonances in the optical response of a broad class of systems, wherein interference effects are generated by coherent perturbation or interaction of dark states. The properties of these resonances can be manipulated to design a desired atomic response.
Multi-photon interference is central to photonic quantum information processing and quantum simulation, usually requiring multiple sources of non-classical light followed by a unitary transformation on their modes. Here, we observe interference in the four-photon events generated by a single silicon waveguide, where the different modes are six frequency channels. Rather than requiring a unitary transformation, the frequency correlations of the source are configured such that photons are generated in superposition states across multiple channels, and interference effects can be seen without fur…
In this paper we study the evolution of the two two-level atoms interacting with a single-mode quantized radiation field, namely, two-atom multiphoton Jaynes-Cummings model when the radiation field and atoms are initially prepared in the superpostion of displaced number states and excited atomic states, respectively. For this system we investigate the atomic inversion, Wigner function, phase distribution and entanglement.
We propose to discriminate chiral molecules by combining one- and two-photon processes in a closed-loop configuration. The one-photon-coupling intrinsic π-phase difference between two enantiomers leads to their different superposition states, which is then followed by a two-photon process through three-mode parallel paths (3MPPs), enabling the discrimination of enantiomers by inducing their entirely-different population distributions. The 3MPPs are constructed by "chosen paths", a method of shortcuts to adiabaticity (STA), exhibiting a fast two-photon process. As an example, we propose to perf…
The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The ana…
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…
Classical linear wave superposition produces the appearance of interference. This observation can be interpreted in two equivalent ways: one can assume that interference is an illusion because input components remain unperturbed, or that interference is real and input components undergo energy redistribution. Both interpretations entail the same observable consequences at the macroscopic level, but the first approach is considerably more popular. This preference was established before the emergence of quantum mechanics. Unfortunately, it requires a non-classical underlying mechanism and fails …
Reflection of a microscopic particle from a mesoscopic/macroscopic `mirror' generates two-body correlated interference from the incident and reflected particle substates and their associated mirror substates. The microscopic momentum exchanged generates two mirror substates which interfere to produce fringes which do not vanish as the mirror mass increases. The small displacement between these mirror states can yield negligible environmental decoherence times. Mirror coherence lengths impose constraints on the extent of this interference, which are mitigated using interference of the two-body …
The interference pattern produced by a quantum particle in Young's double-slit setup is attributed to the particle's wavefunction 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 phot…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states, explaining the interference effects, and the entanglement correlations, in terms of the different orientations that a state-vector can take within the generalized Bloch sphere. We also introduce a tensorial determination of the generators of SU(N), particularly suitable to describe multipartite systems, from the viewpoint of the sub-entities. We then use it to…
The Feynman Path Integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub leading terms in the Path Integral which can be described by wha…
We investigate the quantum interference effects in two types of matter-wave mixing experiments: one with initial matter waves prepared in independent Fock states (type I) and the other with each individual particle prepared in a same coherent superposition of states (type II). In the type I experiment, a symmetric wavefunction of bosons leads to constructive quantum interference and shows final state stimulation, while an anti-symmetric wavefunction of fermions results in destructive quantum interference and inhibited matter wave mixing. In the type II experiment, a coherent superposition stat…
Quantum interferences between non-orthogonal states are the best approximation of a joint realization of the non-commuting physical properties represented by the two states. As I have shown recently, such interferences can be used to demonstrate that quantum physics deviates from classical causality in the limit of small action. Here, I point out that this proof constitutes a failure of the principle of least action and consider possible implications for our understanding of fundamental physics.
Conventional Glauber coherent states (CS) can be defined in several equivalent ways, e.g., by displacing the vacuum or, explicitly, by their infinite Poissonian expansion in Fock states. It is well known that these definitions become inequivalent if applied to finite $d$-level systems (qudits). We present a comparative Wigner-function description of the qudit CS defined (i) by the action of the truncated displacement operator on the vacuum and (ii) by the Poissonian expansion in Fock states of the Glauber CS truncated at $(d-1)$-photon Fock state. These states can be generated from a classical…
It is shown that the degree of polarization of light, generated by superposition in a single-photon interference experiment, may depend on the indistinguishability of the photon-paths.
According to Bohr's principle of complementarity, a quanton can behave either as a wave or a particle, depending on the choice of the experimental setup. Some recent two-path interference experiments have devised methods where one can have a quantum superposition of the two choices, thus indicating that a quanton may be in a superposition of wave and particle nature. These experiments have been of interest from the point of view of Wheeler's delayed-choice experiment. However, it has also been claimed that this experiment can violate complementarity. Here we theoretically analyze a multipath i…
We propose a method to prepare and verify spatial quantum superpositions of a nanometer-sized object separated by distances of the order of its size. This method provides unprecedented bounds for objective collapse models of the wave function by merging techniques and insights from cavity quantum optomechanics and matter wave interferometry. An analysis and simulation of the experiment is performed taking into account standard sources of decoherence. We provide an operational parameter regime using present day and planned technology.
Interferences emerge when multiple pathways coexist together leading towards the same result. A Recent study by Blasing and coworkers [PRL 121(7):073202] showed that in a photo-association reaction of Raman dressed spin orbit coupled $^{87}$Rb Bose Einstein Condensate when the reactant spin state is prepared in a coherent superposition of multiple bare spin states it leads to a destructive interference between reaction pathways. Here we report a theoretical study for a reaction scheme which leads to constructive quantum interference. This is achieved by changing the reactive scattering channel…
We consider how macroscopic quantum superpositions may be created from arrays of Bose-Einstein condensates. We study a system of three condensates in Fock states, all with the same number of atoms and show that this has the form of a highly entangled superposition of different quasi-momenta. We then show how, by partially releasing these condensates and detecting an interference pattern where they overlap, it is possible to create a macroscopic superposition of different relative phases for the remaining portions of the condensates. We discuss methods for confirming these superpositions.
We investigate the influence of superpositional wave function oscillations on the performance of Shor's quantum algorithm for factorization of integers. It is shown that the wave function oscillations can destroy the required quantum interference. This undesirable effect can be routinely eliminated using a resonant pulse implementation of quantum computation, but requires special analysis for non-resonant implementations.
We present the experimental realization of a scheme, based on single-photon interference, for implementing superpositions of distinct quantum operations. Its application to a thermal light field (a well-categorized classical entity) illustrates quantum superposition from a new standpoint and provides a direct and quantitative verification of the bosonic commutation relation between creation and annihilation operators. By shifting the focus towards operator superpositions, this result opens interesting alternative perspectives for manipulating quantum states.
Large spatial quantum superposition of size ${\cal O}(1-10)~{\rm μ\text{m}}$ for mass $m \sim 10^{-17}-10^{-14}~\text{kg}$ is required to probe the foundations of quantum mechanics and testing classical and quantum nature of gravity via entanglement in a laboratory. In this paper, we will show that it is possible to accelerate the two spin states of a macroscopic nano-crystal sourced by the inhomogeneous nonlinear magnetic field in the Stern-Gerlach type setup. We will assume that the electronic spin can be embedded at the centre of the nano-crystal, such as the nitrogen-vacancy (NV) centre of…
We propose a scheme for creating quantum superposition states involving of order $10^{14}$ atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. All experimental requirements appear to be within reach of current technology.
We report the realization of an entangled quantum superposition of M=12 photons by a high gain, quantum-injected optical parametric amplification. The system is found so highly resilient against decoherence to exhibit directly accessible mesoscopic interference effects at normal temperature. By modern tomographic methods the non-separability and the quantum superposition are demonstrated for the overall mesoscopic output state of the dynamic ''closed system''. The device realizes the condition conceived by Erwin Schroedinger with his 1935 paradigmatic ''Cat'' apologue, a fundamental landmark i…
Quantum interference arising from superposition of states is a striking evidence of the validity of Quantum Mechanics, confirmed in many experiments and also exploited in applications. However, as for any scientific theory, Quantum Mechanics is valid within the limits in which it has been experimentally verified. In order to extend such limits, it is necessary to observe quantum interference in unexplored conditions such as moving terminals at large distance in Space. Here we experimentally demonstrate single photon interference at a ground station due to the coherent superposition of two temp…
Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here this appealing idea is considered to analyze both classical and quantum interference, thus providing an alternative and more intuitive framework to understand the time-evolution of waves, either in terms of the flow of energy (for mechanical waves, sound waves, electromagnetic waves, for instance) or, analogously, the flow of probability (quantum waves), respectively. Furthermore, this procedu…
It is a long standing question whether or not one can change the nature of spontaneous emission by a free electron through shaping the electron wavefunction. On one hand, shaping the electron wavefunction changes the respective charge and current densities of the electron. On the other hand, spontaneous emission of an electron is an incoherent process and can often be insensitive to the shape of the electron wavefunction. In this work, we arrive at an affirmative answer examining Bremsstrahlung radiation by free electron superposition states. We find that the radiation can be markedly differen…
We propose a method to generate and detect large quantum superposition states and arbitrary Fock states for the oscillational mode of an optically levitated nanocrystal diamond. The nonlinear interaction required for the generation of non-Gaussian quantum states is enabled through the spin-mechanical coupling with a built-in nitrogen-vacancy center inside the nanodiamond. The proposed method allows the generation of large superpositions of nanoparticles with millions of atoms and the observation of the associated spatial quantum interference under reasonable experimental conditions.
The multiphoton quantum superposition generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The effect can be greatly enhanced if the mirror is part of a cavity structure or is used within an optical interferometer. The overall process will realize an Entangled Macroscopic Quantum Superposition involving a ''microscopic'' singe-photon state of polarization and the coherent ''macroscopic'' displacement of the BEC structure acting in space-l…
We propose and demonstrate a novel method to generate a large-amplitude coherent-state superposition (CSS) via ancilla-assisted photon-subtraction. The ancillary mode induces quantum interference of indistinguishable processes, widening the controllability of quantum superposition at the conditional output. We demonstrate the concept in the time domain, by a simple time-separated two-photon subtraction from cw squeezed light. We observe the largest CSS ever reported without any corrections, which will enable various quantum information applications with CSS states.
We elaborate a theory for the modeling of concepts using the mathematical structure of quantum mechanics. Concepts are represented by vectors in the complex Hilbert space of quantum mechanics and membership weights of items are modeled by quantum weights calculated following the quantum rules. We apply this theory to model the disjunction of concepts and show that experimental data of membership weights of items with respect to the disjunction of concepts can be modeled accurately. It is the quantum effects of interference and superposition, combined with an effect of context, that are at the …
We demonstrate the possibility of realizing sub-Planck-scale structures in the mesoscopic superposition of molecular wave packets involving vibrational levels. The time evolution of the wave packet, taken here as the SU(2) coherent state of the Morse potential describing hydrogen iodide molecules, produces macroscopicquantum- superposition-like states, responsible for the above phenomenon. We investigate the phase-space dynamics of the coherent state through the Wigner function approach and identify the interference phenomena behind the sub-Planck-scale structures. The optimal parameter ranges…
Coherent superpositions are one of the hallmarks of quantum mechanics and are vital for any quantum mechanical device to outperform the classically achievable. Generically, superpositions are verified in interference experiments, but despite their longstanding central role we know very little about how to extract the number of coherently superposed amplitudes from a general interference pattern. A fundamental issue is that performing a phase-sensitive measurement is as challenging as creating a coherent superposition, so that assuming a perfectly implemented measurement for verification of qua…
We present the proposition of an experiment in which the multiphoton quantum superposition consisting of N= 10^5 particles generated by a quantum-injected optical parametric amplifier (QI-OPA), seeded by a single-photon belonging to an EPR entangled pair, is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The overall process will realize a Macroscopic Quantum Superposition (MQS) involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in space-like separated distant places.
The complementary principle of quantum mechanics relates qualitatively the visibility of quantum interference with path indistinguishability. Here we propose a scheme of constructive quantum interference involving superposition between an $N$-photon state and a single-photon state to characterize quantitatively the degree of temporal distinguishability of the $N$-photon state. This scheme is based on a generalized photon bunching effect. Such a scheme can be extended to other more general cases.
We propose measurement based conditional generation of superposition of motional states of nanomechanical resonator. We consider a two level quantum mechanical system coupled with nanomechanical resonator through phonon exchange. An interaction, which produces shifts in the state of nanomechanical resonator depending on the state of the qubit, is realized by driving qubit through two resonant lasers. The measurement of the state of quantum mechanical system produces superposition states of nanomechanical resonator. We show that the quantum interference between states in superposition may lead …
A phase controlled wave packet, recently used in experiment of wave packet interferometry of adiatomic molecule, is investigated to obtain mesoscopic superposition structures, useful in quantum metrology. This analysis provides a new way of obtaining sub-Planck scale structures at smaller time scale of revival dynamics. We study a number of situations for delineating the smallest interference structures and their control by tailoring the relative phase between two subsidiary wave packets. We also find the most appropriate state, so far, for high precision parameter estimation in a system of di…
We apply geometric phase ideas to coherent states to shed light on interference phenomenon in the phase space description of continuous variable Cartesian quantum systems. In contrast to Young's interference characterized by path lengths, phase space interference turns out to be determined by areas. The motivating idea is Pancharatnam's concept of "being in phase" for Hilbert space vectors. Applied to the overcomplete family of coherent states, we are led to preferred one-dimensional integral representations for various states of physical significance, such as the position, momentum, Fock stat…
We analyse tunnelling of a single particle, whose initial state is given by a superposition of spatially separated wave packet modes. It is shown that "pile up" of different components the scatterer may change the tunnelling probabilities, making such states a convenient tool for probing the barrier's scattering times. Interference effects arising in resonance tunnelling in are studied in detail. The analysis allows us to gain further insight into the origin of interference effects in scattering of several identical particles.
We establish an objective scheme to determine the macroscopicity of quantum mechanical superposition tests, which is based on the Bayesian hypothesis falsification of macrorealistic modifications of quantum theory. The measure uses the raw data gathered in an experiment, taking into account all measurement uncertainties, and can be used to directly assess any conceivable quantum test. We determine the resulting macroscopicity for three recent tests of quantum physics: double-well interference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and entanglement generation…
An interferometric scheme for the creation of momentum superposition states of mechanical oscillators, using a quantum mirror kicked by free photons is analyzed. The scheme features ultra-fast preparation with immediate detection and should allow for the observation of signatures of momentum superpositions in a massive macroscopic system at non-zero temperatures. It is robust against thermalized initial states, displacement and movement, mirror imperfections, and the measurements' back-actions.
Two-photon interference with independent classical sources, in which superposition of two indistinguishable two-photon paths plays a key role, is of limited visibility of interference fringes with a maximum value of 50%. By using a random-phase grating to modulate the wavefront of a coherent light, we introduce superposition of multiple indistinguishable two-photon paths, which enhances the two-photon interference effect with a signature of visibility exceeding 50%. The result shows the importance of phase control in the control of high-order coherence of classical light.
Properties and applications of a plasmonic cross-shaped nano-antenna is presented and compared to those of array of holes. A simple analytical model based on the superposition of waves are proposed and compared to the numerical results. A direct consequence of unequal path for two orthogonal surface waves leads to a coherent quantum interferometer with interesting properties. Mechanism behind the rotating surface charge densities and consequently, the formation of rotating resultant dipole moments is identified and the concept of Dipole-SPP-LSP-Stokes coupling is introduced. All of which leads…
We introduce a new topological effect involving interference of two meson loops, manifesting a path-independent topological area dependence. The effect also draws a connection between quark confinement, Wilson-loops and topological interference effects. Although this is only a gedanken experiment in the context of particle physics, such an experiment may be realized and used as a tool to test confinement effects and phase transitions in quantum simulation of dynamic gauge theories.
We study photon localisation and delocalisation in a system of two nonlinear cavities with intensity-dependent coupling. It is shown that complete localisation or delocalisation is possible for proper choices of the strengths of nonlinearity, detuning and inter-cavity coupling. Role of the relative phase in the initial superposition in attaining localisation and delocalisation is discussed. Effects of dissipation and decoherence are considered and the use of quantum interference in reducing dissipation is explored. Many of the features of the system are shown to be the consequences of quantum …
