Particle delocalization is a common feature of quantum random walks in arbitrary lattices. However, in the typical scenario a particle spreads over multiple sites and its evolution is not directly useful for controlled quantum interferometry, as may be required for technological applications. In this paper we devise a strategy to perfectly split the wave-packet of an incoming particle into two components, each propagating in opposite directions, which reconstruct the shape of the initial wavefunction after a particular time $t^*$. Therefore, a particle in a delta-like initial state becomes exactly delocalized between two distant sites after $t^*$. We find the mathematical conditions to achieve the perfect splitting which are satisfied by viable example Hamiltonians with static site-dependent interaction strengths. Our results pave the way for the generation of peculiar many-body interference patterns in a many-site atomic chain (like the Hanbury Brown and Twiss and quantum Talbot effects) as well as for the distribution of entanglement between remote sites. Thus, as for the case of perfect state transfer, the perfect wave-packet splitting can be a new tool for varied applications.
We provide an intuitive interpretation of the optical Stern-Gerlach effect (OSGE) in the dressed-state point of view. We also analyze the effect of atomic damping in an experiment on the OSGE. We show that the atomic damping also causes the wave packet splitting, in a non-mechanical fashion, as opposed to the coherent process that is mechanical.
We propose a simple scheme capable of adiabatically splitting an atomic wave packet using two independent translating traps. Implemented with optical dipole traps, our scheme allows a high degree of flexibility for atom interferometry arrangements and highlights its potential as an efficient and high fidelity atom optical beam splitter.
Coherent manipulation of single-photon wave packets is essentially important for optical quantum communication and quantum information processing. In this paper, we realize controllable splitting and modulation of single-photon-level pulses by using a tripod-type atomic medium. The adoption of two control beams enable us to store one signal pulse into superposition of two distinct atomic collective excitations. By controlling the time delay between the two control pulses, we observe splitting of a stored wave packet into two temporally-distinct modes. By controlling the frequency detuning of t…
We report the first experimental realization of perfect W-state in a superconducting qubit based system. In contrast to maximally entangled state, the perfect W state is different in weights and phases of the terms contained in the maximally entangled W-state. The prefect W state finds important applications in quantum information processing tasks such as perfect teleportation, superdense coding, secret sharing etc. The efficiency of generation is quantified by fidelity which is calculated by performing full quantum state tomography. To verify the presence of genuine nonlocality in the generat…
Following the previous paper in which quantum teleportation is rig orously discussed with coherent entangled states given by beam splittings, we further discuss two types of models, perfect teleportation model and non-perfect teleportation model, in general scheme. Then the difference among several models, i.e., the perfect models and the non-perfect models, is studied. Our teleportation models are constructed by means of coherent states in some Fock space with counting measures, so that our model can be treated in the frame of usual optical communication.
We study wave packet dynamics of a Bose condensate in a periodically shaken trap. Dichotomy, that is, dynamic splitting of the condensate, and dynamic stabilization are analyzed in analogy with similar phenomena in the domain of atoms in strong laser fields.
We show that by adding a quadratic phase to an initial arbitrary wavefunction, its free evolution maintains an invariant structure while it spreads by the action of an squeeze operator. Although such invariance is an approximation, we show that it matches perfectly the exact evolution.
We present a generic treatment of wave-packet revivals for quantum-mechanical systems. This treatment permits a classification of certain ideal revival types. For example, wave packets for a particle in a one-dimensional box are shown to exhibit perfect revivals. We also examine the revival structure of wave packets for quantum systems with energies that depend on two quantum numbers. Wave packets in these systems exhibit quantum beats in the initial motion as well as new types of long-term revivals. As an example, we consider the revival structure of a particle in a two-dimensional box.
We employ a cascaded system approach to numerically simulate the interaction of photon pulses with a two-level scatterer in a chiral waveguide QED setup. It is possible to expand any pure state of two photons as a superposition of orthogonal two-photon pulses. We show that the scattering of a two-photon pulse of suitable duration may lead to an entangled output state between predominately two equally populated two-photon states. In a complementary wave packet basis, this state is a product state of two orthogonal single photon wave packets. The time reversal of the above scattering process all…
Quantum fluctuations of electromagnetic vacuum are investigated in a half-space bounded by a perfectly reflecting plate by introducing a probe described by a charged wave-packet distribution in time-direction. The wave-packet distribution of the probe enables one to investigate the smearing effect upon the measured vacuum fluctuations caused by the quantum nature of the probe particle. It is shown that the wave-packet spread of the probe particle significantly influences the measured velocity dispersion of the probe. In particular, the asymptotic late-time behavior of its $z$-component, $ < \D…
Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the the ac-driven single-particle Krawtchouk Hamiltonian $\hat{H}(t)$ and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of $\hat{H}(t)$ and the conditions for exact wave packet reconstruction (dynamic localization). In p…
We introduce the concept of quantum reliability as an extension of the concept of network reliability in the context of quantum networks. We show that this concept is intimately related to the concept of quantum reliability operator that we also introduce and show a Negami like splitting formula for it. Considering that the simple factorization formula for classical networks which is the basis of most of the calculation algorithms does not hold in the quantum context due to entanglement, a Negami like splitting for the quantum reliability operator becomes relevant.
We observe the phase space trajectory of an entangled wave packet of a trapped ion with high precision. The application of a spin dependent light force on a superposition of spin states allows for coherent splitting of the matter wave packet such that two distinct components in phase space emerge. We observe such motion with a precision of better than 9% of the wave packet extension in both momentum and position, corresponding to a 0.8 nm position resolution. We accurately study the effect of the initial ion temperature on the quantum entanglement dynamics. Furthermore, we map out the phonon d…
Quantum teleportation is rigorously discussed with coherent entang led states given by beam splittings. The mathematical scheme of beam splitti ng has been used to study quantum communication and quantum stochastic. We d iscuss the teleportation process by means of coherent states in this scheme for the following two cases: (1) Delete the vacuum part from coherent states, whose compensation provides us a perfect teleportation from Alice to Bob. (2) Use fully realistic (physical) coherent states, which give s a non-perfect teleportation but shows that it is exact when the average en ergy (densi…
An experiment is proposed that permits the observation of the reduced de Broglie wavelengths of two and four-photon wave packets using present technology. It is suggested to use a Mach-Zehnder setup and feed both input ports with light generated by a single non-degenerate down-conversion source. The strong quantum correlations of the light in conjunction with boson-enhancement at the input beam splitter allow to detect a two- and fourfold decrease in the observed de Broglie wavelength with perfect visibility. This allows a reduction of the observed de Broglie wavelength below the wavelength of…
We demonstrate that a highly excited quantum electromagnetic mode strongly interacting with a single qubit exhibits several distinct resonances in addition to the Bloch-Siegert resonance condition that arises in the interaction with classical radiation. The resonance phenomena are associated with non-classical effects: Collapse of Rabi oscillations, splitting of the photon wave packet, and field-qubit entanglement. The analysis is based on a semiclassical phase-space flow of 2-by-2 matrices and becomes exact when the photon number tends to infinity. The flow equations are solved perturbatively…
The competition between staggered imaginary potentials and lattice dimerization results in a unidirectional propagating coalescing state of a non-Hermitian Su-Schrieffer-Heeger (SSH) ring at an exceptional point. A segment of the SSH ring inherits the unidirectional feature and exhibits some intriguing dynamic behaviors when it is embedded in a Hermitian chain as a $\mathcal{PT}$-symmetric scattering center. Based on the Bethe ansatz scattering solution for the interface between Hermitian and non-Hermitian regions, we show that the SSH scattering center supports the following wave-packet dynam…
A model of the asymmetric coherent scattering process (caused by initial atomic wave-packet splitting in the momentum space) taking place at the large detuning and adiabatic course of interaction for an effective two-state system interacting with a standing wave of laser radiation is discussed. We show that the same form of initial wave-packet splitting may lead to different, in general, diffraction patterns for opposite, adiabatic and resonant, regimes of the standing-wave scattering. We show that the scattering of the Gaussian wave packet in the adiabatic case presents refraction (a limiting…
We present a photonic wave packet construction which is immune against the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated momentum modes. The helicity encoding is considered to be particularly suitable for free-space communication. The integral part of the story is information retrieval on the receiver's side. We employed p…
In this contribution we investigate quantum electrodynamical many-mode aspects by exploring the simplest possible situation in this context, namely the interaction of a single atom, modeled by a simple two-level system, with many-mode one-photon quantum states of the electromagnetic field. In particular, we concentrate on the question how the engineering of electromagnetic field modes influences the atom-field interaction. An interesting problem in this context is the engineering of ideal one-photon multi-mode quantum states which may excite a single atom perfectly [M. Stobińska, G. Alber, and…
The wave function of a moderately cold atom in a stationary near-resonant standing light wave delocalizes very fast due to wave packet splitting. However, we show that frequency modulation of the field may suppress packet splitting for some atoms having specific velocities in a narrow range. These atoms remain localized in a small space for a long time. We propose that in a real experiment with cold atomic gas this effect may decrease the velocity distribution of atoms (the field traps the atoms with such specific velocities while all other atoms leave the field)
In this brief report we present a feasible scheme to split quantum information in the realm of traveling waves. An oversimplified scheme is also proposed for the generation of a class of W states useful for perfect teleportation and superdense coding. The scheme employs only linear optical elements as beam splitters and phase shifters, in addition to photon counters and one-photon sources. It is shown that splitting of quantum information with high fidelity is possible even including inefficiency of the detectors and photoabsorption of the beam splitters.
We experimentally demonstrate a new interferometry paradigm: a self-interfering clock. We split a clock into two spatially separated wave packets, and observe an interference pattern with a stable phase showing that the splitting was coherent, i.e., the clock was in two places simultaneously. We then make the clock wave packets "tick" at different rates to simulate a proper time lag. The entanglement between the clock's time and its path yields "which path" information, which affects the visibility of the clock's self-interference. By contrast, in standard interferometry, time cannot yield "wh…
Properties of time evolution of wave packets built up from rotator eigenstates are discussed. The mechanism of perfect cloning of the initial wave packet for "circular states" at fractional revival times is explained. The smooth transition from "circular" to "linear" through intermediate "elliptic" is described. Example of time evolution of a nuclear wave packet created in Coulomb excitation mechanism is presented.
In this paper we discuss possibilities to manipulate a matter-wave with time-dependent potentials. Assuming a specific setup on an atom chip, we explore how one can focus, accelerate, reflect, and stop an atomic wave packet, with, for example, electric fields from an array of electrodes. We also utilize this method to initiate coherent splitting. Special emphasis is put on the robustness of the control schemes. We begin with the wave packet of a single atom, and extend this to a BEC, in the Gross-Pitaevskii picture. In analogy to laser pulse shaping with its wide variety of applications, we ex…
The wave function of a moderately cold atom in a stationary near-resonant standing light wave delocalizes very fast due to wave packet splitting. However, we show that frequency modulation of the field may suppress packet splitting for some atoms having specific velocities in a narrow range. These atoms remain localized in a small space for a long time. We demonstrate and explain this effect numerically and analytically. Also we demonstrate that modulated field can not only trap, but also cool the atoms. We perform a numerical experiment with a large atomic ensebmble having wide initial veloci…
We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nm excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chai…
We study quantum dynamics of a kicked relativistic spin-half particle in a one dimensional box. Time-dependence of the average kinetic energy and evolution of the wave packet are explored. Kicking potential is introduced as the Lorentz-scalar, i.e., through the mass-term in the Dirac equation. It is found that depending on the values of the kicking parameters E(t) can be periodic, monotonically growing and non-periodic function of time. Particle transport in the system is studied by considering spatio-temporal evolution of the Gaussian wave packet.Splitting of the packet into two symmetric par…
We study quantum dynamics of wave packet motion of Bloch electrons in quantum networks with the tight-binding approach for different types of nearest-neighbor interactions. For various geometrical configurations, these networks can function as some optical devices, such as beam splitters and interferometers. When the Bloch electrons with the Gaussian wave packets input these devices, various quantum coherence phenomena can be observed, e.g., the perfect quantum state transfer without reflection in a Y-shaped beam, the multi- mode entanglers of electron wave by star shaped network and Bloch ele…
Hestenes has shown that a bispinor field on a Minkowski space-time is equivalent to an orthonormal tetrad of one-forms together with a complex scalar field. More recently, the Dirac and Einstein equations were unified in a tetrad formulation of a Kaluza-Klein model which gives precisely the usual Dirac-Einstein Lagrangian. In this model, Dirac's bispinor equation is obtained in the limit for which the radius of higher compact dimensions of the Kaluza-Klein manifold becomes vanishingly small compared with the Planck length. For a small but finite radius, the Kaluza-Klein model predicts velocity…
We present a generalized model for the evolution of atomic wave-packets in matter-wave interferometers. This method provides an efficient tool for analyzing the performance of atomic interferometers using atom clouds prepared in a trap as a Bose-Einstein condensate (BEC) or as a thermal ensemble. Predictions of the model for dynamic properties such as wave-packet size and phase are in excellent agreement with explicit numerical solutions of the non-linear Gross-Pitaevskii equations and enable fast calculations of interferometric performance in regimes where full numerical solutions become impr…
X-ray free-electron lasers (FEL) deliver ultrabright X-ray pulses, but not the sequences of phase-coherent pulses required for time-domain interferometry and control of quantum states. For conventional split-and-delay schemes to produce such sequences the challenge stems from extreme stability requirements when splitting Angstrom wavelength beams where tiniest path length differences introduce phase jitter. We describe an FEL mode based on selective electron bunch degradation and transverse beam shaping in the accelerator, combined with a self-seeded photon emission scheme. Instead of splittin…
