We report an experimental study of group-velocity dispersion effect on an entangled two-photon wavepacket, generated via spontaneous parametric down-conversion and propagating through a dispersive medium. Even in the case of using CW laser beam for pump, the biphoton wavepacket and the second-order correlation function spread significantly. The study and understanding of this phenomenon is of great importance for quantum information applications, such as quantum communication and distant clock synchronization.
Non dispersive electronic Rydberg wave packets may be created in atoms illuminated by a microwave field of circular polarization. We discuss the spontaneous emission from such states and show that the elastic incoherent component (occuring at the frequency of the driving field) dominates the spectrum in the semiclassical limit, contrary to earlier predictions. We calculate the frequencies of single photon emissions and the associated rates in the "harmonic approximation", i.e. when the wave packet has approximately a Gaussian shape. The results agree well with exact quantum mechanical calculat…
The modification of initially entangled light pulses passing through dispersive and absorbing four-port devices is studied, using recently obtained results on quantum state transformations [Phys. Rev. A 59, 4716 (1999)]. The fidelity and indices of quantum correlations based on the von Neumann entropy are calculated. Their dependence on both the pulse shape and the four-port device parameters is studied. It is shown, that due to dispersion and absorption the quantum correlations are reduced substantially for large initial entanglement.
We propose the suppression of dispersive spreading of wave packets governed by the free-space Schrödinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically-dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutions of the nonlinear Schrödinger equation with a constant (time-independent) nonlinearity. Our analytics are strongly supported by full numerical simulations. The predicted dispersionless wave packets can move with arbitrary velocity and can be realiz…
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…
With the exception of the harmonic oscillator, quantum wave-packets usually spread as time evolves. We show here that, using the nonlinear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave-packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave-packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the nonlinear resonance island. We discuss the g…
We propose an extension of coherent control using laser-synthesized free-electron matter waves. In contrast to coherent control schemes exploiting optical coherences to steer the dynamics of matter waves, we analyze the opposite and investigate the control of quantum light emission driven by laser-sculpted coherent free-electron matter waves. We apply this concept to the control of entangled photon-pair emission in electron-atom collisions, in which the incident electron wave packet, colliding with a target atom $B$, is engineered by interferometric resonantly-enhanced multiphoton ionization o…
We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium, and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state, or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The ``overlap fidelity'' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglem…
In the framework of the paraxial and of the slowly varying envelope approximations, with reference to a normally dispersive medium or to vacuum, the electromagnetic field is given as a continuous quantum superposition of non-dispersive and non-diffracting wave-packets (namely X-waves). Entangled states as pairs of elementary excitations traveling at (approximately) the same velocity are found in optical parametric amplification.
Quantum mechanics asserts that a wave packet must inevitably spread as time progresses since the dispersion relation for the quantum waves is assumed to be quadratic in the momentum k. However, this assumption does not consider the standard frequency Doppler shift formula of Galilean relativity. In this article a non-dispersive wave packet is constructed by appropriately considering the transformation rules between the laboratory and the (particle's) rest inertial reference frames.
The Feynman path integral formulation of non-dispersive Airy wave packets and their applications to the heavy meson mass spectra and ultra-cold neutrons
It is conjectured that the effects of reduction, which occur with the individual wavepackets in a system of two separated though entangled packets, occur simultaneously in the center frame (properly defined) of the entangled packets. Existing experiments are compatible with this type of nonlocality. Further experimental tests are suggested.
A quantum teleportation scheme based on the EPR-pair entangled with respect to the ``energy+time'' variables is proposed. Teleportation of the multimode state of a single-photon wave packet is considered.
It is shown that under certain dynamical conditions a material wave packet displays coherent, non-dispersive accelerated evolution in gravitational field over a modulated atomic mirror. The phenomenon takes place as a consequence of simultaneous presence of the dynamical localization and the coherent Fermi acceleration for the same modulation amplitude. It is purely a quantum mechanical effect as the windows of modulation strengths supporting dynamical localization and Fermi acceleration overlap for larger effective Plank constant. Present day experimental techniques make it feasible to realiz…
We show that combination of a linearly polarized resonant microwave field and a parallel static electric field may be used to create a non-dispersive electronic wavepacket in Rydberg atoms. The static electric field allows for manipulation of the shape of the elliptical trajectory the wavepacket is propagating on. Exact quantum numerical calculations for realistic experimental parameters show that the wavepacket evolving on a linear orbit can be very easily prepared in a laboratory either by a direct optical excitation or by preparing an atom in an extremal Stark state and then slowly switchin…
With propagating through a dispersive medium, the temporal-spectral profile of laser pulses should be inevitably modified. Although such dispersion effect has been well studied in classical optics, its effect on a single-photon wave-packet, i.e., the matter wave of a single-photon, has not yet been entirely revealed. In this paper, we investigate the effect of dispersion on indistinguishability of single-photon wave-packets through the Hong-Ou-Mandel (HOM) interference. By dispersively manipulating two indistinguishable single-photon wave-packets before interfering with each other, we observe …
Quantum key distribution (QKD) is a crucial technology for information security in the future. Developing simple and efficient ways to establish QKD among multiple users are important to extend the applications of QKD in communication networks. Herein, we proposed a scheme of symmetric dispersive optics QKD (DO-QKD) and demonstrated an entanglement-based quantum network based on it. In the experiment, a broadband entanglement photon pair source was shared by end users via wavelength and space division multiplexing. The wide spectrum of generated entangled photon pairs was divided into 16 combi…
We present a scheme for demonstrating violation of Bell's inequalities using a spin-1/2 system entangled with a pair of classically distinguishable wave packets in a harmonic potential. In the optical domain, such wave packets can be represented by coherent states of a single light mode. The proposed scheme involves standard spin-1/2 projections and measurements of the position and the momentum of the harmonic oscillator system, which for a light mode can be realized by means of homodyne detection. We discuss effects of imperfections, including non-unit efficiency of the homodyne detector, and…
We derive a master equation describing the collective decay of two-level atoms inside a single mode cavity in the dispersive limit. By considering atomic decay in the collective thermostat, we found a decoherence-free subspace of the multiparticle entangled states of the W-like class. We present a scheme for writing and storing these states in collective thermostat.
We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an alternate wave-packet basis for quantum information in the atom. A change of basis from energy levels to wave packets amounts to a discrete quantum Fourier transform within each atom. The algorithm then reduces to a series of conditional phase transforms between two entangled atoms in mixed energy and wave-packet bases. We show how to implement such transforms …
I want to show situations in which causal relation of two events is entangled and similar to time paradox, without employing time machines. Such situations will be obtained in measurement by two measurement devices moving mutually. According to the concept of the collapse of wave packet and the relativity of simultaneity, the causal relation of two measurements can be entangled.
We study single-photon emission of a classically pumped three-level $Λ$-type emitter in a high-$Q$ cavity. In particular, generation of single-photon time-bin double-peak wave packets is shown.
In this work, we experimentally manipulate the spectrum and phase of a biphoton wave packet in a two-dimensional frequency space. The spectrum is shaped by adjusting the temperature of the crystal, and the phase is controlled by tilting the dispersive glass plate. The manipulating effects are confirmed by measuring the two-photon spectral intensity (TSI) and the Hong-Ou-Mandel (HOM) interference patterns. Unlike the previous independent manipulation schemes, here we perform joint manipulation on the biphoton spectrum. The technique in this work paves the way for arbitrary shaping of a multi-ph…
In this letter, we provide evidence for a classical sector of states in the Hilbert space of Finite Quantum Mechanics (FQM). We construct a subset of states whose the minimum bound of position -momentum uncertainty (equivalent to an effective $\hbar$) vanishes. The classical regime, contrary to standard Quantum Mechanical Systems of particles and fields, but also of strings and branes appears in short distances of the order of the lattice spacing. {}For linear quantum maps of long periods, we observe that time evolution leads to fast decorrelation of the wave packets, phenomenon similar to the…
A simple model allows us to study the nonclassical behavior of slowly moving atoms interacting with a quantized field. Atom and field become entangled and their joint state can be identified as a mesoscopic "Schroedinger-cat". By introducing appropriate observables for atom and field and by analyzing correlations between them based on a Bell-type inequality we can show the corresponding nonclassical behavior.
A pair of optical pulses traveling through two dispersive media will become broadened and, as a result, the degree of coincidence between the optical pulses will be reduced. For a pair of entangled photons, however, nonlocal dispersion cancellation in which the dispersion experienced by one photon cancels the dispersion experienced by the other photon is possible. In this paper, we report an experimental demonstration of nonlocal dispersion cancellation using entangled photons. The degree of two-photon coincidence is shown to increase beyond the limit attainable without entanglement. Our resul…
We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against general coherent attacks. The protocol is additionally compatible with standard fiber telecommunications channels and wavelength division multiplexers. We offer multiple implementations to enhance the transmission rate and describe a heralded qudit source that is easy to im…
We propose a bootstrapping approach to generation of maximally path-entangled states of photons, so called ``NOON states''. Strong atom-light interaction of cavity QED can be employed to generate NOON states with about 100 photons; which can then be used to boost the existing experimental Kerr nonlinearities based on quantum coherence effects to facilitate NOON generation with arbitrarily large number of photons all within the current experimental state of the art technology. We also offer an alternative scheme that uses an atom-cavity dispersive interaction to obtain sufficiently high Kerr-no…
Quantum light spectroscopy, providing novel molecular information non-accessible by classical light, necessitates new computational tools when applied for complex molecular systems. We introduce two computational protocols for the molecular nuclear wave packet dynamics interacting with an entangled photon pair to produce the entangled two-photon absorption signal. The first involves summing over transition pathways in a temporal grid defined by two light-matter interaction times accompanied by the field correlation functions of quantum light. The signal is obtained by averaging over the two-ti…
Controls of waveforms (pulse durations) of single photons are important tasks for effectively interconnecting disparate atomic memories in hybrid quantum networks. So far, the waveform control of single photon that is entangled with an atomic memory remains unexplored. Here, we demonstrated control of waveform length of the photon that is entangled with an atomic spin-wave memory by varying light-atom interaction time in cold atoms. The Bell parameter S as a function of the duration of photon pulse is measured, which shows that violations of Bell equality can be achieved for the photon pulse i…
In the present paper an example of entanglement between two different kinds of interacting particles, photons and electrons is analysed. The initial-value problem of the Schroedinger equation is solved non-perturbatively for the system of a free electron interacting with a quantized mode of the electromagnetic radiation. Wave packets of the dressed states so obtained are constructed in order to describe the spatio-temporal separation of the subsystems before and after the interaction. The joint probability amplitudes are calculated for the detection of the electron at some space-time location …
A class of centrosymmetric molecules support excitons with a well-defined quasi-angular momentum. Cofacial arrangements of these molecules can be engineered so that quantum cutting produces a pair of excitons with angular momenta that are maximally entangled. The Bell state constituents can subsequently travel in opposite directions down molecular chains as ballistic wave packets. This is a direct excitonic analog to the entangled polarization states produced by the spontaneous parametric downconversion of light. As in optical settings, the ability to produce Bell states should enable foundati…
The discovery of Berry and Balazs in 1979 that the free-particle Schrödinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schrödinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the c…
A single 40Ca+ ion is trapped and laser cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S1/2 to D5/2 transition causes a phase shift proportional to the ion's motional quantum state |n>. As the phase shift is conditional upon the ion's motion, we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target state {S,D} is flipped depending on the motional qubit state |n>={|0>,|1>}. Finally, we discuss scaling properties of this universal quantum gate for linear ion crystals and present numeri…
We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a c…
The efficient quantum state reconstruction algorithm described in [P. Six et al., Phys. Rev. A 93, 012109 (2016)] is experimentally implemented on the non-local state of two microwave cavities entangled by a circular Rydberg atom. We use information provided by long sequences of measurements performed by resonant and dispersive probe atoms over time scales involving the system decoherence. Moreover, we benefit from the consolidation, in the same reconstruction, of different measurement protocols providing complementary information. Finally, we obtain realistic error bars for the matrix element…
The dispersion cancellation feature of pulses which are entangled in frequency is employed to synchronize clocks of distant parties. The proposed protocol is insensitive to the pulse distortion caused by transit through a dispersive medium. Since there is cancellation to all orders, also the effects of slowly fluctuating dispersive media are compensated. The experimental setup can be realized with currently available technology, at least for a proof of principle.
An ad hoc quantization scheme for the electromagnetic field in a weakly dispersive, transparent dielectric leads to the definition of canonical and kinetic forms for the momentum of the electromagnetic field in a dispersive medium. The canonical momentum is uniquely defined as the operator that generates spatial translations in a uniform medium, but the quantization scheme suggests two possible choices for the kinetic momentum operator, corresponding to the Abraham or the Minkowski momentum in classical electrodynamics. Another implication of this procedure is that a wave packet containing a s…
In the paper, we employ a wavefunction approach to investigate the evolution of a two-photon wave packet propagating in a one-dimensional waveguide coupled to the Jaynes-Cummings (JC) system. We derive and solve, both analytically and numerically, a set of equations of motion governing the quantum state of the system. That allows us to provide real-time analysis of the evolution of the wave packet two-photon joint spectrum (2PJS) and the excitation dynamics of the JC system in the course of its interaction with the two-photon pulse. We demonstrate that the 2PJS and the spectrum of the wave pac…
We discuss the generation of a macroscopic entangled state in a single atom cavity-QED system. The three-level atom in a cascade configuration interacts dispersively with two classical coherent fields inside a doubly resonant cavity. We show that a macroscopic entangled state between these two cavity modes can be generated under large detuning conditions. The entanglement persists even under the presence of cavity losses.
Recently a new formulation of quantum mechanics has been introduced, based on signed classical field-less particles interacting with an external field by means of only creation and annihilation events. In this paper, we extend this novel theory to the case of many-body problems. We show that, when restricted to spatial finite domains and discrete momentum space, the proposed extended theory is equivalent to the time-dependent many-body Wigner Monte Carlo method. In this new picture, the treatment of entangled systems comes naturally and, therefore, we apply it to the study of quantum entangled…
An energy-time entanglement-based dispersive optics quantum key distribution (DO-QKD) is demonstrated experimentally over optical fibers of 20 km. In the experiment, the telecom band energy-time entangled photon pairs are generated through spontaneous four wave mixing in a silicon waveguide. The arrival time of photons are registered for key generating and security test. High dimensional encoding in the arrival time of photons is used to increase the information per coincidence of photon pairs. The bin sifting process is optimized by a three level structure, which significantly reduces the raw…
We investigate how the polarization correlations of entangled photons described by wave packets are modified when measured by moving detectors. For this purpose, we analyze the Clauser-Horne-Shimony-Holt Bell inequality as a function of the apparatus velocity. Our analysis is motivated by future experiments with entangled photons designed to use satellites. This is a first step towards the implementation of quantum information protocols in a global scale.
The Hanbury Brown-Twiss (HBT) effect, at the quantum level, is essentially an interference of one particle with another, as opposed to interference of a particle with itself. Conventional treatments of identical particles encounter difficulties while dealing with entanglement. A recently introduced label-free approach to indistinguishable particles is described, and is used to analyze the HBT effect. Quantum wave-packets have been used to provide a better understanding of the quantum interpretation of the HBT effect. The effect is demonstrated for two independent particles governed by Bose-Ein…
Nonlinear spectroscopy and microscopy techniques are ubiquitous in a wide range of applications across physics and biology. However, these usually rely on high-powered pulsed laser systems. A promising alternative is to exploit entangled two-photon absorption (ETPA), which can lead to tens of orders of magnitude lower incident flux rates than in conventional two-photon absorption (TPA) schemes. However, the role of different entangled degrees of freedom in ETPA was unclear following recent experimental studies, when compared to earlier theoretical works. Here, we first demonstrate a linear dep…
Entanglement, describing the inseparability of a quantum multiparty system, is one of the most intriguing features of quantum mechanics. Violation of Bell inequality, for ruling out the possibility of local hidden variable theories, is commonly used as a strong witness for quantum entanglement. In previous Bell test experiments with photonic entanglement based on two-photon coincidence measurement, the photon temporal wave packets are absorbed completely by the detectors. That is, the photon coherence time is much shorter than the detection time window. Here we demonstrate generation of freque…
We propose and design a high-brightness, ultra-compact electrically pumped GaSb-based laser source of entangled photons generated by mode-matched intracavity parametric down-conversion of lasing modes. To describe the nonlinear mixing in highly dispersive and dissipative waveguides, we develop a nonperturbative quantum theory of parametric down-conversion of waveguide modes which takes into account the effects of modal dispersion, group and phase mismatch, propagation, dissipation, and coupling to noisy reservoirs. We extend our theory to the regime of quantized pump fields with a new approach…
Quantum error correction protects the quantum state against noise and decoherence in quantum communication and quantum computation, which enables one to perform fault-torrent quantum information processing. We experimentally demonstrate a quantum error correction scheme with a five-wave-packet code against a single stochastic error, the original theoretical model of which is firstly proposed by S. L. Braunstein and T. A. Walker. Five submodes of a continuous variable cluster entangled state of light are used for five encoding channels. Especially, in our encoding scheme the information of the …
Describing and understanding the essence of quantum entanglement and its connection to dynamical chaos is of great scientific interest. In this work, using information geometric (IG) techniques, we investigate the effects of micro-correlations on the evolution of maximal probability paths on statistical manifolds induced by systems whose microscopic degrees of freedom are Gaussian distributed. We use the statistical manifolds associated with correlated and non-correlated Gaussians to model the scattering induced quantum entanglement of two spinless, structureless, non-relativistic particles, t…
Recently the engineering of the entanglement for photon pairs generated during the spontaneous parametric down conversion process (SPDC) can be achieved via manipulation of pump wavelength behind a \c{hi}(2)-based type II SPDC process [1]. Such effect is used in this paper for demonstration of non-classical dispersion cancellation phenomenon in both local and nonlocal detections, theoretically. The following results are analytically achieved: I) For local detection, if narrow pump laser (highly entangled photons) are used, the dispersive broadening cancelation is directly depends on the degree…
Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large scale entangled states is challenging in the presence of decoherence. We present a quantum control strategy using highly nonlinear geometric phase gates for preparing entangled states on spin ensembles which can be used for practical precision metrology. The method uses a dispersive coupling of $N$ spins to a common bosonic mode and does not require addressability, special detunings, or interactions between the spins. Using a control sequence t…
