We study nonlinear dynamics of superposition of quantum wavepackets in various systems such as Kerr medium, Morse oscillator and bosonic Josephson junction. The prime reason behind this study is to find out how the superposition of states influence the dynamics of quantum systems. We consider the superposition states which are potential candidates for quantum computing and quantum communication and so it is most necessary that we study the dynamics for their proper understanding and usage. Methods in nonlinear time series analysis such as first return time distribution, recurrence plot and Lyapunov exponent are used for the qualification and quantification of dynamics. We found that there is a vast change in the dynamics of quantum systems when we consider the superposition of wave packets. These changes are observed in various kinds of dynamics such as periodic, quasi-periodic, ergodic, and chaotic dynamics.
The time-development of photoexcitations in molecular aggregates exhibits specific dynamics of electronic states and vibrational wavefunction. We discuss the dynamical formation of entanglement between electronic and vibrational degrees of freedom in molecular aggregates with theory of electronic energy transfer and the method of vibronic 2D wavepackets [Cina, Kilin, Humble, J. Chem. Phys. 118, 46 (2003)]. The vibronic dynamics is also described by applying Jaynes-Cummings model to the electronic energy transfer [Kilin, Pereverzev, Prezhdo, J. Chem. Phys. 120, 11209 (2004);math-ph/0403023]. Fo…
Binary discrete nonlinear Schrödinger equation is used to describe dynamics of two-species Bose-Einstein condensate loaded into an optical lattice. Linear inter-species coupling leads to Rabi transitions between the species. In the regime of strong nonlinearity, a wavepacket corresponding to condensate separates into localized and ballistic fractions. Localized fraction is predominantly formed by immiscible solitons consisted of only one species. Initial states without spatial separation of occupied sites expose formation of immiscible solitons after a strongly chaotic transient. We calculate …
The dynamics of an initially localized wavepacket is studied for the generalized nonlinear Schroedinger Equation with a random potential, where the nonlinearity term is |ψ|^p*ψand "p" is arbitrary. Mainly short times for which the numerical calculations can be performed accurately are considered. Long time calculations are presented as well. In particular the subdiffusive behavior where the average second moment of the wavepacket is of the form <m_{2}>~t^a is computed. Contrary to former heuristic arguments, no evidence for any critical behavior as function of "p" is found. The properties of α…
Heisenberg in 1929 introduced the "collapse of the wavepacket" into quantum theory. We review here an experiment at Berkeley which demonstrated several aspects of this idea. In this experiment, a pair of daughter photons was produced in an entangled state, in which the sum of their two energies was equal to the sharp energy of their parent photon, in the nonlinear optical process of spontaneous parametric down-conversion. The wavepacket of one daughter photon collapsed upon a measurement-at-a-distance of the other daughter's energy, in such a way that the total energy of the two-photon system …
We analyze a quantum optical memory based on the off-resonant Raman interaction of a single broadband photon, copropagating with a classical control pulse, with an atomic ensemble. The conditions under which the memory can perform optimally are found, by means of a `universal' mode decomposition. This enables the memory efficiency to be specified in terms of a single parameter, and the control field pulse shape to be determined via a simple nonlinear scaling. We apply the same decomposition to determine the optimal configurations for read-out.
We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhances localization in one type, and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of $δ$-like wavepackets in the presence of disorder. A transition from ballistic wavepacket expansion to exponential (Anderson) localization is observed. We find an intermediate…
Wavepacket transport across a nonlinear region is studied numerically at zero and finite temperatures. In contrary to the zero temperature case which demonstrates ballistic transport, finite temperature lattice vibrations suppresses the transport drastically. The interface between the linear and the nonlinear chain plays the role of a high barrier at finite temperature when anharmonicity factor is small compared to the typical inverse cubic interatomic distance. Inverse participation ratio of the central region shows that for small anharmonicity and finite temperatures lattice vibrations give …
Scattering of a Gaussian wavepacket from rectangular potential barriers with increasing widths or heights is studied numerically. It is seen that during a certain time interval the time-evolving transmission probability increases compared to the corresponding unperturbed cases. In the literature this effect is known as superarrival in transmission probability. We present a trajectory-based explanation for this effect by using the concept of quantum potential energy and computing a selection of Bohmian trajectories. Relevant parameters in superarrivals are determined for the case that the barri…
Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and fiel…
It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must play an essential role in such cases. As a striking example, the logical paradoxes usually associated with causality violation can be resolved by quantum effects. We ask whether the explicit construction of a theory that allows causality violation might in turn teach us something about quantum gravity. Taking the toy model of Deutsch as a starting point, in Par…
The dynamics of a three-state quantum walk with amplitude-dependent phase shifts is investigated. We consider two representative inputs whose linear evolution is known to display either full dispersion of the wave packet or intrinsic localization on the initial position. The nonlinear counterpart presents much more involved dynamics featuring self-trapping, solitonic pulses, radiation, and chaotic-like behavior. We show that nonlinearity leads to a metastable self-trapped wavepacket component that radiates in the long-time regime with the survival probability $\propto t^{-1/2}$. A sudden dynam…
Seeing macroscopic quantum states directly remains an elusive goal. Particles with boson symmetry can condense into such quantum fluids producing rich physical phenomena as well as proven potential for interferometric devices [1-10]. However direct imaging of such quantum states is only fleetingly possible in high-vacuum ultracold atomic condensates, and not in superconductors. Recent condensation of solid state polariton quasiparticles, built from mixing semiconductor excitons with microcavity photons, offers monolithic devices capable of supporting room temperature quantum states [11-14] tha…
Two-photon time-frequency entanglement is a valuable resource in quantum information. Resolving the wavepacket of ultrashort pulsed single-photons, however, is a challenge. Here, we demonstrate remote spectral shaping of single photon states and probe the coherence properties of two-photon quantum correlations in the time-frequency domain, using engineered parametric down-conversion (PDC) and a quantum pulse gate (QPG) in nonlinear waveguides. Through tailoring the joint spectral amplitude function of our PDC source we control the temporal mode structure between the generated photon pairs and …
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…
Full control over the spatio-temporal structure of quantum states of light is an important goal in quantum optics, to generate for instance single-mode quantum pulses or to encode information on multiple modes, enhancing channel capacities. Quantum light pulses feature an inherent, rich spectral broadband-mode structure. In recent years, exploring the use of integrated optics as well as source-engineering has led to a deep understanding of the pulse-mode structure of guided quantum states of light. In addition, several groups have started to investigate the manipulation of quantum states by me…
Time-Frequency Continuous-Variable Quantum Teleportation with Single Photons
Telecom Paris, Institut Polytechnique de Paris（巴黎电信学院，巴黎理工学院）；Centre for Nanosciences and Nanotechnology, CNRS, Université Paris-Saclay（纳米科学与工程中心，法国国家科学研究中心，巴黎萨克雷大学）
The large-scale expansion dynamics of quantum gases is a central tool for ultracold gas experiments and poses a significant challenge for theory. In this work we provide an exact reformulation of the Gross-Pitaevskii equation for the ultracold Bose gas in a coordinate frame that adaptively scales with the system size during evolution, enabling simulations of long evolution times during expansion or similar large-scale manipulation. Our approach makes no hydrodynamic approximations, is not restricted to a scaling ansatz, harmonic potentials, or energy eigenstates, and can be generalized readily…
