A phenomenological model of the time evolution of a particle wavepacket is presented that is subject to scattering event with small momentum transfer. It is suited for three dimensions and allows for an additional potential. For a random value of a phase parameter, it is equivalent to the decoherence by scattering off plane wave field states. Imposing some condition on the same phase parameter, the model delivers definite outcomes in a local pointer base. Common sense notions about the quantum-classical transition are readily obtained: Decoherent free particle solutions are localized constant-width wavepackets, quantum barrier scattering results in random reflection and transmission. The scattering process assumed in the phenomenological model is realized by scattering of a particle pair interacting by a force-distance law with small momentum transfer. Particles are localized not by decoherence but by a classical lensing effect. Schmidt paths in the Schmidt representation of the multiparticle state are products of single-particle wavepackets. Therefore the model has a natural 'Many Worlds' interpretation, identifying each Schmidt path with a classical branch. Different runs of the phenomenological model map the state of the same particular particle within different branches.
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk and the first Anderson localization in a discrete quantum walk architecture.
We use a spin-1/2 model to analyze tunnelling in a double well system coupled to an external reservoir. We consider different noise sources such as fluctuations on the height and central position of the barrier and propose an experiment to observe these effects in trapped ions or atoms.
Although coupling to a super-Ohmic bosonic reservoir leads only to partial dephasing on short time scales, exponential decay of coherence appears in the Markovian limit (for long times) if anharmonicity of the reservoir is taken into account. This effect not only qualitatively changes the decoherence scenario but also leads to localization processes in which superpositions of spatially separated states dephase with a rate that depends on the distance between the localized states. As an example of the latter process, we study the decay of coherence of an electron state delocalized over two semi…
Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with their environment. We show that the decoherence distribution has observable effects on the transport. If the decoherence reservoirs are distributed randomly without spatial correlations, a minimal degree of decoherence is necessary to obtain Ohmic conduction. Below this threshold the system is localized and thus, a decoherence driven metal-insulator transitio…
We study and compare the decoherent histories approach, the environment-induced decoherence and the localization properties of thesolutions to the stochastic Schrödinger equation in quantum jump simulationand quantum state diffusion approaches, for a quantum two-level system model. We show, in particular, that there is a close connection between the decoherent histories and the quantum jump simulation, complementing a connection with the quantum state diffusion approach noted earlier by Diósi, Gisin, Halliwell and Percival. In the case of the decoherent histories analysis, the degree of approx…
We investigate numerically the tunneling effect under influence of another particle in a double well system. Such influence from only one degree of freedom makes decoherence and quantum-classical transition, i.e., suppression of the tunneling effect. The decoherence happens even for cases that the influence is from a particle of very small mass, and it has virtually no effect in the corresponding classical dynamics. There are cases similar to dynamical localization that the suppressed tunneling rate is several times smaller than the classical counterpart. This result is relevant for understand…
A more detailed analysis of the measurement problem continues to support the position taken by Shimony and the author that collapse of the wave function takes place in an objective manner in the rhodopsin molecule of the retina. This casts further doubts on the theories involving a spontaneous localization collapse process or a no-collapse decoherence process taking place in the visual cortex in a subjective fashion. The possibility is then raised, as per Anandan, as to whether the solution of the measurement problem in quantum theory allows one to address the problem of quantizing gravitation…
We study the open system dynamics of a circuit QED model operating in the ultrastrong coupling regime. If the resonator is pumped periodically in time the underlying classical system is chaotic. Indeed, the periodically driven Jaynes-Cummings model in the Born-Oppenheimer approximation resembles a Duffing oscillator which in the classical limit is a well-known example of a chaotic system. Detection of the field quadrature of the output field acts as an effective position measurement of the oscillator. We address how such detection affects the quantum chaotic evolution in this bipartite system.…
We consider a wave packet of a charged particle passing through a cavity filled with photons at temperature T and investigate its localization and interference properties. It is shown that the wave packet becomes localized and the interference disappears with an exponential speed after a sufficiently long path through the cavity.
Using the path integral representation of the density matrix propagator of quantum Brownian motion, we derive its asymptotic form for times greater than the localization time, $ (\hbar / γk T )^{\half}$, where $γ$ is the dissipation and $T$ the temperature of the thermal environment. The localization time is typically greater than the decoherence time, but much shorter than the relaxation time, $γ^{-1}$. We use this result to show that the reduced density operator rapidly evolves into a state which is approximately diagonal in a set of generalized coherent states. We thus reproduce, using a co…
The loss of coherence in quantum mechanical superposition states limits the time for which quantum information remains useful. Similarly, it limits the distance over which quantum information can be transmitted, resembling Anderson localization, where disorder causes quantum mechanical states to become localized. Here, we investigate in a nuclear spin-based quantum simulator, the localization of the size of spin clusters that are generated by a Hamiltonian driving the transmission of information, while a variable-strength perturbation counteracts the spreading. We find that the system reaches …
The quantum to classical transition maybe caused by decoherence or by dynamical collapse of the wave-function. We propose quantum discord as a tool, 1) for comparing and contrasting the role of a collapse model (Continuous Spontaneous Localization) and various sources of decoherence (environmental and fundamental), 2) for detecting collapse model and fundamental decoherence for an experimentally demonstrated macroscopic entanglement. We discuss the experimental times which will lead to the detection of either Continuous Spontaneous Localization or fundamental decoherence. We further put bounds…
To account for the phenomenon of quantum decoherence of a macroscopic object, such as the localization and disappearance of interference, we invoke the adiabatic quantum entanglement between its collective states(such as that of the center-of-mass (C.M)) and its inner states based on our recent investigation. Under the adiabatic limit that motion of C.M dose not excite the transition of inner states, it is shown that the wave function of the macroscopic object can be written as an entangled state with correlation between adiabatic inner states and quasi-classical motion configurations of the C…
Motivated by trapping and cooling experiments with non-spherical nanoparticles, we discuss how their combined rotational and translational quantum state is affected by the interaction with a gaseous environment. Based on the quantum master equation in terms of orientation-dependent scattering amplitudes, we evaluate the localization rate for gas collisions off an anisotropic van der Waals-type potential and for photon scattering off an anisotropic dielectric. We also show how pure angular momentum diffusion arises from these open quantum dynamics in the limit of weak anisotropies.
Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum mixing for neutrinos. Once the mass-eigenstates that support flavor oscillations are identified as three-{\em qubit} modes, a decoherence scale can be extracted from correlation quantifiers, namely the entanglement of formation and the logarithmic negativity. Such a decoherence scale is compared with the coherence length of damped oscillations. Damping signat…
The spurious interaction of quantum systems with their environment known as decoherence leads, as a function of time, to a decay of coherence of superposition states. Since the interactions between system and environment are local, they can also cause a loss of spatial coherence: correlations between spatially distant parts of the system are lost and the equilibrium states can become localized. This effect limits the distance over which quantum information can be transmitted, e.g., along a spin chain. We investigate this issue in a nuclear magnetic resonance quantum simulator, where it is poss…
We address decoherence and classicalization of continuous-time quantum walks (CTQWs) on graphs. In particular, we investigate three different models of decoherence, and employ the quantum-classical (QC) dynamical distance as a figure of merit to assess whether, and to which extent, decoherence classicalizes the CTQW, i.e. turns it into the analogue classical process. We show that the dynamics arising from intrinsic decoherence, i.e. dephasing in the energy basis, do not fully classicalize the walker and partially preserves quantum features. On the other hand, dephasing in the position basis, a…
We describe how quasiclassical relative positions of particles emerge in an initially delocalized quantum system as scattering of a probe beam is observed. We show that in the multiparticle case this localization in position space occurs via intermediate states that are quantum superpositions of spatial configurations. These superpositions are robust to consecutive scattering events, and scattering alone does not lead to their decoherence. Instead the free evolution of the system combines with scattering to destroy these superpositions, leading the particles to adopt classical-like positions r…
We show how the ro-translational motion of anisotropic particles is affected by the model of Continuous Spontaneous Localization (CSL), the most prominent hypothetical modification of the Schrödinger equation restoring realism on the macroscale. We derive the master equation describing collapse-induced spatio-orientational decoherence, and demonstrate how it leads to linear- and angular-momentum diffusion. Since the associated heating rates scale differently with the CSL parameters, the latter can be determined individually by measuring the random motion of a single levitated nanorotor.
Postselection-induced localization and coherence in quantum walks on heterogeneous networks
Indian Institute of Science Education and Research Pune（印度科学教育研究所浦那分校）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所蒂鲁瓦南特普朗分校）
We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces decoherence and suppression of tunnelling. These features are widely accepted as definition of classicality, while we believe that classicality implies that quantum delocalized states spontaneously evolve into localized ones. We than show that this evolution take place only when both noise and non linearity in the equations are present.
We investigate decoherence in the quantum kicked rotator (modelling cold atoms in a pulsed optical field) subjected to noise with power-law tail waiting-time distributions of variable exponent (Levy noise). We demonstrate the existence of a regime of nonexponential decoherence where the notion of a decoherence rate is ill-defined. In this regime, dynamical localization is never fully destroyed, indicating that the dynamics of the quantum system never reaches the classical limit. We show that this leads to quantum subdiffusion of the momentum, which should be observable in an experiment.
Aperiodic Dissipation as a Mechanism for Steady-State Localization
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit（MajuLab，CNRS-南锡大学-索邦大学-新加坡国立大学-南洋理工大学国际联合研究单元）
We study the effects of non-hermitian perturbation on a quantum kicked model exhibiting a localization transition. Using an exact renormalization scheme, we show that the critical line separating the extended and localized phases approaches its semiclassical limit as the imaginary part of the kicking parameter is steadily increased. Further, the metastability of the quantum states appears to be directly correlated with the deviation between the semi-classical and quantum results. This direct evidence of quantum-classical correspondence suggests that non-hermitian perturbations may be used to m…
We show how multi-walker quantum walks can be implemented in a quantum quincunx created via cavity quantum electrodynamics. The implementation of a quantum walk with a multi-walker opens up the interesting possibility to introduce entanglement and more advanced walks. With different coin tosses and initial states the multi-walker quantum walk shows different probability distributions which deviate strongly from the classical random walks with quadratic enhanced spreadings and localization effects. By introducing decoherence, the transition from quantum walks to the classical versions is observ…
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. This aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This …
The experimental observation of a clear quantum signature of gravity is believed to be out of the grasp of current technology. However, several recent promising proposals to test the possible existence of non-classical features of gravity seem to be accessible by the state-of-art table-top experiments. Among them, some aim at measuring the gravitationally induced entanglement between two masses which would be a distinct non-classical signature of gravity. We explicitly study, in two of these proposals, the effects of decoherence on the system's dynamics by monitoring the corresponding degree o…
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior than that of classical random walks such as ballistic propagation or localization due to disorder. Physical implementations of quantum walks have only been made in very small scale systems severely limited by decoherence. Here we show that the propagation of photons in waveguide lattices, which have been studied extensively in recent years, are essentially …
We study the process of observation (measurement), within the framework of a `perspectival' (`relational', `relative state') version of the modal interpretation of quantum mechanics. We show that if we assume certain features of discreteness and determinism in the operation of the measuring device (which could be a part of the observer's nerve system), this gives rise to classical characteristics of the observed properties, in the first place to spatial localization. We investigate to what extent semi-classical behavior of the object system itself (as opposed to the observational system) is ne…
We propose a mechanism for testing the theory of collapse models such as continuous spontaneous localization (CSL) by examining the parametric heating rate of a trapped nanosphere. The random localizations of the centre-of-mass for a given particle predicted by the CSL model can be understood as a stochastic force embodying a source of heating for the nanosphere. We show that by utilising a Paul trap to levitate the particle and optical cooling, it is possible to reduce environmental decoherence to such a level that CSL dominates the dynamics and contributes the main source of heating. We show…
In a closed single-particle quantum system, spatial disorder induces Anderson localization of eigenstates and halts wave propagation. The phenomenon is vulnerable to interaction with environment and decoherence, that is believed to restore normal diffusion. We demonstrate that for a class of experimentally feasible non-Hermitian dissipators, which admit signatures of localization in asymptotic states, quantum particle opts between diffusive and ballistic regimes, depending on the phase parameter of dissipators, with sticking about localization centers. In diffusive regime, statistics of quantu…
Biological information processing is generally assumed to be classical. Measured cellular energy budgets of both prokaryotes and eukaryotes, however, fall orders of magnitude short of the power required to maintain classical states of protein conformation and localization at the Å, fs scales predicted by single-molecule decoherence calculations and assumed by classical molecular dynamics models. We suggest that decoherence is limited to the immediate surroundings of the cell membrane and of intercompartmental boundaries within the cell, and that bulk cellular biochemistry implements quantum in…
Geometry-Only CSL/DP Ratios and the Nonuniqueness of Decoherence Kernels
FirstPrinciples；Department of Computational Applied Mathematics and Operations Research, Rice University（莱斯大学计算应用数学与运筹学系）；School of Mathematics and Physics, The University of Sussex（萨塞克斯大学数学与物理学院）；National Quantum Computing Centre, Rutherford Appleton Laboratory（拉瑟福·阿普顿实验室国家量子计算中心）
The inflationary paradigm provides a mechanism to generate the primordial perturbations needed to explain the observed large scale structures in the universe. Inflation traces back all the inhomogeneities to quantum fluctuations although the structures look classical today. Squeezing of primordial quantum fluctuations along with the mechanism of decoherence accounts for many aspects of this quantum to classical transition, although it remains a matter of debate as to whether this is sufficient to explain the issue of realization of a single outcome (i.e. the issue of macro-objectification) fro…
We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, epsilon-classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamica…
We study excitation transport in a two-dimensional system of randomly assembled spins with power-law hopping in two dimensions. This model can be realized in cold atom quantum simulators with Rydberg atoms. In these experiments, due to the Rydberg blockade effect, the degree of disorder in the system is effectively tunable by varying the spin density. We study dynamics and eigenstate properties of the model as a function of disorder strength and system size and discuss potential limitations for experiments. At strong disorder we predominantly observe localized eigenstates with power-law tails.…
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a novel and useful characterization of quantum states in higher dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in t…
