In this Thesis we study the quantum to classical transition process in the context of quantum mechanics and quantum field theory. We shall analyze the effects that general environments, namely ohmic and non-ohmic, at zero and high temperature induce over a quantum Brownian particle. We state that the evolution of the system can be summarized in terms of two main environmental induced physical phenomena: decoherence and energy activation. In this Thesis, we shall show that the latter is a post-decoherence phenomenon. As the energy is an observable, the excitation process can be consider a direct indicator of the system-environment entanglement particularly useful at zero temperature.
From other point of view, we shall study different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and for neutral particles with permanent dipole moments. In this context, we shall show that the interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. In this context, we shall apply our results to a real matter wave interferometry experiment. We shall also show under which general conditions the geometry phase of a quantum open system can be observed.Finally, we shall study the decoherence process during a quantum phase transition. In this framework, we shall show that it can be phrased easily in terms of the decoherence functional, without having to use the master equation. To demonstrate this, we shall consider the decohering effects due to the displacement of domain boundaries, with implications for the displacement of defects, in general. We shall see that decoherence arises so quickly in this event, that it is negligible in comparison to decoherence due to field fluctuations in the way defined in previous papers.
Using the spin wave approximation, we study the decoherence dynamics of a central spin coupled to an antiferromagnetic environment under the application of an external global magnetic field. The external magnetic field affects the decoherence process through its effect on the antiferromagnetic environment. It is shown explicitly that the decoherence factor which displays a Gaussian decay with time depends on the strength of the external magnetic field and the crystal anisotropy field in the antiferromagnetic environment. When the values of the external magnetic field is increased to the critic…
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…
The elimination of decoherence of a multiphoton two-state quantum system by using an appropriate external driving field is considered. The multiphoton process caused by the noise field has a supersymmetric Lie algebraic structure. The time-evolution equations for the off-diagonal elements of the density operator of the two-state system are derived in the interaction picture. A simple explicit formula is given for the time-dependent external driving field used to eliminate the decoherence of the multiphoton two-state system.
"Decoherence of quantum superpositions through coupling to engineered reservoirs" is the topic of a recent article by Myatt et al. [Nature {\underline{403}}, 269 (2000)] which has attracted much interest because of its relevance to current research in fundamental quantum theory, quantum computation, teleportation, entanglement and the quantum-classical interface. However, the preponderance of theoretical work on decoherence does not consider the effect of an {\underline{external field}}. Here, we present an analysis of such an effect in the case of the random delta-correlated force discussed b…
We investigate nonclassical properties of the output of a Bose-Einstein condensate in Milburn's model of intrinsic decoherence. It is shown that the squeezing property of the atom laser is suppressed due to decoherence. Nevertheless, if some very special conditions were satisfied, the squeezing properties of atom laser could be robust against the decoherence.
We present expressions demonstrating that collisional decoherence of ultracold atoms or molecules in a coherent superposition of non-degenerate quantum states is suppressed when both the real and imaginary parts of the scattering lengths for the states in the coherent superposition are equal. We show that the rate of collisional decoherence can be enhanced or suppressed by varying an external magnetic field near a Feshbach resonance. For some resonances, the suppression is very dramatic. We propose a method for measuring the scattering length of ultracold particles in excited quantum states ex…
We derive an influence action for the heat diffusion equation and from its spectral dependence show that long wavelength hydrodynamic modes are most readily decohered. The result is independent of the details of the microscopic dynamics, and follows from general principles alone.
By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-xi Liu et.al. [Phys. Rev. A {\bf 63}, 033816 (2001)]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed states of the excitons is investigated. Our result shows that, thought the characteristic time of decoherence does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the external parameters.
We study the interference of C70 fullerenes in a Talbot-Lau interferometer with a large separation between the diffraction gratings. This permits the observation of recurrences of the interference contrast both as a function of the de Broglie wavelength and in dependence of the interaction with background gases. We observe an exponential decrease of the fringe visibility with increasing background pressure and find good quantitative agreement with the predictions of decoherence theory. From this we extrapolate the limits of matter wave interferometry and conclude that the influence of collisio…
We present a method to determine the decay of multiparticle quantum correlations as quantified by the geometric measure of entanglement under the influence of decoherence. With this, we compare the robustness of entanglement in GHZ-, cluster-, W- and Dicke states of four qubits and show that the Dicke state is most robust. Finally, we determine the geometric measure analytically for decaying GHZ and cluster states of an arbitrary number of qubits.
This study was started to know mysterious classicality of nuclei. Using three particles model without external environments, it is found that decisions of respective state of three particles by decoherence are not simultaneous. Furthermore, in this model, wave function of total three body system collapses spontaneously without any external environments. Therefore we may able to insist that a wavefunction of our universe has already collapsed spontaneously without any external observer, because of the same mechanism with this model.
Reducing decoherence is an essential step toward realizing general-purpose quantum computers beyond the present noisy intermediate-scale quantum (NISQ) computers. To this end, dynamical decoupling (DD) approaches in which external fields are applied to qubits are often adopted. We numerically study DD using a two-level model system (qubit) under the influence of Markovian decoherence by using quantum optimal control theory with slightly modified settings, in which the physical objective is to maximally create and maintain a specified superposition state in a specified control period. An optima…
The dynamics of coherence in a two-qubit Heisenberg XXX model with magnetic field in the presence of the intrinsic decoherence is investigated. We discuss the influence of dipole parameter, spin distance, magnetic field and initial state parameter on coherence of the long time limit situation. Then, we discuss how decoherence changes with time with the initial state parameter and the decoherence parameter.
Gaussian state decoherence aspects due to interacting magnetic-like and gravitational fields are quantified through the quantum fidelity and Shannon entropy in the scope of the phase-space representation of elementary quantum systems. For Gaussian Wigner functions describing harmonic oscillator states, an interacting external field destroys the quantum fidelity and introduces a quantum beating behavior. Likewise, it introduces harmonic profiles for free particle systems. Some aspects of quantum decoherence for the quantum harmonic oscillator and for the free particle limit are also quantified …
We investigate the characteristics of entanglement teleportation of a two-qubit Heisenberg XYZ model under different Dzyaloshinskii-Moriya interaction with intrinsic decoherence taken into account. The comparison of the two different Dzyaloshinskii-Moriya interaction, the effects of the initial state and the inputting state on the entanglement teleportation are presented. The results reveal that the dynamics of entanglement is a symmetry function about for the system, whereas it is not for the system. The ferromagnetic case is superior to the antiferromagnetic case for restrain decoherence whe…
An array of ultracold polar molecules trapped in an external electric field is regarded as a promising carrier of quantum information. Under the action of this field, molecules are compelled to undergo pendular oscillations by the Stark effect. Particular attention has been paid to the influence of intrinsic decoherence on the model of linear polar molecular pendular states, thereby we evaluate the tripartite entanglement with negativity, as well as fidelity of bipartite quantum systems for input and output signals using electric dipole moments of polar molecules as qubits. According to this s…
We reformulate the quantum Monty Hall problem in the presence of decoherence. The decoherence destroys the fairness of the game. A new Nash equilibrium for a particular strategy profile in the presence of decoherence emerges. It is shown that in the presence of decoherence under the action of amplitude damping channel, Bob's winning probability is always higher than three-forth, irrespective of Alice's strategy, if he does not switch to the other door and always wins for a fully decohered case of the channel. Depolarizing channel damps up Bob's winning probability and gets better off if he sti…
The effect induced by an environment on a composite quantum system is studied. The model considers the composite system as comprised by a subsystem A coupled to a subsystem B which is also coupled to an external environment. We study all possible four combinations of subsystems A and B made up with a harmonic oscillator and an upside down oscillator. We analyzed the decoherence suffered by subsystem A due to an effective environment composed by subsystem B and the external reservoir. In all the cases we found that subsystem A decoheres even though it interacts with the environment only through…
We present an open loop (bang-bang) scheme to control decoherence in a generic one-qubit quantum gate and implement it in a realistic simulation. The system is consistently described within the spin-boson model, with interactions accounting for both adiabatic and thermal decoherence. The external control is included from the beginning in the Hamiltonian as an independent interaction term. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. The controls are determined ex…
Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice's payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice's payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around …
We study the dynamics of multipartite entanglement under the influence of decoherence. A suitable generalization of concurrence reveals distinct scaling of the entanglement decay rate of GHZ and W states, for various environments.
Some of the simplest modifications to general relativity involve the coupling of additional scalar fields to the scalar curvature. By making a Weyl rescaling of the metric, these theories can be mapped to Einstein gravity with the additional scalar fields instead being coupled universally to matter. The resulting couplings to matter give rise to scalar fifth forces, which can evade the stringent constraints from local tests of gravity by means of so-called screening mechanisms. In this talk, we derive evolution equations for the matrix elements of the reduced density operator of a toy matter s…
We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice's quantum strategy. Where as in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, the Bob's payoffs are found symmetrical with maximum at p=0.5 against his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob's classical strat…
Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms of energy and matter causing decoherence. This may have subtle implications on precision laboratory experiments and astronomical observations and could limit the ultimate capacities for quantum technologies prone to decoherence. To establish the essential physical mechanism of decoherence under weak spacetime fluctuations, we carry out a sequence of analytica…
We study the dynamics of a two-level quantum system interacting with an external environment that takes the form of an XY spin chain in the presence of an external magnetic field. While the presence of the bath itself can enhance the transition probability from the lower level to the upper level of the system, we show that this noise-assisted phenomenon is sensitive to a change of the quantum phase of the environment. The derivative of the transition probability displays a maximum in correspondence with the critical value of the applied field both in the case of isotropic and anisotropic chain…
We investigate the optimal control problem for non-Markovian open, dissipative quantum system. Optimal control using Pontryagin maximum principle is specifically derived. The influences of Ohmic reservoir with Lorentz-Drude regularization are numerically studied in a two-level system under the following three conditions: ω_0\llω_c, ω_0\approxω_c or ω_0\ggω_c, where ω_0 is the characteristic frequency of the quantum system of interest, and ω_c the cut-off frequency of Ohmic reservoir. The optimal control process shows its remarkable influences on the decoherence dynamics. The temperature is a k…
We study the spontaneous decoherence of the coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the hidden couplings between the center-of-mass and relative degrees of freedoms, which actually originates from the symmetries of the ring geometry and corresponding nont…
We show how it is possible to suppress decoherence using tailored external forcing acting as pulses. In the limit of infinitely frequent pulses decoherence and dissipation are completely frozen; however, a significant decoherence suppression is already obtained when the frequency of the pulses is of the order of the reservoir typical frequency scale. This method could be useful in particular to suppress the decoherence of the center-of-mass motion in ion traps.
We present a quantum interference approach to preserve coherence in the external states of an atom trapped in an optical lattice. We show that this is possible by suitably choosing the initial state of the atom. We demonstrate this in context of decoherence due to spontaneous emission in an one-dimensional optical double-well lattice.
Dielectric constant and absorption measurements on boron doped silicon samples show that transitions between the acceptor energy levels can be induced by an applied resonant ac electric field and the Stark tuning of level spacing with an external DC electric field. The relatively longer decoherence times were observed by the electric echo measurement in a low boron dopant concentration Si sample. The scalable acceptor-based system is a promising candidate of the charge qubit for quantum computing.
In the pursuit of speculative new particles, forces, and dimensions with vanishingly small influence on normal matter, understanding the ultimate physical limits of experimental sensitivity is essential. Here, I show that quantum decoherence offers a window into otherwise inaccessible realms. There is a standard quantum limit for diffusion that restricts some entanglement-generating phenomena, like soft collisions with new particle species, from having appreciable classical influence on normal matter. Such phenomena are classically undetectable but can be revealed by the anomalous decoherence …
The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath $\varrho_{B}(t)$ and of the system $\varrho_{S}(t)$ are written. Formal solution of the equation for $\varrho_{B}(t)$ in the 2-nd approximation in interaction yields a specific extra term, related to the intrinsic bath dynamics. This term is nonlinear in the reduced density matrix $\varrho_{S}(t)$, and vanishes in the Markovian limit. To verify the consistence a…
We study the dynamics of pure phase decoherence for a particle hopping around an N-site ring, coupled both to a spin bath and to an Aharonov-Bohm flux which threads the ring. Analytic results are found for the dynamics of the influence functional and of the reduced density matrix of the particle, both for initial single wave-packet states, and for states split initially into 2 separate wave-packets moving at different velocities. We also give results for the dynamics of the current as a function of time.
We show that classical-quantum correspondence of center of mass motion in two coupled delta-kicked rotors can be obtained from intrinsic decoherence of the system itself which occurs due to the entanglement of the center of mass motion to the internal degree of freedom without coupling to external environment.
We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems like ion traps, semicondutor quantum dots and atoms. We show that the interactions lead to a phenomenon of periodic disentanglement and entanglement between the qubits. The disentanglement is primarily caused by environmental perturbations. The qubits are seen to remain disentangled for a finite time before getting entangled again. We find that the phenomenon is generic and occurs for wide variety of …
We consider a strongly driven two-level (spin) system, with a periodic external field that induces a sequence of avoided level crossings. The spin system interacts with a bosonic reservoir which leads to decoherence. A Markovian dynamical equation is introduced without relying on the rotating wave approximation in the system-external field interaction. We show that the time evolution of the two-level system is directed towards an incoherent sum of periodic Floquet states regardless of the initial state and even the type of the coupling to the environment. Analyzing the time scale of approachin…
Decoherence is the process by which quantum systems interact and become correlated with their external environments; quantum trajectories are a powerful technique by which decohering systems can be resolved into stochastic evolutions, conditioned on different possible ``measurements'' of the environment. By calling on recently-developed tools from quantum information theory, we can analyze simplified models of decoherence, explicitly quantifying the flow of information and randomness between the system, the environment, and potential observers.
We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (``wobbling'') of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac-component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctu…
We investigate the influence of environmental noise on polarization entangled light generated by parametric emission in a cavity. By adopting a recently developed separability criterion, we show that: i) self-stimulation may suppress the detrimental influence of noise on entanglement; ii) when self-stimulation becomes effective, a classical model of parametric emission incorporating noise provides the same results of quantum theory for the expectation values involved in the separability criterion. Moreover we show that, in the macroscopic limit, it is impossible to observe violations of local …
When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes-Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.
We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.
We investigate entanglement properties of multipartite states under the influence of decoherence. We show that the lifetime of (distillable) entanglement for GHZ-type superposition states decreases with the size of the system, while for a class of other states -namely all graph states with constant degree- the lifetime is independent of the system size. We show that these results are largely independent of the specific decoherence model and are in particular valid for all models which deal with individual couplings of particles to independent environments, described by some quantum optical mas…
We study the decoherence process associated with the scattering of stochastic backgrounds of gravitational waves. We show that it has a negligible influence on HYPER-like atomic interferometers although it may dominate decoherence of macroscopic motions, such as the planetary motion of the Moon around the Earth.
The non-unitary evolution of initial number states in general Gaussian environments is solved analytically. Decoherence in the channels is quantified by determining explicitly the purity of the state at any time. The influence of the squeezing of the bath on decoherence is discussed. The behavior of coherent superpositions of number states is addressed as well.
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.
We study the effect of quantum noise on history dependent quantum Parrondo's games by taking into account different noise channels. Our calculations show that entanglement can play a crucial role in quantum Parrondo's games. It is seen that for the maximally entangled initial state in the presence of decoherence, the quantum phases strongly influence the payoffs for various sequences of the game. The effect of amplitude damping channel leads to winning payoffs. Whereas the depolarizing and phase damping channels lead to the losing payoffs. In case of amplitude damping channel, the payoffs are …
In the last years noncommutative quantum mechanics has been investigated intensively. We consider the influence of magnetic field on decoherence of a system in the noncommutative quantum plane. Particularly, we point out a model in which the magnetic field allows {\it in situ} dynamical control of decoherence as well as, in principle, observation of noncommutativity.
We consider quantum decoherence in solid-state systems by studying the transverse dynamics of a single qubit interacting with a fermionic bath and driven by external pulses. Our interest is in investigating the extent to which the lost coherence can be restored by the application of external pulses to the qubit. We show that the qubit evolution under various pulse sequences can be mapped onto Keldysh path integrals. This approach allows a simple diagrammatic treatment of different bath excitation processes contributing to qubit decoherence. We apply this theory to the evolution of the qubit co…
We study decoherence of the external degree of freedom of a tracer particle moving in a one dimensional dilute Boltzmann gas. We find that phase averaging is the dominant decoherence effect, rather than information exchange between tracer and gas particles. While a coherent superposition of two wave packets with different mean positions quickly turns into a mixed state, it is demonstrated that such superpositions of different momenta are robust to phase averaging, until the two wave packets acquire a different position due to the different velocity of each wave packet.
Decoherence in quantum computer memory due to the inevitable coupling to the external environment is examined. We take the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits are decohered collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of…
The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of environment on quantum computation is probed on the basis of its analogy to the problem of wave function collapse in quantum measurement.Techniques from the Hepp-Colemen approach and its generalization are used to deal with decoherence problems in quantum computation including dynamic mechanism of decoherence, quantum error avoiding tricks and calculation of decoh…
Quantum decoherence happens when the system interacts with the environment. Quantum correlation behaviours in the two-qubit spin squeezing model are studied under the influence of intrinsic decoherence. Quantitative results were determined, which depend on parameters of the physical system by checking different quantifiers of quantum correlation such as entanglement, local quantum uncertainty, trace distance discord and uncertainty-induced quantum nonlocality. We show that the entanglement suffers from intrinsic decoherence and exhibits sudden death, whereas the other measures are more robust …
The time evolution of a spin-1/2 particle under the influence of a locally applied external magnetic field, and interacting with anisotropic spin environment in thermal equilibrium at temperature $T$ is studied. The exact analytical form of the reduced density matrix of the central spin is calculated explicitly for finite number of bath spins. The case of an infinite number of environmental spins is investigated using the convergence of the rescaled bath operators to normal Gaussian random variables. In this limit, we derive the analytical form of the components of the Bloch vector for antifer…
