Decoherence of quantum Brownian motion in noncommutative space

The decoherence of a harmonic oscillator under two-dimensional quantum Brownian motion on a noncommutative plane is investigated. The interaction with the environment is considered by two separate models so-called coupled and uncoupled. The two-dimensional master equation and its noncommutative counterpart are derived for both employed models. The rate of the linear entropy (predictability sieve) is chosen as a criterion to investigate the purity in the presence of the space noncommutativity. Besides, a two-dimensional charged harmonic oscillator on a plane which is imposed by a perpendicular magnetic field is introduced as a realization of our model. Therefore, our approach provides a formalism to investigate the influence of the magnetic field on the decoherence of the pure states. We show that in the high magnetic field limit the rate of the decoherence will be decreased.     

Non-Markovian weak coupling limit of quantum Brownian motion

We derive and solve analytically the non-Markovian master equation for harmonic quantum Brownian motion proving that, for weak system-reservoir couplings and high temperatures, it can be recast in the form of the master equation for a harmonic oscillator interacting with a squeezed thermal bath. This equivalence guarantees preservation of positivity of the density operator during the time evolution and allows one to establish a connection between the dynamics of Schrödinger cat states in squeezed environments and environment-induced decoherence in quantum Brownian motion.

     

Master equation for a quantum particle in a gas

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.     

Quantum Zeno control of decoherence

We demonstrate the possibility of controlling the quantum to classical transition by means of the quantum Zeno and anti-Zeno effects. We consider a quantum harmonic oscillator initially prepared in a Schrödinger cat state and interacting with an engineered amplitude reservoir. We show that the environment induced decoherence transforming the cat state into a statistical mixture can be strongly inhibited by means of either appropriate sequences of measurements or shuttered reservoirs.     

Dynamics of driven Brownian inverted oscillator

In this paper, we derive the quantum Langevin equation for a driven Brownian inverted oscillator in the framework of the Heisenberg picture for the Caldeira-Leggett model. We describe the influence of an arbitrary time-dependent force on an open inverted oscillator dynamics. We take into account environment through the integral operator of relaxation and the force correlation function. The resulting behavior of the system is represented as a combination the time evolution of the position expectation and the variance, being induced simultaneously by spreading the wave packet and the chaotic Brownian motion. We discuss the possibility of stabilization of an open inverted oscillator, when applying external alternating force.     

Quantum decoherence in the theory of open systems

Within the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time scale and analyze the transition from quantum to classical behavior of the considered system. The text was submitted by the author in English.     

Nonlinear Theory of Quantum Brownian Motion

A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrödinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum Smoluchowski-like equation, which is proven to reproduce key results from the quantum and classical physics. The application of the theory to a free quantum Brownian particle results in a nonlinear dependence of the position dispersion on time, being quantum generalization of the Einstein law of Brownian motion. It is shown that the time of decoherence from quantum to classical diffusion is proportional to the square of the thermal de Broglie wavelength divided by the classical Einstein diffusion constant.     

Quantum decoherence of the damped harmonic oscillator

In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations. The text was submitted by the author in English.     

Information and Entropy in Quantum Brownian Motion

We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two entropies which are due to the fact that the Brownian particle and its environment are entangled. We give an explanation for these findings and point out that these deviations become important in cases where statements about the information capacity of the subsystem are associated with thermodynamic properties, as it is the case for the Landauer principle.     

Suppression of decoherence in a wave packet via nonlinear resonance

We propose a simple approach for suppressing decoherence of a wave packet excited in an anharmonic oscillator. We show that when a resonant external field forces the oscillator to follow the driving force, motion around the resonant trajectory inside a stable resonant island can be made almost completely immune to the environment. As an example, we study suppression of decoherence due to coupling to thermally populated rotations in vibrational wave packets in a Na2 molecule.     

Quantum decoherence and classical correlations of the harmonic oscillator in the Lindblad theory

In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical behaviour of the considered system is analysed and it is shown that the classicality takes place during a finite interval of time. We calculate also the decoherence time and show that it has the same scale as the time after which statistical fluctuations become comparable with quantum fluctuations.     

Parallel decoherence in composite quantum systems

For the standard quantum Brownian motion (QBM) model, we point out the occurrence of simultaneous (parallel), mutually irreducible and autonomous decoherence processes. Besides the standard Brownian particle, we show that there is at least another system undergoing the dynamics described by the QBM model. We do this by selecting the two mutually irreducible, global structures (decompositions into subsystems) of the composite system of the QBM model. The generalization of this observation is a new, challenging task in the foundations of the decoherence theory. We do not place our findings in any interpretational context.     

Zeno and anti-Zeno effects for quantum Brownian motion

In this Letter, we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behavior of environment induced decoherence is ultimately responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally, we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context.     

Multipartite entanglement dynamics and decoherence from a quantum-critical environment

We investigate the entanglement dynamics and decoherence of a multipartite system under an environment which can exhibit a quantum phase transition. Our result implies that the entanglement evolution depends not only on the size of the system and the quantum states of concern but also on the environment. In the sense of the linear entropy to measure decoherence induced by the environment, the decoherence-free subspaces have been identified for our model.     

Decoherence by correlated noise and quantum error correction

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.     

Circuit design based manipulation of decoherence and disentanglement

In the process of quantum information transport, environment inevitably causes decoherence and disentanglement. It is effective to constitute a hybrid qubit system by taking advantages of different types of qubits to overcome the effects of decoherence and achieve quantum information transport. We find that energy relaxation exists in the process of information exchange bewteen the hybrid qubits. Combining this kind of energy relaxation with the decoherence effects from external environment, quantum information transport of non-disentangled effect can be achieved in phase damping channel if the exchange decay rate and decoherence time satisfy certain constraint relations. We discuss the scheme to achieve the constraint relations through combining specific quantum circuits.     

The Lee–Friedrichs Model: Continuous Limit and Decoherence

We analyze the thermodynamic limit of the Hamiltonian, states and observables, of a system containing an oscillator interacting with a thermal bath We use the results to a compare environment and self induced decoherence.     

Exact master equation for a noncommutative Brownian particle

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.