In this paper, we analyze two different techniques based on reservoir engineering method and quantum Zeno effect for controlling decoherence of a dissipative charged oscillator in the presence of an external magnetic field. Our main focus is to investigate the sensitiveness of these decoherence control techniques on the details of different environmental spectrum (
J(ω)), and on the crucial role played by different system and reservoir parameters, e.g., external magnetic field (
rc), confinement length (
r0), temperature (T), cut-off frequency of reservoir spectrum (
ωcut), and measurement interval (
τ). First, we consider the charged quantum oscillator in an initial nonclassical Schrodinger cat state and analyze the non-Markovian dynamics for the magneto-oscillator in contact with Ohmic, sub-Ohmic, and super-Ohmic environments. We show the procedure to control the quantumness of the Schrodinger cat state by tuning the parameters
rc,
r0, and
J(ω). On the other hand, we investigate the effect of nonselective energy measurement process on the mortification of quantumness of an initial Fock-Darwin state of the charged magneto-oscillator. We investigate in details the strategy to manipulate the continuous passage from decay suppression to decay acceleration by engineered reservoirs and by tuning the system or reservoir parameters, e.g.,
rc,
r0, T or
τ. As a result of that one can control environment induced decoherence (EID).
The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic, and super-Ohmic environments, without performing the Markovian approximation. Our results allow one to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.
We investigate the quantum dissipative dynamics of a charged magneto-oscillator(CMO) coupled to a heat bath of harmonic oscillators in the presence of an additional field-bath interaction. The problem is formulated within the framework of the generalized quantum Langevin equation, where the external confining potential modifies the random force correlations and the memory kernel of the environment, and the effective spring constant. Using the corresponding non-Markovian master equation, we examine the influence of the field-bath coupling on the temporal decay of the reduced density matrix of the system. We show that the additional interaction leads to an enhancement of the decoherence rate by altering the dissipative response of the bath. Thus our results shed light on the role of field-bath coupling in the quantum to classical transition of a CMO. The resulting fluctuation-dissipation relation is analyzed, and the position autocorrelation, position-velocity correlation and velocity autocorrelation are obtained explicitly. The dependence of these experimentally accessible quantities on the field-bath coupling parameter is discussed. We outline an experimental proposal for testing our theoretical predictions. The study sheds light on reservoir engineering which is central to quantum technologies.
Abstract The study of decoherence plays a key role in our understanding of the transition from the quantum to the classical world. Typically, one considers a system coupled to an external bath which forms a model for an open quantum system. While most of the studies pertain to a position coupling between the system and the environment, some involve a momentum coupling, giving rise to an anomalous diffusive model. Here we have gone beyond existing studies and analyzed the non-Markovian master equation, involving the quantum Langevin dynamics of a harmonically oscillating charged Brownian particle in the presence of a magnetic field and coupled to Ohmic (s = 1), sub-Ohmic (s < 1) and super-Ohmic (s > 1) heat baths via both position and momentum couplings. The presence of both position and momentum couplings leads to a stronger interaction with the environment, resulting in a faster loss of coherence compared to a situation where only position coupling is present. The rate of decoherence can be tuned by controlling the relative strengths of the position and momentum coupling parameters. In addition, the magnetic field results in the slowing down of the loss of information from the system, irrespective of the nature of coupling between the system and the bath. A faster decoherence rate is observed for higher values of the Ohmicity parameter ‘s’. Our results can be experimentally verified by designing a suitable ion trap setup.
Abstract We derive a non-Markovian master equation for a charged particle in a magnetic field coupled to a bath and study decoherence by analyzing the temporal decay of the off-diagonal elements of the reduced density matrix in the position basis. The coherent oscillations characterized by the cyclotron frequency get suppressed as a result of decoherence due to coupling with the environment. We consider an Ohmic bath with three distinct models for the high-frequency cutoff for the spectral density of the bath and compare the three cases. As expected, the three cutoff models converge in the limit of the uppermost frequency of the bath tending to infinity. We notice a dramatic slowing down of loss of coherence in the low-temperature limit dominated by zero point quantum fluctuations compared to the high-temperature classical limit dominated by thermal fluctuations. We also go beyond the Ohmic model and study super-Ohmic and sub-Ohmic baths with the spectral densities deviating from a linear dependence on the frequency. Our results are testable in a state of the art cold atom laboratory.
In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.