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.
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.
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.
The loss of coherence in a general open quantum system interacting with a bosonic environment is analyzed. The reservoir is initially in a thermal state. The reduced dynamics is described by a non-Markovian time-local master equation. We consider spectral densities that are sub- or super-Ohmic at low frequencies and arbitrarily shaped at high frequencies. In the super-Ohmic regime, for noninteger frequency powers larger than 2, long time survival of coherence appears. In the latter regime, at vanishing temperature, the asymptotic amount of surviving coherence is stabilized to its initial value, up to a phase factor, by properly increasing the bandwidth and decreasing the low-frequency profile of the spectral density. For noninteger positive frequency powers less than 2, stretched exponential-like decoherence is found over long times. The relaxations to the asymptotic configurations become arbitrarily slow by approaching the frequency power 2 of the super-Ohmic regime. The same dependence on temperature, spectral density, and scale frequency appears for purity and concurrence of two qubits and coherence of a qubit.
In this work, we consider the dissipative dynamics of a quantum Brownian magneto-oscillator in contact with different types of environment at zero temperature as well as at high temperatures. We derive closed-form expressions of decay rate and heating rate for the magneto-oscillator in contact with Ohmic, sub-Ohmic, and super-Ohmic environments with non-Markovian characteristics. The present study is useful in determining the relationship between the thermalization dynamics of a magneto-oscillator and different forms of environmental spectrum and external magnetic field. Although our study is limited to the short-time (Non-Markovian) and long-time (Markovian) regimes, it manifests that one can actually tune the effective coupling of the system reservoir either by tuning oscillator frequency through reservoir engineering techniques or changing external magnetic field. Thus the present work establishes the essential role of non-Markovian dissipation and the crucial role of magnetic field in the environment induced decoherence and decay processes of the dissipative magneto-oscillator.
We study the non-Markovian dynamics of a qubit made up of a two-level atom interacting with an electromagnetic field (EMF) initially at finite temperature. Unlike most earlier studies where the bath is assumed to be fixed, we study the complete evolution of the combined qubit-EMF system, thus allowing for the coherent backaction from the bath on the qubit and the qubit on the bath in a self-consistent manner. In this way we can see the development of quantum correlations and entanglement between the system and its environment, and how that affects the decoherence and relaxation of the system. We find nonexponential decay for both the diagonal and nondiagonal matrix elements of the qubit's reduced density matrix in the pointer basis. The former shows the qubit relaxing to thermal equilibrium with the bath, while the latter shows the decoherence rate beginning at the usually predicted thermal rate, but changing to the zero-temperature value as the qubit and bath become entangled. The decoherence and relaxation rates are comparable, as in the zero-temperature case. On the entanglement of a qubit with the EMF we calculated the fidelity and the von Neumann entropy, which is a measure of the purity of the density matrix. The present more accurate non-Markovian calculations predict lower loss of fidelity and purity as compared with the Markovian results. Generally speaking, with the inclusion of quantum correlations between the qubit and its environment, the non-Markovian processes tend to slow down the drive of the system to equilibrium, prolonging the decoherence and better preserving the fidelity and purity of the system.
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.
Understanding the behavior of a quantum system coupled to its environment is of fundamental interest in the general field of quantum technologies. It also has important repercussions on foundational problems in physics, such as the process of decoherence and the so-called quantum measurement problem. There have been many approaches to explore Markovian and non-Markovian dynamics within the framework of open quantum systems, but the richness of the ensuing dynamics is still not fully understood. In this paper we develop a non-Markovian extension of the standard Caldeira-Leggett model, based on expanding the dynamics of the reduced system at high temperature in inverse powers of the high-frequency cutoff of the Ohmic spectral density of the environment and derive a non-Markovian master equation for the reduced density matrix for the case of a general potential. We also obtain a fully analytical solution in the free particle case. While the short-time behavior of this solution does not diverge substantially from the Markovian behavior, at intermediate times we find a resurgence of coherence, which we name lateral coherence. We identify this with a corresponding transient negative entropy production rate, which is understood to be characteristic of non-Markovian dynamics. We also analyze the positivity of the reduced density matrix and derive the corresponding Fokker-Planck equation in the classical limit.