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Register a new userNon-Hermitian wave packet approximation for coupled two-level systems in weak and intense fields
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Added by
Raiju Puthumpally-Joseph
Publication date
2016
fields
Physics
and research's language is
English
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We introduce an accurate non-Hermitian Schrodinger-type approximation of Bloch optical equations for two-level systems. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics in both weak and strong laser fields. In this approach, it is sufficient to propagate the wave function of the quantum system instead of the density matrix, providing that relaxation and dephasing are taken into account via automatically-adjusted time-dependent gain and decay rates. The developed formalism is applied to the problem of scattering and absorption of electromagnetic radiation by a thin layer comprised of interacting two-level emitters.
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We introduce a non-Hermitian approximation of Bloch optical equations. This approximation provides a complete description of the excitation, relaxation and decoherence dynamics of ensembles of coupled quantum systems in weak laser fields, taking into account collective effects and dephasing. In the proposed method one propagates the wave function of the system instead of a complete density matrix. Relaxation and dephasing are taken into account via automatically-adjusted time-dependent gain and decay rates. As an application, we compute the numerical wave packet solution of a time-dependent non-Hermitian Schrodinger equation describing the interaction of electromagnetic radiation with a quantum nano-structure and compare the calculated transmission, reflection, and absorption spectra with those obtained from the numerical solution of the Liouville- von-Neumann equation. It is shown that the proposed wave packet scheme is significantly faster than the propagation of the full density matrix while maintaining small error. We provide the key ingredients for easy-to-use implementation of the proposed scheme and identify the limits and error scaling of this approximation.
The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decays. In the limit of very high decay rates, on the basis of this effective description we can predict the occurrence of a quantum Zeno dynamics which is interpreted as the removal of some coupling terms and the vanishing of an operatorial pseudo-Lamb shift.
Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLSs). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant $pi$-pulses in which the Rabi frequency is approximately 40% or higher of the transition frequency do not achieve complete inversion in TLSs. Hence, guided by analytical results based on the averaging technique, we propose two methods for obtaining population
Entanglement is essential in quantum information science. Typically, the inevitable coupling between quantum systems and environment inhibits entanglement from being created between long-distance subsystems and being maintained for a long time. In this paper, we show that when the environment is composed of a bath of massive scalar fields, the region of the separation within which entanglement can be generated is significantly enlarged, and the decay rate of entanglement is significantly slowed down compared with those in the massless case, when the mass of the field $m$ is smaller than but close to the transition frequency of the qubits $omega$. When $mgeqomega$, the initial entanglement can be maintained for an arbitrarily long time, regardless of the environmental temperature. Therefore, in principle, it is possible to achieve long-distance entanglement generation and long-lived entanglement by manipulating the energy level spacing of the two-level systems with respect to the mass of the field.
Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection have been analyzed to characterize the topology of these systems. While the topological classification of non-Hermitian systems is being developed, little attention has been paid to the impact of the new geometric phases on dynamics and transport. In this work, we derive the full set of semiclassical equations of motion for wave-packet dynamics in a system governed by a non-Hermitian Hamiltonian, including corrections induced by the Berry connection. We show that non-Hermiticity is manifested in anomalous weight rate and velocity terms that are present already in one-dimensional systems, in marked distinction from the Hermitian case. We express the anomalous weight and velocity in terms of the Berry connections defined in the space of left and right eigenstates and compare the analytical results with numerical lattice simulations. Our work specifies the conditions for observing the anomalous contributions to the semiclassical dynamics and thereby paves the way to their experimental detection, which should be within immediate reach in currently available metamaterials.
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