Journal of Physics Conference Series

Dissipative effects in Multilevel Systems

A. I. Solomon, S. G. Schirmer

Published Nov 1, 2007• 2 citations

Abstract

Dissipation is sometimes regarded as an inevitable and regrettable presence in the real evolution of a quantum system. However, the effects may not always be malign, although often non-intuitive and may even be beneficial. In this note we we display some of these effects for N-level systems, where N = 2,3,4. We start with an elementary introduction to dissipative effects on the Bloch Sphere, and its interior, the Bloch Ball, for a two-level system. We describe explicitly the hamiltonian evolution as well as the purely dissipative dynamics, in the latter case giving the t → ∞ limits of the motion. This discussion enables us to provide an intuitive feeling for the measures of control-reachable states. For the three-level case we discuss the impossibility of isolating a two-level (qubit) subsystem; this is a Bohm-Aharonov type consequence of dissipation. We finally exemplify the four-level case by giving constraints on the decay of two-qubit entanglement.

DOI: 10.1088/1742-6596/87/1/012015

Related papers

Dissipative "Groups" and the Bloch Ball

A. I. Solomon, Sonia G. Schirmer

We show that a quantum control procedure on a two-level system including dissipation gives rise to a semi-group corresponding to the Lie algebra semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in the Bloch ball.

arXiv:quant-ph/0211027Nov 6, 20025 citations

Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems

Thomas E. Skinner

The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which provides information towards control of the dissipative process. The Bloch equation also describes a system of three coupled harmonic oscillators, providing additional perspective on dissipative systems.

Physical Review AJan 12, 20186 citations

Dissipative dynamics of an entangled three-qubit system via non-Hermitian Hamiltonian: Its correspondence with Markovian and non-Markovian regimes

M Rastegarzadeh, Mohammad Kazem Tavassoly

We investigate an entangled three-qubit system in which only one of the qubits experiences the decoherence effect by considering a non-Hermitian Hamiltonian, while the other two qubits are isolated, i.e., do not interact with environment, directly. Then, the time evolution of the density matrix (for the pure as well as mixed initial density matrix) and the corresponding reduced density matrices are obtained, by which we are able to utilize the dissipative non-Hermitian Hamiltonian model with Markovian and non-Markovian regimes via adjusting the strange of the non-Hermitian term of the total Hamiltonian of the under-considered system.

Chinese Physics BOct 20, 20202 citations

Dissipative dynamics of a two-qubit system: Four-level lasing

E. A. Temchenko, Sergey N Shevchenko, A. N. Omelyanchouk

The dissipative dynamics of a two-qubit system is studied theoretically. We make use of the Bloch-Redfield formalism which explicitly includes the parameter-dependent relaxation rates. We consider the case of two flux qubits, when the controlling parameters are the partial magnetic fluxes through the qubits' loops. The strong dependence of the interlevel relaxation rates on the controlling magnetic fluxes is demonstrated for the realistic system. This allows us to propose several mechanisms for lasing in this four-level system.

arXiv:1011.5598Physical Review BApr 13, 201117 citations

Qubit-oscillator relationships in the open quantum Rabi model: the role of dissipation

G. Di Bello, Loris Maria Cangemi, V. Cataudella +3 more

Abstract Using a dissipative quantum Rabi model, we study the dynamics of a slow qubit coupled to a fast quantum harmonic oscillator interacting with a bosonic bath from weak to strong and ultra-strong coupling regimes. Solving the quantum Heisenberg equations of motion, perturbative in the internal coupling between qubit and oscillator, we derive functional relationships directly linking the qubit coordinates in the Bloch sphere to oscillator observables. We then perform accurate time-dependent Matrix Product State simulations and compare our results both with the analytical solutions of the Heisenberg equations of motion, and with numerical solutions of a Lindblad master equation, perturbative in the external coupling between oscillator and environment. Indeed, we show that, up to the strong coupling regime, the qubit state accurately fulfils the derived functional relationships. We analyse in detail the case of a qubit starting with generic coordinates on the Bloch sphere of which we evaluate the three components of the Bloch vector through the averages of oscillator observables. Interestingly, a weak to intermediate oscillator coupling to the bath is able to simplify the Bloch vector evaluation since qubit-oscillator relationships are more immediate. Moreover, by monitoring the qubit fidelity with respect to free limit, we find the parameter regime where the combined effect of internal and external couplings is able to hinder the reliable evaluation of the qubit Bloch vector. Finally, in the ultra-strong coupling regime, non-Markovian effects become robust and the dynamics of qubit and oscillator are inextricably entangled making the qubit Bloch vector evaluation difficult. Graphical Abstract

arXiv:2208.00708The European Physical Journal PlusFeb 8, 20232 citations

Influence of the dissipation on the N-level atom interacting with a two two-level atoms in presence of qubit–qubit interaction

S. Abdel‐Khalek, Hashim M. Alshehri, Eied Mahmoud Khalil +1 more

The interacting of two qubits and an N-level atom based on su(2) Lie algebra in the presence of both qubit-qubit interaction and dissipation term is considered. The effects of the qubit-qubit interaction and the dissipation term on the dynamics of the proposed system are discussed in detail for certain values of the number of levels. The dynamical expressions of the observable operators are obtained using the Heisenberg equation of motion. The population inversion and linear entropy, as well as the concurrence formula as a measure of entanglement between the two qubits are calculated and discussed. The roles of the number of levels, the qubit-qubit coupling parameter and the dissipation rate on these quantities are also discussed. We explore the sudden birth and sudden death of the entanglement phenomena with and without the dissipation term.

Scientific ReportsApr 1, 20211 citation