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arXiv:2004.03863

The effect of the second nearest neighbor interaction on the population transfer in a four-particle Landau-Zener system

Aarash Maroufian, Mehdi Hosseini

Published Apr 8, 2020• 0 citations
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Abstract

Population transfer in quantum systems has always been an interesting area in physics since the introduction of quantum mechanics. In this paper, transition probabilities for a coupled system consisting of four two - level particles are studied by solving Landau - Zener Hamiltonian. The effects of the first and second nearest neighbors interactions are investigated. Presented results indicate that the second nearest neighbors interactions will decrease the transition probability when the coupling strength for each neighborhood has the same sign. The fast sweep effect on transition probability is also studied here.

DOI
10.48550/arxiv.2004.03863

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Population transfer in quantum systems has always been an interesting area in physics since the introduction of quantum mechanics. In this paper, transition probabilities for a coupled system consisting of four two - level particles are studied by solving Landau - Zener Hamiltonian. The effects of the first and second nearest neighbors interactions are investigated. Presented results indicate that the second nearest neighbors interactions will decrease the transition probability when the coupling strength for each neighborhood has the same sign. The fast sweep effect on transition probability is also studied here.
The study of transition probabilities in few-body systems and their long-range interactions using the Landau-Zener method could be helpful for solving a wide range of problems in fields of quantum simulations, Rydberg blockade, quantum gates, and dipole transition in Rydberg atoms. Here, the transition probabilities for a four-particle system in a square-shaped lattice are studied by solving the many-body Landau-Zener Hamiltonian in the next-nearest-neighbor approximation. It is observed that the complete transition occurs for the anti-ferromagnetic coupling while it is limited to a constant probability for the ferromagnetic coupling. These probabilities suppress when the magnetic field's energy rate is increased. We demonstrate that in the presence of the next-nearest-neighbor's interactions, the final probabilities’ behavior is different. Considering the next-nearest-neighbor's interactions, it is possible to achieve the complete transition in imperfect anti-ferromagnetic regions. At the same time, the complete transition does not occur in perfect anti-ferromagnetic regions for certain values of the sweeping rate. These results emphasize that it is necessary to consider the next-nearest-neighbors’ interactions in a many-body system. Furthermore, the implementation of this Hamiltonian in the dipole-dipole and van der Waals interaction reveals that a steeper decrease for dipole-dipole interaction.
By considering a quantum critical Lipkin-Meshkov-Glick model we analyze a new type of Landau-Zener transitions where the population transfer is mediated by interaction rather than from a direct diabatic coupling. For this scenario, at a mean-field level the dynamics is greatly influenced by quantum interferences. In particular, regardless of how slow the Landau-Zener sweep is, for certain parameters almost no population transfer occurs, which is in stark contrast to the regular Landau-Zener model. For moderate system sizes, this counterintuitive mean-field behaviour is not duplicated in the quantum case. This can be attributed quantum fluctuations and the fact that multi-level Landau-Zener-Stückelberg interferences have a `dephasing' effect on the above mentioned phenomenon. We also find a discrepancy between the quantum and mean-field models in terms of how the transfer probabilities scale with the sweep velocity.
Landau-Zener (LZ) transitions of a two-level system (e.g., electronic spin in molecular magnets) coupled to one or many environmental spins (e.g., nuclear spins) are studied. For rather general interactions the LZ problem is reduced to that of a Landau-Zener grid. It is shown analytically that environmental spins initially in their ground state do not influence the staying probability PPP. This changes if they are prepared in a statistical ensemble. For a more specific model with environmental spins in a transverse field, LZ transitions are studied in the case of well-separated resonances in the LZ grid. The full evolution of the system is described as a succession of elementary transitions at avoided crossings and free evolution between them. If the environmental spins are strongly coupled to the central spin, their effect on PPP is weak. In other cases LZ transitions are strongly suppressed and PPP is decreasing very slowly with the sweep-rate parameter $\ensuremath{\epsilon}\ensuremath{\propto}1/v$, vvv being the energy sweep rate.
For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, to survive the transition and to remain in the first level, does not depend on whether or not the second level is broadened [V. M. Akulin and W. P. Schleich, Phys. Rev. A 46, 4110 (1992)]. In other words, the seminal Landau-Zener result applies regardless of the broadening of the second level. The same question for the multistate Landau-Zener transition is addressed in the present paper. While for integrable multistate models, where the transition does not involve interference of the virtual paths, it can be argued that the independence of the broadening persists, we focus on nonintegrable models involving interference. For a simplest four-state model, which allows an analytical treatment, we demonstrate that the decay of the excited states affects the survival probability provided that the widths of the final states are different.
Considering a temperature dependent two-level quantum system, we have numerically solved the Landau-Zener transition problem.The method includes the incorporation of temperature effect as a thermal noise added Schrödinger equation for the construction of the Hamiltonian.Here, the obtained results which describe the changes in the system including the quantum states and the transition probabilities are investigated and discussed.The results successfully describe the behavior of the transition probabilities by sweeping the temperature.
We study Landau-Zener transitions between two states with the addition of a shared discretized continuum. The continuum allows for population decay from the initial state as well as indirect transitions between the two states. The probability of nonadiabatic transition in this multichannel model preserves the standard Landau-Zener functional form except for a shift in the usual exponential factor, reflecting population transfer into the continuum. We provide an intuitive explanation for this behavior assuming individual, independent transitions between pairs of states. In contrast, the ground state survival probability at long time shows a novel, non-monotonic, functional form with an oscillatory behavior in the sweep rate at low sweep rate values. We contrast the behavior of this open-multistate model to other generalized Landau-Zener models incorporating an environment: the stochastic Landau-Zener model and the dissipative case, where energy dissipation and thermal excitations affect the adiabatic region. Finally, we present evidence that the continuum of states may act to shield the two-state Landau-Zener transition probability from the effect of noise.