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OSA Continuum

Effect of the next-nearest-neighbor's interaction on the population transfer in a four-particle Landau-Zener system

Aarash Maroufian, Mehdi Hosseini, Fatemeh Ahmadinouri

Published Jan 13, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1364/osac.416739

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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.
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 asymptotic staying probability PPP in the Landau-Zener effect with interaction is analytically investigated at fast sweep $\ensuremath{\epsilon}=\ensuremath{\pi}{\ensuremath{\Delta}}^{2}∕(2\ensuremath{\hbar}v)⪡1$. We have rigorously calculated the value of I0{I}_{0}I0​ in the expansion $P\ensuremath{\cong}1\ensuremath{-}\ensuremath{\epsilon}+{\ensuremath{\epsilon}}^{2}∕2+{\ensuremath{\epsilon}}^{2}{I}_{0}$ for arbitrary couplings and relative resonance shifts of individual tunneling particles. The results essentially differ from those of the mean-field approximation. It is shown that strong long-range interactions such as dipole-dipole interaction generate huge values of I0{I}_{0}I0​ because a flip of one particle strongly influences many others. However, in the presence of strong static disorder, making the resonances for individual particles shifted with respect to each other, the influence of interactions is strongly reduced. In molecular magnets the main source of static disorder is the coupling to nuclear spins. Our calculations using the actual shape of the Fe8{\mathrm{Fe}}_{8}Fe8​ crystal studied in the Landau-Zener experiments [Wernsdorfer et al., Europhys. Lett. 50, 552 (2000)] yield a value of I0{I}_{0}I0​ that is in good agreement with the value extracted from the experimental data.
The Landau-Zener-Stueckelberg (LZS) effect in a model system of interacting tunneling particles is studied numerically and analytically. Each of N tunneling particles interacts with each of the others with the same coupling J. This problem maps onto that of the LZS effect for a large spin S=N/2.S=N/2.S=N/2. The mean-field limit $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ corresponds to the classical limit $\stackrel{\ensuremath{\rightarrow}}{S}\ensuremath{\infty}$ for the effective spin. It is shown that the ferromagnetic coupling J>0J>0J>0 tends to suppress the LZS transitions. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ there is a critical value of J above which the staying probability P does not go to zero in the slow sweep limit, unlike the standard LZS effect. For J<0J<0J<0 LZS transitions are boosted and P=0P=0P=0 for a set of finite values of the sweep rate for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}.$ Various limiting cases such as strong and weak interaction, slow and fast sweep are considered analytically. It is shown that the mean-field approach works well for arbitrary N if the interaction J is weak.
Dynamical Crossover in Landau−-−Zener Tunneling in Dissipative Rydberg Lattices
In this work, we investigate the excitation dynamics of a Rabi-coupled dissipative Rydberg lattice with a time-dependent detuning. The system is analyzed using (i) a Lindblad master equation within a mean-field approximation and (ii) an effective non-Hermitian Hamiltonian framework. While the mean-field approach captures the emergence of an antiferromagnetic order in the Rydberg excitation profile, the non-Hermitian description provides direct insight into the complex energy spectrum and its avoided crossings, which govern the Landau−-−Zener dynamics. We identify a regime in which the sublattice population imbalance vanishes near the avoided crossing, resulting in identical Landau−-−Zener probabilities on the two sublattices. Beyond a critical effective blockade strength there is a dynamical crossover to another regime in which the sublattice population imbalance persists through the avoided crossing, giving rise to sublattice-dependent Landau−-−Zener probabilities. Furthermore, Rydberg interactions prolong the lifetime of Landau−-−Zener-induced excitations in the presence of weak dissipation and strong Rabi coupling. In contrast, for weak Rabi coupling, the Rydberg blockade inhibits excitation and suppresses the Landau−-−Zener transition probability.
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.
We report the observation of a controlled Landau-Zener transition (LZT) in Rydberg atoms by breaking the symmetry of the underlying Hamiltonian. For a nonhydrogenic Rydberg atom inside a changing electric (F) field, a LZT occurs between the avoided crossing energy levels of neighboring Rydberg states only for a sufficiently high changing rate. If a transverse magnetic (B) field is applied as we implement, the atomic level symmetry is broken, which causes the Stark manifolds denoted by a different |m| (m is the magnetic quantum number) to interact with each other. The mixed state levels end up pushing the adiabatically repelled target states closer and additionally they serve as stepping stones for the sequential LZTs between the neighboring sublevels. Such a feature significantly decreases the changing rate required for an efficient LZT inside a pure electric field. We report experimental observations that support the above scenario. It opens a versatile approach for engineering a controlled LZT in more general systems.