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arXiv:2207.02017 · Nature Communications

Dissipative Landau-Zener tunneling in the crossover regime from weak to strong environment coupling

Xi Dai, Robbyn Trappen, Huo Chen, Denis Melanson, Muhammet Ali Yurtalan, Daniel Tennant, Antonio Martinez, Yongchao Tang, Evgeny Mozgunov, J. Gibson, Jeffrey A. Grover, Steven Disseler, James I. Basham, S. Novikov, Rabindra Nath Das, Alexander J. Melville, Bethany M. Niedzielski, Cyrus F. Hirjibehedin, Kyle Serniak, Steven J. Weber, Jonilyn Yoder, William D. Oliver, Kenneth M. Zick, Daniel A. Lidar, Adrian Lupaşcu

Published Jan 2, 2025• 8 citations

Abstract

Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.

DOI: 10.1038/s41467-024-55588-x

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Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.

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.

We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.

We study Landau-Zener transitions in a fermionic dissipative environment where a two-level (up and down states) system is coupled to two metallic leads kept with different chemical potentials at zero temperature. The dynamics of the system is simulated by an iterative numerically exact influence functional path integral method. In the pure Landau-Zener problem, two kinds of transition (from up to down state and from down to up state) probability are symmetric. However, this symmetry is destroyed by coupling the system to the bath. In addition, in both kinds of transitions, there exists a nonmonotonic dependence of the transition probability on the sweep velocity; meanwhile nonmonotonic dependence of the transition probability on the system-bath coupling strength is only shown in one of them. As in the spin-boson model, these phenomena can be explained by a simple phenomenological model.

We study Landau-Zener-St\"uckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from an LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to ten energy levels.

We report an experimental measurement of Landau-Zener transitions on an individual flux qubit within a multiqubit superconducting chip. The method used isolates a single qubit, tunes its tunneling amplitude $\ensuremath{\Delta}$ into the limit where $\ensuremath{\Delta}$ is much less than both the temperature

T

and the decoherence-induced energy level broadening, and forces it to undergo a Landau-Zener transition. We find that the behavior of the qubit agrees to a high degree of accuracy with theoretical predictions for Landau-Zener transition probabilities for a double-well quantum system coupled to a nonMarkovian

1/f

magnetic flux noise.

Abstract We study the dynamics of a quantum two-state system driven through an avoided crossing under the influence of a super-Ohmic environment. We determine the Landau–Zener probability employing the numerical exact quasi-adiabatic path integral and a Markovian weak coupling approach. Increasing the driving time in the numerical protocol, we find converged results which shows that super-Ohmic environments only influence the Landau Zener probability within a finite crossing time window. This crossing time is qualitatively determined by the environmental cut-off energy. At weak coupling, we show that the Markovian weak coupling approach provides an accurate description. Since pure dephasing of a super-Ohmic bath is non-Markovian, this highlights that pure dephasing hardly influences the Landau–Zener probability. The finite crossing time window, thus, results from the suppression of relaxation once the energy splitting exceeds the environmental cut-off energy. Graphical abstract