Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Quantum interference and exceptional points in a nonreciprocal two-level system

Jing Dong, Xiao-Lin Li, Fu-Quan Dou, Wen-Yuan Wang

Published Dec 8, 2023• 9 citations
Publisher

Abstract

Non-Hermitian systems with complex-valued energy spectra and exceptional points show unconventional dynamics. Here we investigate the quantum interference of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. We propose the multiple-passage Landau-Zener-St\"uckelberg-Majorana scheme to realize the quantum interferometry of such a non-Hermitian system, that is, the energy bias between two levels is periodically modulated, which may result in constructive or destructive interference. In the absence of nonlinear self-interaction, it exhibits obvious interference fringes in the weak nonreciprocal regime, whereas the interference is completely suppressed in the strong nonreciprocal regime due to the parity-time-symmetry breaking. The explicit expressions for the occupation probabilities are obtained within an effective rotating-wave approximation, which is consistent with the numerical results. In the presence of nonlinear interaction, the system shows a rich variety of dynamics and interference fringes. We further obtain phase diagrams for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate quantum interference within the nonlinear non-Hermitian system. The present work unlocks quantum interference characteristics from a nonreciprocal two-level system and provides a theoretical perspective for the manipulation of quantum states in non-Hermitian systems.

DOI
10.1103/physreva.108.063506

Related papers

Nonlinear non-Hermitian Landau–Zener–Stückelberg–Majorana interferometry

Xin Wang, H. D. Liu, Libin Fu

Abstract In this work, we have studied the non-Hermitian nonlinear Landau–Zener–Stückelberg–Majorana (LZSM) interferometry in a non-Hermitian N -body interacting boson system in which the non-Hermiticity is from the nonreciprocal tunnelings between the bosons. By using the mean-field approximation and projective Hilbert space, the effect of nonreciprocity and nonlinearity on the energy spectrum, the dynamics, and the formation of the interference fringes have been studied. The different symmetries and the impact of the two different types of reciprocity, i.e. the in-phase tunneling and anti-phase tunneling, on the energy spectrum and the phase transition between the Josephson oscillations and the self-trapping have been investigated. For the LZSM interferometry, the strength of the nonreciprocity is found to take an essential role in the population of the projective state and the strengths of the interference patterns in the projective space. While the conditions of destructive and constructive interference under the weak-coupling approximation still only depend on the strength of nonlinearity. Our result provides an application of the nonlinear non-Hermitian LZSM interferometry in studying the parameters of a two-level system which related to the nonlinearity and the non-Hermiticity.

arXiv:2301.00734•New Journal of Physics•Apr 1, 2023•18 citations

Adiabaticity in nonreciprocal Landau-Zener tunneling

Wen-Yuan Wang, Bin Sun, Jie Liu

We investigate the Landau-Zener tunneling (LZT) of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. In such a non-Hermitian system, when the energy bias between two levels is adjusted very slowly, i.e., in the adiabatic limit, we find that a quantum state can still closely follow the eigenstate solution until it encounters the exceptional points (EPs) at which two eigenvalues and their corresponding eigenvectors coalesce. In the absence of the nonlinear self-interaction, we can obtain explicit expressions for the eigenvectors and eigenvalues and analytically derive the adiabatic LZT probability from invariants at EPs. In the presence of the nonlinear interaction, the dynamics of the adiabatic evolutions are explicitly demonstrated with the help of classical trajectories in the plane of the two canonical variables of the corresponding classical Josephson Hamiltonian. We show that the adiabatic tunneling probabilities can be precisely predicted by the classical action at EPs in the weak nonreciprocal regime. In a certain region of strong nonreciprocity, we find that interestingly, the nonlinear interaction effects can be completely suppressed so that the adiabatic tunneling probabilities are identical to their linear counterparts. We also obtain a phase diagram for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate where the adiabaticity can break down, i.e., the emergence of the nonzero tunneling probabilities even in adiabatic limit.

arXiv:2201.02934•Physical Review A•Dec 14, 2022•29 citations

Nonlinear Landau-Zener-Stückelberg-Majorana interferometry

Sheng-Chang Li, Libin Fu, Jie Liu

We investigate Landau-Zener-St\"uckelberg-Majorana (LZSM) interferometry in a nonlinear two-level system subjected to a sinusoidal driving field. A comprehensive analysis for the interference patterns is shown from which we can analytically obtain the condition of constructive and destructive interferences in some cases. In the presence of nonlinear interaction, the level structure is changed, which can lead to an asymmetric deformation of the interference patterns and a significant position shift of the interference fringes. Our findings suggest an application of the nonlinear LZSM interferometry in accurately calibrating the parameters characterizing a nonlinear two-level system, as well as its coupling with the driven fields.

Physical Review A•Jul 2, 2018•22 citations

Landau–Zener without a qubit: multiphoton sidebands interaction and signatures of dissipative quantum chaos

Léo Peyruchat, Fabrizio Minganti, Marco Scigliuzzo +5 more

Abstract Landau–Zener–Stückelberg–Majorana (LZSM) interference occurs when qubit parameters are periodically modulated across avoided level crossings. We explore this phenomenon in nonlinear multilevel bosonic systems, where interference is influenced by multiple energy levels. We fabricate two superconducting resonators with flux-tunable Josephson junction arrays. The first device, exhibiting weak nonlinearity, behaves like a linear resonator under weak driving but shows LZSM interference akin to two-level systems. With stronger driving, nonlinear effects alter the interference pattern. We theoretically demonstrate that merging LZSM peaks can lead to dissipative quantum chaos. In the second device, where nonlinearity exceeds photon-loss rates, we observe additional LZSM peaks from Kerr multiphoton resonances. Under Floquet theory, these resonances represent synthetic modes of coupled nonlinear cavities, revealing effective coupling as modulation parameters vary. Our findings advance the understanding of LZSM physics and emphasize the control of nonlinear Floquet states and the emergence of chaos in engineered systems, with significant implications for novel applications in quantum dynamics and quantum control.

arXiv:2404.10051•npj Quantum Information•Apr 7, 2025•4 citations

Nonlinear Landau-Zener-Stückelberg-Majorana problem with non-Hermitian models

Y. Cao, T. F. Xu

We study nonlinear Landau-Zener-St\"uckelberg-Majorana (LZSM) tunneling with a $\mathcal{PT}$-symmetric potential, which can be converted to a non-Hermitian nonlinear two-level model by a two-mode approximation. Then, we construct an equivalent Hermitian model through a transformation, verify that the tunneling probabilities obtained by the two models are consistent, and comprehensively analyze the effect of the gain-dissipation term on tunneling. In addition, due to the gain-dissipation properties, the total population density of the non-Hermitian model is no longer a conserved quantity, which will increase or decay to a fixed value as the model evolves. Finally, we prove that the spatial inversion symmetry breaking of the Hamiltonian leads to nonreciprocal tunneling, and the numerical simulation results confirm our analysis. These studies provide alternative ideas to study the nonlinear dynamics of non-Hermitian systems in the future.

Physical Review A•Jan 30, 2024•5 citations

Rosen–Zener transition in a nonlinear nonreciprocal two-level system

Keyan Liu, Han Zhang, Haiyu Cheng +3 more

The dynamics of the Rosen–Zener transition (RZT) in interacting two-level systems within nonreciprocal systems is examined, where nonreciprocity stems from asymmetric couplings between energy levels. For the linear case, an analytical expression for the RZT probability is derived. In the nonlinear scenario, numerical experiments are utilized to investigate the impact of various initial states and scanning periods on transition probabilities under adiabatic conditions . Additionally, an equivalent classical Hamiltonian is formulated to elucidate the origin of transition asymmetry under different initial state conditions. The influence of energy level detuning on the RZT is explored, leading to the suggestion of new applications for studying parameters of two-level systems related to nonlinearity and nonreciprocity. This opens avenues for potential Rosen–Zener–Stückelberg interferometry implementations.

Results in Physics•Aug 28, 2024•2 citations
Non-Hermitian systems with complex-valued energy spectra and exceptional points show unconventional dynamics. Here we investigate the quantum interference of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. We propose the multiple-passage Landau-Zener-St"uckelberg-Majorana scheme to realize the quantum interferometry of such a non-Hermitian system, that is, the energy bias between two levels is periodically modulated, which may result in constructive or destructive interference. In the absence of nonlinear self-interaction, it exhibits obvious interference fringes in the weak nonreciprocal regime, whereas the interference is completely suppressed in the strong nonreciprocal regime due to the parity-time-symmetry breaking. The explicit expressions for the occupation probabilities are obtained within an effective rotating-wave approximation, which is consistent with the numerical results. In the presence of nonlinear interaction, the system shows a rich variety of dynamics and interference fringes. We further obtain phase diagrams for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate quantum interference within the nonlinear non-Hermitian system. The present work unlocks quantum interference characteristics from a nonreciprocal two-level system and provides a theoretical perspective for the manipulation of quantum states in non-Hermitian systems.
Abstract In this work, we have studied the non-Hermitian nonlinear Landau–Zener–Stückelberg–Majorana (LZSM) interferometry in a non-Hermitian N -body interacting boson system in which the non-Hermiticity is from the nonreciprocal tunnelings between the bosons. By using the mean-field approximation and projective Hilbert space, the effect of nonreciprocity and nonlinearity on the energy spectrum, the dynamics, and the formation of the interference fringes have been studied. The different symmetries and the impact of the two different types of reciprocity, i.e. the in-phase tunneling and anti-phase tunneling, on the energy spectrum and the phase transition between the Josephson oscillations and the self-trapping have been investigated. For the LZSM interferometry, the strength of the nonreciprocity is found to take an essential role in the population of the projective state and the strengths of the interference patterns in the projective space. While the conditions of destructive and constructive interference under the weak-coupling approximation still only depend on the strength of nonlinearity. Our result provides an application of the nonlinear non-Hermitian LZSM interferometry in studying the parameters of a two-level system which related to the nonlinearity and the non-Hermiticity.
We investigate the Landau-Zener tunneling (LZT) of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. In such a non-Hermitian system, when the energy bias between two levels is adjusted very slowly, i.e., in the adiabatic limit, we find that a quantum state can still closely follow the eigenstate solution until it encounters the exceptional points (EPs) at which two eigenvalues and their corresponding eigenvectors coalesce. In the absence of the nonlinear self-interaction, we can obtain explicit expressions for the eigenvectors and eigenvalues and analytically derive the adiabatic LZT probability from invariants at EPs. In the presence of the nonlinear interaction, the dynamics of the adiabatic evolutions are explicitly demonstrated with the help of classical trajectories in the plane of the two canonical variables of the corresponding classical Josephson Hamiltonian. We show that the adiabatic tunneling probabilities can be precisely predicted by the classical action at EPs in the weak nonreciprocal regime. In a certain region of strong nonreciprocity, we find that interestingly, the nonlinear interaction effects can be completely suppressed so that the adiabatic tunneling probabilities are identical to their linear counterparts. We also obtain a phase diagram for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate where the adiabaticity can break down, i.e., the emergence of the nonzero tunneling probabilities even in adiabatic limit.
We investigate Landau-Zener-St\"uckelberg-Majorana (LZSM) interferometry in a nonlinear two-level system subjected to a sinusoidal driving field. A comprehensive analysis for the interference patterns is shown from which we can analytically obtain the condition of constructive and destructive interferences in some cases. In the presence of nonlinear interaction, the level structure is changed, which can lead to an asymmetric deformation of the interference patterns and a significant position shift of the interference fringes. Our findings suggest an application of the nonlinear LZSM interferometry in accurately calibrating the parameters characterizing a nonlinear two-level system, as well as its coupling with the driven fields.
Abstract Landau–Zener–Stückelberg–Majorana (LZSM) interference occurs when qubit parameters are periodically modulated across avoided level crossings. We explore this phenomenon in nonlinear multilevel bosonic systems, where interference is influenced by multiple energy levels. We fabricate two superconducting resonators with flux-tunable Josephson junction arrays. The first device, exhibiting weak nonlinearity, behaves like a linear resonator under weak driving but shows LZSM interference akin to two-level systems. With stronger driving, nonlinear effects alter the interference pattern. We theoretically demonstrate that merging LZSM peaks can lead to dissipative quantum chaos. In the second device, where nonlinearity exceeds photon-loss rates, we observe additional LZSM peaks from Kerr multiphoton resonances. Under Floquet theory, these resonances represent synthetic modes of coupled nonlinear cavities, revealing effective coupling as modulation parameters vary. Our findings advance the understanding of LZSM physics and emphasize the control of nonlinear Floquet states and the emergence of chaos in engineered systems, with significant implications for novel applications in quantum dynamics and quantum control.
We study nonlinear Landau-Zener-St\"uckelberg-Majorana (LZSM) tunneling with a PT\mathcal{PT}PT-symmetric potential, which can be converted to a non-Hermitian nonlinear two-level model by a two-mode approximation. Then, we construct an equivalent Hermitian model through a transformation, verify that the tunneling probabilities obtained by the two models are consistent, and comprehensively analyze the effect of the gain-dissipation term on tunneling. In addition, due to the gain-dissipation properties, the total population density of the non-Hermitian model is no longer a conserved quantity, which will increase or decay to a fixed value as the model evolves. Finally, we prove that the spatial inversion symmetry breaking of the Hamiltonian leads to nonreciprocal tunneling, and the numerical simulation results confirm our analysis. These studies provide alternative ideas to study the nonlinear dynamics of non-Hermitian systems in the future.
The dynamics of the Rosen–Zener transition (RZT) in interacting two-level systems within nonreciprocal systems is examined, where nonreciprocity stems from asymmetric couplings between energy levels. For the linear case, an analytical expression for the RZT probability is derived. In the nonlinear scenario, numerical experiments are utilized to investigate the impact of various initial states and scanning periods on transition probabilities under adiabatic conditions . Additionally, an equivalent classical Hamiltonian is formulated to elucidate the origin of transition asymmetry under different initial state conditions. The influence of energy level detuning on the RZT is explored, leading to the suggestion of new applications for studying parameters of two-level systems related to nonlinearity and nonreciprocity. This opens avenues for potential Rosen–Zener–Stückelberg interferometry implementations.