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arXiv:2301.00734 · New Journal of Physics

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

Xin Wang, H. D. Liu, Libin Fu

Published Apr 1, 2023• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/accca3

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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.
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.
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.
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 nonlinear Landau-Zener-Stückelberg-Majorana (LZSM) tunneling dynamics and interferometry of an extended Bose-Hubbard flux ladder are studied. Based on the mean-field theory, the dispersion relation of the system is given, and it is found that loop structures periodically appear in the band structure and the nonlinear LZSM interference occurs naturally without Floquet engineering, which can be effectively modulated by atomic interactions. The nonlinear energy bands and the unique chirality feature of the flux ladder system can be identified through the dynamics of nonlinear Landau-Zener tunneling. Remarkably, the critical position of the noise in the interference pattern can be employed to identify the loop structure in the energy band, establishing an effective link between the nonlinear loop structure and LZSM interferometry. The position, intensity, symmetry, and width of interference patterns strongly depend on the magnetic field, atomic interactions, rung-to-leg coupling ratio, and energy bias, which provides an effective way to measure these parameters using the nonlinear LZSM interferometry. This paper further expands the dynamics of flux ladder systems to complex interaction regions and has potential applications in the precise measurement of related nonlinear systems.
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 systematically investigate the non-Hermitian generalizations of the Landau-Zener (LZ) transition and the Landau-Zener-St\"uckelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behavior is analyzed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulas for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasized. In particular, the geometrical phase originated from the sign change of the mass term at the two level crossings is still present in the non-Hermitian system, indicating its robustness against the non-Hermiticity. We further apply our non-Hermitian LZS theory to describing the Bloch oscillation in one-dimensional parity-time (PT)(\mathcal{PT})(PT) reversal symmetric non-Hermitian Su-Schrieffer-Heeger model and propose an experimental scheme to simulate such dynamics using photonic waveguide arrays. The Landau-Zener transition, as well as the LZS interferometry, can be visualized through the beam intensity profile and the transition probabilities measured by the center of mass of the profile.