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Chinese Physics B

Periodic modulation of adiabatic dynamics in non-reciprocal Landau–Zener systems

Rong 蓉 Chang 常, Sheng-Chang Li

Published Jan 17, 2025• 2 citations
Publisher

Abstract

Abstract The control of adiabatic dynamics is essential for quantum manipulation. We investigate the effects of both periodic modulating field and linear sweeping field on adiabatic dynamics based on a non-reciprocal Landau–Zener model with periodic modulation. We obtain adiabatic phase diagrams in the (ω, δ) parameter space, where the adiabatic region is bounded by the modulating frequency ω greater than a critical value ω c and the non-reciprocal parameter δ less than one. The results show that the adiabaticity of the system is not sensitive to the modulating amplitude. We find that the critical modulating frequency can be expressed as a power function of the modulating period number or the sweeping rate. Our findings suggest that one can change the adiabatic region or improve the adiabaticity by adjusting the parameters of both the modulating and the sweeping fields, which provides an effective means to flexibly control the adiabatic dynamics of non-reciprocal systems.

DOI
10.1088/1674-1056/adab64

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We consider dynamics of Dicke models, with and without counterrotating terms, under slow variations of parameters which drive the system through a quantum phase transition. The model without counterrotating terms and sweeped detuning is seen in the contexts of a many-body generalization of the Landau-Zener model and the dynamical passage through a second-order quantum phase transition (QPT). Adiabaticity is destroyed when the parameter crosses a critical value. Applying semiclassical analysis based on concepts of classical adiabatic invariants and mapping to the second Painleve equation (PII), we derive a formula which accurately describes particle distributions in the Hilbert space at wide range of parameters and initial conditions of the system. We find striking universal features in the particle distributions which can be probed in an experiment on Feshbach resonance passage or a cavity QED experiment. The dynamics is found to be crucially dependent on the direction of the sweep. The model with counterrotating terms has been realized recently in an experiment with ultracold atomic gases in a cavity. Its semiclassical dynamics is described by a Hamiltonian system with two degrees of freedom. Passage through a QPT corresponds to passage through a bifurcation, and can also be described by PII (after averaging over fast variables), leading to similar universal distributions. Under certain conditions, the Dicke model is reduced to the Lipkin-Meshkov-Glick model.
We present a detailed analysis of the Landau–Zener problem for an interacting Bose–Einstein condensate in a time-varying double-well trap, especially focusing on the relation between the full many-particle problem and the mean-field approximation. Due to the nonlinear self-interaction a dynamical instability occurs, which leads to a breakdown of adiabaticity and thus fundamentally alters the dynamics. It is shown that essentially all the features of the Landau–Zener problem including the depletion of the condensate mode can be already understood within a semiclassical phase-space picture. In particular, this treatment resolves the formerly imputed incommutability of the adiabatic and semiclassical limits. The possibility of exploiting Landau–Zener sweeps to generate squeezed states for spectroscopic tasks is analyzed in detail. Moreover, we study the influence of phase noise and propose a Landau–Zener sweep as a sensitive yet readily implementable probe for decoherence, since the noise has significant effect on the transition rate for slow parameter variations.
We compare various types of adiabatic dynamics that occur during atomic collisions and molecular dynamics. Born–Oppenheimer and non-adiabatic effects in molecular dynamics are contrasted with the time-dependent Landau–Zener transition problem for transitions that occur when a parameter in the Hamiltonian is varied slowly, and these are contrasted with the coherent many-body transitions that occur for a degenerate gas of atoms when an external parameter is tuned slowly near a Feshbach resonance to create loosely bound molecules. Analysis of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms shows that the dependence of the remaining atomic fraction on the sweep rate α varies from exponential Landau–Zener behaviour for a single pair of particles to a power-law dependence for large particle number N.