By driving a 3D transmon with microwave fields, we generate an effective avoided energy-level crossing. Then we chirp microwave frequency, which is equivalent to driving the system through the avoided energy-level crossing by sweeping the avoided crossing. A double-passage chirp produces Landau-Zener-Stückelberg-Majorana (LZSM) interference that agree well with the numerical results, especially with the initial state being an eigen-energy state in the center of an avoided level crossing. A time-resolved state tomography measurement is performed in the evolution of LZSM interference, showing an experimental evidence for the dynamical evolution of quantum state. Our method is fully applicable to other quantum systems that contain no intrinsic avoided level crossing, providing an alternative approach for quantum control and quantum simulation.
By driving a 3D transmon with microwave fields, we generate an effective avoided energy-level crossing. Then we chirp microwave frequency, which is equivalent to driving the system through the avoided energy-level crossing by sweeping the avoided crossing. A double-passage chirp produces Landau-Zener-Stückelberg-Majorana (LZSM) interference that agree well with the numerical results, especially with the initial state being an eigen-energy state in the center of an avoided level crossing. A time-resolved state tomography measurement is performed in the evolution of LZSM interference, showing an experimental evidence for the dynamical evolution of quantum state. Our method is fully applicable to other quantum systems that contain no intrinsic avoided level crossing, providing an alternative approach for quantum control and quantum simulation.
In this study, Landau–Zener–Stückelberg–Majorana (LZSM) dynamics of tunneling transmon quantum bits (qubits) and related interference effects (interferometry) in symmetrical Josephson junctions (JJs) are theoretically investigated. Accordingly, the deviation of the driving parameters from the symmetry point and the transmon frequency are introduced, leading to fluctuations of a superconducting gap that limit the computational power of state-of-the-art transmon qubits and micro-processors. Indeed, the theoretical approach is carried withing the framework of the dynamic matrix approach (DMA) and numerical experiment measurements are reported after both single and double passages through a complexity of the transmon qubit polarization energy . Therefore, we derive generalized analytical expressions of LZSM quantum tunneling probabilities (QTP) and energy eigenvalues for multiple passages processes, which allow us to efficiently establish the transmon frequency and determine the driving parameters. Our theoretical results seem relevant for the interpretation of several LZSM interferometry mechanisms in the modulation of superconducting gap through different transmon qubit spectroscopy experiments in which tunable LZSM transitions and quantum interference patterns are demonstrated by the use of universal nonadiabatic control to implement quantum emulations. Additionally, this mapping enables the investigation of JJ effects through the identification of the corresponding modulated topological phases accumulated during the LZSM transitions, which offer new opportunities to coherently manipulate qubit states and address the energy transfer of transmon qubits on the one hand. On the other hand, it suggests possibilities to reduce sensitivity and to suspected sources of imperfection from different superconducting qubit architectures, particularly in the context of materials optimization strategies that dig out nontrivial phenomena possessing powerful quantum interferometer functionality with realistic quantum controls of tunneling transmon qubit states.
Landau–Zener–Stückelberg–Majorana (LZSM) interference describes the coherent superposition of nonadiabatic transitions when a quantum system is driven through an avoided crossing, but its classical optical analog remains largely unexplored. This work establishes an optical-resonator-based platform for exploring LZSM interference in atomic polarization dynamics using temporal coupled-mode theory. By exploiting the formal correspondence between the cavity mode and atomic polarization in a weakly driven two-level system (TLS), exact analytical solutions are derived for linear frequency sweeps and sinusoidal modulation. The results reveal that the Landau–Zener transition of atomic polarization occurs even when the input frequency transiently sweeps across resonance. The finite temporal memory inherent in the cavity response gives rise to Stückelberg interference, manifesting as oscillations in transmission and cavity energy. The dependence of the interference pattern on sweep rate, linewidth, and modulation is systematically analyzed, and a non-monotonic behavior of oscillation amplitude versus the cavity linewidth is identified. Furthermore, the conventional critical coupling concept is reexamined in the nonadiabatic regime, where counterintuitively the deepest transmission dip occurs under over-coupling rather than critical coupling. Finally, an inverse-design approach engineering both the amplitude and frequency of the input frequency is introduced to tailor the LZSM interference pattern. Our results provide a new platform to all-optical simulation of complex quantum interference.
Harnessing second-order processes enables new control schemes in quantum dynamics. We show that the Landau-Zener-Stückelberg-Majorana (LZSM) transition can be generalized to a virtual-state process in a three-level system, employing a phase modulated drive whereby two photons excite the system from the first to the third level while avoiding the second one. We implement experimentally this process in a transmon, achieving 98% population transfer. We predict and observe the doubling of LZSM velocity. Furthermore, we demonstrate robustness to amplitude and frequency offsets, made possible by the nearly exact cancellation of the two-photon ac Stark shift due to the presence of the fourth state.
Since the pioneering works by Landau, Zener, Stückelberg, and Majorana (LZSM), it has been known that driving a quantum two-level system results in tunneling between its states. Even though the interference between these transitions is known to be important, it is only recently that it became both accessible, controllable, and useful for manipulating a growing number of quantum systems. Here, we systematically study various aspects of LZSM physics and review the relevant literature, significantly expanding the review article in Ref. [504].
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 investigate the transfer between spin quantum bit (qubit) states and study the Landau–Zener–Stückelberg–Majorana (LZSM)-like dynamics of tunneling spin qubits in a multiband two-state magnetic quantum wire. Indeed, within the framework of an optical parabolic potential in a three-dimensional (3D) heterostructure quantum wire and under the influence of an external time-varying magnetic field, a model for a multiband two-state magnetic quantum wire is developed. Here, the external magnetic field is used to coherently manipulate and control spin qubit states. By driving the system through an avoided crossing, we consider the associated effective quantum two-level system (TLS) related to the spin qubit states in each band, driving by an external coherent magnetic field in which the related Hamiltonian is Hermitian, and which generally paves a way to LZSM interferometry. Thus, we establish the analytical expressions of the energy eigenvalues in each band and derive the analytical solution of the dynamical evolution of the tunneling probabilities of the associated TLS. Accordingly, nonadiabatic and adiabatic tunneling probabilities (survival and transition) are calculated for each band of the multiband TLS. In this respect, the nonadiabatic and adiabatic dynamical evolutions of the tunneling probabilities of spin qubit populations in the first four bands, with band quantum numbers n = 0, 1, 2 and 3 are analyzed. As a result, depending on the amplitude strength of the driven magnetic field and the magnitude of the driving frequency, we report two striking nonadiabatic and adiabatic scenarios in each band for both the diabatic and adiabatic states. In this context, driving the two states of each band of the multiband TLS related to the spin qubit states through an avoided level crossing can result in nontrivial and incoherent dynamics at certain phases, resulting to apparent inaccurate probabilities, especially in the case of strong driven magnetic field and high driving frequency.