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arXiv:2110.10271 · Physical Review A

Time-domain Landau-Zener-Stückelberg-Majorana interference in an optical lattice clock

Weixin Liu, Tao Wang, Xue‐Feng Zhang, Weidong Li

Published Nov 22, 2021• 15 citations
arXivHTMLPDF

Abstract

The interference between a sequence of Landau-Zener (LZ) transitions can produce Rabi oscillations (LZROs). This phenomenon is a kind of time-domain Landau-Zener-St\"uckelberg-Majorana (LZSM) interference. However, experimental demonstrations of this LZSM interference induced Rabi oscillation are extremely hard due to the short coherence time of the driven quantum system. Here, we study theoretically the time-domain LZSM interference between the clock transition in a one-dimensional $^{87}\mathrm{Sr}$ optical lattice clock (OLC) system. With the help of both the adiabatic-impulse model and Floquet numerical simulation method, the LZROs with special steplike structure are clearly found both in the fast- and slow-passage limit in the real experiment parameter regions. In addition, the dephasing effect caused by the system temperature can be suppressed with destructive interference in the slow-passage limit. Finally, we discuss the possible Bloch-Siegert shift while the pulse time is away from the half-integer and integer periods. Our work provides a clear road map to observe the LZROs on the OLC platform.

DOI
10.1103/physreva.104.053318

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The interference between a sequence of Landau-Zener (LZ) transitions can produce Rabi oscillations (LZROs). This phenomenon is a kind of time-domain Landau-Zener-St"uckelberg-Majorana (LZSM) interference. However, experimental demonstrations of this LZSM interference induced Rabi oscillation are extremely hard due to the short coherence time of the driven quantum system. Here, we study theoretically the time-domain LZSM interference between the clock transition in a one-dimensional 87Sr^{87}\mathrm{Sr}87Sr optical lattice clock (OLC) system. With the help of both the adiabatic-impulse model and Floquet numerical simulation method, the LZROs with special steplike structure are clearly found both in the fast- and slow-passage limit in the real experiment parameter regions. In addition, the dephasing effect caused by the system temperature can be suppressed with destructive interference in the slow-passage limit. Finally, we discuss the possible Bloch-Siegert shift while the pulse time is away from the half-integer and integer periods. Our work provides a clear road map to observe the LZROs on the OLC platform.
Manipulating quantum states is at the heart of quantum information processing and quantum metrology. Landau-Zener Rabi oscillation (LZRO), which arises from a quantum two-level system swept repeatedly across the avoided crossing point in the time domain, has been suggested for widespread use in manipulating quantum states. Cold atom is one of the most prominent platforms for quantum computing and precision measurement. However, LZRO has never been observed in cold atoms due to its stringent requirements. By compensating for the linear drift of the clock laser and optimizing experimental parameters, we successfully measured LZRO on the strontium atomic optical clock platform under both fast and slow passage limits within 444 to 666 driving periods. Compared to previous results on other platforms, the duration of the plateau is 10410^4104 times longer in the optical lattice clock. The experimental data also suggest that destructive Landau-Zener interference can effectively suppress dephasing effects in the optical lattice clock, paving the way for manipulating quantum states against various environmental effects in cold atomic systems.
Manipulating quantum states is at the heart of quantum information processing and quantum metrology. Landau-Zener Rabi oscillation (LZRO), which arises from a quantum two-level system swept repeatedly across the avoided crossing point in the time domain, has been suggested for widespread use in manipulating quantum states. Cold atoms are one of the most prominent platforms for quantum computing and precision measurement. However, LZRO has never been observed in cold atoms due to its stringent requirements. By compensating for the linear drift of the clock laser and optimizing experimental parameters, we successfully measured LZRO on the strontium atomic optical clock platform under both fast- and slow-passage limits within four to six driving periods. Compared to previous results on other platforms, the duration of the plateau is 104{10}^{4}104 times longer in the optical lattice clock. The experimental data also suggests that destructive Landau-Zener interference can effectively suppress dephasing effects in the optical lattice clock, paving the way for manipulating quantum states against various environmental effects in cold atomic systems.
Landau-Zener (LZ) transition has received renewed interest as an alternative approach to control single-qubit states. An LZ transition occurs when a system passes through an avoided crossing that arises from quantum mechanical coupling of two levels, taking the system to a coherent superposition of the two states. Then, multiple LZ transitions induce interference known as Landau-Zener-Stückelberg (LZS) interference whose amplitude strongly depends on the velocity or adiabaticity of the passage. Here, we study the roles of LZ transitions and LZS interference in coherent charge oscillations of a one-electron semiconductor double quantum dot by time-domain experiments using standard rectangular voltage pulses. By employing density matrix simulations, we show that, in the standard setup using rectangular pulses, even a small distortion of the pulse can give rise to LZ transitions and hence LZS interference, which significantly enhances the measured oscillation amplitude. We further show experimentally that the nature of the coherent charge oscillations changes from Rabi-type to LZS oscillations with increasing pulse distortion. Our results thus demonstrate that it is essential to take into account LZS interference for both precise control of charge qubits and correct interpretation of measurement results.
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.
We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"uckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"uckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given.
We theoretically investigate geometric Stückelberg interferometry in a doubly driven optical lattice clock (OLC). By tuning the relative phase between the two driving fields, we control the relative sign of the effective coupling strengths at the avoided crossings. Within the adiabatic-impulse model, we analyze the time evolution of the two-level system, where nonadiabatic transitions occur only near the crossing points and adiabatic evolution takes place between them. We show that, besides the usual dynamical phase and the Stokes phase, a gauge-invariant noncyclic geometric phase contributes to the final transition probability. This geometric contribution yields a stable π-phase shift in the Stückelberg interference fringes. Moreover, we demonstrate that, under realistic experimental conditions, this geometric Stückelberg interferometer remains insensitive to inhomogeneities in atom-light coupling arising from the finite temperature of the atomic ensemble. Our results provide a general framework for engineering and detecting geometric phases on the OLC platform.