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arXiv:2603.05820

Robust coherent control in non-Hermitian cavity electromagnonics using counterdiabatic driving

Guang-Hui Zhang, Yu-Wen Li, Xue-Ke Song, Liu Ye, Dong Wang

quant-phSubmitted Mar 6, 2026• Announced Mar 9, 2026
arXivHTMLPDF

Abstract

We propose to use counterdiabatic driving (CD) shortcut and the Floquet engineering to realize the robust and fast state transfer in the dissipation cavity magnon-polaritons non-Hermitian (NH) system. For the two-level NH cavity magnon-polaritons Hamiltonian, an accurate and fast population transfer is achieved from the microwave photon to the magnon by two coherent control techniques; counterdiabatic driving shortcut and non-Hermitian shortcuts (NHSs). Additionally, by using the CD technique, the population evolution speed of non-Hermitian systems is faster than that via the NHS technique in the broken-symmetric regime. Furthermore, we compare their performances in the presence of the coupling strength and systematic errors, the CD technique features a broad range of high efficiencies of the transition probability above 99.9%, showing that the CD technique is more robustness against these errors than the NHS technique. It is worth noting that this advantage becomes more significant as the gain rate of system parameters increases. The work provides a basis for achieving the robust coherent control in NH cavity electromagnonics.

Journal reference
Frontiers of Physics 21(7), 075201 (2026)
DOI
10.15302/frontphys.2026.075201
Comments
9 pages, 8 figures

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Abstract In this work, we study the counterdiabatic (CD) driving scheme and population transfer in pseudo- and antipseudo-Hermitian systems. By discussing the adiabatic condition for non-Hermitian system and the relation between the adiabatic evolution and the real energy spectrum, we derive the CD driving scheme for pseudo- and antipseudo-Hermitian systems. Based on these, we derive the condition that an eigenstate of a non-Hermitian Hamiltonian is self-normalized to guarantee the normalized populations of the bare states in non-Hermitian systems. Our results are illustrated by studying the CD driving for a non-Hermitian three-level system. A scheme to realize the perfect population transfer between the bare states is proposed in the antipseudo-Hermitian case.
The stimulated Raman adiabatic passage (STIRAP) allows selective, coherent population transfer in a three-level quantum system by the adiabatic control of two suitably chosen envelopes and delayed laser pulses. However, the long operation time involved with the adiabatic protocols makes them more susceptible to decay and decoherence. A shortcut-to-adiabaticity technique, namely, counterdiabatic driving (CD), suppresses the decoherence-induced loss by speeding up the STIRAP process, thereby enhancing the efficiency and fidelity of population transfer. The superadiabatic STIRAP (saSTIRAP) method requires the application of a shortcut drive or CD pulse, which couples the coherently trapped states in a three-level quantum system. Hence, the closed-loop $\mathrm{\ensuremath{\Lambda}}$ system consisting of all electric dipole-allowed transitions is an essential requirement for saSTIRAP, which is rarely admissible in a natural atom. This paper theoretically investigates an experimentally feasible model for implementing saSTIRAP using a closed-loop $\mathrm{\ensuremath{\Lambda}}$ system with doubly dressed polariton states in a driven circuit QED system. We show a population transfer with efficiencies close to 80.7580.75%80.75 and 98.1098.10%98.10 with fidelities of 89.8689.86%89.86 and 99.0499.04%99.04 for the resonant STIRAP and saSTIRAP protocols, respectively, with experimentally feasible parameters. The efficiency of the population transfer can be further increased by improving the coherence times of the cavity and the transmon qubit. This work may be useful in designing fast, efficient quantum gates for applications in quantum technologies.
Shortcuts to adiabaticity are alternative fast processes which reproduce the same final state as the adiabatic process in a finite or even shorter time, which have been extended from Hermitian systems to non-Hermitian systems in recent years, but they are barely explored for general non-Hermitian systems where off-diagonal elements of the Hamiltonian are not Hermitian. In this paper, we propose a shortcuts to adiabaticity technique which is based on a transitionless quantum driving algorithm to realize population transfer for general two-level non-Hermitian systems and give both exact and approximate analytical solutions of the corresponding counteradiabatic driving Hamiltonian, where the latter can be extended to the zeroth-order and first-order terms by applying perturbative theory. We find that the first-order correction term is different from the previous results, which is caused by the non-Hermiticity of the off-diagonal elements. We work out an exact expression for the control function and present examples consisting of a general two-level system with gain and loss to show the theory. The results suggest that the high-fidelity population transfer can be implemented in general non-Hermitian systems by our method, which works even with strong non-Hermiticity and without rotating wave approximation. Furthermore, we show that the general Hamiltonian the off-diagonal elements of which are not conjugate to each other can be implemented in many physical systems with the present experimental technology, such as an atom-light interaction system and whispering-gallery microcavity, which might have potential applications in quantum information processing.
Shortcuts to adiabaticity (STA) is a common protocol to realize high-fidelity and robust quantum control in various quantum systems. To date, STA has been widely applied in two- and three-level systems, whereas designing feasible strategies to achieve perfect quantum state engineering in multi-level systems still remains a challenging task. Here, we propose to use counterdiabatic (CD) driving and time-rescaling (TR) methods to construct multi-state stimulated Raman shortcut-to-adiabatic passage protocols for realizing robust and fast population transfer in chainwise-connected five-state systems. The first protocol is implemented by initially reducing the original five-state system to an equivalent two-state counterpart, and then designing the corresponding driving field by combining CD driving and unitary transformation. Further, we introduce the TR method to optimize the first protocol and thus offers an alternative solution. Numerical calculations show that both protocols can achieve complete population transfer and effectively suppress transient populations of all intermediate states. Compared with the first protocol, the optimized second exhibits better performance within a shorter evolution time.
Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.
Cavity magnomechanics provides a readily controllable hybrid system, consisting of a cavity mode, magnon mode, and phonon mode, for quantum state manipulation and transfer. To implement a fast-and-robust state transfer between the hybrid photon-magnon mode and the phonon mode, we apply two accelerated-adiabatic-passage protocols based on the counterdiabatic Hamiltonian for transitionless quantum driving and the Levis-Riesenfeld invariant for inverse engineering. We construct the counterdiabatic Hamiltonian in a state-resolved way and express it through the creation and annihilation operators rather than the system eigenstates and their time derivatives. We can optimize the invariant-based inverse-engineering protocol with respect to the stability against the systematic errors of the coupling strength and frequency detuning. Both protocols apply for continuous-variable systems with arbitrary target states. We also discuss the decoherence effects from the thermal environment and the counterrotating interactions on both protocols. Our work contributes to the quantum memory for photonic and magnonic quantum information.