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arXiv:2306.07729 · Physical Review Letters

How to Cross an Energy Barrier at Zero Kelvin without Tunneling Effect

Seiji Miyashita, B. Barbara

Published Aug 9, 2023• 10 citations
arXivHTMLPDF

Abstract

This Letter deals with the broad class of magnetic systems having a single or collective spin S with an energy barrier, such as rare-earth elements and their compounds, single molecule magnets with uniaxial anisotropy, and more generally any other anisotropic quantum system made of single or multiple objects with discrete energy levels. Till now, the reversal of the magnetization of such systems at zero kelvin required making use of quantum tunneling with a significant transverse field or transverse anisotropy term, at resonance. Here, we show that another very simple method exists. It simply consists in the application of a particular sequence of electromagnetic radiations in the ranges of optical or microwave frequencies, depending on the characteristics of the system (spin and anisotropy values for magnetic systems). This produces oscillations of the Rabi type that pass above the barrier, thus extending these oscillations between the two energy wells with mixtures of all the 2S+1 states. In addition to its basic character, this approach opens up new directions of research in quantum information with possible breakthroughs in the current use of multiple quantum bits.

DOI
10.1103/physrevlett.131.066701

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This Letter deals with the broad class of magnetic systems having a single or collective spin S with an energy barrier, such as rare-earth elements and their compounds, single molecule magnets with uniaxial anisotropy, and more generally any other anisotropic quantum system made of single or multiple objects with discrete energy levels. Till now, the reversal of the magnetization of such systems at zero kelvin required making use of quantum tunneling with a significant transverse field or transverse anisotropy term, at resonance. Here, we show that another very simple method exists. It simply consists in the application of a particular sequence of electromagnetic radiations in the ranges of optical or microwave frequencies, depending on the characteristics of the system (spin and anisotropy values for magnetic systems). This produces oscillations of the Rabi type that pass above the barrier, thus extending these oscillations between the two energy wells with mixtures of all the 2S+1 states. In addition to its basic character, this approach opens up new directions of research in quantum information with possible breakthroughs in the current use of multiple quantum bits.
We propose two potential realizations for quantum bits based on nanometre-scale magnetic particles of large spin S and high-anisotropy molecular clusters. In case (1) the bit-value basis states |0⟩ and |1⟩ are the ground and first excited spin states S z = S and S -1, separated by an energy gap given by the ferromagnetic resonance frequency. In case (2), when there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, |0⟩, and antisymmetric, |1⟩, combinations of the twofold degenerate ground state S z = ± S . In each case the temperature of operation must be low compared to the energy gap, Δ, between the states |0⟩ and |1⟩. The gap Δ in case (2) can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware.
Motivated by the experimental observation of resonant tunneling in systems of half-integer spin, such as V15 and Mn4, we study the mechanism of the adiabatic change of the magnetization in systems with time-reversal symmetry. Although tunneling between the degenerate ground states is suppressed in a simple Kramers doublet, some types of perturbational interactions cause an avoided level crossing structure in the energy level structures when the system possesses additional degeneracy of the ground state. We show that a nonadiabatic transition governed by the Landau-Zener-Stückelberg mechanism occurs in many cases, and also find more general cases of adiabatic change of the magnetization in which LZS mechanism cannot be applied directly.
Proton transfer plays a key role in the applications of advanced energy materials as well as in the functionalities of biological systems. In this work, based on the transfer matrix method, we study the quantum effects of proton transfer in a series of one-dimensional (1D) model potentials and numerically calculate the quantum probability of transferring across single and double barriers (wells). In the case of single barriers, when the incident energies of protons are above the barrier height, the quantum oscillations in the transmission coefficients depend on the geometric shape of the barriers. It is found that atomic resonant tunneling (ART) not only presents in the rectangular single well and rectangular double barriers as expected, but also exists in the other types of potential wells and double barriers. For hetero-structured double barriers, there is no resonant tunneling in the classical forbidden zone, i.e., in the case when the incident energy (E i) is lower than the barrier height (E b). Furthermore, we have provided generalized analysis on the characteristics of transmission coefficients of hetero-structured rectangular double barriers.
A method for solving the problem of quantum transmission through potential barriers or potential wells for a compound system consisting of several identical particles coupled via pair oscillator-type potentials in the oscillator representation of the symmetrized coordinates is considered. The efficiency of the proposed approach, algorithms and programs is demonstrated by the examples of calculation of complex energy values and analysis of metastable states of compound systems of two, three, and four identical particles on a straight line, which lead to the effect of quantum transparency of the potential barriers or quantum reflection from the wells.
Electrical control of single spin qubits is a major frontier for nanoscale, high-speed, and scalable quantum devices. Yet, extending it to highly shielded rare-earth 4f electrons remains an experimental challenge across solid-state platforms. Here we demonstrate all-electrical coherent control of a single Er electron spin, which is exchange-coupled to a nearby Ti atom. Scanning tunneling microscopy-based electron spin resonance with three-dimensional magnetic-field control enables comprehensive mapping of the resonance and Rabi frequencies, revealing pronounced anisotropies in both the Er g-tensor and the Er-Ti exchange interaction. The electrical modulation of the anisotropic Er-Ti coupling results in an efficient drive of the Er spin, allowing us to achieve near-gigahertz Rabi frequencies - a ten-fold improvement over the present record for rare-earth spin qubits. By establishing anisotropic exchange as a general resource for electrically accessing shielded rare-earth spins, our results open a new route to ultrafast and local control of rare-earth spins in solid-state quantum devices.
The characterization of the material properties of Single Molecule Magnets (SMMs) has grown in importance over the last few decades with the rise of novel applications such as high-density magnetic storage and quantum computation. Many of the applications require the probing of SMMs with spectroscopic methods that make use of electromagnetic radiation. The interaction with these timedependent fields leads to energy shifts, which can be attributed to the geometric phase acquired by the system or the Bloch-Siegert shift. We model an SMM by a giant spin Hamiltonian, and use Floquet perturbation theory to find the geometric phase shifts. The locations where the phase shift between two levels is zero is useful for performing accurate spectroscopies, whereas the regions where relative phase differences exist are useful in applications like quantum computing. Using the same giant spin Hamiltonian, we can use Floquet theory and Salwen perturbation theory to determine the Bloch-Siegert shift and derive a modified version of the Rabi formula for transition probabilities between the energy states Eα → Eα±1, Eα → Eα±3, and Eα → Eα±5, where α is the index of an arbitrary initial state. The shifted eigenvalues and modified transition probabilities can be useful in spectroscopies where accurate values for the energy-splitting between magnetic states needs to be determined.