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We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive. We find that when the detuning Δ between the frequency of the oscillator and the second subharmonic of the drive equals an even multiple of the Kerr coefficientK, $\mathrm{\Delta }/K=2m$, the oscillator displays $m+1$exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. These degeneracies can be explained by the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime, thus creating a protected cat qubit in the ground state manifold of our oscillator. Our results illustrate the relationship between degeneracies and noise protection in a driven quantum system. 

By applying a microwave drive to a specially designed Josephson circuit, we have realized a double-well model system: a Kerr oscillator submitted to a squeezing force. We have observed, for the first time, the spectroscopic fingerprint of a quantum double-well Hamiltonian when its barrier height is increased: a pairwise level kissing (coalescence) corresponding to the exponential reduction of tunnel splitting in the excited states as they sink under the barrier. The discrete levels in the wells also manifest themselves in the activation time across the barrier which, instead of increasing smoothly as a function of the barrier height, presents steps each time a pair of excited states is captured by the wells. This experiment illustrates the quantum regime of Arrhenius’s law, whose observation is made possible here by the unprecedented combination of low dissipation, time-resolved state control, 98.5% quantum nondemolition single shot measurement fidelity, and complete microwave control over all Hamiltonian parameters in the quantum regime. Direct applications to quantum computation and simulation are discussed. Published by the American Physical Society2024 

Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be able to efficiently capture all the relevant physics of the original system. In this work, we investigate the conditions for the validity of the usual low-order static effective Hamiltonian used to describe a Kerr oscillator under a squeezing drive. This system is of fundamental and technological interest. In particular, it has been used to stabilize Schrödinger cat states, which have applications for quantum computing. We compare the states and energies of the effective static Hamiltonian with the exact Floquet states and quasi-energies of the driven system and determine the parameter regime where the two descriptions agree. Our work brings to light the physics that is left out by ordinary static effective treatments and that can be explored by state-of-the-art experiments. 

Since the demonstration of the unique properties of single-layer graphene and transition metal dichalcogenides (TMDs), research on two-dimensional (2D) materials has become one of the hottest topics, with the family of 2D materials quickly expanding. This expansion is mainly attributable to the development of new synthesis methods to create new materials. This review will summarize and critically analyze topochemical synthesis methods for synthesizing novel 2D materials. For example, the emerging family of 2D transition metal carbides, nitrides and carbonitrides (MXenes) are synthesized primarily by selective etching of “A” (metal) elements from MAX phases. Another 2D material, hydrogenated germanene is produced by selective etching of calcium digermanide (CaGe 2 ). The topochemical transformation of one dichalcogenide into another and 2D oxides into 2D carbides or nitrides have attracted great attention because materials with many useful and diverse properties can be obtained by these methods. Topochemical synthesis methods provide alternative ways of synthesizing 2D materials not requiring van der Waals bonded solid precursors or vapor phase deposition, but they have not been comprehensively reviewed. In this review, we describe common principles of topochemical synthesis of 2D materials, explain synthesis mechanisms and offer an outlook for future research. 

Abstract The synthesis of low‐dimensional transition metal nitride (TMN) nanomaterials is developing rapidly, as their fundamental properties, such as high electrical conductivity, lead to many important applications. However, TMN nanostructures synthesized by traditional strategies do not allow for maximum conductivity and accessibility of active sites simultaneously, which is a crucial factor for many applications in plasmonics, energy storage, sensing, and so on. Unique interconnected two‐dimensional (2D) arrays of few‐nanometer TMN nanocrystals not only having electronic conductivity in‐plane, but also allowing transport of ions and electrolyte through the porous nanosheets, which are obtained by topochemical synthesis on the surface of a salt template, are reported. As a demonstration of their application in a lithium–sulfur battery, it is shown that 2D arrays of several nitrides can achieve a high initial capacity of >1000 mAh g⁻¹at 0.2 C and only about 13% degradation over 1000 cycles at 1 C under a high areal sulfur loading (>5 mg cm⁻²).