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The interplay of superconductivity with non-trivial spin textures is promising for the engineering of non-Abelian Majorana quasiparticles. Spin–orbit coupling is crucial for the topological protection of Majorana modes as it forbids other trivial excitations at low energy but is typically intrinsic to the material1–7. Here, we show that coupling to a magnetic texture can induce both a strong spin–orbit coupling of 1.1 meV and a Zeeman effect in a carbon nanotube. Both of these features are revealed through oscillations of superconductivity-induced subgap states under a change in the magnetic texture. Furthermore, we find a robust zero-energy state—the hallmark of devices hosting localized Majorana modes—at zero magnetic field. Our findings are generalizable to any low-dimensional conductor, and future work could include microwave spectroscopy and braiding operations, which are at the heart of modern schemes for topological quantum computation.

Remarkably, complex assemblies of superconducting wires, electrodes, and Josephson junctions are compactly described by a handful of collective phase degrees of freedom that behave like quantum particles in a potential. Almost all these circuits operate in the regime where quantum phase fluctuations are small—the associated flux is smaller than the superconducting flux quantum—although entering the regime of large fluctuations would have profound implications for metrology and qubit protection. The difficulty arises from the apparent need for circuit impedances vastly exceeding the resistance quantum. Independently, exotic circuit elements that require Cooper pairs to form pairs in order to tunnel have been developed to encode and topologically protect quantum information. In this work, we demonstrate that pairing Cooper pairs magnifies the phase fluctuations of the circuit ground state. We measure a tenfold suppression of flux sensitivity of the first transition energy only, implying a twofold increase in the vacuum phase fluctuations and showing that the ground state is delocalized over several Josephson wells.

Semiconductor quantum dots are an attractive platform for the realisation of quantum processors. To achieve long-range coupling between them, quantum dots have been integrated into microwave cavities. However, it has been shown that their coherence is then reduced compared to their cavity-free implementations. Here, we manipulate the quantum states of a suspended carbon nanotube double quantum dot with ferromagnetic contacts embedded in a microwave cavity. By performing quantum manipulations via the cavity photons, we demonstrate coherence times of the order of 1.3 μ s, two orders of magnitude larger than those measured so far in any carbon quantum circuit and one order of magnitude larger than silicon-based quantum dots in comparable environment. This holds promise for carbon as a host material for spin qubits in circuit quantum electrodynamics. Carbon nanotubes are promising hosts for spin qubits, however existing demonstrations show limited coherence times. Here the authors report quantum states in a carbon-nanotube-based circuit driven solely by cavity photons and exhibiting a coherence time of about 1.3 μ s.

Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an L C oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance L C oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics. In superconducting circuits, the nonlinearity of Josephson junctions mediates photon interactions, but they are typically dominated by two-photon processes. Here the authors observe multi-photon interactions in a superconducting circuit with Cooper-pair pairing, revealing a new regime of microwave quantum optics.

The control of light-matter interaction at the most elementary level has become an important resource for quantum technologies. Implementing such interfaces in the THz range remains an outstanding problem. Here, we couple a single electron trapped in a carbon nanotube quantum dot to a THz resonator. The resulting light-matter interaction reaches the deep strong coupling regime that induces a THz energy gap in the carbon nanotube solely by the vacuum fluctuations of the THz resonator. This is directly confirmed by transport measurements. Such a phenomenon which is the exact counterpart of inhibition of spontaneous emission in atomic physics opens the path to the readout of non-classical states of light using electrical current. This would be a particularly useful resource and perspective for THz quantum optics. Strong light-matter coupling has been realized at the level of single atoms and photons throughout most of the electromagnetic spectrum, except for the THz range. Here, the authors report a THz-scale transport gap, induced by vacuum fluctuations in carbon nanotube quantum dot through the deep strong coupling of a single electron to a THz resonator.

In a quantum dot in the Kondo regime, electrical charges are effectively frozen, but the quantum dot remains electrically conducting owing to strong electron–electron correlations. Conduction from a frozen charge A central theme in condensed matter physics is the understanding of many-body electron–electron interactions, and nanoscale devices enable us to study the underlying principles at the single-electron level. Matthieu Desjardins et al . reveal a remarkable electron–electron interaction effect by examining a carbon nanotube quantum dot placed within a microwave circuit. They tune the quantum dot to the Kondo regime—an archetype of strong electronic correlations—and use combined electronic and microwave measurements to show that, even though electrical charges are effectively frozen because tunnelling of electrons into the dot is not possible, the dot remains electronically conducting. This is due to the strong Kondo correlations. The authors suggest that their measurement platform could be a useful tool for probing charge dynamics in a range of other correlated systems. The ability to control electronic states at the nanoscale has contributed to our modern understanding of condensed matter. In particular, quantum dot circuits represent model systems for the study of strong electronic correlations, epitomized by the Kondo effect 1 , 2 , 3 . We use circuit quantum electrodynamics architectures to study the internal degrees of freedom of this many-body phenomenon. Specifically, we couple a quantum dot to a high-quality-factor microwave cavity to measure with exceptional sensitivity the dot’s electronic compressibility, that is, its ability to accommodate charges. Because electronic compressibility corresponds solely to the charge response of the electronic system, it is not equivalent to the conductance, which generally involves other degrees of freedom such as spin. Here, by performing dual conductance and compressibility measurements in the Kondo regime, we uncover directly the charge dynamics of this peculiar mechanism of electron transfer. The Kondo resonance, visible in transport measurements, is found to be ‘transparent’ to microwave photons trapped in the high-quality cavity, thereby revealing that (in such a many-body resonance) finite conduction is achieved from a charge frozen by Coulomb interaction. This freezing of charge dynamics 4 , 5 , 6 is in contrast to the physics of a free electron gas. We anticipate that the tools of cavity quantum electrodynamics could be used in other types of mesoscopic circuits with many-body correlations 7 , 8 , providing a model system in which to perform quantum simulation of fermion–boson problems.

Single-spin qubits in semiconductor quantum dots hold promise for universal quantum computation with demonstrations of a high single-qubit gate fidelity above 99.9% and two-qubit gates in conjunction with a long coherence time. However, initialization and readout of a qubit is orders of magnitude slower than control, which is detrimental for implementing measurement-based protocols such as error-correcting codes. In contrast, a singlet-triplet qubit, encoded in a two-spin subspace, has the virtue of fast readout with high fidelity. Here, we present a hybrid system which benefits from the different advantages of these two distinct spin-qubit implementations. A quantum interface between the two codes is realized by electrically tunable inter-qubit exchange coupling. We demonstrate a controlled-phase gate that acts within 5.5 ns, much faster than the measured dephasing time of 211 ns. The presented hybrid architecture will be useful to settle remaining key problems with building scalable spin-based quantum computers. The race to produce a quantum computer has driven the development of many different qubit designs with different benefits and drawbacks. Noiri et al. demonstrate a hybrid device with two coupled semiconductor spin qubits of different designs, which should allow each qubit’s advantages to be exploited.

Topological excitations, such as Majorana zero modes, are a promising route for encoding quantum information. Topologically protected gates of Majorana qubits, based on their braiding, will require some form of network. Here, we propose to build such a network by entangling Majorana matter with light in a microwave cavity QED set-up. Our scheme exploits a light-induced interaction which is universal to all the Majorana nanoscale circuit platforms. This effect stems from a parametric drive of the light-matter coupling in a one-dimensional chain of physical Majorana modes. Our set-up enables all the basic operations needed in a Majorana quantum computing platform such as fusing, braiding, the crucial T-gate, the read-out, and importantly, the stabilization or correction of the physical Majorana modes.

Non-collinear spin transport is at the heart of spin or magnetization control in spintronics devices. The use of nanoscale conductors exhibiting quantum effects in transport could provide new paths for that purpose. Here we study non-collinear spin transport in a quantum dot. We use a device made out of a single-wall carbon nanotube connected to orthogonal ferromagnetic electrodes. In the spin transport signals, we observe signatures of out of equilibrium spin precession that are electrically tunable through dissipation. This could provide a new path to harness spin precession in nanoscale conductors. Control over the orientation of electronic spins forms the basis for spintronic devices in both classical and quantum systems. Here, the authors observe electrically-tunable dissipation-controlled spin precession in a carbon nanotube quantum dot bridging two non-collinearly magnetized electrodes.

Engineering the interaction between light and matter is an important goal in the emerging field of quantum opto-electronics. Thanks to the use of cavity quantum electrodynamics architectures, one can envision a fully hybrid multiplexing of quantum conductors. Here we use such an architecture to couple two quantum dot circuits. Our quantum dots are separated by 200 times their own size, with no direct tunnel and electrostatic couplings between them. We demonstrate their interaction, mediated by the cavity photons. This could be used to scale up quantum bit architectures based on quantum dot circuits or simulate on-chip phonon-mediated interactions between strongly correlated electrons. Controlling the interaction between distant quantum dots is important if they are to be used in quantum information devices. Delbecq et al . place two quantum dot circuits in a microwave cavity and show that they interact via cavity photons, even though they are separated by 200 times their own size.