Hole-spins localized in semiconductor structures, such as quantum dots or defects, serve to the realization of efficient gate-tunable solid-state quantum bits. Here we study two electrically driven spin $3/2$ holes coupled to the electromagnetic fiel
d of a microwave cavity. We show that the interplay between the non-Abelian Berry phases generated by local time-dependent electrical fields and the shared cavity photons allows for fast manipulation, detection, and long-range entanglement of the hole-spin qubits in the absence of any external magnetic field. Owing to its geometrical structure, such a scheme is more robust against external noises than the conventional hole-spin qubit implementations. These results suggest that hole-spins are favorable qubits for scalable quantum computing by purely electrical means.
Spin pumping consists in the injection of spin currents into a non-magnetic material due to the precession of an adjacent ferromagnet. In addition to the pumping of spin the precession always leads to pumping of heat, but in the presence of spin-orbi
tal entanglement it also leads to a charge current. We investigate the pumping of charge, spin and heat in a device where a superconductor and a quantum spin Hall insulator are in proximity contact with a ferromagnetic insulator. We show that the device supports two robust operation regimes arising from topological effects. In one regime, the pumped charge, spin and heat are quantized and related to each other due to a topological winding number of the reflection coefficient in the scattering matrix formalism -- translating to a Chern number in the case of Hamiltonian formalism. In the second regime, a Majorana zero mode switches off the pumping of currents owing to the topologically protected perfect Andreev reflection. We show that the interplay of these two topological effects can be utilized so that the device operates as a robust charge, spin and heat transistor.
We study the spin transport through a 1D quantum Ising-XY-Ising spin link that emulates a topological superconducting-normal-superconducting structure via Jordan-Wigner (JW) transformation. We calculate, both analytically and numerically, the spectru
m of spin Andreev bound states and the resulting $mathbb{Z}_2$ fractional spin Josephson effect (JE) pertaining to the emerging Majorana JW fermions. Deep in the topological regime, we identify an effective time-reversal symmetry that leads to $mathbb{Z}_4$ fractional spin JE in the $textit{presence}$ of interactions within the junction. Moreover, we uncover a hidden inversion time-reversal symmetry that protects the $mathbb{Z}_4$ periodicity in chains with an odd number of spins, even in the $textit{absence}$ of interactions. We also analyze the entanglement between pairs of spins by evaluating the concurrence in the presence of spin current and highlight the effects of the JW Majorana states. We propose to use a microwave cavity setup for detecting the aforementioned JEs by dispersive readout methods and show that, surprisingly, the $mathbb{Z}_2$ periodicity is immune to $textit{any}$ local magnetic perturbations. Our results are relevant for a plethora of spin systems, such as trapped ions, photonic lattices, electron spins in quantum dots, or magnetic impurities on surfaces.
A trijunction made of three topological semiconducting wires, each supporting a Majorana bound state at its two extremities, appears as one of the simplest geometry in order to perform braiding of Majorana fermions. By embedding the trijunction into
a microwave cavity allows to study the intricate dynamics of the low-energy Majorana bound states (MBSs) coupled to the cavity electric field under a braiding operation. Extending a previous work (Phys. Rev. Lett. 2019, 122, 236803), the full time evolution of the density matrix of the low-energy states, including various relaxation channels, is computed both in the adiabatic regime, as well as within the Floquet formalism in the case of periodic driving. It turns out that in the stationary state the observables of the system depend on both the parity of the ground state and on the non-Abelian Berry phase acquired during braiding. The average photon number and the second order photon coherence function $g^{(2)}(0)$ are explicitly evaluated and reveal the accumulated non-Abelian Berry phase during the braiding process.
A minimally invasive technique is proposed for detecting the differential spin conductance and spin current noise across a junction between two quantum magnets using a high-quality microwave resonator coupled to a transmission line which is impedance
matched to a photon detector downstream. Photons in the microwave resonator couple inductively to the spins in the spin subsystem, and the noise in the junction spin current imprints itself into the output photons propagating along the transmission line. The technique is capable of extracting both the dc and finite frequency noise via the output photon flux and of measuring the junction spin conductance by driving the electromagnetic environment into a different temperature regime.
We study the dynamical process of braiding Majorana bound states in the presence of the coupling to photons in a microwave cavity. We show theoretically that the $pi/4$ phase associated with the braiding of Majoranas, as well as the parity of the gro
und state are imprinted into the photonic field of the cavity, which can be detected by dispersive readouts techniques. These manifestations are purely dynamical, they occur in the absence of any splitting of the MBS that are exchanged, and they disappear in the static setups studied previously. Conversely, the cavity can affect the braiding phase, which in turn should allow for cavity controlled braiding.
We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-
dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana states populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, thus far unexplored in the context of Majorana physics, allows to probe accurately the presence of Majorana bound states in the junction.
We study theoretically a chain of precessing classical magnetic impurities in an $s$-wave superconductor. Utilizing a rotating wave description, we derive an effective Hamiltonian that describes the emergent Shiba band. We find that this Hamiltonian
shows non-trivial topological properties, and we obtain the corresponding topological phase diagrams both numerically and analytically. We show that changing the precession frequency offers a control over topological phase transitions and the emergence of Majorana bound states. We propose driving the magnetic impurities or magnetic texture into precession by means of spin-transfer torque in a spin-Hall setup, and manipulate it using spin superfluidity in the case of planar magnetic order.
We consider a superconducting microwave cavity capacitively coupled to both a quantum conductor and its electronic reservoirs. We analyze in details how the measurements of the cavity microwave field, which are related to the electronic charge suscep
tibility, can be used to extract information on the transport properties of the quantum conductor. We show that the asymmetry of the capacitive couplings between the electronic reservoirs and the cavity plays a crucial role in relating optical measurements to transport properties. For asymmetric capacitive couplings, photonic measurements can be used to probe the finite low frequency admittance of the quantum conductor, the real part of which being related to the differential conductance. In particular, when the quantum dot is far from resonance, the charge susceptibility is directly proportional to the admittance for a large range of frequencies and voltages. However, when the quantum conductor is near a resonance, such a relation generally holds only at low frequency and for equal tunnel coupling or low voltage. Beyond this low-energy near equilibrium regime, the charge susceptibility and thus the optical transmission offers new insights on the quantum conductors since the optical observables are not directly connected to transport quantities. For symmetric lead capacitive couplings, we show that the optical measurements can be used to reveal the Korringa-Shiba relation, connecting the reactive to the dissipative part of the susceptibility, at low frequency and low bias.
We find a superradiant quantum phase transition in the model of triangular molecular magnets coupled to the electric component of a microwave cavity field. The transition occurs when the coupling strength exceeds a critical value which, in sharp cont
rast to the standard two-level emitters, can be tuned by an external magnetic field. In addition to emitted radiation, the molecules develop an in-plane electric dipole moment at the transition. We estimate that the transition can be detected in state of the art microwave strip-line cavities containing $10^{15}$ molecules.
