We propose triplet superconductors, such as ruthenates, as prospective materials for qubit construction. The vectorial nature of the order parameter in triplet superconductors makes it conceptually easy to estimate the performance of the qubits. The Cooper condensate of pairs in triplet superconductors has all the attributes of Bose–Einstein condensates and should facilitate long decoherence times for these qubits, relative to other vectorial schemes for qubits, such as small ferromagnets. There are other benefits, which the superconducting state provides for requirements such as entanglement between qubits via the proximity effect, etc. We consider these benefits in detail, although our consideration is only preliminary and further experimental and theoretical research will undoubtedly introduce correctives.
Triplet-pairing superconductors with broken time-reversal symmetry such as ruthenates, Sr2RuO4, have potential application as a basis for quantum computing (QC). The prerequisite here is the requirement of achieving superconductivity in single domain mesoscopic samples. One possible fabrication approach is application of thin film technologies. Initially some attempts were made by other groups to achieve epitaxial Sr2RuO4 films by pulsed laser deposition, but they failed. We propose an alternative method that makes small pieces of the material from larger crystals without destroying the crystal Meanwhile, experimental demonstration of quantum dynamics of triplet superconductors, such as Sr2RuO4, requires small structures on the order of the size of a single domain. QC done using triplet state superconductivity is potentially advantageous because the qubit is only a tiny piece of metal, yet a complete QC system can be implemented building upon this kind of qubit as the foundation. The supporting technology for initiation, entanglement and readout is described. Some of it involves application of ferromagnetic components, used in gate mechanisms. Ultimately, the approach presented here brings together triplet superconductivity in mesoscopic structures with ferromagnetic techniques.
Hybrid devices integrating quantum dots with Josephson junctions are gaining interest because they combine spin-based quantum computing with circuit quantum electrodynamics (circuit QED) methods. In particular, Andreev spin qubits have shown significant experimental progress including strong two-qubit coupling, and are predicted to exhibit all-to-all connectivity. Here we propose superconducting singlet-triplet (SST) qubits that rely on parallel-aligned double quantum dots in Josephson junctions. While Andreev spin qubits require spin-orbit interaction to unlock the spin degree-of-freedom, SST qubits do not require spin-orbit interaction, making the advantages of hybrid devices available to a wider range of materials. Similar to Andreev spin qubits, the qubit states couple to the superconducting phase across the junction, which allows for control and readout using circuit QED, and supports all-to-all connectivity. Only
N flux lines are required to perform any single- and two-qubit gate among
N qubits, and thus the overhead of control lines is small. Finally, linear protection from charge or flux noise makes these qubits interesting candidates for a future quantum processor.
We show how superconductors can be used to couple, initialize, and read out spatially separated spin qubits. When two single-electron quantum dots are tunnel coupled to the same superconductor, the singlet component of the two-electron state partially leaks into the superconductor via crossed Andreev reflection. This induces a gate-controlled singlet-triplet splitting which, with an appropriate superconductor geometry, remains large for dot separations within the superconducting coherence length. Furthermore, we show that when two double-dot singlet-triplet qubits are tunnel coupled to a superconductor with finite charging energy, crossed Andreev reflection enables a strong two-qubit coupling over distances much larger than the coherence length.
We show that the fully polarized triplet
s-wave component is characterized not only by the spin direction, but also by chirality. Interaction of a polarized triplet component and a singlet one results in creation of triplet Cooper pairs with opposite spin direction or of different chiralities. Such spin transformation leads to interesting phenomena in multiterminal magnetic Josephson junctions. We calculate the dc Josephson current
IJ in a multiterminal Josephson contact of the ${S}_{\text{m}}/n/{S}_{\text{m}}^{\ensuremath{'}}$ type with ``magnetic'' superconductors
Sm that generate fully polarized triplet components. The superconductors
Sm are attached to magnetic insulators (filters) which let pass electrons with a fixed spin direction only. The filter axes are assumed to be oriented antiparallel to each other. The Josephson current is zero in two-terminal Josephson junction, i.e., in
S/n/Sm or in ${S}_{\text{m}}/n/{S}_{\text{m}}^{\ensuremath{'}}$ contact. But in the three-terminal Josephson junction, with another
S superconductor attached to the normal wire, the finite current
IJ appears flowing from the
S superconductor to
Sm superconductors. The currents through the right (left) superconductors
Sm are opposite in sign, ${I}_{\text{R}}\ensuremath{\equiv}{I}_{\text{J}}={I}_{\text{c}}sin({\ensuremath{\chi}}_{\text{R}}+{\ensuremath{\chi}}_{\text{L}}\ensuremath{-}2\ensuremath{\chi})=\ensuremath{-}{I}_{\text{L}}$, where ${\ensuremath{\chi}}_{\text{L/R}}$ and $\ensuremath{\chi}$ are the phases of superconductors ${S}_{\text{m}},{S}_{\text{m}}^{\ensuremath{'}}$, and
S, respectively. We discuss possibilities of experimental observation of the effect.
It was theoretically proposed that a forward-biased $p\ensuremath{-}n$ junction with a superconducting layer (P-N-S) would produce pure, polarization-entangled photons due to inherent spin-singlet pairing of electrons. However, any heterostructure interface generically induces Rashba spin-orbit coupling, which in turn generates a mixed singlet-triplet superconducting order parameter. Here we study the effect of triplet pairing on the purity of photons produced through Cooper pair recombination. A unique directional dependence of the state purity is found for a triplet superconductor with fixed $\mathbit{d}$: pure, entangled photons are produced when the photon polarization axis is parallel to $\mathbit{d}$. Induced triplet pairing in a singlet superconductor is shown to degrade the state purity, while induced singlet pairing in a triplet superconductor is shown to enhance the production of entangled pairs. These considerations may aid the design of functional devices to produce entangled photons.