Quantum dynamics of
superconducting topological systems
Quantum dynamics of
superconducting topological systems
Up to now there exist two major distinct methods to avoid dephasing and thermalization in classical and quantum computing devices and preserve the initial state information. The first one considered in the previous research direction is based on the quenched disorder.
Up to now there exist two major distinct methods to avoid dephasing and thermalization in classical and quantum computing devices and preserve the initial state information. The first one considered in the previous research direction is based on the quenched disorder.
This research direction considers another method to retain the coherence of superconducting qubits using topological systems for quantum computations. Such a topological protection of the desired states is actively used for fault-tolerant quantum computations and is usually associated to braiding protocols of Majorana modes. A key feature of superconducting materials with nontrivial topological properties is their ability to support exotic localized vortex or edge excitations called Majorana modes, which are robust to most decoherence effects.
This research direction considers another method to retain the coherence of superconducting qubits using topological systems for quantum computations. Such a topological protection of the desired states is actively used for fault-tolerant quantum computations and is usually associated to braiding protocols of Majorana modes. A key feature of superconducting materials with nontrivial topological properties is their ability to support exotic localized vortex or edge excitations called Majorana modes, which are robust to most decoherence effects.
Despite quite a number of theoretical proposals and experimental evidences of Majorana mode observation, there are still significant limitations preventing realization of their braiding and its relevant theoretical description. The main difficulty is to include the interaction preserving the particle parity into the considered picture. Thus, in this direction we develop the coherent quantum mechanical description of a Majorana nanowire subject to the Coulomb blockade.
Despite quite a number of theoretical proposals and experimental evidences of Majorana mode observation, there are still significant limitations preventing realization of their braiding and its relevant theoretical description. The main difficulty is to include the interaction preserving the particle parity into the considered picture. Thus, in this direction we develop the coherent quantum mechanical description of a Majorana nanowire subject to the Coulomb blockade.
The work done by us in the paper "Nonlocality and dynamic response of Majorana states in fermionic superfluids" is the first step in this direction . It clarifies the fundamental physical limits on times of operations with Majorana states, the peculiarities of their dynamics accounting of specificity of the physical systems (see Fig. on the left). This problem is one of milestones necessary for realization of braiding and observability of non-Abelian statistics of Majorana states.
The work done by us in the paper "Nonlocality and dynamic response of Majorana states in fermionic superfluids" is the first step in this direction . It clarifies the fundamental physical limits on times of operations with Majorana states, the peculiarities of their dynamics accounting of specificity of the physical systems (see Fig. on the left). This problem is one of milestones necessary for realization of braiding and observability of non-Abelian statistics of Majorana states.
Another fundamental issue with the Majorana modes is the so-called quasiparticle poisoning which occurs at any finite temperature due to the smallness of the superconducting gap induced in the topologically non-trivial system.
Another fundamental issue with the Majorana modes is the so-called quasiparticle poisoning which occurs at any finite temperature due to the smallness of the superconducting gap induced in the topologically non-trivial system.
In the paper "Inverse proximity effect in semiconductor Majorana nanowires" we have addressed the issue of the small induced superconducting gap in the system of a semiconducting nanowire with the strong spin-orbit coupling and large Lande g-factor covered by the superconducting shell. Such system being one of the most promising candidates for realizing Majorana modes, needs the application of the strong magnetic field along the wire. The topological phase transition occurs when the effective exchange field in the wire exceeds its chemical potential. As shown in the paper within the microscopic model of induced superconductivity due to the van Hove singularity at the crossing of the topological transition the inverse proximity effect might suppress the superconductivity not only in the wire, but also in the primary superconducting shell (see Fig. on the right).
In the paper "Inverse proximity effect in semiconductor Majorana nanowires" we have addressed the issue of the small induced superconducting gap in the system of a semiconducting nanowire with the strong spin-orbit coupling and large Lande g-factor covered by the superconducting shell. Such system being one of the most promising candidates for realizing Majorana modes, needs the application of the strong magnetic field along the wire. The topological phase transition occurs when the effective exchange field in the wire exceeds its chemical potential. As shown in the paper within the microscopic model of induced superconductivity due to the van Hove singularity at the crossing of the topological transition the inverse proximity effect might suppress the superconductivity not only in the wire, but also in the primary superconducting shell (see Fig. on the right).
Yet another interesting effect relevant for quantum dynamics of Majorana modes (such as braiding), is the presence of the collective excitations of the superconducting order parameter amplitude under the drive or quench of the parameters of the system. By the analogy with the high energy physics, such collective modes of the amplitude of the order parameter are called Higgs boson modes. However, in order to excite such modes the perturbation should contain the frequencies of the order of two superconducting gaps.
Yet another interesting effect relevant for quantum dynamics of Majorana modes (such as braiding), is the presence of the collective excitations of the superconducting order parameter amplitude under the drive or quench of the parameters of the system. By the analogy with the high energy physics, such collective modes of the amplitude of the order parameter are called Higgs boson modes. However, in order to excite such modes the perturbation should contain the frequencies of the order of two superconducting gaps.
In hybrid superconducting systems, like considered in our work "Higgs modes in superconducting systems with proximity effect" (see Fig. on the left), the latter restrictions might be lifted. Indeed, due to the presence of the non-superconducting subsystem, new Higgs modes are formed with smaller eigenfrequencies given by the sum of the primary Δ0 and induced Δi gaps as well as by the doubled induced gap 2Δi. The primary Higgs mode obtains the exponential damping due to the incoherent Cooper pair breaking.
In hybrid superconducting systems, like considered in our work "Higgs modes in superconducting systems with proximity effect" (see Fig. on the left), the latter restrictions might be lifted. Indeed, due to the presence of the non-superconducting subsystem, new Higgs modes are formed with smaller eigenfrequencies given by the sum of the primary Δ0 and induced Δi gaps as well as by the doubled induced gap 2Δi. The primary Higgs mode obtains the exponential damping due to the incoherent Cooper pair breaking.
In this direction the relevant outline is to consider the emergent Higgs modes in the topologically non-trivial systems with the induced superconductivity, used for the realization of the Majorana modes. This consideration allows to understand the interplay of such new Higgs modes with Majorana excitations and their mutual dynamics.
In this direction the relevant outline is to consider the emergent Higgs modes in the topologically non-trivial systems with the induced superconductivity, used for the realization of the Majorana modes. This consideration allows to understand the interplay of such new Higgs modes with Majorana excitations and their mutual dynamics.