Dmitriy S. Shapiro

We study charge transport in a single-electron transistor implemented as an interferometer such that the Coulomb blockaded middle island contains a circular chiral Majorana or Dirac edge mode. We concentrate on the regime of small conductance and provide an asymptotic solution in the limit of high transport voltage exceeding the charging energy. The solution is achieved using an instanton-like technique. The distinctions between Majorana and Dirac cases appears when the tunnel junctions are unequal. The main difference is in the offset current at high voltages which can be higher up to $50\%$ in Majorana case. It is caused by an additional particle-hole symmetry of the distribution function in the Majorana case. There is also an eye-catching distinction between the oscillations patterns of the current as a function of the gate charge. We conjecture this distinction survives at lower transport voltages as well.

We explore experimentally a quantum metamaterial based on a superconducting chip with 25 frequency-tunable transmon qubits coupled to a common coplanar resonator. The collective bright and dark modes are probed via the microwave response, i.e., by measuring the transmission amplitude of an external microwave signal. All qubits have individual control and readout lines. Their frequency tunability allows the number $N$ of resonantly coupled qubits to change and a disorder in their excitation frequencies to be introduced with preassigned distributions. While increasing $N$, we demonstrate the expected $N^{1/2}$ scaling law for the energy gap (Rabi splitting) between bright modes around the cavity frequency. By introducing a controllable disorder and averaging the transmission amplitude over a large number of realizations, we demonstrate a decay of mesoscopic fluctuations which mimics an approach towards the thermodynamic limit. The collective bright states survive in the presence of disorder when the strength of individual qubit coupling to the cavity dominates over the disorder strength.

A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of a one-dimensional system with a nontrivial band topology. An interplay of disorder and topological ordering in the SSH model is of great interest owing to experimental advancements in synthesized quantum simulators. In this paper, we investigate a special sort of a disorder when intercell hopping amplitudes are random. Using a definition for ${\mathbb{Z}}_2$-topological invariant $\nu \in \{0;1\}$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $\langle \nu \rangle$ averaged by random realizations. This allows to find: (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite-size fluctuations of $\nu$ for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for the finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green's function method for a thermodynamic limit.

We explore experimentally a quantum metamaterial based on a superconducting chip with 25 frequency-tunable transmon qubits coupled to a common coplanar resonator. The collective bright and dark modes are probed via the microwave response, i.e., by measuring the transmission amplitude of an external microwave signal. All qubits have individual control and readout lines. Their frequency tunability allows to change the number N of resonantly coupled qubits and also to introduce a disorder in their excitation frequencies with preassigned distributions. While increasing N, we demonstrate the expected $N^{1/2}$ scaling law for the energy gap (Rabi splitting) between bright modes around the cavity frequency. By introducing a controllable disorder and averaging the transmission amplitude over a large number of realizations, we demonstrate a decay of mesoscopic fluctuations which mimics an approach towards the thermodynamic limit. The collective bright states survive in the presence of disorder when the strength of individual qubit coupling to the cavity dominates over the disorder strength.