Geometric nature of the environment-induced Berry phase and geometric dephasing

We investigate the geometric phase or Berry phase acquired by a spin half which is both subject to a slowly varying magnetic field and weakly coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original Berry phase (for an isolated system) is the flux of a monopole field through the loop traversed by the magnetic field, the environment-induced modification of the phase is the flux of a quadrupolelike field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the Berry phase, this geometric dephasing is gauge invariant for open paths of the magnetic field.     

Nondemolition measurements of a single quantum spin using Josephson oscillations

We consider a single localized spin-1/2 between the singlet superconducting leads of a Josephson junction (e.g., a superconducting STM). For the spin subject to a dc magnetic field B parallel z, we study the spin dynamics and the possibility to measure the spin state via transport through the junction embedded in a dissipative circuit. Turning on the tunneling or a voltage bias induces oscillations of the Josephson current, with an amplitude sensitive to the initial value of the z component of the spin, S(z)=+/-1/2. At low temperatures, when effects of quasiparticles are negligible, this procedure realizes a quantum nondemolition measurement of S(z).     

Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system

A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the "atomic" levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.     

Geometric phase via adiabatic manipulations of the environment

It has been shown that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system, this phase is expressed in terms of the geometry of the path, traversed by the slowly varying direction and amplitude of the fluctuations. The origin of this phase and the possibilities of separating it from the known environment-induced modification of the Berry phase are discussed. The text was submitted by the authors in English.     

Entanglement Spectrum in Superfluid Phases of <Superscript>3</Superscript>He

Processes of single and pair production of heavy quarkonia under LHC conditions have been studied within nonrelativistic quantum chromodynamics. Constraints on the matrix elements of color-singlet and color-octet states have been obtained by analyzing the existing experimental data. It has been shown that the leading contribution to the cross sections for these processes comes from the color singlet mechanism with the singlet matrix elements exceeding phenomenological values obtained from the solutions of potential models or experimental decay widths of the corresponding mesons. It has also been found that the contribution from color-octet states should be taken into account to describe the ratio of the cross sections for the production of tensor and axial charmonia. These results have been used to analyze the single production of bottomonia, the pair production of heavy quarkonia, and the production of vector charmonium in jets. The resulting theoretical predictions are in good agreement with experimental data.     

Topological Josephson Junction in Transverse Magnetic Field

JETP Letters - We consider Majorana zero modes in a Josephson junction on top of a topological insulator in transverse magnetic field. Majorana zero modes reside at periodically located nodes of...     

Dephasing of solid-state qubits at optimal points

Motivated by recent experiments with Josephson-junction circuits, we analyze the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We study the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. For 1/f noise strong higher-order effects influence the evolution.     

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.     

A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem

We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type \({{\tilde{A}}}_{n-1}\), i.e., corresponding to the affine Lie algebra \({{\widehat{\mathfrak {sl}}}}_n\). Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation. Our formula can be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion’s theorem and then apply it to our polyhedron to prove the formula.     

Two-Qubit Operation on Majorana Qubits in Ordinary-Qubit Chains

Majorana zero modes can be simulated in structures based on spin or quasi-spin degrees of freedom, e.g., Josephson-qubit chains. Braiding of Majorana degrees of freedom is realized using T-junctions supplied with an auxiliary spin (ancilla). Motivated by prospective experiments, we analyze the braiding in the spin representation, which provides the basis for the analysis of imperfections characteristic to the spin and qubit designs. The result of the braiding operation is straightforwardly found for the initial basis states of the two qubits and the ancilla, up to phase factors. Here, we fix these phase factors and thus describe the complete two-qubit operation. This result is relevant for physical simulation of the Majorana qubits in Josephson-qubit chains and other spin or qubit structures.