Phonon-induced decoherence and dissipation in donor-based charge qubits

We investigate the phonon-induced decoherence and dissipation in a donor-based charge quantum bit realized by the orbital states of an electron shared by two dopant ions which are implanted in a silicon host crystal. The dopant ions are taken from the group-V elements Bi, As, P, Sb. The excess electron is coupled to deformation potential acoustic phonons which dominate in the Si host. The particular geometry tailors a non-monotonous frequency distribution of the phonon modes. We determine the exact qubit dynamics under the influence of the phonons by employing the numerically exact quasi-adiabatic propagator path integral scheme thereby taking into account all bath-induced correlations. In particular, we have improved the scheme by completely eliminating the Trotter discretization error by a Hirsch-Fye extrapolation. By comparing the exact results to those of a Born-Markov approximation we find that the latter yields appropriate estimates for the decoherence and relaxation rates. However, noticeable quantitative corrections due to non-Markovian contributions appear.Comment: 8 pages, 8 figures, published online in Eur.Phys.J.B, article in press; the original publication is avaiable at www.eurphysj.or

Decoherence and dissipation during a quantum XOR gate operation

The dynamics of a quantum XOR gate operation in a two-qubit system being coupled to a bath of quantum harmonic oscillators is investigated. Upon applying the numerical quasiadiabatic propagator path integral method, we obtain the numerically precise time-resolved evolution of this interacting two-qubit system in presence of time-dependent external fields without further approximations. We simulate the dissipative gate operation for characteristic experimental realizations of condensed matter qubits; namely, the flux and charge qubits realized in superconducting Josephson systems and qubits formed with semiconductor quantum dots. Moreover, we study systematically the quality of the XOR gate by determining the four characteristic gate quantifiers: fidelity, purity, the quantum degree, and the entanglement capability of the gate. Two different types of errors in the qubits have been modelled, i.e., bit-flip errors and phase errors. The dependence of the quality of the gate operation on the environmental temperature, on the friction strength stemming from the system-bath interaction, and on the strength of the interqubit coupling is systematically explored: Our main finding is that the four gate quantifiers depend only weakly on temperature, but are rather sensitive to the friction strength.Comment: 16 pages including 1 table and 5 figure

Dynamical bistability in the driven circuit QED

We show that the nonlinear response of a driven circuit quantum electrodynamics setup displays antiresonant multiphoton transitions, as recently observed in a transmon qubit device. By including photon leaking, we explain the lineshape by a perturbative and a semiclassical analysis. We derive a bistable semiclassical quasienergy surface whose lowest quasienergy eigenstate is squeezed, allowing for a squeezing-dependent local effective temperature. We study the escape dynamics out of the metastable state and find signatures of dynamical tunneling, similar as for the quantum Duffing oscillator.Comment: submitted to PR

BCS theory of driven superconductivity

We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature $T_c$, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of $T_c$. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify $T_c$. Our results hold universally for the large class of normal BCS superconductors