Low-frequency measurement of the tunneling amplitude in a flux qubit

Abstract

We have observed signatures of resonant tunneling in an Al three-junction qubit, inductively coupled to a Nb LC tank circuit. The resonant properties of the tank oscillator are sensitive to the effective susceptibility (or inductance) of the qubit, which changes drastically as its flux states pass through degeneracy. The tunneling amplitude is estimated from the data. We find good agreement with the theoretical predictions in the regime of their validity.PACS numbers: 85.25. Cp, 85.25.Dq, 84.37.+q, 03.67.Lx Several groups, using different devices, have by now established that superconductors can behave as macroscopic quantum objects.1-3 These are natural candidates for a qubit, the building block of a quantum computer. Qubits are effectively two-level systems with timedependent parameters. One of them is a superconducting loop with low inductance L, including three Josephson junctions (a 3JJ qubit).4 Its potential energy, U = For suitable parameters, U (φ 1 , φ 2 ) has two minima corresponding to qubit states Ψ l and Ψ r , carrying opposite supercurrents around the loop. These become degenerate for Φ x = 1 2 Φ 0 . The Coulomb energy E C (≡ e 2 /2C, with C the capacitance of junction 1) introduces quantum uncertainty in the φ j . Hence, near degeneracy the system can tunnel between the two potential minima.(Since E C ≪ E J ≡ E J1 , we deal with a flux qubit; E C ≫ E J yields a charge qubit. Coherent tunneling was demonstrated in both.)In the basis {Ψ l , Ψ r } and near Φ x = 1 2 Φ 0 , the qubit can be described by the Hamiltonian∆ is the tunneling amplitude. At bias ǫ = 0 the two lowest energy levels of the qubit anticross [ Fig. 1(a)], with a gap of 2∆. Increasing ǫ slowly enough, the qubit can adiabatically transform from Ψ l to Ψ r , staying in the ground state E − . Since dE − /dΦ x is the persistent loop current, the curvature d

Multiphoton transitions in Josephson-junction qubits (Review Article)

“…(51) allows to describe both the suppression and widening of the zero-bias dip (that is at f dc = 0) as it was experimentally demonstrated in Ref. [134]. Indeed, the suppression of the zero-bias dip (at f dc = 0) is described by the first term in Eq.…”

Измерение Параметров Сверхпроводникового Потокового Кубита В Квазидисперсионном Режиме

“…Первые два параметра можно определить либо в дисперсионном режиме, когда резонансная частота сверхпроводникового резонатора [6][7][8], либо методом двухчастотной спектроскопии, когда в допол-нение к пробному сигналу кубит возбуждается высокой частотой, близкой к расстоянию между энергетическими уровнями кубита [5]. Что касается двух других парамет-ров, то g обычно рассчитывается численно, исходя из дизайна структуры кубит−резонатор, а γ определяется как подгоночный параметр для характерного провала в зависимости коэффициента прохождения от смещения кубита на фиксированной частоте [5].…”

Engineering Dissipative Channels for Realizing Schrödinger Cats in SQUIDs

“…We note that there already exist schemes for realizing non-classical states via engineered dissipative channels (Amico et al, 2008;Diehl et al, 2008;Kraus et al, 2008;Schirmer and Wang, 2010;Ticozzi et al, 2010;Zhang et al, 2010;Busch et al, 2011;Pechen, 2011;Scully et al, 2011;Chen et al, 2012;Ticozzi and Viola, 2012;Yamamoto, 2012;Ikeda and Yamamoto, 2013) as well as a number of experimental realizations (Barreiro et al, 2011;Krauter et al, 2011;Leghtas et al, 2013). We also note that SQUIDs are an ideal candidate system for realizing this protocol as they have already been shown able to support appropriate quantum states (Nakamura et al, 1999;Friedman et al, 2000;Grajcar et al, 2004;Il'Ichev et al, 2004) and, as we shall later show, existing circuit designs can be used to engineer an environment with the suitable characteristics (Deng et al, 2010;Kumar and DiVincenzo, 2010).…”