We demonstrate the Bloch-Siegert effect in a dispersively coupled qubit-cavity system which is driven through a quantum-to-classical transition. The observed dispersive shift of theresonance frequency displays strongly non-monotonic dependence on the number of cavity photons and escapes the scope of the analytic results obtained with either a simple rotating-wave approximation, or with a more refined counter-rotating hybridized rotating wave approach. We measured the transition energy with a weak resonant probe, and the obtained data is in a good agreement with our numerical simulations of the quasienergy spectrum.
The adiabatic manipulation of quantum states is a powerful technique that has opened up new directions in quantum engineering, enabling tests of fundamental concepts such as the Berryphase and its nonabelian generalization, the observation of topological transitions, and holds the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage process for circuit quantum electrodynamics, by using the first three levels of a transmon qubit. We demonstrate a population transfer efficiency above 80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses coupled to the first and second transition. The advantage of this techniques is robustness against errors in the timing of the control pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time-domain. We also show that this protocol can be reversed by applying a third adiabatic pulse on the first transition. Furthermore, we demonstrate a hybrid adiabatic-nonadiabatic gate using a fast pulse followed by the adiabatic Raman sequence, and we study experimentally the case of a quasi-degenerate intermediate level.
When the transition frequency of a qubit is modulated periodically across an avoided crossing along its energy dispersion curve, tunnelling to the excited state – and consequentlyLandau-Zener-St\“uckelberg interference – can occur. The types of modulation studied so far correspond to a continuous evolution of the system along the dispersion curve. Here we introduce a type of modulation called periodic latching, in which the qubit’s free phase evolution is interrupted by sudden switches in the transition frequency. In this case, the conventional Landau-Zener-St\“uckelberg theory becomes inadequate and we develop a novel adiabatic-impulse model for the evolution of the system. We derive the resonance conditions and we identify two regimes: a slow-modulation regime and a fast-modulation regime, in which case the rotating wave approximation (RWA) can be applied to obtain analytical results. The adiabatic-impulse model and the RWA results are compared with those of a full numerical simulation. These theoretical predictions are tested in an experimental setup consisting of a transmon whose flux bias is modulated with a square wave form. A rich spectrum with distinctive features in the slow-modulation and fast-modulation (RWA) regimes is observed and shown to be in very good agreement with the theoretical models. Also, differences with respect to the well known case of sinusoidal modulation are discussed, both theoretically and experimentally.
Superconducting circuits with Josephson junctions are promising candidates
for developing future quantum technologies. Of particular interest is to use
these circuits to study effectsthat typically occur in complex
condensed-matter systems. Here, we employ a superconducting quantum bit
(qubit), a transmon, to carry out an analog simulation of motional averaging, a
phenomenon initially observed in nuclear magnetic resonance (NMR) spectroscopy.
To realize this effect, the flux bias of the transmon is modulated by a
controllable pseudo-random telegraph noise, resulting in stochastic jumping of
the energy separation between two discrete values. When the jumping is faster
than a dynamical threshold set by the frequency displacement of the levels, the
two separated spectral lines merge into a single narrow-width,
motional-averaged line. With sinusoidal modulation a complex pattern of
additional sidebands is observed. We demonstrate experimentally that the
modulated system remains quantum coherent, with modified transition
frequencies, Rabi couplings, and dephasing rates. These results represent the
first steps towards more advanced quantum simulations using artificial atoms.