Superadiabatic driving of a three-level quantum system

We study superadiabatic quantum control of a three-level quantum system whose energy spectrum exhibits multiple avoided crossings. In particular, we investigate the possibility of treating the full control task in terms of independent two-level Landau-Zener problems. We first show that the time profiles of the elements of the full control Hamiltonian are characterized by peaks centered around the crossing times. These peaks decay algebraically for large times. In principle, such a power-law scaling invalidates the hypothesis of perfect separability. Nonetheless, we address the problem from a pragmatic point of view by studying the fidelity obtained through separate control as a function of the intercrossing separation. This procedure may be a good approach to achieve approximate adiabatic driving of a specific instantaneous eigenstate in realistic implementations.Comment: 11 pages, 7 figure

Counterintuitive transitions between crossing energy levels

We calculate analytically the probabilities for intuitive and counterintuitive transitions in a three-state system, in which two parallel energies are crossed by a third, tilted energy. The state with the tilted energy is coupled to the other two states in a chainwise linkage pattern with constant couplings of finite duration. The probability for a counterintuitive transition is found to increase with the square of the coupling and decrease with the squares of the interaction duration, the energy splitting between the parallel energies, and the tilt (chirp) rate. Physical examples of this model can be found in coherent atomic excitation and optical shielding in cold atomic collisions

Amplitude Spectroscopy of a Solid-State Artificial Atom

The energy-level structure of a quantum system plays a fundamental role in determining its behavior and manifests itself in a discrete absorption and emission spectrum. Conventionally, spectra are probed via frequency spectroscopy whereby the frequency \nu of a harmonic driving field is varied to fulfill the conditions \Delta E = h \nu, where the driving field is resonant with the level separation \Delta E (h is Planck's constant). Although this technique has been successfully employed in a variety of physical systems, including natural and artificial atoms and molecules, its application is not universally straightforward, and becomes extremely challenging for frequencies in the range of 10's and 100's of gigahertz. Here we demonstrate an alternative approach, whereby a harmonic driving field sweeps the atom through its energy-level avoided crossings at a fixed frequency, surmounting many of the limitations of the conventional approach. Spectroscopic information is obtained from the amplitude dependence of the system response. The resulting ``spectroscopy diamonds'' contain interference patterns and population inversion that serve as a fingerprint of the atom's spectrum. By analyzing these features, we determine the energy spectrum of a manifold of states with energies from 0.01 to 120 GHz \times h in a superconducting artificial atom, using a driving frequency near 0.1 GHz. This approach provides a means to manipulate and characterize systems over a broad bandwidth, using only a single driving frequency that may be orders of magnitude smaller than the energy scales being probed.Comment: 12 pages, 13 figure