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Nonlinear transmons

PhD - Leuven | About a week ago

A multilevel quantum system where each of the energy levels can be addressed unambiguously via a single microwave pulse

A transmon qubit can be thought of as a non-linear capacitor-inductor system where the inducting element is replaced by a pair of Josephson junctions. These provide the sufficient nonlinearities to result in a system with discreet energy levels, where each pair of consecutive levels are split out by a different energy. This makes possible to address the two lowest levels independently from the others and use the transmon as a two-level quantum mechanical system, i.e., a qubit.

Transmon qubits are typically capacitively coupled to resonators (transmission lines) and the qubit-resonator coupling is well described by the Jaynes-Cummings (or Tavis-Cummings) Hamiltonian. But this model has some limitations. One of them is that higher levels of the transmon qubit can only be excited sequentially after exciting the lowest ones. Of course this is usually regarded as an advantage, since for quantum computation purposes it is convenient to limit the Hilbert space to two states only and disregard higher states and their coupling to the resonator. But an extended coupling where we can selectively excite any transmon level can offer new possibilities for quantum information transmission and processing.

This extended behavior can be accomplished by replacing the conventional capacitor, which has an energy quadratic in the potential with a “nonlinear capacitor”. This is an element composed of two parallel plates—very much like a capacitor—with carbon nanotubes between the plates. This results into an energy containing an additional quartic term in the potential that depends on the details of the nanostructure [1,2]. The fabrication of such device has been shown to be feasible [3], but a theoretical description of such a system as well as an analysis of its possible applications is still missing. Furthermore the exploration for other materials or structures that can lead to such non-linear behavior will also be part of this PhD. 

[1] S. Ilani, L. Donev, M. Kindermann, et al. Nature Phys 2, 687–691 (2006).

[2] D. Akinwande, Y. Nishi and H. -. P. Wong, IEEE Transactions on Nanotechnology, 8, 31-36, (2009).

[3] M. Mergenthaler, A Nersisyan, A Patterson, et al. arXiv preprint arXiv:1904.10132.

Required background: Physics, Electrical engineering, Engineering physics

Type of work: 80% Modeling/simulation 20% literature

Supervisor: Christian Maes

Co-supervisor: Bart Soree

Daily advisor: Bart Soree

The reference code for this position is 2021-057. Mention this reference code on your application form.

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