Analytical Methods for the Calculation of Quasienergy States of Quantum Systems

P. V. Elyutin, Timur V. Filippov

Matti Silveri, Jani Tuorila, Mika Kemppainen +1 more

The present qubit technology, in particular, in Josephson qubits, allows an unprecedented control of discrete energy levels. This motivates a new study of the old pump-probe problem, where a discrete quantum system is driven by a strong drive and simultaneously probed by a weaker one. The strong drive is included by the Floquet method and the resulting quasienergy states are then studied with the probe. We study a qubit where the harmonic drive has a significant longitudinal component relative to the static equilibrium state of the qubit. Both analytical and numerical methods are used to solve the problem. We present calculations with realistic parameters and compare the results with recent experimental results. A short introduction to the Floquet method and the probe absorption is given.

Yuri A. Rylov

V. O. Chaltykyan, G. G. Grigoryan, A. A. Hovhannisyan +1 more

We consider a medium of multilevel atomic systems interacting with radiation pulses. A relatively simple technique of analytic calculations is proposed, which allows revealing all necessary conditions (with sufficient conditions to be checked separately) imposed on the interaction parameters, for which the mean dipole moment of a multilevel atomic medium vanishes, i.e., the medium becomes transparent via adiabatic interaction. The proposed technique is based on the method of quasienergies and illustrated for three- and five-level atomic systems.

Cristian M. Le, Ryosuke Akashi, Shinji Tsuneyuki

We reformulate the Floquet theory for periodically driven quantum systems following a perfect analogy with the proof of the Bloch theorem. We observe that the current standard method for calculating the Floquet eigenstates using the quasienergy alone is incomplete and unstable and pinpoint an overlooked quantum number, the average energy. This new quantum number resolves many shortcomings of the Floquet method stemming from the quasienergy degeneracy issues, particularly in the continuum limit. Using the average-energy quantum number, we get properties similar to those of the static energy, including a unique lower-bounded ordering of the Floquet states, from which we define a ground state, and a variational method for calculating the Floquet states. This is a first step towards reformulating Floquet first-principles methods, which have long been thought to be incompatible due to the limitations of the quasienergy.

P. V. Elyutin, Timur V. Filippov