Floquet space exploration for the dual-dressing of a qubit

Abstract

The application of a periodic nonresonant drive to a system allows the Floquet engineering of effective fields described by a broad class of quantum simulated Hamiltonians. The Floquet evolution is based on two different elements. The first one is a time-independent or stroboscopic evolution with an effective Hamiltonian corresponding to the quantum simulation target. The second element is the time evolution at the frequencies of the nonresonant driving and of its harmonics, denoted as micromotion. We examine experimentally and theoretically the harmonic dual-dressing Floquet engineering of a cold atomic two-level sample. Our focus is the dressing operation with small bare energies and large Rabi frequencies, where frequencies and amplitudes of the stroboscopic/micromotion time evolutions are comparable. At the kHz range of our dressed atom oscillations, we probe directly both the stroboscopic and micromotion components of the qubit global time evolution. We develop ad-hoc monitoring tools of the Floquet space evolution. The direct record of the time evolution following a pulsed excitation demonstrates the interplay between the two components of the spin precession in the Floquet space. From the resonant pumping of the dressed system at its evolution frequencies, Floquet eigenenergy spectra up to the fifth order harmonic of the dressing frequency are precisely measured as function of dressing parameters. Dirac points of the Floquet eigenenergies are identified and, correspondingly, a jump in the dynamical phase shift is measured. The stroboscopic Hamiltonian eigenfrequencies are measured also from the probe of the micromotion sidebands.These monitoring tools are appropriate for quantum simulation/computation investigations. Our results evidence that the stroboscopic phase shift of the qubit wavefunction contains an additional information that opens new simulation directions.

Atoms Dressed by Virtual and Real Photons

“…The spin time evolution contains additional components produced by the kick operator centered around the multiple of the ω dressing frequency measured in the dual-dressing investigation in Refs. [37,38,40].…”

“…Lately, monitoring the spin transverse magnetization ⟨σ i (t)⟩, i = x, y, for instance, by Faraday detection, has provided a more effective detection tool, mainly with ultracold atoms [40,[43][44][45][46]. In this configuration, the spin system is initially prepared in a superposition of the bare atom eigenstates; for instance, the ⟨σ x (t = 0)⟩ = 1 mean value and the ⟨σ y (t)⟩ mean value of the dressed atom eigenstates, oscillating mainly at Ω L , is monitored.…”

“…In that context the pump action is very often described by dressed atom that we present below in Section 3.4. Here, we expand to two commensurate dressing fields [40,46,69] the strong dressing regime, which is characterized by Ω x ω as described in Section 3.2. We investigate the following Hamiltonian written in the τ adimensional time:…”