Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system

Abstract

Near-resonant periodic driving of quantum systems promises the implementation of a large variety of novel quantum states, though their preparation and measurement remains challenging. We address these aspects in a model system consisting of interacting fermions in a periodically driven array of double wells created by an optical lattice. The singlet and triplet fractions and the double occupancy of the Floquet states are measured, and their behavior as a function of the interaction strength is analyzed in the high-and low-frequency regimes. We demonstrate full control of the Floquet state population and find suitable ramping protocols and time-scales which adiabatically connect the initial ground state to different targeted Floquet states. The micromotion which exactly describes the time evolution of the system within one driving cycle is observed. Additionally, we provide an analytic description of the model and compare it to numerical simulations.Floquet engineering aims to create novel quantum states through periodic driving, by realising effective Hamiltonians beyond the reach of static systems [1][2][3]. These effective Hamiltonians have been implemented with photons [4,5], solids [6] and ultracold gases in optical lattices [3]. However, preparing and controlling a specific quantum state in a driven system remains in general a challenge. This is particularly the case for many interesting schemes which were realised by driving at low frequencies [4,7] or even close to a characteristic energy scale of the underlying static Hamiltonian. Indeed, driving near-resonantly to the band structure was used to modify kinetic terms in the Hamiltonian [8][9][10][11][12][13][14][15], and modulating close to the interaction energy was proposed to engineer novel interaction terms [16][17][18][19][20]. For all these schemes, the periodic drive strongly couples the static eigenstates, which makes the full control of the population of the different Floquet states and the analysis of their exact time evolution demanding.One important aspect lies in the fundamental differences between Floquet-engineered systems and static Hamiltonians. For example, a periodically driven system is described by a periodic quasi-energy spectrum, and thus has no ground state. Its absence raises an important experimental challenge: How to adiabatically connect the ground state of the initial static Hamiltonian to the targeted Floquet eigenstate? Theory suggests that the population of Floquet states has a non-trivial dependence on the ramp speed and on the exact trajectory which is used in parameter-space [21][22][23][24][25][26], particularly in the case of near-resonant driving which leads to the formation of avoided crossings between quasi-energy levels [27]. In addition to this aspect, we now have to measure observables that are affected by micromotion describing the dynamics of the Floquet system within a driving period. Whilst this micromotion tends to become negligible for infinite driving frequencies, it alters the states significantly for nea...

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Realization of density-dependent Peierls phases to engineer quantized gauge fields coupled to ultracold matter

“…The atoms interact via a repulsive on-site interaction energy U , which can be tuned in a range between 5 and 10 kHz using a magnetic Feshbach resonance. The drive consists of a sinusoidal modulation of the lattice position in time, which in a comoving frame correponds to a modulation of the energy offset ∆ tot (τ ) = ∆ 0 + ∆(τ ) within the dimers [27]. We simultaneously apply two frequencies ω/(2π) and 2ω/(2π) to break TRS.…”

Floquet perturbation theory: formalism and application to low-frequency limit

“…In 5. We note that while agreement is good in the first half of the cycle, it becomes less reliable in the second half.…”

“…In quantum systems, a well-known consequence of periodic driving is the Rabi oscillation in a twolevel system [2]. More recently, the repertoire of such phenomena has been expanded to many-body quantum systems [3][4][5], including the appearance of non-equilibrium topological phases [6][7][8][9][10][11][12][13][14][15][16][17][18][19] and, in the presence of interactions and/or disorder, many-body localized phases [20][21][22] that exhibit subharmonic oscillations, thus realizing a time crystal [23][24][25][26]. Also, recent experimental advances have allowed the realization of driven optical lattices [27][28][29][30][31].…”