Quasienergies and Floquet states of two weakly coupled Bose-Einstein condensates under periodic driving

Abstract

We investigate the quasi-energies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasi-energies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasi-energy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second quantized model, we find also a triangular structure in the quantum quasi-energy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasi-energies is further explored by a semi-classical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasi-energies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.

Solvable model of a generic driven mixture of trapped Bose-Einstein condensates and properties of a many-boson Floquet state at the limit of an infinite number of particles

“…which are the relations between the individual species' center-of-mass coordinates and the respective Jacobi coordinates [118]. We see that, in the laboratory frame, both contributing poles (31) are intermixed and the time-dependent translation of each species is more intricate.…”

Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

“…A particularly exciting arena for quantum dynamics across many disciplines is that in which the system’s Hamiltonian is periodic in time [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 ]. The time-periodic Hamiltonian defines the Floquet Hamiltonian and governs the Floquet eigenvalue equation in an extended Hilbert space [ 11 , 12 ], in analogy to the static Hamiltonian, which governs the Schrödinger eigenvalue equation in the standard Hilbert space of a time-independent system.…”

Floquet eigenspectra of a nonlinear two-mode system under periodic driving: the emergence of "ring" structures

“…A first step towards the understanding of a driven interacting bosonic system is the study of level transitions in the presence of a self-consistent mean-field interaction. On the one hand, there have been numerous theoretical studies on nonlinear Landau-Zener [16,17] or interacting two-mode Bose systems with periodic modulations either in the level spacing [21][22][23][24][25][26][27][28][29][30][31][32] or an off-diagonal coupling [33][34][35][36][37], or both of them [38][39][40]. Phenomena such as the coherent destruction of tunneling (originally studied in [41][42][43] for different setups) realizing a dynamical localization [29,31,40,44], macroscopic self-trapping [2,21,22,26,27,32,38], assisted higher-order co-tunneling [36,40], as well as the emergence of Hamiltonian chaos [23,28,33,35,37] have been uncovered.…”

“…We numerically solve the nonlinear Schrödinger equation (as realized by GPE for a two-mode BEC) focusing on a few regimes (from high-to low-frequency driving) where complex eigenspectrum structures can emerge. While the Floquet analysis has been applied to the nonlinear two-mode system by many authors so far [21,22,27,30,32,33,37,49], there are only a few works which studies the Floquet quasienergy spectrum in depth. Even in the latter, they only focus on high frequency regime [30], or employ an effective Hamiltonian description, which is valid only for high-frequency driving, without a Floquet analysis [34,35].…”

“…While the Floquet analysis has been applied to the nonlinear two-mode system by many authors so far [21,22,27,30,32,33,37,49], there are only a few works which studies the Floquet quasienergy spectrum in depth. Even in the latter, they only focus on high frequency regime [30], or employ an effective Hamiltonian description, which is valid only for high-frequency driving, without a Floquet analysis [34,35]. Here, our work is no longer restricted to a particular frequency range, provided that the solution assumes a Floquet form.…”