Floquet engineering with quasienergy bands of periodically driven optical lattices

Holthaus, Martin

doi:10.1088/0953-4075/49/1/013001

Cited by 233 publications

(237 citation statements)

References 94 publications

(254 reference statements)

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“…In order to understand these driven systems better, a new theoretical approach known as 'Floquet engineering' [1], has evolved. This approach provides an opportunity to manipulate the interactions of an atomic system with a periodic driving force while transforming the time dependent interaction Hamiltonian to a 'stroboscopic' Hamiltonian [2].…”

Section: Introductionmentioning

confidence: 99%

Resonance enhancement of two photon absorption by magnetically trapped atoms in strong rf-fields

Chakraborty¹,

Mishra²

2018

Physics Letters A

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Applying a many mode Floquet formalism for magnetically trapped atoms interacting with a polychromatic rf-field, we predict a large two photon transition probability in the atomic system of cold 87 Rb atoms. The physical origin of this enormous increase in the two photon transition probability is due to the formation of avoided crossings between eigen-energy levels originating from different Floquet sub-manifolds and redistribution of population in the resonant intermediate levels to give rise to the resonance enhancement effect. Other exquisite features of the studied atom-field composite system include the splitting of the generated avoided crossings at the strong field strength limit and a periodic variation of the single and two photon transition probabilities with the mode separation frequency of the polychromatic rf-field. This work can find applications to characterize properties of cold atom clouds in the magnetic traps using rf-spectroscopy techniques.

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Section: Introductionmentioning

confidence: 99%

Resonance enhancement of two photon absorption by magnetically trapped atoms in strong rf-fields

Chakraborty¹,

Mishra²

2018

Physics Letters A

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“…In this case, the Hamiltonian is modulated periodically in time, invalidating a direct description in terms of the powerful methods of time-independent quantum mechanics. But due to the periodicity of the Hamiltonian, it is possible to incorporate the time-dependence into the basis states leading to a description in terms of time-periodic Floquet modes and their quasi-energies [100][101][102][103]. This is in complete analogy with the better-known space-periodic case, where Bloch waves and their quasi-momenta give valuable insight into condensed matter systems [104].…”

Section: Non-equilibrium Protocolsmentioning

confidence: 99%

“…integer multiples of the driving period, the time evolution can be described in terms of a hermitian operator, the so-called Floquet Hamiltonian. This quasi-Hamiltonian depends on the specific system and driving parameters, making it possible to engineer systems with properties very different to [105][106][107] and the Haldane model [108], and there exist numerous theoretical proposals [103,[109][110][111][112][113][114][115][116][117][118][119][120][121][122][123][124] and experimental realizations of a wide range of systems .…”

Section: Non-equilibrium Protocolsmentioning

confidence: 99%

“…6.2(f). Small avoided crossings can be problematic numerically, because truncated finite-basis size calculations might not be converged sufficiently [103,399,400]. Due to the Brioullin zone structure, there will be many of these, and we discuss this issue in more detail in Sec.…”

Section: Fidelity and Quasi-energy Spectrummentioning

confidence: 99%

“…Approximating an infinite basis by a finite subset has to be done carefully in the case of Floquet theory because the Brioullin-zone structure of the quasi-energies means that there are infinitely many points in a finite interval [103,399,401]. As we saw in Sec.…”

Section: Numerical Considerationsmentioning

confidence: 99%

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Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Zill¹

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This thesis is concerned with non-equilibrium phenomena in interacting quantum manybody systems. Specifically, we investigate the time-evolution and relaxation dynamics of Bose gases in a highly restricted geometry, which constrains the dynamics to one spatial dimension. This leads to a description of the system in terms of a simple model Hamiltonian which permits exact many-body quantum mechanical solutions due to its integrability.In the first part of this thesis, a computational method is developed to obtain experimentally relevant correlation functions in the framework of the coordinate Bethe ansatz.We employ this method to compute exact ground-state correlation functions of the LiebLiniger gas for up to seven particles covering the whole regime of repulsive interactions. We also investigate the dynamics of the system after an instantaneous change of the interaction strength. This quantum quench deposits large amounts of energy that cannot be dissipated due to the system being closed, and so the dynamics far from equilibrium are probed. We prepare the system in two different initial states, and quench to the same final interaction strength. The latter is determined in such a way that the added energy due to the quench is the same for both scenarios. Conventional statistical mechanics predicts the same relaxed state, but due to the integrability of the system all considered correlation functions of the relaxed states differ from each other and also from the thermal ones.We then investigate the dynamics and relaxed state for a quench from zero to repulsive interactions in more detail, focussing on the mechanism of relaxation and the involved time-scales. We find that local correlation functions relax on time-scales determined by the interaction strength, in contrast to non-local correlation functions, whose relaxation time-scale is proportional to the system size.Next, we employ the same methodology to study the one-dimensional Bose gas with attractive interactions. In this case many-body bound states are permissible solutions of the Lieb-Liniger model. We compare exact ground-state correlation functions of up to seven particles to their corresponding mean-field solution. The latter displays a quantum phase transition at a critical interaction strength, marking the transition from a uniformdensity state to a localized bright soliton. Our exact results agree remarkably well with the corresponding mean-field solution past the critical point. We also investigate the dynamics following an interaction strength quench, starting again from the non-interacting ground state. Bound states strongly influence correlation functions for all post-quench interaction strengths, and local correlation functions are largely increased compared to their initial value.In the last part of this thesis, we investigate the behavior of the one-dimensional Bose gas under periodic driving of the interaction strength. To this end, we extend the coordinate Bethe-ansatz formalism by employing Floquet theory to obtain solutions for the...

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Quantum Emulation of Extreme Non‐Equilibrium Phenomena with Trapped Atoms

et al. 2017

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Floquet engineering with quasienergy bands of periodically driven optical lattices

Cited by 233 publications

References 94 publications

Resonance enhancement of two photon absorption by magnetically trapped atoms in strong rf-fields

Resonance enhancement of two photon absorption by magnetically trapped atoms in strong rf-fields

Nonequilibrium dynamics of a one-dimensional Bose gas via the coordinate Bethe ansatz

Quantum Emulation of Extreme Non‐Equilibrium Phenomena with Trapped Atoms

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