Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

Bukov, Marin; Polkovnikov, Anatoli

doi:10.1103/physreva.90.043613

Cited by 40 publications

(61 citation statements)

References 46 publications

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“…[4][5][6][7][8] These systems can be prepared in such a way that they are very well isolated from the environment. There is also, however, great interest in using periodic driving to design transport and band-structure properties of solid state systems, such as semiconductors and semiconductor heterostructures, 9,10 graphene, [11][12][13][14][15] and topological insulator surface states.…”

Section: Introductionmentioning

confidence: 99%

Floquet systems coupled to particle reservoirs

Iadecola

Chamon

2015

Phys. Rev. B

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Open quantum systems, when driven by a periodic field, can relax to effective statistical ensembles that resemble their equilibrium counterparts. We consider a class of problems in which a periodicallydriven quantum system is allowed to exchange both energy and particles with a thermal reservoir. We demonstrate that, even for noninteracting systems, effective equilibration to the grand canonical ensemble requires both fine tuning the system-bath coupling and selecting a sufficiently simple driving protocol. We study a tractable subclass of these problems in which the long-time steady state of the system can be determined analytically, and demonstrate that the system effectively thermalizes with fine tuning, but does not thermalize for general values of the system-bath couplings. When the driven system does not thermalize, it supports a tunable persistent current in the steady state without external bias. We compute this current analytically for two examples of interest: 1) a driven double quantum dot, where the current is interpreted as a DC electrical current, and 2) driven Dirac fermions in graphene, where it is interpreted as a valley current.

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Section: Introductionmentioning

confidence: 99%

Floquet systems coupled to particle reservoirs

Iadecola

Chamon

2015

Phys. Rev. B

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“…These issues are complicated, since all schemes for realizing the HH Hamiltonian use some form of temporal lattice modulation and therefore are described by a time-dependent Floquet formalism. The HH model arises after time averaging the Floquet Hamiltonian, but it is an open question to what extent finite interactions and micromotion lead to transitions between Floquet modes and therefore heating [21][22][23][24]. Bose-Einstein condensation has been achieved in staggered flux configurations [15,25] and in small ladder systems [26,27] further highlighting its noted absence in the uniform field configuration.…”

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confidence: 99%

Observation of Bose–Einstein condensation in a strong synthetic magnetic field

et al. 2015

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Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new states of matter with topological properties. Traditionally, this has been achieved using gauge fields created by magnetic fields or spin orbit interactions which couple only to charged particles. For neutral ultracold atoms, synthetic magnetic fields have been created which are strong enough to realize the Harper-Hofstadter model. Despite many proposals and major experimental efforts, so far it has not been possible to prepare the ground state of this system. Here we report the observation of BoseEinstein condensation for the Harper-Hofstadter Hamiltonian with one-half flux quantum per lattice unit cell. The diffraction pattern of the superfluid state directly shows the momentum distribution on the wavefuction, which is gauge-dependent. It reveals both the reduced symmetry of the vector potential and the twofold degeneracy of the ground state. We explore an adiabatic many-body state preparation protocol via the Mott insulating phase and observe the superfluid ground state in a three-dimensional lattice with strong interactions.Topological states of matter are an active new frontier in physics. Topological properties at the single particle level are well understood; however, there are many open questions when strong interactions and correlations are introduced [1, 2] as in the ν = 5/2 state of the fractional quantum Hall effect [3] and in Majorana fermions [4][5][6]. For neutral ultracold atoms, new methods have been developed to create synthetic gauge fields. Forces analogous to the Lorentz force on electons are engineered either through the Coriolis force in rotating systems [7][8][9], by phase imprinting via photon recoil [10][11][12][13][14], or lattice shaking [15,16]. Much of the research with ultracold atoms has focused on the paradigmatic HarperHofstadter (HH) Hamiltonian, which describes particles in a crystal lattice subject to a strong homogeneous magnetic field [17][18][19]. For magnetic fluxes on the order of one flux quantum per lattice unit cell, the radius of the smallest possible cyclotron orbit and the lattice constant are comparable, and their competition gives rise to the celebrated fractal spectrum of Hofstadfer's butterfly whose sub-bands have non-zero Chern numbers [20] and Dirac points.So far, it has not been possible to observe the ground state of the HH Hamiltonian, which for bosonic atoms is a superfluid Bose-Einstein condensate. It is unknown whether this is due to heating associated with technical noise, non-adiabatic state preparation, or inelastic collisions. These issues are complicated, since all schemes for realizing the HH Hamiltonian use some form of temporal lattice modulation and therefore are described by a time-dependent Floquet formalism. The HH model arises after time averaging the Floquet Hamiltonian, but it is an open question to what extent finite interactions and micromotion lead to transitions between Floquet modes and therefore heating [21][22][23][24]. Bose-Einstein condensat...

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“…Recently, the importance of the kick operators in the stroboscopic and non-stroboscopic dynamics of Floquet systems has been highlighted by several authors [34][35][36][37]. For the rotated Hamiltonian in Eq.…”

Section: Modelmentioning

confidence: 99%

“…It is well known that in the limit of very large frequency or small period one can calculate the Floquet Hamiltonian and the kick operator perturbatively using a high frequency expansion. In this paper, we use a particular van Vleck expansion, which is invariant under the choice of the driving phase in the rotating frame [34,36,38]:…”

Section: Modelmentioning

confidence: 99%

“…Using the Floquet formalism [34][35][36][37][38], we also derive an effective time-independent Hamiltonian for the system in the presence of a high-frequency driving force, and compare the results coming from this effective theory by solving the model numerically using the time dependent Density Matrix Renormalization Group method (tDMRG) [39,40].…”

Section: Introductionmentioning

confidence: 99%

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Unconventional fermionic pairing states in a monochromatically tilted optical lattice

2017

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We study the one-dimensional attractive Fermionic Hubbard model under the influence of periodic driving with the time-dependent density matrix renormalization group method. We show that the system can be driven into an unconventional pairing state characterized by a condensate made of Cooper-pairs with a finite center-of-mass momentum similar to a Fulde-Ferrell state. We obtain results both in the laboratory and the rotating reference frames demonstrating that the momentum of the condensate can be finely tuned by changing the ratio between the amplitude and the frequency of the driving. In particular, by quenching this ratio to the value corresponding to suppression of the tunnelling and the Coulomb interaction strength to zero, we are able to "freeze" the condensate. We finally study the effects of different initial conditions, and compare our numerical results to those obtained from a time-independent Floquet theory in the large frequency regime. Our work offers the possibility of engineering and controlling unconventional pairing states in fermionic condensates.

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Stroboscopic versus nonstroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian

Cited by 40 publications

References 46 publications

Floquet systems coupled to particle reservoirs

Floquet systems coupled to particle reservoirs

Observation of Bose–Einstein condensation in a strong synthetic magnetic field

Unconventional fermionic pairing states in a monochromatically tilted optical lattice

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