Realizing and Detecting the Quantum Hall Effect without Landau Levels by Using Ultracold Atoms

Shao, L. B.; Zhu, Shi-Liang; Sheng, L.; Xing, D. Y.; Wang, Z. D.

doi:10.1103/physrevlett.101.246810

Cited by 135 publications

(130 citation statements)

References 36 publications

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“…3. With noninteracting fermions in this setup, it will exhibit quantum anomalous Hall effect with quantized Hall conductance, which can be measured by various methods [15,20].…”

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confidence: 99%

Floquet topological states in shaking optical lattices

2014

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In this letter we propose realistic schemes to realize topologically nontrivial Floquet states by shaking optical lattices, using both one-dimension lattice and two-dimensional honeycomb lattice as examples. The topological phase in the two-dimensional model exhibits quantum anomalous Hall effect. The transition between topological trivial and nontrivial states can be easily controlled by shaking frequency and amplitude. Our schemes have two major advantages. First, both the static Hamiltonian and the shaking scheme are sufficiently simple to implement. Secondly, it requires relatively small shaking amplitude and therefore heating can be minimized. These two advantages make our scheme much more practical.Topological state of matters such as quantum Hall effect and topological insulator have been extensively studied in equilibrium systems. Recently, topological classification of quantum states in a periodically driven nonequilibrium system has been proposed [1,2], in which the topologically nontrivial states are named as "Floquet topological insulator" [1]. Floquet topological band has been first realized in photonic crystal and the edge state of light has been observed [3]. While so far it has not been realized in any solid-state or cold-atom system.Realizing and studying topological state of matter is also one of the major treads for cold atom physics nowadays, for which Raman laser coupling [4][5][6][7] and shaking optical lattice [8][9][10] have been developed as two major schemes. In several recent experiments, it has been demonstrated that fast shaking optical lattices can generate synthetic abelian gauge field and magnetic flux [8,9]. In this letter we propose that shaking optical lattice is also a powerful tool to realize Floquet topological state in cold atom systems.We first demonstrate that in one-dimension lattice it realizes a system equivalent to Su-Schrieffer-Heeger model [11] with nonzero Zak phase; Then, we show that in two-dimension honeycomb lattice [12] it realizes a system equivalent to the Haldane model which exhibits quantum anomalous Hall effect [13]. So far, quantum anomalous Hall effect has only been found in chromium-doped (Bi,Sb) 2 Te 3 , and growing this material is extremely challenging [14]. It is therefore highly desirable that one can quantum simulate this effect with cold atom system. However, despite of several proposals [15] this effect has not yet been successfully simulated in cold atom setup. Our scheme has two major advantages for which it becomes much practical.The first is its simplicity. To realize a topological state in a static system, it usually requires particular form of hopping term. For instance, in order to realize the Haldane model [13], one needs to generate a special nextnearest range hopping term, which usually requires engineering laser-assisted tunneling in cold atom system [4][5][6][7]. In contrast, in our scheme, the static Hamiltonian is quite simple (it only contains normal nearest neighboring hopping without extra phase factor) and has been realized in...

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“…3. With noninteracting fermions in this setup, it will exhibit quantum anomalous Hall effect with quantized Hall conductance, which can be measured by various methods [15,20].…”

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confidence: 99%

Floquet topological states in shaking optical lattices

2014

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“…8(a). The spacial periodic magnetic field in the Haldane model can be simulated by use of the laser-inducedgauge-field method in an optical lattice 27 . With a similar method, we can design two other kinds of effective magnetic field.…”

Section: Discussion and Summarymentioning

confidence: 99%

“…In the new basis space |χ ={|χ 1 , |χ 2 , |χ 3 }, the primary atom HamiltonianĤ= 2 +V with M the atom mass and A and V the matrix with matrix elements A n,m =i χ n (r) |∇χ m (r) and V n,m =λ n (r) δ n,m + χ n (r)|V (r) |χ m (r) , respectively. One can see that in the new basis the atom can be considered as moving in gauge potential A, which corresponds to an effective magnetic field 27,28 . We focus on the subspace spanned by the two lower eigenstates {|χ 1 , |χ 2 }, which is redefined by |χ ↑ ≡ |χ 1 and |χ ↓ ≡ |χ 2 in the spin language.…”

Section: Discussion and Summarymentioning

confidence: 99%

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Quantum Hall effects in a non-Abelian honeycomb lattice

Hao

Liu

et al. 2015

Phys. Rev. A

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We study the tunable quantum Hall effects in a non-Abelian honeycomb optical lattice which is a multi-Dirac-point system. We find that the quantum Hall effects present different features with the change in relative strengths of several perturbations. Namely, the quantum spin Hall effect can be induced by gauge-field-dressed next-nearest-neighbor hopping, which together with a Zeeman field can induce the quantum anomalous Hall effect characterized by different Chern numbers. Furthermore, we find that the edge states of the multi-Dirac-point system represent very different features for different boundary geometries, in contrast with the generic two-Dirac-point system. Our study extends the borders of the field of quantum Hall effects in a honeycomb optical lattice with multivalley degrees of freedom.

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“…The ultra-cold atom gas associated with optical lattice technology provide an ideal platform to realize and investigate the topological phases [12][13][14][15][16] due to the controllability and cleanity. In particular, some chiral pwave TSFs [13,15] have been proposed based on the laserinduced artificial gauge fields [17,18] in cold atom systems.…”

Section: Introductionmentioning

confidence: 99%

Chiralf-wave topological superfluid in triangular optical lattices

Hao

Liu

et al. 2013

Phys. Rev. A

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We demonstrate that an exotically chiral f -wave topological superfluid can be induced in coldfermionic-atom triangular optical lattices through the laser-field-generated effective non-Abelian gauge field, controllable Zeeman fields and s-wave Feshbach resonance. We find that the chiral f -wave topological superfluid is characterized by three gapless Majorana edge states located on the boundary of the system. More interestingly, these Majorana edge states degenerate into one Majorana fermion bound to each vortex in the superfluid. Our proposal enlarges topological superfluid family and specifies a unique experimentally controllable system to study the Majorana fermion physics.

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Realizing and Detecting the Quantum Hall Effect without Landau Levels by Using Ultracold Atoms

Cited by 135 publications

References 36 publications

Floquet topological states in shaking optical lattices

Floquet topological states in shaking optical lattices

Quantum Hall effects in a non-Abelian honeycomb lattice

Chiralf-wave topological superfluid in triangular optical lattices

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