2020
DOI: 10.1103/physrevlett.124.050502
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Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate

Abstract: We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the momentum lattice is dictated by a periodically driven Su-Schieffer-Heeger model, which is equivalent to a discretetime topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements i… Show more

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Cited by 93 publications
(56 citation statements)
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References 77 publications
(88 reference statements)
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“…The MCD was first introduced as a dynamical probe to the winding numbers of 1D topological insulators in the symmetry classes AIII and BDI [ 98 ], and later extended to Floquet systems [ 93 , 99 , 100 ], two-dimensional systems [ 101 ], many-body systems [ 102 ], systems in other symmetry classes [ 84 ], and recently also to non-Hermitian systems [ 50 , 51 , 53 ]. In the meantime, the MCD has also been measured experimentally in photonic [ 98 , 103 ] and cold atom [ 104 , 105 ] setups. In this section, we further generalize the MCD to non-Hermitian Floquet systems in the CII symmetry class, and employ it to dynamically characterize the topological phases found in the non-Hermitian PQTLL model.…”
Section: Dynamical Probe To the Topological Phasesmentioning
confidence: 99%
See 1 more Smart Citation
“…The MCD was first introduced as a dynamical probe to the winding numbers of 1D topological insulators in the symmetry classes AIII and BDI [ 98 ], and later extended to Floquet systems [ 93 , 99 , 100 ], two-dimensional systems [ 101 ], many-body systems [ 102 ], systems in other symmetry classes [ 84 ], and recently also to non-Hermitian systems [ 50 , 51 , 53 ]. In the meantime, the MCD has also been measured experimentally in photonic [ 98 , 103 ] and cold atom [ 104 , 105 ] setups. In this section, we further generalize the MCD to non-Hermitian Floquet systems in the CII symmetry class, and employ it to dynamically characterize the topological phases found in the non-Hermitian PQTLL model.…”
Section: Dynamical Probe To the Topological Phasesmentioning
confidence: 99%
“…Furthermore, a quantized jump of the MCD is observed every time when the system passes through a topological phase transition point. Experimentally, the MCDs have been measured in both the cold atom [ 104 , 105 ] and photonic systems [ 98 , 103 ], in which non-Hermiticity and driving fields can also be implemented [ 1 ]. Furthermore, the MCDs may also be detected directly in momentum space with the help of a recently proposed setup certaining the nitrogen-vacancy-center in diamond [ 36 ].…”
Section: Dynamical Probe To the Topological Phasesmentioning
confidence: 99%
“…Now the periodically driven Hamiltonian for the system in Fig. 3(a) can be written as [60] H =v(t) where θ 2 = Ωτ 2 /2. Once we choose the duration τ 1 such that θ 1 = π/4, such a scheme forms a standard discrete-time quantum walk.…”
Section: Quantum Walk With Periodic Drivingmentioning
confidence: 99%
“…Since quantum walks are Floquet systems in which time evolves in a discrete manner, topological phases can be different from those which are described by time-independent Hamiltonians. Floquet topological phases of quantum walks have been intensively studied for the last decade [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69], and topological edge states have been observed in experiments of both closed [70][71][72][73] and open [36,47,74,75] systems. Specifically, much attention has been paid to Floquet systems with chiral symmetry.…”
Section: Introductionmentioning
confidence: 99%