Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. Our work unequivocally establishes the non-Hermitian bulk-boundary correspondence as a general principle underlying non-Hermitian topological systems, and paves the way for a complete understanding of topological matter in open systems.

We study non-Bloch bulk-boundary correspondence in a non-Hermitian Su-Schieffer-Heeger model in a domain-wall configuration where the left and right bulks have different parameters. Focusing on the case where chiral symmetry is still conserved, we show that non-Hermitian skin effects of bulk states persist in the system, while the definition of the non-Bloch winding number of either bulk depends on parameters on both sides of the boundary. Under these redefined non-Bloch topological invariants, we confirm non-Bloch bulk-boundary correspondence under the domain-wall configuration, which exemplifies the impact of boundary conditions in non-Hermitian topological systems. II. MODEL AND BLOCH TOPOLOGICAL INVARIANTSAs illustrated in Fig. 1, we consider a non-Hermitian SSH model in a domain-wall configuration on a ring. The arXiv:1903.03811v3 [cond-mat.quant-gas]

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 in different time frames, which are consistent with our experimental observation of topological phase transitions. The high tunability of the system further enables us to observe robust helical Floquet channels in the one-dimensional momentum lattice, which derive from the winding of Floquet quasienergy bands. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.Exploring topological phases is a main theme in modern physics. Characterized by topological invariants which reflect the global geometric properties of the system wave function, topological phases host a range of fascinating features, which are robust to local perturbations and are potentially useful for applications in quantum information and quantum computation [1,2]. Besides conventional topological materials in solid-state systems, topological phenomena also emerge away from equilibrium. For example, topological phases and emergent topological phenomena exist in non-Hermitian open systems [3][4][5][6][7][8][9][10][11][12][13][14], in periodically driven Floquet systems and quench processes [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], which have stimulated intense interest recently due to the rapid progress in synthetic quantum-simulation platforms such as cold atoms [34][35][36][37], photonics [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52], phononics [53], and superconducting qubits [54].A particularly interesting subject is topologies in periodically driven Floquet systems, which are shown to have a rich structure and host novel topological phases with no counterparts in static systems [20][21][22][23]. A paradigmatic example of topological Floquet dynamics is discrete-time quantum walks, which, besides potential applications in quantum information [55][56][57], have been widely used in photonics for the exploration of Floquet topological phases [38][39][40][41][42][43][44][45][46][47]. In cold atoms, whereas Floquet topological phases [34] and quantum walks [58] have been respectively implemented, quantum walks with topological properties are yet to be experimentally realized.Here we report the experimental implementation of discrete-time topological quantum walks in momentum space for a Bose-Einstein condensate (BEC). Combining the generation of momentum lattice [59-63] with stroboscopic driving sequences, dynamics of the conden-sate atoms is governed b...

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We identify emergent topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time (PT ) symmetry. Their occurrence in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the states do not evolve in time. We construct a theoretical formalism for characterizing topological properties in non-unitary dynamics within the framework of biorthogonal quantum mechanics, and prove the existence of fixed points for quenches between distinct static topological phases in the PT -symmetry-preserving regime. We then reveal the interesting relation between different dynamic topological phenomena through the momentumtime spin texture characterizing the dynamic process. For quenches involving Hamiltonians in the PT -symmetry-broken regime, these topological phenomena are not ensured.The exploration of topological matter constitutes a major theme in modern physics [1,2]. With rapid progress in the discovery and understanding of topological phases in solid-state materials, a challenging quest lies in extending the study of conventional topological matter to novel regimes. Prominent examples include the investigation of emergent topological properties in out-of-equilibrium dynamics [3-28] and the characterization of topological phases in non-Hermitian systems [29? -40]. With the flexible controls afforded by synthetic systems such as ultracold atoms and engineered photonic configurations, the experimental implementation of these interesting scenarios is already within reach [41][42][43][44][45][46][47][48][49][50].An exemplary situation for the study of topological properties in out-of-equilibrium dynamics is the quantum quench of a topological system, where the ground state of the initial Hamiltonian H i is subject to a unitary time evolution governed by the final Hamiltonian H f . Whereas the topological invariant characterizing the instantaneous state is unchanged during the unitary dynamics [8,9], previous studies have revealed the emergence of intriguing phenomena such as dynamic quantum phase transitions (DQPTs) [13-18, 45, 51] and quantized non-equilibrium Hall responses in quench processes [19][20][21]. Further, in a series of recent theoretical and experimental studies, it has been established that dynamic topological invariants can be defined in unitary quantum quenches, which are related to the topology of initial and final Hamiltonians in equilibrium [23][24][25]44].Here arises an interesting question: what if the quench dynamics is non-unitary and governed by non-Hermitian Hamiltonians? The question is particularly relevant in light of recent studies on topological phenomena in parity-time(PT )-symmetric non-Hermitian systems [32][33][34][46][47][48]. Under PT symmetry, eigenenergies of a non-Hermitan Hamiltonian are entirely real in the PTsymmetry-preserving regime, in contrast to regimes with spontaneously broken PT symmetry [52][53][54]. Whereas it has be...

We study the impurity problem in a gas of 173 Yb atoms near the recently discovered orbital Feshbach resonance. In an orbital Feshbach resonance, atoms in the electronic ground state 1 S0 interact with those in the long-lived excited 3 P0 state with magnetically tunable interactions. We consider an impurity atom with a given hypferine spin in the 3 P0 state interacting with a singlecomponent Fermi sea of atoms in the ground 1 S0 manifold. Close to the orbital Feshbach resonance, the impurity can induce collective partilce-hole excitations out of the Fermi sea, which can be regarded as the polaron state. While as the magnetic field decreases, a molecular state becomes the ground state of the system. We show that a polaron to molecule transition exists in 173 Yb atoms close to the orbital Feshbach resonance. Furthermore, due to the spin-exchange nature of the orbital Feshbach resonance, the formation of both the polaron and the molecule involve spin-flipping processes with interesting density distributions among the relevant hyperfine spin states. We show that the polaron to molecule transition can be detected using Raman spectroscopy.

We show that dynamical quantum phase transitions (DQPTs) in the quench dynamics of twodimensional topological systems can be characterized by a dynamical topological invariant defined along an appropriately chosen closed contour in momentum space. Such a dynamical topological invariant reflects the vorticity of dynamical vortices responsible for the DQPTs, and thus serves as a dynamical topological order parameter in two dimensions. We demonstrate that when the contour crosses topologically protected fixed points in the quench dynamics, an intimate connection can be established between the dynamical topological order parameter in two dimensions and those in one dimension. We further define a reduced rate function of the Loschmidt echo on the contour, which features non-analyticities at critical times and is sufficient to characterize DQPTs in two dimensions. We illustrate our results using the Haldane honeycomb model and the quantum anomalous Hall model as concrete examples, both of which have been experimentally realized using cold atoms.

We characterize properties of the so-called repulsive polaron across the recently discovered orbital Feshbach resonance in alkaline-earth(-like) atoms. Being a metastable quasiparticle excitation at the positive energy, the repulsive polaron is induced by the interaction between an impurity atom and a Fermi sea. By analyzing in detail the energy, the polaron residue, the effective mass, and the decay rate of the repulsive polaron, we reveal interesting features that are intimately related to the two-channel nature of the orbital Feshbach resonance. In particular, we find that the life time of the repulsive polaron is non-monotonic in the Zeeman-field detuning bewteen the two channels, and has a maximum on the BEC-side of the resonance. Further, by considering the stability of a mixture of the impurity and the majority atoms against phase separation, we show that the itinerant ferromagnetism may exist near the orbital Feshbach resonance at appropriate densities. Our results can be readily probed experimentally, and have interesting implications for the observation of itinerant ferromagnetism near an orbital Feshbach resonance.