Yongguan Ke

Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions

We investigate continuous-time quantumwalks of two indistinguishable particles [two bosons, or two fermions, or two hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are consistent with the recent experimental observation of two-magnon dynamics [Fukuhara et al., Nature (London) 502, 76 (2013)]. The two interacting particles can undergo independent walking and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with a statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk speed of bosons is found to be exactly three times that of fermions and HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.

Quantum metrology with spin cat states under dissipation.

Quantum metrology aims to yield higher measurement precisions via quantum techniques such as entanglement. It is of great importance for both fundamental sciences and practical technologies, from testing equivalence principle to designing high-precision atomic clocks. However, due to environment effects, highly entangled states become fragile and the achieved precisions may even be worse than the standard quantum limit (SQL). Here we present a high-precision measurement scheme via spin cat states (a kind of non-Gaussian entangled states in superposition of two quasi-orthogonal spin coherent states) under dissipation. In comparison to maximally entangled states, spin cat states with modest entanglement are more robust against losses and their achievable precisions may still beat the SQL. Even if the detector is imperfect, the achieved precisions of the parity measurement are higher than the ones of the population measurement. Our scheme provides a realizable way to achieve high-precision measurements via dissipative quantum systems of Bose atoms.The maximally entangled states are excellent candidates for achieving Heisenberg-limited measurements in ideal quantum metrology, however, they are fragile against dissipation such as particle losses and their achievable precisions may become even worse than the standard quantum limit (SQL). Here we present a robust high-precision measurement scheme via spin cat states (a kind of non-Gaussian entangled states in superposition of two spin coherent states) in the presence of particle losses. The input spin cat states are of excellent robustness against particle losses and their achievable precisions may still beat the SQL. For realistic measurements based upon our scheme, comparing with the population measurement, the parity measurement is more suitable for yielding higher precisions. In phase measurement with realistic dissipative systems of bosons, our scheme provides a robust and realizable way to achieve high-precision measurements beyond the SQL.

Topological phase transitions and Thouless pumping of light in photonic waveguide arrays

Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-Andre-Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In contrast to incommensurate AAH models, diagonal and off-diagonal commensurate AAH models are not topologically equivalent. In particular, there appear nontrivial topological phases with large Chern numbers and topological phase transitions. By implementing Thouless pumping of light in photonic waveguide arrays, we propose a simple scheme to measure the bulk Chern numbers.

Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound-states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingale-den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms [Phys. Rev. Lett. \textbf{111}, 185301 (2013); Phys. Rev. Lett. \textbf{111}, 185302 (2013)]. Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound-states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound-states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

Bloch-Landau-Zener dynamics in single-particle Wannier-Zeeman systems

Stimulated by the experimental realization of spin-dependent tunneling via gradient magnetic field [Phys. Rev. Lett. 111, 225301 (2013); Phys. Rev. Lett. 111, 185301 (2013)], we investigate dynamics of Bloch oscillations and Landau-Zener tunneling of single spin-half particles in a periodic potential under the influence of a spin-dependent constant force. In analogy to the Wannier-Stark system, we call our system as the Wannier-Zeeman system. If there is no coupling between the two spin states, the system can be described by two crossing Wannier-Stark ladders with opposite tilts. The spatial crossing between two Wannier-Stark ladders becomes a spatial anti-crossing if the two spin states are coupled by external fields. For a wave-packet away from the spatial anti-crossing, due to the spin-dependent constant force, it will undergo spatial Landau-Zener transitions assisted by the intrinsic intra-band Bloch oscillations, which we call the Bloch-Landau-Zener dynamics. If the inter-spin coupling is sufficiently strong, the system undergoes adiabatic Bloch-Landau-Zener dynamics, in which the spin dynamics follows the local dressed states. Otherwise, for non-strong inter-spin couplings, the system undergoes non-adiabatic Bloch-Landau-Zener dynamics.

Topological magnon bound states in periodically modulated Heisenberg XXZ chains

Strongly interacting topological states in multi-particle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multi-particle quantum states, which enables us to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and Chern numbers of the two-magnon bound-states and show the existence of topological protected edge bound-states. Our study not only opens a new prospect to pursue topological magnon bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.

Multiparticle Wannier states and Thouless pumping of interacting bosons

The study of topological effects in physics is a hot area of research, and only recently have researchers been able to address the important issues of topological properties of interacting quantum systems. But it is still a great challenge to describe multiparticle and interaction effects. Here, we introduce the multiparticle Wannier states for interacting systems with cotranslational symmetry, which provide an orthogonal basis for constructing effective Hamiltonians for the isolated bands. We reveal how the shift of multiparticle Wannier state relates to the Chern number of the multiparticle Bloch band and study the Thouless pumping of two interacting bosons in a one-dimensional superlattice. In addition to the Thouless pumping of bound states when two bosons move unidirectionally as a whole, we describe topologically resonant tunneling when two bosons move unidirectionally, one by the other, provided the neighboring-well potential bias matches the interaction energy. Our work creates a paradigm for multiparticle topological effects and provides a way to detect topological states in interacting multiparticle systems.

Kibble-Zurek dynamics in an array of coupled binary Bose condensates

Universal dynamics of spontaneous symmetry breaking is central to understanding the universal behavior of spontaneous defect formation in various system from the early universe, condensed-matter systems to ultracold atomic systems. We explore the universal real-time dynamics in an array of coupled binary atomic Bose-Einstein condensates in optical lattices, which undergo a spontaneous symmetry breaking from the symmetric Rabi oscillation to the broken-symmetry self-trapping. In addition to Goldstone modes, there exist gapped Higgs mode whose excitation gap vanishes at the critical point. In the slow passage through the critical point, we analytically find that the symmetry-breaking dynamics obeys the Kibble-Zurek mechanism. From the scalings of bifurcation delay and domain formation, we numerically extract two Kibble-Zurek exponents

Floquet Bound States in a Driven Two-Particle Bose–Hubbard Model with an Impurity

b_{1}=\nu/(1+\nu z)

Cluster mean-field signature of entanglement entropy in bosonic superfluid-insulator transitions

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