Observation of dynamical vortices after quenches in a system with topology

Abstract

Recently, the identification of non-equilibrium signatures of topology in the dynamics of such systems has attracted particular attention [3][4][5][6] . Here, we experimentally study the dynamical evolution of the wavefunction using time-and momentum-resolved full state tomography for spin-polarized fermionic atoms in driven optical lattices 7 . We observe the appearance, movement and annihilation of dynamical vortices in momentum space after sudden quenches close to the topological phase transition. These dynamical vortices can be interpreted as dynamical Fisher zeros of the Loschmidt amplitude 8 , which signal a so-called dynamical phase transition 9,10 . Our results pave the way to a deeper understanding of the connection between topological phases and non-equilibrium dynamics.The discovery of topological matter has revolutionized our understanding of band theory: not only are the dispersions of the energy bands important, but so is the geometry of the corresponding eigenstates 1 . The non-local nature of the topological invariants characterizing such phases goes beyond the Landau paradigm of local order parameters and leads to topological protection, for example, against disorder. Ultracold quantum gases in optical lattices allow for controlled studies of archetypal topological models [11][12][13][14] . In addition, compared with, for example condensed-matter systems, they also allow for detailed studies of the relation between dynamics and topology as the timescales are experimentally easier to access. Dynamical studies of driven systems have recently attracted attention in terms of their high T c superconductivity 15 . A particular challenge is to identify non-equilibrium signatures of topology in the dynamics of highly excited states 3,4,16 . Here, we observe the time evolution of the wavefunction after a sudden quench in a Haldanelike model and find dynamical vortices as a signature of the topological nature of the underlying ground state.In the experiments described here, the state tomography method allows mapping of the full quantum-mechanical wavefunction of non-interacting ultracold fermionic quantum gases in an optical lattice for any time after a sudden quench of the system close to or into a Chern insulating phase. As a key result, we identify in an intense series of measurements the appearance, movement and annihilation In the initial system, tunnelling J AB between the A and B sites is suppressed by a large energy offset. In the final Floquet system, tunnelling is re-established by means of near-resonant driving. b, At each momentum, the Hamiltonian describes the coupling between the states of the A and B sublattices, and can be visualized on a Bloch sphere. In the initial system, the Hamiltonian for all momenta points to the north pole, whereas in the Floquet system, the Hamiltonian covers a large surface of the Bloch sphere. c, Phase diagram for the Floquet Hamiltonian as a function of shaking amplitude and detuning with respect to the sublattice offset for the case of circular lattice shaking...

Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System

“…Our work complements the very recent observation of a dynamical topological order parameter for DQPTs in systems of ultra-cold atoms in optical lattices [18]. We study DQPTs in a trapped-ion quantum simulator, realising the dynamics of an effective transverse-field Ising Hamiltonian [19][20][21],…”

“…1a and b), many essential concepts such as universality and scaling [12] as well as robustness [13][14][15] carry over to them. Moreover, order parameters have recently been identified theoretically and also measured experimentally [16][17][18].…”

Connecting dynamical quantum phase transitions and topological steady-state transitions by tuning the energy gap

“…An example is the universal logarithmic divergence of the Hall conductance in the steady state of topological insulators after a quench [16,17]. Another important concept is that of dynamical quantum phase transitions (DQPTs) [15], recently observed experimentally [18,19], which occur on transient and intermediate time scales accompanied by a nonanalytic behavior as a function of time instead of a conventional order parameter. In the context of such developments, it is then a natural question to ask, whether and how these two notions of phase transitions are connected.…”

“…Dynamics of the vortices: A recent experiment [18] measured the real-time dynamics of the k-dependent Loschmidt echo L k , i.e. the Loschmidt echo of a particle at the momentum k. L k is expressed as…”

Quantum Phase Transitions Go Dynamical

“…Moreover, order parameters have recently been identified theoretically [16,17]. Very recently, a dynamical topological order parameter for DQPTs has been observed in a system of ultracold atoms in an optical lattice [18]. Here, we report on the first direct observation of a DQPT by resolving the nonanalyticity in the evolution of a quantum many-body system at a DQPT.…”