Persistence of Topological Phases in Non-Hermitian Quantum Walks
- URL: http://arxiv.org/abs/2007.15500v2
- Date: Wed, 19 May 2021 05:57:27 GMT
- Title: Persistence of Topological Phases in Non-Hermitian Quantum Walks
- Authors: Vikash Mittal, Aswathy Raj, Sanjib Dey, Sandeep K. Goyal
- Abstract summary: We investigate the behavior of topological states in quantum walks in the presence of a lossy environment.
We show that the topological phases of the quantum walks are robust against moderate losses.
Although the topological nature persists in two-dimensional quantum walks, the $mathcalPT$-symmetric has no role to play there.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Discrete-time quantum walks are known to exhibit exotic topological states
and phases. Physical realization of quantum walks in a noisy environment may
destroy these phases. We investigate the behavior of topological states in
quantum walks in the presence of a lossy environment. The environmental effects
in the quantum walk dynamics are addressed using the non-Hermitian Hamiltonian
approach. We show that the topological phases of the quantum walks are robust
against moderate losses. The topological order in one-dimensional split-step
quantum walk persists as long as the Hamiltonian is $\mathcal{PT}$-symmetric.
Although the topological nature persists in two-dimensional quantum walks as
well, the $\mathcal{PT}$-symmetry has no role to play there. Furthermore, we
observe the noise-induced topological phase transition in two-dimensional
quantum walks.
Related papers
- Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - Geometric phases along quantum trajectories [58.720142291102135]
We study the distribution function of geometric phases in monitored quantum systems.
For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle.
For the same parameters, the density matrix does not show any interference.
arXiv Detail & Related papers (2023-01-10T22:05:18Z) - Topological transitions with continuously monitored free fermions [68.8204255655161]
We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits.
We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
arXiv Detail & Related papers (2021-12-17T22:01:54Z) - Dynamical Topological Quantum Phase Transitions at Criticality [0.0]
We contribute to expanding the systematic understanding of the interrelation between the equilibrium quantum phase transition and the dynamical quantum phase transition (DQPT)
Specifically, we find that dynamical quantum phase transition relies on the existence of massless it propagating quasiparticles as signaled by their impact on the Loschmidt overlap.
The underlying two dimensional model reveals gapless modes, which do not couple to the dynamical quantum phase transitions, while relevant massless quasiparticles present periodic nonanalytic signatures on the Loschmidt amplitude.
arXiv Detail & Related papers (2021-04-09T13:38:39Z) - Observing a Topological Transition in Weak-Measurement-Induced Geometric
Phases [55.41644538483948]
Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control.
We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength.
Our results open new horizons for measurement-enabled quantum control of many-body topological states.
arXiv Detail & Related papers (2021-02-10T19:00:00Z) - Unraveling the topology of dissipative quantum systems [58.720142291102135]
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories.
We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
arXiv Detail & Related papers (2020-07-12T11:26:02Z) - Topological delocalization in the completely disordered two-dimensional
quantum walk [0.0]
We investigate the effect of spatial disorder on two-dimensional split-step discrete-time quantum walks with two internal "coin" states.
We find that spatial disorder of the most general type, i.e., position-dependent Haar random coin operators, does not lead to Anderson localization but to a diffusive spread instead.
This is a delocalization, which happens because disorder places the quantum walk to a critical point between different anomalous Floquet-Anderson insulating topological phases.
arXiv Detail & Related papers (2020-05-01T03:57:37Z) - Topological Quantum Walk with Discrete Time-Glide Symmetry [0.0]
We formulate discrete space-time symmetry in quantum walks and evaluate the corresponding symmetry protected topological phases.
Due to discrete nature of time evolution, the topological classification is found to be different from that in conventional Floquet systems.
arXiv Detail & Related papers (2020-04-20T14:24:14Z) - Exploring 2D synthetic quantum Hall physics with a quasi-periodically
driven qubit [58.720142291102135]
Quasi-periodically driven quantum systems are predicted to exhibit quantized topological properties.
We experimentally study a synthetic quantum Hall effect with a two-tone drive.
arXiv Detail & Related papers (2020-04-07T15:00:41Z) - Second-order topological insulator in a coinless discrete-time quantum
walk [3.7528520149256006]
We construct a two-dimensional coinless quantum walk to simulate second-order topological insulator with zero-dimensional corner states.
We show that both of the corner and edge states can be observed through the probability distribution of the walker.
We propose a possible experimental implementation to realize this discrete-time quantum walk in a three-dimensional integrated photonic circuits.
arXiv Detail & Related papers (2020-03-19T09:07:34Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.