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arXiv:1604.03630 · Physical review. B./Physical review. B

Generation of chiral spin state by quantum simulation

Tetsufumi Tanamoto

Published Jun 20, 2016• 0 citations
arXivHTMLPDF

Abstract

Chirality of materials in nature appears when there are asymmetries in their lattice structures or interactions in a certain environment. Recent development of quantum simulation technology has enabled the manipulation of qubits. Accordingly, chirality can be realized intentionally rather than passively observed. Here we theoretically provide simple methods to create a chiral spin state in a spin-1/2 qubit system on a square lattice. First, we show that switching on and off the Heisenberg and $XY$ interactions produces the chiral interaction directly in the effective Hamiltonian without controlling local fields. Moreover, when initial states of spin qubits are appropriately prepared, we prove that the chirality with desirable phase is dynamically obtained. Finally, even for the case where switching on and off the interactions is infeasible and the interactions are always on, we show that, by preparing an asymmetric initial qubit state, the chirality whose phase is $\ensuremath{\pi}/2$ is dynamically generated.

DOI
10.1103/physrevb.93.235137

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Chirality of materials in nature appears when there are asymmetries in their lattice structures or interactions in a certain environment. Recent development of quantum simulation technology has enabled the manipulation of qubits. Accordingly, chirality can be realized intentionally rather than passively observed. Here we theoretically provide simple methods to create a chiral spin state in a spin-1/2 qubit system on a square lattice. First, we show that switching on and off the Heisenberg and XYXYXY interactions produces the chiral interaction directly in the effective Hamiltonian without controlling local fields. Moreover, when initial states of spin qubits are appropriately prepared, we prove that the chirality with desirable phase is dynamically obtained. Finally, even for the case where switching on and off the interactions is infeasible and the interactions are always on, we show that, by preparing an asymmetric initial qubit state, the chirality whose phase is \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 is dynamically generated.
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Spin-orbit coupling (SOC) in ultracold atoms is engineered by light-atom interaction, such as two-photon Raman transitions between two Zeeman spin states. In this paper, we propose and experimentally realize chiral Raman coupling to generate SOC in ultracold atomic gases, which exhibits high quantization axis direction dependence. Chiral Raman coupling for SOC is created by chiral light-atom interaction, in which a circularly polarized electromagnetic field generated by two Raman lasers interacts with two Zeeman spin states $\ensuremath{\delta}{m}_{F}=\ifmmode\pm\else\textpm\fi{}1$ (chiral transition). We present a simple scheme of chiral one-dimensional (1D) Raman coupling by employing two Raman lasers at an intersecting angle ${90}^{\ensuremath{\circ}}$ with the proper polarization configuration. In this case, Raman coupling for SOC exists in one direction of the magnetic quantization axis and disappears in the opposite direction. Then we extend this scheme into a chiral two-dimensional (2D) optical square Raman lattice configuration to generate the 1D SOC. There are two orthogonal 1D SOCs, which exist in the positive and negative directions of the magnetic quantization axis respectively. This case is compared with 2D SOC based on the nonchiral 2D optical Raman lattice scheme for studying the topological energy band. This paper broadens the horizon for understanding chiral physics and simulating topological quantum systems.
Numerical simulation is typically used to study the dynamics of complex quantum systems, namely 1-dimensional many-body spin systems and 2-dimensional spin lattice models. Systems of this nature tend to have large or complicated to experimentally realise Hilbert spaces. This results in a difficulty in producing realistic experimental methods of creating interacting spin systems and non-abelian topological phenomena. It also gives a limited success in numerical simulation, requiring advanced methods of quantum simulation to achieve results on an interesting scale. In this thesis we verify known theoretical properties and uncover new features of two such models: a many-body XX Hamiltonian modified with an interacting chiral term and a quantum double model utilised in the manipulation of topological particles. The interacting chiral spin chain has previously shown a rich variety of properties, from the semi-classical black hole background found in its continuum limit, to measurements of Hawking radiation and maximal information scrambling abilities. Our work builds upon these findings. First by analysing the phase order transition from the dominance of the chiral coupling and identifying the role interactions play in the chiral phase that define the interior of a black hole. The interactions of this model are then broken down with the Trotter-Suzuki method into a set of local evolutionary ’gates’. This quantum circuit decomposition of the chiral many-body dynamics gives rise to a potential method of experimental realisation, both of black hole geometry and of its maximal scrambling. Then a lattice model capable of manipulating topological particles is introduced. With this model we produce a methodology of extracting the braiding statistics of a simple non-abelian set of topological quasiparticles based on the S3 group with minimal resources. Within the limitations of this model, we manage to produce the result that the braiding operator this particle set has the ability to produce quantum magic states. This indicates a capability to perform universal quantum computation that can be demonstrated in the laboratory with current technology.