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Register a new userTwo-dimensional topological quantum walks in the momentum space of structured light
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Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an innovative approach to the photonic simulation of a quantum walk in two dimensions, where walker positions are encoded in the transverse wavevector components of a single light beam. The desired dynamics is obtained by means of a sequence of liquid-crystal devices, which apply polarization-dependent transverse kicks to the photons in the beam. We engineer our quantum walk so that it realizes a periodically-driven Chern insulator, and we probe its topological features by detecting the anomalous displacement of the photonic wavepacket under the effect of a constant force. Our compact, versatile platform offers exciting prospects for the photonic simulation of two-dimensional quantum dynamics and topological systems.
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We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the topological phases in one, two dimensions and take the first initiatives to build necessary protocols for three-dimensional cases. We also highlight the possible boundary states that can be observed for each protocol in different dimensions and extract the conditions for their emergences or absences. To further enrich the simulation of the topological phenomenas, we include step-dependent coins in the evolution operators of the quantum walks. Consequently, this leads to step-dependency of the simulated topological phenomenas and their properties which in turn introduce dynamicality as a feature to simulated topological phases and boundary states. This dynamicality provides the step-number of the quantum walk as a mean to control and engineer the number of topological phases and boundary states, their populations, types and even occurrences.
We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalues at symmetry protected points, and satisfy a mild locality condition. No translation invariance is assumed. The classification is parameterized by three indices, taking values in a group, which is either trivial, the group of integers, or the group of integers modulo 2, depending on the type of symmetry. The classification is complete in the sense that two walks have the same indices if and only if they can be connected by a norm continuous path along which all the mentioned properties remain valid. Of the three indices, two are related to the asymptotic behaviour far to the right and far to the left, respectively. These are also stable under compact perturbations. The third index is sensitive to those compact perturbations which cannot be contracted to a trivial one. The results apply to the Hamiltonian case as well. In this case all compact perturbations can be contracted, so the third index is not defined. Our classification extends the one known in the translation invariant case, where the asymptotic right and left indices add up to zero, and the third one vanishes, leaving effectively only one independent index. When two translationally invariant bulks with distinct indices are joined, the left and right asymptotic indices of the joined walk are thereby fixed, and there must be eigenvalues at $1$ or $-1$ (bulk-boundary correspondence). Their location is governed by the third index. We also discuss how the theory applies to finite lattices, with suitable homogeneity assumptions.
We present an optomechanical device designed to allow optical transduction of orbital angular momentum of light. An optically induced twist imparted on the device by light is detected using an integrated cavity optomechanical system based on a nanobeam slot-mode photonic crystal cavity. This device could allow measurement of the orbital angular momentum of light when photons are absorbed by the mechanical element, or detection of the presence of photons when they are scattered into new orbital angular momentum states by a sub-wavelength grating patterned on the device. Such a system allows detection of a $l = 1$ orbital angular momentum field with an average power of $3.9times10^3$ photons modulated at the mechanical resonance frequency of the device and can be extended to higher order orbital angular momentum states.
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in position and momentum variables, during a tunable time span. We study two cases: the reconstruction of the wavefunctions of pure states and the direct measurement of the density matrix of mixed states. We show that our method can be applied to several physical systems where high quantum control can be experimentally achieved.
One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t to infty$ of all joint moments of two components of walkers pseudovelocity, $X_t/t$ and $Y_t/t$, is proved and the probability density of limit distribution is derived. Dependence of the two-dimensional limit density function on the parameter of quantum coin and initial four-component qudit of quantum walker is determined. Symmetry of limit distribution on a plane and localization around the origin are completely controlled. Comparison with numerical results of direct computer-simulations is also shown.
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