Janos K. Asboth

Computable Measure of Nonclassicality for Light

We propose the entanglement potential (EP) as a measure of nonclassicality for quantum states of a single-mode electromagnetic field. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states, and ideal photodetectors. The EP detects nonclassicality, has a direct physical interpretation, and can be computed efficiently. These three properties together make it stand out from previously proposed nonclassicality measures. We derive closed expressions for the EP of important classes of states and analyze as an example of the degradation of nonclassicality in lossy channels.

Scattering theory of cooling and heating in optomechanical systems

We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front of a mirror

Correlated motion of two atoms trapped in a single-mode cavity field

We study the motion of two atoms trapped at distant positions in the field of a driven standing-wave high-Q optical resonator. Even without any direct atom-atom interaction the atoms are coupled through their position dependent influence on the intracavity field. For sufficiently good trapping and low cavity losses the atomic motion becomes significantly correlated and the two particles oscillate in their wells preferentially with a 90 deg. relative phase shift. The onset of correlations seriously limits cavity cooling efficiency, raising the achievable temperature to the Doppler limit. The physical origin of the correlation can be traced back to a cavity mediated crossfriction, i.e., a friction force on one particle depending on the velocity of the second particle. Choosing appropriate operating conditions allows for engineering these long range correlations. In addition this cross-friction effect can provide a basis for sympathetic cooling of distant trapped clouds.

Robustness of topologically protected edge states in quantum walk experiments with neutral atoms

Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one- and two-dimensional discrete-time quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental proposal based on neutral atoms in spin-dependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spin-dependent discrete shift operations in a two-dimensional optical lattice. We analyze under realistic decoherence conditions the experimental feasibility of observing unidirectional, dissipationless transport of matter waves along boundaries separating distinct topological domains.

Detecting topological invariants in chiral symmetric insulators via losses

We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak measurements on one sublattice only, which interrupt the dynamics periodically. When these do not detect the particle, they realize negative measurements. Our repeated measurement scheme covers both time-independent and periodically driven (Floquet) topological insulators, with or without spatial disorder. In the limit of rapidly repeated, vanishingly weak measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy Su-Schrieffer-Heeger model of Phys. Rev. Lett. 102, 065703 (2009). We find, contrary to intuition, that the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. We illustrate our results on a discrete-time quantum walk, and propose ways of testing them experimentally.

Collective excitations and instability of an optical lattice due to unbalanced pumping

We solve self-consistently the coupled equations of motion for trapped particles and the field of a one-dimensional optical lattice. Optomechanical coupling creates long-range interaction between the particles, whose nature depends crucially on the relative power of the pump beams. For asymmetric pumping, traveling density wavelike collective oscillations arise in the lattice, even in the overdamped limit. By increasing the lattice size or pump asymmetry, these waves can destabilize the lattice.

Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk

Quantum walks are promising for information processing tasks because on regular graphs they spread quadratically faster than random walks. Static disorder, however, can turn the tables: unlike random walks, quantum walks can suffer Anderson localization, whereby the spread of the walker stays within a finite region even in the infinite time limit. It is therefore important to understand when we can expect a quantum walk to be Anderson localized and when we can expect it to spread to infinity even in the presence of disorder. In this work we analyze the response of a generic one-dimensional quantum walk -- the split-step walk -- to different forms of static disorder. We find that introducing static, symmetry-preserving disorder in the parameters of the walk leads to Anderson localization. In the completely disordered limit, however, a delocalization sets in, and the walk spreads subdiffusively. Using an efficient numerical algorithm, we calculate the bulk topological invariants of the disordered walk, and interpret the disorder-induced Anderson localization and delocalization transitions using these invariants.

Edge-state-enhanced transport in a two-dimensional quantum walk

Quantum walks on translation-invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits or even stops t ...

Topological bound states of a quantum walk with cold atoms

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically nontrivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atoms position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.

Localization, delocalization, and topological transitions in disordered two-dimensional quantum walks

We investigate time-independent disorder on several two-dimensional discrete-time quantum walks. We find numerically that, contrary to claims in the literature, random onsite phase disorder, spin-dependent or otherwise, cannot localize the Hadamard quantum walk; rather, it induces diffusive spreading of the walker. In contrast, split-step quantum walks are generically localized by phase disorder. We explain this difference by showing that the Hadamard walk is a special case of the split-step quantum walk, with parameters tuned to a critical point at a topological phase transition. We show that the topological phase transition can also be reached by introducing strong disorder in the rotation angles. We determine the critical exponent for the divergence of the localization length at the topological phase transition, and find nu = 2.6, in both cases. This places the two-dimensional split-step quantum walk in the universality class of the quantum Hall effect.